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Four-XTM

Whittle Multi-ElementOpen Pit Optimization Software

USER MANUAL

DECEMBER 1997

Copyright 1997 Whittle Programming Proprietary LimitedMelbourne, Australia (A.C.N. 065 377 004)

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26 April, 1998 Whittle Four-X User Manual

TABLE OF CONTENTS – Main Headings

About This Release ........................................................................................................................................ 9

1. INTRODUCTION ...................................................................................................................................... 10

2. GETTING STARTED................................................................................................................................ 15

3. USING THE PACKAGE............................................................................................................................ 18

4. TUTORIALS AND EXERCISES................................................................................................................ 20

5. DATA FILES............................................................................................................................................. 59

6. PROGRAM OPERATION – GENERAL .................................................................................................... 82

7. OPERATION OF THE EDIT PROGRAM – FXED..................................................................................... 88

8. OPERATION THE RE-BLOCKING PROGRAM – FXRB .......................................................................... 92

9. OPERATION OF THE STRUCTURE ARCS PROGRAM – FXST .......................................................... 105

10. OPERATION OF THE OPTIMIZATION PROGRAM – FXOP................................................................ 107

11. OPERATION OF THE PRINT PROGRAM – FXPR .............................................................................. 110

12. OPERATION OF THE ANALYSIS PROGRAM – FXAN ....................................................................... 112

13. OPERATION OF THE UTILITY PROGRAM – FXUT............................................................................ 122

14. OPERATION OF THE MINING WIDTH PROGRAM - FXMW............................................................... 128

15. TECHNIQUES ...................................................................................................................................... 132

16. APPENDICES ...................................................................................................................................... 149

GLOSSARY................................................................................................................................................ 229

INDEX ........................................................................................................................................................ 237

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TABLE OF CONTENTS – All Headings

About This Release ........................................................................................................................................ 9

1. INTRODUCTION ...................................................................................................................................... 101.1. History .....................................................................................................................................................101.2. Whittle Four-X .........................................................................................................................................111.3. Hardware and software requirements.........................................................................................................11

1.3.1. IBM compatible PCs .................................................................................................................111.3.2. UNIX workstations....................................................................................................................12

1.4. This manual..............................................................................................................................................121.5. Terminology .............................................................................................................................................12

2. GETTING STARTED................................................................................................................................ 152.1. Installing Four-X ......................................................................................................................................152.2. Menu facility ............................................................................................................................................16

2.2.1. Program selection ......................................................................................................................162.2.2. Exit ...........................................................................................................................................172.2.3. Main menu bar ..........................................................................................................................172.2.4. Files submenu ...........................................................................................................................172.2.5. Option submenu ........................................................................................................................17

3. USING THE PACKAGE............................................................................................................................ 18

4. TUTORIALS AND EXERCISES................................................................................................................ 204.1. Introduction ..............................................................................................................................................204.2. Preparation ...............................................................................................................................................204.3. Tutorial 1 - The basics ..............................................................................................................................21

4.3.1. Examining your data with FXUT...............................................................................................214.3.2. Producing the STructure arcs with FXST...................................................................................244.3.3. Doing the OPtimization with FXOP...........................................................................................254.3.4. PRinting plans and sections of the pits with FXPR .....................................................................274.3.5. ANalyzing the Results File with FXAN......................................................................................304.3.6. File summary ............................................................................................................................364.3.7. What you have learnt.................................................................................................................36

4.4. Exercise 1 – Using different pit sizes .........................................................................................................364.5. Tutorial 2 – More analysis of the Results File............................................................................................38

4.5.1. Running FXAN with a Log File and spreadsheet output .............................................................394.5.2. Examining the Log File..............................................................................................................414.5.3. Examining the spreadsheet output ..............................................................................................414.5.4. File Summary............................................................................................................................424.5.5. What you have learnt.................................................................................................................43

4.6. Exercise 2 – Varying silver prices .............................................................................................................434.7. Tutorial 3 – Improving the value by using contract mining.........................................................................44

4.7.1. Doing the analysis run ...............................................................................................................444.7.2. Further manipulating the output .................................................................................................454.7.3. What you have learnt.................................................................................................................46

4.8. Exercise 3 – Improving the value by using two push-backs ........................................................................464.9. Tutorial 4 – Re-arranging a model.............................................................................................................47

4.9.1. Extending the model ..................................................................................................................484.9.2. What you have learnt.................................................................................................................49

4.10. Exercise 4 – Adding positional mining CAFs...........................................................................................494.11. Tutorial 5 – Dealing with an obstruction..................................................................................................50

4.11.1. Preparing the special Model File ..............................................................................................514.11.2. Repeating the optimization.......................................................................................................524.11.3. Examining the output...............................................................................................................524.11.4. What you have learnt...............................................................................................................52

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4.12. Exercise 5 – Should the mill be moved?...................................................................................................534.13. Tutorial 6 - The basics of mining width control........................................................................................53

4.13.1. Establishing the push-backs and final pit..................................................................................534.13.2. Running FXMW......................................................................................................................53

4.14. Exercise 6 - Further tidying up ................................................................................................................57

5. DATA FILES............................................................................................................................................. 595.1. Overview..................................................................................................................................................595.2. Additional Arcs Files ................................................................................................................................595.3. Mining Sequence Files ..............................................................................................................................595.4. Model Files...............................................................................................................................................59

5.4.1. Which blocks to include.............................................................................................................605.5. Opti-Cut Files...........................................................................................................................................605.6. Parameters Files .......................................................................................................................................61

5.6.1. The dimensions of a block..........................................................................................................625.6.2. The dimensions of the model framework.....................................................................................625.6.3. The origin co-ordinates ..............................................................................................................635.6.4. General formatting requirements ................................................................................................635.6.5. The active blocks indicator ........................................................................................................635.6.6. The restart interval ....................................................................................................................645.6.7. The reference mining cost ..........................................................................................................645.6.8. The mining dilution factor..........................................................................................................655.6.9. The mining recovery factor ........................................................................................................655.6.10. The general default rock tonnage..............................................................................................655.6.11. The ore selection method flag...................................................................................................665.6.12. Air flag A................................................................................................................................665.6.13. Air flag B................................................................................................................................675.6.14. The positional mining CAF flag ...............................................................................................685.6.15. The positional processing CAF flag .........................................................................................685.6.16. The print unprocessed mineralisation flag.................................................................................685.6.17. The required revenue factor values...........................................................................................685.6.18. For each sub-region: ................................................................................................................69

a) The block limits ................................................................................................................69b) The number of benches for arc generation..........................................................................69c) The sub-region default rock tonnage ..................................................................................70d) For each slope angle:.........................................................................................................70

The bearing................................................................................................................70The slope ...................................................................................................................71

5.6.19. For any grade-dependent expression:........................................................................................715.6.20. For each element:.....................................................................................................................72

a) The element type code .......................................................................................................72b) The Position in Model File ................................................................................................72c) The element formatting requirements .................................................................................72d) The Selling Cost per Unit ..................................................................................................72e) The Price per Unit .............................................................................................................72

5.6.21. For each rock type: ..................................................................................................................73a) The rock type code ............................................................................................................73b) The rock type mining CAF................................................................................................73c) The rehabilitation cost per tonne ........................................................................................73d) The processing throughput factor ......................................................................................74

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5.6.22. For each processing-method/rock-type for open pit mining:.......................................................74a) The processing method code ..............................................................................................74b) The rock type code............................................................................................................74c) The processing cost ...........................................................................................................74d) For each element ...............................................................................................................75

The element type code ................................................................................................75The cut-off control flag ..............................................................................................75The element processing cost per unit...........................................................................75The processing recovery fraction ................................................................................75The processing recovery threshold ..............................................................................76The minimum.............................................................................................................76The maximum............................................................................................................77

5.6.23. For each method/type for underground mining:.........................................................................775.6.24. For each processing method group: ..........................................................................................77

5.7. Pit List Files .............................................................................................................................................785.8. Polygon Files ............................................................................................................................................785.9. Results Files .............................................................................................................................................785.10. Spreadsheet Files ....................................................................................................................................795.11. Structure Files ........................................................................................................................................795.12. Work Files..............................................................................................................................................805.13. Auxiliary Files ........................................................................................................................................80

5.13.1. The Initialization File...............................................................................................................805.13.2. The Language File...................................................................................................................815.13.3. Log Files .................................................................................................................................81

6. PROGRAM OPERATION – GENERAL .................................................................................................... 826.1. At the keyboard ........................................................................................................................................82

6.1.1. Prompts and answers .................................................................................................................826.1.2. Editing the defaults....................................................................................................................826.1.3. File names.................................................................................................................................83

a) Default..............................................................................................................................83b) Extensions ........................................................................................................................83c) Upper and lower case ........................................................................................................84d) Overwriting files with the same name ................................................................................84e) Length...............................................................................................................................84

6.2. Log Files ..................................................................................................................................................856.3. Running the programs in batch mode.........................................................................................................87

7. OPERATION OF THE EDIT PROGRAM – FXED..................................................................................... 887.1. Purpose ....................................................................................................................................................887.2. Menu operation.........................................................................................................................................887.3. Menu navigation .......................................................................................................................................907.4. Operation..................................................................................................................................................91

8. OPERATION THE RE-BLOCKING PROGRAM – FXRB .......................................................................... 928.1. Purpose ....................................................................................................................................................928.2. Explanation ..............................................................................................................................................93

8.2.1. Framework extension and truncation..........................................................................................958.2.2. Multiple input models ................................................................................................................968.2.3. Combining and splitting blocks ..................................................................................................97

8.3. Information required .................................................................................................................................988.4. Operation................................................................................................................................................ 104

9. OPERATION OF THE STRUCTURE ARCS PROGRAM – FXST .......................................................... 1059.1. Purpose .................................................................................................................................................. 1059.2. Information required ............................................................................................................................... 1059.3. Operation................................................................................................................................................ 105

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10. OPERATION OF THE OPTIMIZATION PROGRAM – FXOP................................................................ 10710.1. Purpose ................................................................................................................................................ 10710.2. Information required ............................................................................................................................. 10710.3. Operation.............................................................................................................................................. 108

11. OPERATION OF THE PRINT PROGRAM – FXPR .............................................................................. 11011.1. Purpose ................................................................................................................................................ 11011.2. Information required ............................................................................................................................. 11011.3. Operation.............................................................................................................................................. 111

12. OPERATION OF THE ANALYSIS PROGRAM – FXAN ....................................................................... 11212.1. Purpose ................................................................................................................................................ 11212.2. Explanation .......................................................................................................................................... 11212.3. Information required ............................................................................................................................. 11312.4. Entering request values ......................................................................................................................... 115

12.4.1. Error correction ..................................................................................................................... 11512.4.2. Default values ....................................................................................................................... 11512.4.3. Large values.......................................................................................................................... 11512.4.4. Value ranges.......................................................................................................................... 11512.4.5. Values that change with time.................................................................................................. 11712.4.6. Period length ......................................................................................................................... 11812.4.7. Discount percentage............................................................................................................... 11812.4.8. Throughput limits .................................................................................................................. 11912.4.9. Varying the period length....................................................................................................... 11912.4.10. Schedules with specified push-backs .................................................................................... 119

12.5. Spreadsheet output................................................................................................................................ 12012.6. Operation.............................................................................................................................................. 121

13. OPERATION OF THE UTILITY PROGRAM – FXUT............................................................................ 12213.1. Purpose ................................................................................................................................................ 12213.2. Information required ............................................................................................................................. 12213.3. Operation.............................................................................................................................................. 124

13.3.1. Summarising a data file ......................................................................................................... 12413.3.2. Showing block value calculations........................................................................................... 12513.3.3. Showing cut-off variation with processing CAF ..................................................................... 12613.3.4. Showing Four-X system limits ............................................................................................... 127

14. OPERATION OF THE MINING WIDTH PROGRAM - FXMW............................................................... 12814.1. Purpose ................................................................................................................................................ 12814.2. Information required ............................................................................................................................. 12814.3. Operation.............................................................................................................................................. 12914.4. The FXMW print file ............................................................................................................................ 13014.5. Air blocks in the input Results File ........................................................................................................ 13014.6. Additional Arcs..................................................................................................................................... 13014.7. Initial push-back printouts..................................................................................................................... 131

15. TECHNIQUES ...................................................................................................................................... 13215.1. Calculating costs for use with Four-X ................................................................................................... 132

15.1.1. What costs to include............................................................................................................. 13215.1.2. The reference block ............................................................................................................... 13315.1.3. Extra ore mining costs ........................................................................................................... 13315.1.4. Examples .............................................................................................................................. 133

a) Processing mill................................................................................................................ 134b) Trucks ............................................................................................................................ 134c) Administration costs........................................................................................................ 135d) Bank loans for initial costs .............................................................................................. 135e) Bank loans for recoverable costs...................................................................................... 135f) Grade control costs .......................................................................................................... 135

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g) Support – cable bolts ...................................................................................................... 13515.1.5. Sample cost calculation ......................................................................................................... 13615.1.6. Time cost handling during analysis......................................................................................... 136

15.2. Reagent costs........................................................................................................................................ 13715.3. Block sizes............................................................................................................................................ 137

15.3.1. For outlining the ore body...................................................................................................... 13715.3.2. For calculating values............................................................................................................ 13815.3.3. For designing a pit ................................................................................................................. 13815.3.4. For sensitivity work ............................................................................................................... 139

15.4. Re-blocking and bias............................................................................................................................. 13915.5. Restricting the number of parcels in a block........................................................................................... 14015.6. From optimized outline to design ........................................................................................................... 14115.7. Minimum mining width ......................................................................................................................... 14215.8. Pits that hit the side of the model framework.......................................................................................... 14415.9. Immovable objects ................................................................................................................................ 14515.10. Extending the ore body........................................................................................................................ 14515.11. Slopes that vary with rock type............................................................................................................ 14615.12. Sensitivity example ............................................................................................................................. 14715.13. Complex processing methods............................................................................................................... 147

15.13.1. Element extraction at different stages ................................................................................... 14715.13.2. Separation ........................................................................................................................... 14815.13.3. Different selling costs .......................................................................................................... 148

16. APPENDICES ...................................................................................................................................... 14916.1. Detailed file formats.............................................................................................................................. 149

16.1.1. The Additional Arcs File format............................................................................................. 14916.1.2. The Mining Sequence File format........................................................................................... 15016.1.3. The Model File format ........................................................................................................... 15116.1.4. The Parameters File format.................................................................................................... 15216.1.5. The Pit List File format ......................................................................................................... 16416.1.6. The Polygon File format ........................................................................................................ 16416.1.7. The Results File format ......................................................................................................... 16516.1.8. The Spreadsheet Definition File format .................................................................................. 166

a) Values set by the user...................................................................................................... 167b) Derived values ................................................................................................................ 168c) Spreadsheet code overview .............................................................................................. 174

16.1.9. The Spreadsheet Output File format....................................................................................... 17716.2. The block model.................................................................................................................................... 17716.3. Sub-regions........................................................................................................................................... 17816.4. Slope handling ...................................................................................................................................... 179

16.4.1. The slope cone....................................................................................................................... 17916.4.2. Generating the possible arcs for a block ................................................................................. 18016.4.3. Generating the Structure File ................................................................................................. 181

16.5. Ore selection methods ........................................................................................................................... 18216.5.1. Ore selection by cut-off.......................................................................................................... 18216.5.2. Ore selection by cash flow ..................................................................................................... 182

16.6. Cut-off calculation ................................................................................................................................ 18216.6.1. The simple case ..................................................................................................................... 18216.6.2. Mining dilution and recovery ................................................................................................. 18316.6.3. Positional processing cost adjustment factor........................................................................... 18416.6.4. Element processing cost ......................................................................................................... 18416.6.5. Non-linear processing recovery .............................................................................................. 18416.6.6. Selling cost............................................................................................................................ 18516.6.7. Rehabilitation cost ................................................................................................................. 18516.6.8. Derivation of the formula for a cut-off ................................................................................... 186

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16.6.9. Multiple processing methods.................................................................................................. 18916.6.10. The formula for a cut-over................................................................................................... 19016.6.11. Multiple elements ................................................................................................................ 19016.6.12. Display of cut-offs and cut-overs ......................................................................................... 19116.6.13. Cut-off scaling..................................................................................................................... 191

16.7. Ore selection by cash flow example ....................................................................................................... 19216.8. The effects of minima and maxima ........................................................................................................ 193

16.8.1. Minimum and maximum cut-offs ........................................................................................... 19316.8.2. Minimum and maximum parcel grades................................................................................... 196

16.9. The concepts behind Four-X nested pits................................................................................................. 19716.10. How Four-X calculates a block value .................................................................................................. 199

16.10.1. Definition of terms............................................................................................................... 19916.10.2. Procedure ............................................................................................................................ 20016.10.3. Allowing for underground mining......................................................................................... 202

16.11. Expressions......................................................................................................................................... 20416.11.1. Constants ............................................................................................................................ 20416.11.2. Variables............................................................................................................................. 20516.11.3. Operators ............................................................................................................................ 20516.11.4. Functions............................................................................................................................. 20616.11.5. Example expression ............................................................................................................. 20716.11.6. Input ................................................................................................................................... 207

a) Positional CAF expressions ............................................................................................. 207b) Grade-dependent expressions........................................................................................... 208

16.12. Merging elements from different Model Files ....................................................................................... 20916.13. How FXMW works ............................................................................................................................ 211

16.13.1. Mining width ....................................................................................................................... 21116.13.2. Small drop cuts.................................................................................................................... 21216.13.3. Small walls.......................................................................................................................... 21316.13.4. Small stumps....................................................................................................................... 21416.13.5. Small holes.......................................................................................................................... 21416.13.6. Sharp corners ...................................................................................................................... 21516.13.7. Slopes ................................................................................................................................. 21516.13.8. Additional arcs .................................................................................................................... 216

16.14. Interfacing with Opti-Cut .................................................................................................................... 21716.15. Precision within Four-X ...................................................................................................................... 21816.16. Four-X / Four-D comparison............................................................................................................... 218

16.16.1. Data files............................................................................................................................. 21816.16.2. FXED ................................................................................................................................. 21916.16.3. FXRB ................................................................................................................................. 21916.16.4. FXST.................................................................................................................................. 21916.16.5. FXOP.................................................................................................................................. 21916.16.6. FXPR.................................................................................................................................. 21916.16.7. FXAN ................................................................................................................................. 21916.16.8. FXUT ................................................................................................................................. 21916.16.9. Spreadsheet codes................................................................................................................ 220

16.17. Error messages.................................................................................................................................... 22216.17.1. Four-X data checks.............................................................................................................. 22216.17.2. Four-X problem traps .......................................................................................................... 22216.17.3. System error Messages ........................................................................................................ 222

16.18. The Lerchs-Grossmann method ........................................................................................................... 22316.19. Request for program enhancement ....................................................................................................... 228

GLOSSARY................................................................................................................................................ 229

INDEX ........................................................................................................................................................ 237

____________________________________________________________________About This Release 9


About This Release

This version of the Four-X manual was released with revision 1.00 of the software.

Four-X enables users to track multiple elements. It is very similar in usage to Whittle Four-D (which onlyhandles one element). Four-D users can refer to page 218 for an overview of the differences.

The major changes to the software included in this revision are:

1. Grade-dependent expressions can now be used for prices, costs and recoveries.

2. It is now possible to use cash flow rather than cut-offs to control what happens to potential ore. Thisusually makes no difference, but there are some significant cases where it does.

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1. INTRODUCTION

1.1. History

In 1964, Lerchs and Grossmann published a mathematical method for determining the exact optimalshape for an open pit in three dimensions.

The method works on a block model of the ore body, and progressively constructs lists of relatedblocks that should, or should not, be mined. The final lists define a pit outline that has the highestpossible total value, subject to the required pit slopes. This outline includes every block that is“worth mining” when waste stripping is taken into account. It also excludes every block that is not“worth mining”. (The definition of a block model appears on page 177, and a more detailedexplanation of the Lerchs-Grossmann method appears on page 223).

The method uses the values of the blocks and what are called “Structure Arcs” as input. Forexample, a structure arc from block A to block B indicates that, if we mine block A, we must mineblock B to uncover it, but not necessarily the reverse.

In 1985, Whittle released “Three-D”, a computer implementation of the Lerchs-Grossmann method.

Three-D operates on a regular block model of the ore body. That is, a volume filled with rectangularblocks that all have the same dimensions. Some of these blocks will contain material of sufficientgrade to make them worth processing, once they are exposed. These blocks are allocated positiveeconomic values consisting of the value of the recoverable product, less the mining and processingcosts. That is, their value is the net cash flow that would result from mining the block in isolation.Waste blocks and air blocks have negative and zero values respectively.

Provided that you do not wish to discount future cash flows with time, the block list produced byThree-D defines the optimal pit outline, and thus provides an excellent starting point for design.

However, if you do wish to discount future cash flows with time, and your expected mine life is morethan two or three years, then Three-D is not sufficient. It cannot allow for the discounting, and wenow know that discounting can have a profound effect on the size of the optimal pit.

Whittle introduced “Four-D” in 1987 to deal with this problem. This package uses the Three-Doptimization technique to produce a set of nested optimal pits, where each is optimal for a differentset of cost/price ratios. The nested pits are then used to guide the mining sequence during simulationof the operation of the mine. The mining sequence is translated into a long-term productionschedule, with cash flows and discounted cash flows. This allows you to select the pit which is mostsuitable for your company’s corporate aims. Typical aims are to maximize the Net Present Value orthe Internal Rate of Return, but almost any criterion can be used. At the same time, Four-D makessensitivity work very easy indeed.

In 1996 Whittle introduced “Four-X”. This program works in a similar fashion to Four-D, but itallows the user to handle resources containing more than one element.

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1.2. Whittle Four-X

The Whittle Programming Four-X package consists of eight separate programs. These are:

FXED – A program for editing and validating the Parameters Files containing the data thatdescribes your model layout, dimensions, slopes, materials and processing methods.

FXRB – A program for manipulating Model, Results and Pit List Files.FXST – A program for generating the structure arcs that ensure that your slope requirements

are met during optimization.FXOP – A program for producing the nested optimal pits.FXPR – A program for printing simple plans and sections of the pits, and for printing plans and

sections of mining phases.FXAN – A program for analysing the nested pits, by doing life-of-mine simulations for different

mining sequences and different economic situations.FXUT – A utility program that can summarise Model, Results and Mining Sequence Files; can

give details of how particular block values are calculated; can give details ofcut-offs; and, can show the various package limits.

FXMW – A program which can adjust push-backs based on pit shells, so as to ensure that miningwidth requirements are met.

Of these FXAN is by far the most important, and you will spend most of your time working with it.

Four-X has been designed to cater for all the different types of mining and processing which canoccur, and to allow designers the maximum scope for creativity. Some of the major features offeredby Four-X are:

• Multiple rock types.• Multiple Elements.• Multiple production processes with variable processing costs limits and throughputs.• Recoveries for each process for each element with optional element processing costs,

production limits and selling costs.• Variable mining costs, limits and throughputs.• User definable economic scenarios that allow full variation with time of all variables.• Discount rates, capital costs and time costs.• Selection of ore by cut-off or by cash flow.• The use of grade-dependent expressions for prices, costs and recoveries.• Spreadsheet output to allow further analysis and plotting of the results.

1.3. Hardware and software requirements

1.3.1. IBM compatible PCs

The minimum requirement is a PC 386 with 4MB of memory, a maths co-processor and30MB of free disk space. The preferred specification is a Pentium, 32MB of memory and100MB of free disk space.

Four-X will run under DOS, Windows 3.x, Windows 95, Windows NT and OS/2.

When used in a multi-tasking environment it can be run as either a foreground or backgroundtask.

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1.3.2. UNIX workstations.

In general, workstations have plenty of memory and hard disk space so that the above limitsdo not apply. Four-X has been ported to all the major UNIX platforms (DEC, HP, SGI andSUN). Check with Whittle Programming for a current list of manufacturers.

1.4. This manual

This manual contains everything you need to know in order to use the Four-X package effectively.

On page 15, there is a section that tells you how to install the package on your machine.

Starting on page 20, there are a number of tutorials and exercises designed to help you learnabout Four-X, and to help you build up the necessary skills to use it.

Starting on page 82, there are a number of chapters giving details of how to run theprograms.

Starting on page 132, there is a chapter on the techniques involved in using Four-X.

Starting on page 149, there are a number of appendices that cover a range of detailedtechnical matters.

The column positions of the various fields in the fixed format versions of the files canbe found in an appendix starting on page 149.

Finally, there is a Glossary and comprehensive Index.

To get a further overview of the manual, we suggest that you take a minute to look through the twoTables of Contents at the front.

1.5. Terminology

There are a number of terms that have meanings that are peculiar to Four-X. These are explained inthe body of the text and in the Glossary, but are also explained here to make it easier to read thismanual for the first time.

CAF See Cost adjustment factor.

Cost adjustment factor The cost of mining and the cost of processing can vary with bothposition in the pit, and with rock type. Four-X deals with this byusing “cost adjustment factors” (CAFs). The costs at the ReferenceBlock are multiplied by the appropriate CAFs to get the actual cost.

“Cost of mining” In this manual, unless the context indicates otherwise, the term “costof mining” means the cost of blasting, loading and hauling a tonne ofrock as waste. See also Reference Mining Cost.

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“Cost of processing” This is the difference between the total cost of blasting, loading,hauling and processing a tonne of material as ore, and the cost ofblasting, loading and hauling the same material in the same positionas waste.

Element A substance of interest in the mineralised material. It need not be aproduct.

Parcel This is part of a block for which the rock type, tonnage and elementcontent (if any) are known. A block may contain zero or moreparcels. The total tonnage of the parcels may be the same as thetonnage of the block, or it may be less. If it is less, the difference iscalled undefined waste, that is, it is waste of unknown rock type. Ifa block has no parcels, the total tonnage of the block is undefinedwaste.

Neither the position of a parcel within a block, nor its shape, isdefined.

Product An “element” which may be extracted for sale.

Examples are gold, copper, diamonds, etc.

Reference block A particular block in the model, chosen by the user, for which allmining and processing costs are calculated. If the costs are differentin other parts of the model, this is handled by rock type CAFs and bypositional CAFs for mining and/or processing.

Reference MiningCost

The cost of mining a tonne of undefined waste at the ReferenceBlock.

The cost of mining a defined rock type as waste at the ReferenceBlock is obtained by multiplying the Reference mining cost by therock type mining CAF.

The cost of mining any type of rock as waste at another block isobtained by multiplying the cost of mining the same rock as waste atthe Reference Block by the positional mining CAF for the block inquestion.

Revenue Factor This is the factor by which the revenue for each block is scaled inorder to produce one of the nested pits. Different Revenue Factorsproduce different pits.

Rock This refers to all material, not just waste.

Time costs Costs that continue during mining regardless of the amount mined,processed or sold. These are often called overheads or G&A(General & Administration) costs.

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Units In Four-X, the units used for quantities of rock, elements andcurrency are arbitrary and it is possible to have different units foreach element.

The units for rock and elements are set by the units used in theModel File, and grades are expressed throughout, as the ratio ofquantities measured in these units.

For example, if the Model File contains rock quantities measured inmetric tonnes, gold quantities measured grams and copper inpounds, then the grades and cut-offs will be expressed in grams pertonne and pounds per tonne respectively. (This manual and Four-Xrefer to tonnes, but no particular scaling is implied by this).

Four-X makes no assumptions about the units of distance, exceptthat they must be the same for the block dimensions and the originco-ordinates in the Parameters File.

The symbol for the unit of currency, which appears in the printedoutput from program FXAN, can be controlled by the user. Thedefault symbol is “$”.

_______________________________________________________________________ Getting Started 15


2. GETTING STARTED

2.1. Installing Four-X

Installation of a PC version of Four-X is very simple.

Either get into DOS mode or open up a DOS window on your Windows system. Then insert the firstdiskette into a diskette drive and, from your hard drive, execute program INSTALL, which is on thatdiskette.

e.g. C:>x:INSTALL

where “x” is the drive letter A or B

After this, carefully follow the instructions on the screen.

If you are using any version of Windows, you may want to install the icons provided on a separatediskette. To do this you need to run the INSTALL program on that diskette. In Windows 3.1 this isdone from the File/Run… menu option. In Windows 95 and NT it is done from the Start/Run…menu option.

Also on a separate diskette, you will have been provided with your fx.ini file. This should be copiedinto your tutorial data directory (e.g. \4x\tutor) and into any directory where you plan to do workwith Four-X.

If you have any difficulty with the installation, refer to the more detailed instructions given to you,both as hard copy, and as file READ.ME on the first diskette.

If you get an error message when you run any of the Four-X programs, refer to the section on errormessages on page 222.

Detailed installation instructions are provided with UNIX versions of Four-X both as hard copy andas a file called read.me which is included with the programs.

_______________________________________________________________________ Getting Started 16


2.2. Menu facility

There is a menu facility in Four-X. This can be used in both DOS and Windows environments. Thereis a slightly different version for use under UNIX. The menu is accessed in DOS or UNIX by typingfxmenu, or from Windows via the Whittle menu icon:

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿³ Files Options Selections ³ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´³ ßÛßßßßÛ ßÛ Ûß ---WORKING DIRECTORY--- ³³ Û Û Û C:\123\MINING ³³ Ûßßßß ÛßßßßÛ ßÛ ßÛ ßÛÜßßÛ Û ³³ Û Û Û Û Û Û ßßß Û Û ³³ ÜÛÜ ÛÜÜÜÜÛ ÛÜÜÜÛÜ ÜÛ ÜÛ ÛÜ tm ---SELECTION MENU--- ³³Four Dimensional Open Pit Economic Optimization ³³ (c) Whittle Programming Pty Ltd, Australia Edit parameters ³ÃÄÄÂÄÄÂÄÄÂÄÄÂÄÄÂÄÄÂÄÄÂÄÄÂÄÄÂÄÄÂÄÄÂÄÄÂÄÄÂÄÄÂÄÄ¿ Reblocking ³³ ³ ³ ³ ³ ³ ³ ³ ³ ³ ³ ³ ³ ³ ³ ³ Structure arcs ³Ã°°°°ÛÛÛÛÅÄÄÅÄÄÅÄÄÅÄÄÅÄÄÅÄÄÅÄÄÅÄÄÅÜÛÛÛÛ°°°°°±´ Optimization ³³±°°°°ÛÛÛÛÜ ³ ³ ³ ³ ³ ³ ³ ÜÛÛÛÛÛ°°°°°±±³ Plan printing ³Ã±±°°°°°ÛÛÛÛÜÄÄÅÄÄÅÄÄÅÄÄÅÄÄÅÄÄÜÛÛÛÛ°°°°°°±±±±´ Mining width ³³±±±°°°°°ÛÛÛÛÛÜÜ ³ ³ ³ ÜÛÛÛÛÛÛÛ°°°°°°±±±±²³ Analysis program ³Ã²±±±°°°°°ÛÛÛÛÛÛÛÄÅÄÄÅÄÄÅÛÛÛÛÛÛÛ°°°°°°±±±±±²²´ Utility routines ³³²²±±±°°°°°ÛÛÛÛÛÛÛ³ ³ ÜÛÛÛÛÛÛÛ°°°°°°±±±±±²²²³ ³Ã²²²²±±°°°°°°ÛÛÛÛÛÛÛÜÜÛÛÛÛÛÛÛÛ°°°°°°±±±±²²²²²´ View output ³³²²²²²±±±±°°°°°°°°°°°°°°°°°°°°°°°°°±±±±²²²²²²³ Invoke editor ³Ã²²²²²²±±±±±±±°°°°°°°°°°°°°°°°°°°°±±±±²²²²²²²´ ³³²²²²²²²²²²²±±±±±±±±±±±±±±±±±±±±±±±±±²²²²²²²²³ eXit from menu ³ÃÄÄÁÄÄÁÄÄÁÄÄÁÄÄÁÄÄÁÄÄÁÄÄÁÄÄÁÄÄÁÄÄÁÄÄÁÄÄÁÄÄÁÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´³ Press <ESC> to Abort ³ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

Menus can be accessed by hot key, arrow keys or a mouse. The instructions may be slightly differentfor UNIX.

2.2.1. Program selection

By default the menu comes up ready to select a program. Item selection can be carried out inthree ways:

a) moving the highlighted bar with the up or down arrow keys. Pressing “Enter” willselect the item.

b) entering one of the highlighted letters, for example E for edit, will select and run theitem.

c) If you have a mouse installed on your computer, then you can operate the menu usingthe point and click method. Items selected by a single click are run.

All programs return to the menu on completion after a “Press any key to continue...”.

You will note that there are options to view output or to edit files. The user can set up his orher preferences in the Files submenu.

_______________________________________________________________________ Getting Started 17


2.2.2. Exit

The menu program can be exited in three ways:

a) Choose eXit from the general selection menu.b) Choose eXit from the Files selection menu.c) Press “Esc” from the main menu bar.

2.2.3. Main menu bar

In a similar manner, other items on the main menu bar can be selected by using the left orright arrow keys, using a highlighted letter or using the mouse. Use the “Esc” key to movefrom a selected submenu to the main menu.

2.2.4. Files submenu

A working directory is maintained from session to session and can be updated files submenu.The working directory is displayed on the menu. Programs are executed from within theworking directory. The system will check that the directory exists.

The program path is automatically set up during the installation process. If you change thelocation of the programs, then this field must be updated. The system will check to ensurethat the programs exist in the directory you specify.

Users can configure the system to their needs or preferences. They can specify the path totheir favourite editor and file viewer. Remember that you only need a text-based editor. Atypical path could be:

c:\dos\edit.com or c:\util\list.com

EDIT is provided with MS-DOS 5.0 and above. LIST is shareware. It is almost universallyavailable, however, if you have difficulty in locating a copy, please contact WhittleProgramming. UNIX users can use emacs, jove, vi etc. The system will verify that theprogram exists.

2.2.5. Option submenu

The colour of the screen can be changed to monochrome or to a variety of colour schemes.

____________________________________________________________________ Using the Package 18


3. USING THE PACKAGE

The minimum that you have to do to design a pit using Four-X is to:

A. Export a Model File from your Generalised Mining Package (GMP).

B. Work out your expected costs.

C. Decide on your slope requirements, allowing for the location of the haul roads.

D. Use program FXST to pre-calculate the slopes and to create a Structure File.

E. Use program FXOP to create a Results File containing nested pits.

F. Use program FXAN to analyse the Results File and to decide which pit to use.

G. Import the pit outline into the GMP from the Results File and do the detailed pit design, using theoutline as a guide.

However, such a simple approach is unlikely to lead to the best design, because it makes no allowance fordata checking, and makes only limited allowance for sensitivity work.

A more sensible approach goes through two stages, using two different block sizes.

Stage one - sensitivity work:

A. Export a Model File from your GMP. (The first time you do this, it is a good idea to prepare plansand sections of the file, using program FXPR, to check that the exporting procedure puts the blockswhere you expect them to be. You can also check quantities, rock types, etc. with FXUT).

B. If the model is too big for sensitivity work, use program FXRB to re-block it. (Keep the original filefor later use).

C. Work out your expected costs.

D. Decide on your slope requirements, allowing for the location of the haul roads.

E. Use program FXST to pre-calculate the slopes and prepare a Structure File.

F. Use program FXOP to produce a Results File containing nested pits. This will only take a shortwhile.

____________________________________________________________________ Using the Package 19


G. Do some preliminary analysis runs for different pit sizes, and then select the best pit for yourpurposes.

H. Use program FXPR to prepare plans and sections of this pit. Check that it is roughly the shape andsize you expected, and that the haul roads will fit where you laid back the slopes to allow for them. Ifthe haul roads will not fit as expected, adjust the slopes accordingly and go back to step E.

I. Do more extensive analysis runs to explore all the economic and throughput sensitivities of theproject. If you are using multiple push-backs, use FXMW to tidy up the outlines. During this work,you will probably find that you settle on a size and sequence of operation that best meets yourrequirements. If you find that the scale of the operation is radically different from what you hadexpected, you may need to re-calculate the costs and go back to step F.

If, after this, you want to explore the sensitivity of the project in relation to the pit slopes, you willhave to go back to step E.

In this first stage you will undoubtedly generate a large number of files. You will find it easier to keep trackof these if you are very systematic in your use of file names, and if you keep notes on what you do.

Stage two - design work:

J. If the model that you exported from your GMP is too big for design work, use program FXRB tore-block it.

K. Use program FXST to pre-calculate the slopes and to prepare the corresponding Structure File.

L. Use program FXOP to do the optimization. Depending on the computer you are using, this may takesome time.

M. If you are using multiple push-backs, use FXMW to tidy up the outlines.

N. Repeat your final analysis runs on this larger Results File to check that there are no significantchanges.

O. Import the pit outline into your GMP and do the detailed design using the outline as a guide.

P. Compare the ore and waste tonnages of the outline with the detailed design. If they differ by morethan two or three percent and this is not due to deliberate deviations from the outline, you probablydid not lay the slopes back correctly. If this is the, adjust them and go back to step K.

This approach will give you a good understanding of the economic and slope sensitivity of the pit, and shouldlead to a design that is stable in the face of change. There are many possible variations of this approach on it,which you will develop with experience.

To simplify this explanation, we have made no mention of Parameters Files. You will require severalversions of the parameters files, and these can be prepared with program FXED. This will become obviouswhen you read the details of the different files, and the details of how to run the programs. For moreinformation, see Parameters Files starting on page 61.

_________________________________________________________________Tutorials and Exercises 20


4. TUTORIALS AND EXERCISES

4.1. Introduction

This section contains six tutorials and six related exercises that are of increasing complexity anddifficulty.

If you are unfamiliar with Four-D or Four-X, we strongly suggest that you first work through thefollowing preparation, Tutorial 1 and Exercise 1, to get a feel for Four-X. Next, read the rest of thismanual. Finally, return to the remaining tutorials and exercises, and work through each of them.This may take you a few hours, but will leave you much better equipped to work on your own data.You will need about 50 megabytes of disk space.

The tutorials and exercises make use of a small set of demonstration data files that are supplied withyour software.

Four-X is a large package with a wide range of facilities. You may only need to use a subset of thesefacilities, but you need to know what facilities exist, and what they can do for you, in order to be ableto choose the subset required for your project.

Note that all of the tutorials use ore selection by cut-off. There is another approach, but this is muchless common. The different ore selection methods are explained on page 182.

4.2. Preparation

The instructions assume that you are working in the directory containing the demonstration data files.On a PC, this is usually directory c:\4x\tutor. Please check this by using the “DIR” command on aPC, the “ls” command under UNIX, or an equivalent command under any other operating system.

You should find at least the following files:

fxtut.modfxtut.partut2.ssdexer3.ssdtut5.mil

fxtut.mod is a Model File for a multi-element model. It contains details of the contents of theblocks. The model represents a small gold/silver deposit.

fxtut.par is a Parameters File that gives information about the model as a whole and about theslope and economic requirements.

tut2.ssd is a Spreadsheet Definition File that is used in Tutorial 2.

exer3.ssd is a Spreadsheet Definition File that is used in Exercise 3.

tut5.mil is a small portion of a Model File that is used in Tutorial 5.



In addition, you must have a license file that is called

fx.ini

in your current, or default, directory. This file, often called an “INI file” or a “dot INI file”, is usuallysupplied to you separately from the programs and tutorial data.

The instructions assume that you know how to start a program, and that the eight Four-X programsare available for you to run. On a PC, they are usually stored in directory c:\4x, and this directory isusually inserted in your “path”, so that the programs can be run from anywhere on your disk merelyby typing in their name. Alternatively, you can use fxmenu, as described on page 16.

4.3. Tutorial 1 - The basics

In working through this tutorial, which will take you an hour or two, you will carry out astraightforward optimization and preliminary analysis of the Results File. The object is to familiariseyou with the general operation of the programs. Details will come later.

In general, there are five steps:

1. You examine your data with FXUT.

2. You convert your slope requirements into a form that is suitable for optimization, usingprogram FXST - the structure arcs program.

3. You do the optimization using program FXOP - the four-dimensional multi-elementoptimization program.

4. You examine the resulting outlines using program FXPR - the print program.

5. You use the analysis program FXAN to analyse the Results File.

4.3.1. Examining your data with FXUT

Start up program FXUT. It will display a heading similar to the one shown below, and willthen ask for certain information.

Whittle Four-X UTILITY PROGRAM Rev 1.00 Licensed for use by -Your Company name will appear here- ------------------------------------------------------------------------------

Note that, on a PC, the alphabetic case of the responses you give is irrelevant. On othersystems, particularly with file names under UNIX, where it is usual to use lower case, thealphabetic case may be important.



It asks:

For a name for the print fileuse tut1.pru1

Whether you want to summarise a data file, show block values, calculate cut-offs, orshow limits- type 1

If you want to use a Parameters File- the answer is Y (yes) for this tutorial

Parameters File- use fxtut.par

What you see on the screen looks like the following. Your responses are shown in bold type,and the symbol “¿¿” indicates that you press the “Enter” key:

Please enter a name for the print file

: tut1.pru¿¿

SELECT MAIN OPTION

1. Summarise a data file 2. Show block value calculations 3. Show cut-off variation with processing CAF 4. Show Four-X system limits

Your choice : 1¿¿

Do you want to use a Parameters File (Y/N) [Y] ? ¿¿

Please enter the name of the input Parameters File

: fxtut.par¿¿

Note that in response to the third question you need only press the “Enter” key, as shownabove. This is because the “[Y]” in the prompt indicates that “Y” is the default answer.Since this is the answer you want to give, there is no need to type it. Whenever a Four-Xprogram asks a question and shows a possible response in square brackets, pressing “Enter”will have the same effect as keying in that response.

The system then asks:

What type of file you want to summarise- in this case you want to summarise a Model File

For the name of the Model File- use fxtut.mod

SELECT FILE TYPE

1. Use Model File 2. Use Results File 3. Use Mining Sequence File

Your choice : 1¿¿

Please enter the name of the input Model File

: fxtut.mod¿¿

1 If an output file already exists, as a result of a previous run, the program will let you know of this fact and will ask for thefile name again. Enter the name again, but put a cross hatch (#) in front of it to indicate that you want to overwrite the existing file.Alternatively you can just enter the cross hatch, which will have the same effect.



A new screen is displayed, and you are asked:

To select the type of summary- enter 1

For rock types which are to be excluded from the summary- leave this blank

If you want to exclude any ore- answer N (no)

If you want to output data for spreadsheet use- answer N (no)

SELECT TYPE OF SUMMARY

1. Counts only 2. Distribution graphs only 3. Both counts and graphs

Your choice : 1¿¿

Rock types may be excluded from the summary.

Enter a list of rock type codes to exclude (separated by a space) or leave blank for no exclusions

: ¿¿

Do you want to exclude any ore (Y/N) [N] ? ¿¿

Do you want to output data for spreadsheet use (Y/N) [Y] ? n¿¿

The program then starts its run, which takes only a few seconds.

Now take the time to examine the Print File in detail, by printing it out, or by putting it onthe screen. Apart from page headings, the print file contains the following:

• A listing of the contents of the Parameters File.• File count information.• Total tonnage and element content.• A summary by rock type.• A summary by bench.

The rock type summary shows that there are approximately 18.8 million tonnes of rock and7.3 million tonnes of ore, with average oxide and sulphide gold grades of .0505 and .0349 ozper tonne, respectively. The corresponding silver grades are .8585 and 2.6689.

Summary by rock type -

Rock No of Mine Proc Total Total ---- Grade distribution --- Type Parcels CAF CAF Tonnes Element Minimum Average Maximum

-------------- ------ ------ --------- --------- -------- -------- --------

WASTE 6818 1.000 1.000 11454240 OXID 348 1.000 1.000 640320 GOLD 32338 0.0185 0.0505 0.1144 SLVR 549736 0.1709 0.8585 2.1434 SULF 3087 1.000 1.000 6667920 GOLD 232906 0.0090 0.0349 0.1102 SLVR 17795885 0.5833 2.6689 7.5412 -------------- ------ ------ --------- --------- -------- -------- --------

TOT 10253 1.000 1.000 18762480 GOLD 265244 0.0090 0.0363 0.1144 SLVR 18345620 0.1709 2.5103 7.5412



4.3.2. Producing the STructure arcs with FXST

Start up program FXST.

It asks:

For a name for the print fileuse tut1.prs2

For the name of the input Parameters File- use fxtut.par

Whether you want to use an Additional Arcs File- the answer is No for this tutorial

For a name for the output Structure File- use tut1.stu2


: tut1.prs¿¿


[fxtut.par] : ¿¿

Do you have a file of additional arcs to add (Y/N) [N] ? ¿¿

Please enter a name for the Structure File

: tut1.stu¿¿

The program then starts its run, which takes only a minute or two. The first thing it does isto report on the screen the slope accuracy for each of the two sub-regions. The report lookslike this:

Preparing the possible arcs list for sub-region 1

With 4 levels, there are 17 possible arcs per block.

This gives an average slope error of 1.8 degrees.

Preparing the possible arcs list for sub-region 2

With 10 levels, there are 53 possible arcs per block.

This gives an average slope error of 1.1 degrees.

A more detailed report on slope accuracies appears in the print file.

FXST gives progress reports as it generates the structure arcs and writes them out as theStructure File. In this case, it should report 1,630,450 arcs as being output.

Now take the time to examine the print file in detail. The print file contains the following:

• A listing of the contents of the Parameters File, and a detailed explanation of theparameters pertaining to structure arcs.

• The name of the output file.• For each sub-region:

• More information on the slope accuracy.• A diagram showing the blocks influenced by the slopes.

2 If an output file already exists, as a result of a previous run, the program will complain and ask for the file name again. Enter thename again, but put a cross hatch (#) in front of it to indicate that you want to overwrite the existing file. Alternatively you can justenter the cross hatch, which will have the same effect.



4.3.3. Doing the OPtimization with FXOP

Start up program FXOP. It will display a heading like the one shown on page 21, exceptthat the program description will be different.

The program then asks:

For a name for the print fileuse tut1.pro

Whether this is a restart run- answer No

For the name of the Parameters File- use fxtut.par

For the name of the Model File- use fxtut.mod

For the name of the Structure File that you have just created- use tut1.stu

For a name for the Work File- use tut1.wrk

For a name for the Results File- use tut1.res

What you see on the screen looks like the following. Again your responses are shown in boldtype. Note how the package has remembered three of the file names from previous runs.This information is stored in the file fx.ini, that is re-written after the user has entered all thefile names and data at the keyboard.


: tut1.pro¿¿

Is this a restart run (Y/N) [N] ? ¿¿


[fxtut.par] : ¿¿

Please enter the name of the input Model File

[fxtut.mod] : ¿¿

Please enter the name of the Structure File

[tut1.stu] : ¿¿

Please enter a name for the Work File

: tut1.wrk¿¿

Please enter a name for the output Results File

: tut1.res¿¿

The program then does the optimizations required to produce a set of nested pits. Variousmessages on the screen tell you what is happening at each stage. (Do not be concerned bythe fact that the first optimization is number 2. This is because optimization 1 is completedduring the preliminary scan).

The time taken for the optimizations depends on your computer, but will be measured inminutes rather than hours. (While you are waiting, you might like to turn to page 223 andread about how the optimization process works).

The last message on the screen, apart from the run-time message, should tell you that it isprinting pit 49.



You may find it surprising that, after 55 optimizations, there are only 49 pit outlines. This isbecause, in some cases, the economic change between two optimizations was too small tochange the outline by even one block, and there were no pits for Revenue Factors less than0.5.

Again, please take the time to examine the print file, tut1.pro. This file is quite big, so lookat it on the screen rather than by printing it out. It contains:

• A listing of the contents of the Parameters File, and a detailed explanation of theparameters pertaining to optimization.

• Details of the files used.• Counts of the blocks read from tut1.mod (12,840).• Details of the progress of each of the 55 optimizations.• Counts of the blocks written to tut1.res (13,691).• For each of the 49 pit outlines starting with the smallest:

• The pit number, and a letter if the number is greater than9 (this is used when printing plans and sections of thepits).

• The Revenue Factor value(s) for which it is optimal.• The applicable cut-offs.• For each bench:

• The tonnes mined (Rock) with the stripping ratio.• The tonnes, element content and grade of the

material processed for both gold and silver.• The tonnes, element content and grade of

unprocessed mineralised material (Reject).• Grand totals of the tonnages and grades.

Pit 1 is an example of the details given for a pit, for a specific Revenue Factor:

Pit 1 which is optimal for ======= a Revenue Factor of 0.50000

--------------------------------- Rock Process Cut-off Type Method Element /over OXID MILL GOLD 0.1118 SLVR 10.6250 SULF MILL GOLD 0.1042 SLVR 9.3750 ---------------------------------

Strip Bench Method Product Tonnes /Element Grade

22 Rock 1840 0.00 MILL GOLD 1840 194 0.1052 SLVR 3189 1.7330 --------- --------- --------- Totals Rock 1840 0.00 MILL GOLD 1840 194 0.1052 SLVR 3189 1.7330 --------- --------- ---------



Pit 48 is an example of the details given for a pit which is optimal for a range of RevenueFactors:

Pit 48 (m) which is optimal for ======= a Revenue Factor range 1.97000 to 2.00000

--------------------------------- ----------------------------- Rock Process Cut-off Cut-off Type Method Element /over /over OXID MILL GOLD 0.0284 0.0280 SLVR 2.6967 2.6562 SULF MILL GOLD 0.0264 0.0260 SLVR 2.3794 2.3437 --------------------------------- -----------------------------

Strip Strip Bench Method Product Tonnes /Element Grade Tonnes /Element Grade

23 Rock 248640 999.99 999.99

22 Rock 1284960 23.08 23.08 MILL GOLD 53360 3002 0.0563 53360 3002 0.0563 SLVR 51454 0.9643 51454 0.9643 Reject GOLD 1840 46 0.0247 1840 46 0.0247 SLVR 525 0.2852 525 0.2852 . . . . . . --------- --------- --------- --------- --------- --------- Totals Rock 22136640 2.11 2.11 MILL GOLD 7117040 260858 0.0367 7125680 261007 0.0366 SLVR 18076407 2.5399 18083364 2.5378 Reject GOLD 89680 1458 0.0163 81040 1308 0.0161 SLVR 63826 0.7117 56869 0.7017 --------- --------- --------- --------- --------- ---------

Note: although the pit outline, and hence the total tonnage, is the same for the two RevenueFactors, the cut-offs, and hence the tonnes and grades processed, are different.

4.3.4. PRinting plans and sections of the pits with FXPR

In order to get some idea of the shape of the nested pits, start up program FXPR. After aheading, this will ask for certain information, as is shown below:


: tut1.prp¿¿


[fxtut.par] : ¿¿

Three types of file can be read:

1. Results File (with defined pits) 2. Model File (with optional zones) 3. Mining Sequence (with periods)

Your choice [1] : ¿¿

Please enter the name of the input Results File

[tut1.res] : ¿¿

There are two ways of displaying blocks containing rock:

1. Using pit numbers (1-9,A-Z,a-z) 2. Using value signs (+mineral,-waste)

Your choice [1] : ¿¿

Do you want to emphasise a particular pit number (Y/N) [Y] ? n¿¿

Which planes do you want to display (1=XY, 2=XZ, 3=YZ) [1 2 3] ? ¿¿

The program then starts its run, reads in the Results File and prints plans and sections of themodel. These can be found in the print file, which you named tut1.prp. You should viewthis file on the screen.

You will find plans and sections laid out like the following simple plans. Note that theproportions are incorrect because the characters used to represent each block are not thesame shape as a block.



The plan below shows the top bench of the model. The dots represent air blocks. Thus, thetopography slopes upwards to the right. The letters indicate the smallest pit that includeseach block.

XY plane for Z = 23 facing in the direction of -ve Z

Symbols: "." is air, "1-9,A-Z,a-z" denote pits

**********|*********|*********|**** *............................... * *............................... * *............................... * *............................... * -............................... - *..............................L * *..............................9M * *..............................9BU* *..............................9BK* *..............................ABD* *..............................ADD* *..............................ADD* *..............................ADD* *..............................DDD* -.............................AADD- *.............................AADF* *.............................AAFF* *.............................ACFI* *.............................BCFI* *.............................BCFH* *.............................CCFH* *.............................CFFH* *.............................CFFI* *.............................CFFI* -.............................DFFI- *.............................DFFI* *.............................DFFI* *............................DDFII* *............................DFFII* *............................DFHIO* *............................FFIIO* ............................FHINO* Y............................GINOY* ...........................FHNOY * -...........................GMOY - *...........................GMW * *..........................GIMY * *..........................GIU * *..........................GNa * *..........................GN * *.........................GIN * *.........................INO * *.........................IN * *.........................LO * -.........................OO - *.........................Of * *........................Of * *........................T * *........................k * *........................ * *........................ * *....................... * *....................... * *...................... * -...................... - *..................... * *..................... * *.................... * *.................... * *.................... * *.................... * *.................... * *.................... * *.................... * **********|***** X *|*********|****



The plan below shows the third bench from the top, and the full extent of the pits can now beseen.


Symbols: "." is air, "1-9,A-Z,a-z" denote pits

**********|*********|*********|**** * * * * * * * Eb * - EEEb - * 9999Eb * * bC999999L * * bC99999999M * * MGGC99999999BBU * * KDBBB99994999ADKU * * KDBBB999999799ADDKU* * KKDBBBA999999999ADDDK* * JHHDBBB9999999999ADDDD * * UHDDCBBB9999999999AADDDPh* - UGDCCCBB9999999599AAADDFP - * UGDCCCBBB9999995999AAAAFFS * * UGDCCCB999999999999AAAACFIOS* * UGDCCCC999999999999AAAABCFINS* * WGDCCCC9999992999999AAABBCFIIP* * bGGCCCC9999939999999AAABBCCFIIO* * kWGECCC99999999699999AABBBCFFHIO* * bGGDCC99999999666999BBBBBCCFFIIO* * bGDDCC9999997996999ABBBBBCCFFIIO* *kWGDDCC9999999999999BBBBBCCDFFIIO* -bHGDDCC999999999999ABBBBBCCDFFIIO- *bGGDDCCB9999999999ABBBBBCCCDFFIIO* *bGEDCCCBB99999999ABBBBBBCCDDFIIOY* *HGDDCCCBBB999999ABBBBBBBCDDFFIIOZ* *GGDDCCCBBBB9AAAABBBBBBBCCDDFHIOO * *GEDDCCCBBBBBAABBBBBBBBBCDDFFIIOO * *GEDDCCCBBBBBBBBBBBBBBBCDDFFHINOY * EEDDDCCCBBBBBBBBBBBBBCDDEFGINOY * YEEDDDCCCCBBBBBBBBBBBCDDEFFHNOY * EEDDDDCCCCBBBBBBBBCCDDEFFGMOY * -GEEDDDCCCCCBBBCCCCCDDEEFGGMW - *GEEEDDDCCCCCCCCCCCDDEEFGGIMY * *GGEEEDDDCCCCCCCCCDDEEFGGGIU * *JGGEEEDDDDCCCCCCDDEEFGGGGNa * *JIGFEEEDDDDDDEEEEEEFGGGGGN * *JJGGFEEEDDDEEEEEEEFFGGGGIN * *SJIGGFEEEEEEEEEEEFFGGGGINO * *SJJIGGFFEEEEEEEEFFGGGGIIN * *mSJJIGGFFFEEEEFFGGGGGIILO * *mTMJIIGGGGGGGGGGGGGGIILOO * - TSMJIIGGGGGGGGGGGGIIJNOf - * TSMJIIGGGGGGGGGGIIJNOf * * TTSMJJIGGGGGGGGIIJNOT * * TTSMJJIIGGGGGIJJNOTk * * TTSNJJJIIIJJJNNOTk * * TTSNNJJJJJNNOOTk * * TTSNNNNNNNOOTk * * lTTSSSOOOSSTk * * lTTTTTTTTkk * * lkkkkkkkk * - lllll - * * * * * * * * * * * * * * * * * * **********|***** X *|*********|****

If you examine the print carefully, you will see that pits 2, 3 and 4 each add one block beforepit 5 adds two, etc.



4.3.5. ANalyzing the Results File with FXAN

Now do a preliminary analysis of the Results File and its nested pits by starting programFXAN. After a heading, this will ask for certain information as is shown below. Do not beconcerned at this stage if some of the items do not mean very much to you. If you make amistake after the spreadsheet question, there are two ways of making corrections. You cantype in the caret symbol “^” to go back to the previous question, or you can continueentering values and just respond with “n” when the program asks if the “above values arecorrect”. It will then repeat all the questions with your previous responses as defaults, andyou can correct your error when you get to it.

First you set up the necessary files and initialize the run:


: tut1.pra¿¿


[fxtut.par] : ¿¿


[tut1.res] : ¿¿

Do you want to output data for spreadsheet use (Y/N) [Y] ? n¿¿

RUN DESCRIPTION

: Multi-element tutorial 1¿¿

Do you wish to enter time/replacement costs explicitly (Y/N) [N] ? ¿¿

Next you enter the required economic values:

Please enter an analysis request

ECONOMIC VARIABLES

Initial capital expenditure

[0] : ¿¿

Reference mining cost

[1.25] : 1¿¿

Price to be obtained for the GOLD

[400.00] : 380¿¿

Price to be obtained for the SLVR

[5.00] : 5.1¿¿

Select a pit number ( 1 to 48)

: 19¿¿

Discount percentage per period

[0] : 10¿¿

Maximum TONNES of rock per period

[0] : 4m¿¿

Maximum TONNES per period for method MILL

[0] : 1m¿¿

Maximum units of GOLD per period

[0] : ¿¿

Maximum units of SLVR per period

[0] : ¿¿



The program then offers to modify the other Parameters File values:

OTHER VALUES (* indicates a modified value)

Mining dilution: 1.000 recovery: 1.000

Elements: GOLD SLVR Selling cost: 0 0

Rock types: WTHR OXID SULF Mining CAF: 1.000 1.000 1.000 Rehabilitation cost: 0 0 0 Throughput factor: 1.000 1.000

Processes: MILL.OXID MILL.SULF

Do you want to modify any of these values (Y/N) [N] ? ¿¿

You now tell the program what schedules you want to produce:

SCHEDULE VARIABLES

Do you want to produce a specified schedule (Y/N) [N] ? ¿¿

Do you want to produce the worst case schedule (Y/N) [Y] ? ¿¿

Do you want to produce the best case schedule (Y/N) [Y] ? ¿¿

Finally you tell it what you want to do next:

Are the values for that request correct (Y/N) ? y¿¿

1 analysis scenarios have been defined so far

Enter another analysis request (Y/N) ? n¿¿

Do you want a full print (Y/N) ? y¿¿

The run time will be only a minute or two.

We strongly suggest that you print out the six pages of the print file tut1.pra at this point. Itcontains a wide range of information that we will now discuss in detail.

First, there is a listing of the Parameters File and the expanded details of the relevant parts ofthis file. This appears at the start of every Four-X print file. Next, there are the countsobtained in reading through the Results File. The program should have read 13,691 blocks,of which 2,587 were air.

The remainder of the print file consists of details of the consequences of sequencing andscheduling pit 19 in two different ways. The first is a “worst case schedule”, with eachbench mined completely before the next bench is started. This is almost always practicable,but generally produces the worst possible Net Present Value (NPV). The second schedule isa “best case schedule” in which pit 19 is mined out in a series of 19 push-backs! This is, ofcourse, almost never practicable, but, if it were, it would give the best possible NPV. It isvery useful as a target to aim for when devising a working schedule. We will discuss thislater.



Please examine the details of the two schedules that you have just produced.

Whittle Four-X ANALYSIS OF PIT OPTIMIZATION RESULTS FILE Page 4 Rev 1.00 10:55 Licensed for use by -Your Company name will appear here- 17-NOV-97 ------------------------------------------------------------------------------ Multi-element tutorial 1

General cost of mining ($/TONNE) : 1.00 GOLD price ($/UNIT) : 380.00 SLVR price ($/UNIT) : 5.10 Pit number : 19 (J) Discount rate (% per period) : 10.00 Calculation based on selection by : Cut-off Maximum mining per period (TONNES) : 4000000 Maximum MILL per period (TONNES) : 1000000 Results File : tut1.res

Rock Proc Meth Proc T/R Recov Thresh Minimum Maximum Cut-off Type Element Cost adj Ratio Grade cut-off cut-off /over

OXID MILL 21.25 GOLD 0.950 0.0589 SLVR 0.800 5.2083 SULF MILL 18.75 GOLD 0.900 0.0548 SLVR 0.800 4.5956 ==============================================================================

WORST CASE SCHEDULE: with each bench mined completely before proceeding

Each starts with a heading like the above, setting out the economic scenario for which theschedule was developed. It includes all the figures that you entered when running FXAN,plus some figures from the Parameters File and cut-offs worked out by the program (basedon the presence of each element on its own). You will probably recognise most of thesevalues. The heading is the same for both schedules. The letter “J” next to the pit number isthe character used to identify the pit in the plans and sections output by FXPR.

Each schedule then gives details of what will happen in each time period.

The first line for a typical period is explained below.

Category Element Process Strip Costs and NPV Method\rock Units Tonnes /Feed Income Discounted Period Element Limit Input Input Grade Cash Flow Cash Flow ==============================================================================

4 Rock MILL 2600190 1.60 -2600190 -1705985

(1) (2) (3) (4) (5) (6) (7)

(1) The period number was 4.(2) The category “Rock” indicates that this line gives figures for all the material mined.(3) The “MILL” throughput sets the limit on material handled in the period.(4) 2,600,190 tonnes of material (ore and waste) was mined in the period.(5) The stripping ratio (material not processed/material processed) was 1.60.(6) The cost of mining all of the material as waste was $2,600,190.(7) The discounted cost of mining all of the material as waste was $1,705,985.



The second line in a period is explained below:


4 Rock MILL 2600190 1.60 -2600190 -1705985 MILL SULF 1000000 -18750000 -12301875

(1) (2) (3) (4) (5)

(1) This indicates that this line gives figures for processing method “MILL”.If more than one processing method is used, this line is repeated as required.

(2) This indicates that this line gives figures for rock type “SULF”.If more than one rock type is used, this line is repeated as required.

(3) 1,000,000 tonnes of material was fed to this processing method.(4) The cost of processing associated with this processing method was $18,750,000.

“Processing cost” includes any extra mining cost for ore.(5) The discounted cost is $12,301,875.

The processing method lines are followed by lines giving details of the products beingextracted.


4 Rock MILL 2600190 1.60 -2600190 -1705985 MILL SULF 1000000 -18750000 -12301875 GOLD 40038 0.0400 13692937 8983936

(1) (2) (3) (4) (5)

(1) This indicates that this line gives figures for product “GOLD”. If more than oneelement is present, this line is repeated as required. In this case, the next line givesthe details for SLVR.

(2) The material processed contained 40,038 units of GOLD.(3) The average grade of the material processed was 0.04.

Note that this grade is below the cut-off (0.0548) given for gold, in rock type SULF.This is because the program allows a combination of gold and silver to contributetowards the revenue. This is further explained on page 190.

(4) The revenue associated with this element was $13,692,937.(5) The discounted revenue cash flow is $8,983,936.

A line giving similar figures for SLVR follows the one for GOLD.



The processing method lines are followed by (optional) lines giving details of material thatwas associated with a processing method, but which was rejected because the grade wasbelow cut-off:


4 Rock MILL 2600190 1.60 -2600190 -1705985 MILL SULF 1000000 -18750000 -12301875 GOLD 40038 0.0400 13692937 8983936 SLVR 3335028 3.3350 13606916 8927497 Rejected 530443 GOLD 13046 0.0246

(2) (1) (3)

(1) The rejected tonnage was 530,443.(2) The rejected material contained 13,046 units of GOLD. If more than one element is

present, this line is repeated as required.(3) The average grade of the rejected material was 0.0246.

A line giving similar figures for SLVR follows the one for GOLD.

The printout for each period ends with a totals line:


4 Rock MILL 2600190 1.60 -2600190 -1705985 MILL SULF 1000000 -18750000 -12301875 GOLD 40038 0.0400 13692937 8983936 SLVR 3335028 3.3350 13606916 8927497 Rejected 530443 GOLD 13046 0.0246 SLVR 809944 1.5269 ---------- ---------- Bench 14 to bench 11 5949662 3903573

(1) (2) (3)

(1) During this period, mining started somewhere on bench 14 and ended somewhere onbench 11. (The layout of the information given here depends on the miningsequence).

(2) The total cash flow for the period was $5,949,662.(3) The total discounted cash flow for the period was $3,903,573.

At the end of each schedule, the grand total figures appear, together with the mine life inperiods:

------------------------------------------------------------------------------ Totals Rock 17004000 3.15 -17004000 -12861577 MILL OXID 281520 -5982300 -5183677 GOLD 18924 0.0672 6831383 5919961 SLVR 314322 1.1165 1282434 1111486 MILL SULF 3818880 -71604000 -47183487 GOLD 154716 0.0405 52912700 34822934 SLVR 12909876 3.3805 52672295 34685344 Rejected 2220720 GOLD 60425 0.0272 SLVR 3019696 1.3598 Internal rate of return % N/A ---------- ---------- Total number of periods 5.52 19108512 11310984 ==============================================================================



Note that a period is whatever length you wish, and you define it by the discount rate andthroughputs that you supply. The mine life is worked out on the assumption that all periods,except the last, are of equal length. However, periods can be of different lengths if you wish,as is explained on page 119.

The grand total of the discounted cash flows given at the bottom right of the printout shownabove is the Net Present Value of the operating cash flows. (If we subtract the up-frontcapital costs, we obtain the NPV of the mine). Note that these values are very different inthe two schedules. Clearly, the order in which this pit is mined can have a profound effect onNPV. FXAN can be used to explore different long-term mining sequences.

Look at the tonnages mined and milled in each period in relation to both schedules.Although the grand totals of the tonnages mined and milled are the same in both cases, theperiod tonnages follow quite different patterns. You will notice that the rock tonnage in thefirst period of the worst case schedule is exactly the limit of 4,000,000 tonnes, but the milldoes not receive its desired input of 1,000,000 tonnes. This is repeated in periods 2 and 3,but in periods 4 and 5 the stripping rate falls off and the mill is fully supplied. Period 6 justuses up the remaining tonnages. If this deposit is to be mined in the worst case sequence,then something will have to be done about the high stripping in the earlier years. We willreturn to this later.

Conversely, in the best case schedule, the mill is fully supplied in periods 1 and 2, butunder-utilised for the rest of the mine life. In other words, in worst case mining, strippingratio starts high and ends low, whereas in best case mining the reverse is true. This is, ofcourse, exactly what you would expect.



4.3.6. File summary

The following diagram gives a summary of the files used by each program in this tutorial. Ineach case, the input files are on the left and the output files are on the right. The output filesalways start with the print file.

Input Program Output

fxtut.parfxtut.mod FXUT

tut1.pru

fxtut.parFXST

tut1.prstut1.stu

fxtut.parfxtut.modtut1.stu

FXOPtut1.protut1.wrktut1.res

fxtut.partut1.res FXPR

tut1.prp

fxtut.partut1.res FXAN

tut1.pra

4.3.7. What you have learnt

In working through this tutorial, you have learnt how to run five of the programs and youhave learnt what files are required. You have also seen how Four-X takes note of thefile names that you use, and provides them as defaults, to save you repeatedly re-typingthem. You have also seen how you can look at the pit outlines and how you can start tosimulate the operation of the mine, with all its tonnages, grades and cash flows.

Although you have now completed this tutorial, it is important to keep the files that yougenerated, including the print files, because some of them are used again in the tutorials andexercises that follow.

4.4. Exercise 1 – Using different pit sizes

In the analysis done in Tutorial 1, you examined the consequences of mining pit 19 in two differentsequences. We now suggest that you do the same analysis for a range of different pit numbers, sayfrom 14 to 21, so as to find the pit with the best NPV under the same economic conditions.

You do this by running FXAN again. Use a different print file name, such as exer1.pra, butotherwise enter the same file names and values except for the pit number, which should be 14 the firsttime through. When you get to the question which asks you if you want to enter another scenario,answer “y” or “Y”. FXAN will return to the question about the reference mining cost, but now thedefault response will be what you entered the first time through.



All you have to do to repeat the same study for a different pit number is to press “Enter” at everyquestion except the pit number question, and there, you key in the pit number you require (15).Continue looping round the questions, entering a new pit number each time (16,17,18,19,20,21),until you have entered all you require. At this point, answer “N” to the question about anotherscenario.

Since, with five economic scenarios, you would produce a great deal of printed output and you onlyrequire the totals, answer “N” to the question about a full print. FXAN will then complete the run.This will take a minute or two.

Examine the print file from this run (you may find it convenient to print it out). You will find that,because of your response to the question about a full print, the period information is missing but thegrand total information remains.

Concentrate on the grand total of the discounted cash flows, that is, the Net Present Value. Whichpit has the highest NPV for worst case scheduling, and which has the highest NPV for best casescheduling? Look at the difference in total rock and ore tonnage for the two pits.

You should find that, if the pit is to be mined in the worst case sequence, mining pit 15 rather than pit19 will increase the NPV of the cash flows by 6% while mining 32% less and processing 22% less.Indeed, if pit 14 is mined, we still get an increase in NPV of 5%, and the pit is 40% smaller! Thesepercentage changes of NPV become much greater when we subtract the initial capital expenditure.

Conversely, for the best case sequence, pit 19 has the highest NPV.

The following graph shows the relevant values:

0

2

4

6

8

10

12

14

16

18

14 15 16 17 18 19 20 21

Pit number

NP

V a

nd

To

nn

es (

mill

ion

s)

Tonnage

Worst casemaximum NPV

Best casemaximum NPV

We deliberately got you to do this analysis the hard way, with each scenario being entered separately.There is, in fact a much easier way, and that is to enter “14-1-21” as the pit number the first timethrough. This tells FXAN to use 14 as the first pit number, 14+1 as the second etc. until 21 isreached. This is the equivalent of entering 8 scenarios in one hit. There are a number of facilities inFour-X that make repetitive work much easier, and we will introduce you to others later.



4.5. Tutorial 2 – More analysis of the Results File

Unless you have already done so, we strongly suggest that you read through the whole manual beforeworking through the remainder of these tutorials and exercises. If you do not, you may find themhard to follow.

With FXAN you are able to run a large number of simulations very quickly, and the output from thesimulations can be voluminous. To make FXAN more useful, you need tools that make it easy to setup large numbers of simulations simply and systematically. You also need tools to extract, from theflood of output, just the data that you are interested in. This tutorial introduces you to these tools.

In a study of a Results File, it is very common to want to re-run FXAN with small variations in thescenario values. The easiest way to do this is to “log” your keyboard responses to a Log File whichyou can then edit and re-play, as required. An example of this is given in this tutorial. Anexplanation of Log Files starts on page 85.

In Exercise 1, we mentioned the use of ranges as a means of entering a series of values, and we givean example of their use in this tutorial. A full explanation starts on page 115.

When you do a lot of simulations, you generate a large print file even if you opt not to have a fullprint, and the task of extracting the figures that you are interested in can become quite onerous.Four-X includes a facility to output selected values to a separate file, and, because users often wantto do further manipulations of the figures, these are output in a format that is suitable for input to aspreadsheet program. There are two files involved in this. One is a small text file that lists theparticular items that you want to output. This is called a Spreadsheet Definition File and it can easilybe prepared with a text editor. The other file is the output itself that can be viewed on the screen,printed out, or input to a spreadsheet program. An explanation of spreadsheet files starts on page 79,and a description of the detailed formats starts on page 166.



The Spreadsheet Definition File used in this tutorial is called tut2.ssd. It contains the followingsingle line of text:

Gra GOLD/Price Pit/FI Rock/tgw Mill/tiw OPVALUE/DTW

The items in the line have the following meanings:

Gra Indicates that the remaining codes on the line refer to grand total amounts.

GOLD/Price Indicates that we want to output the gold price.

Pit/FI Indicates that we want to output the final pit number.

Rock/tgw Indicates that we want to output total rock (ore and waste) in-groundtonnage for the worst case schedule.

Mill/tiw Indicates that we want to output the total tonnage input to the mill for theworst case schedule.

OPVALUE/DTW Indicates that we want to output the total open pit value for discounted worstcase, that is the NPV of the cash flows.

As you can see, the codes can be in upper case and/or lower case, or a mixture of both. There aremany other codes that we could have used, and these are detailed on pages 167 to 173.

In this tutorial you are going to find the best pit sizes for a range of gold prices, under the assumptionof worst case scheduling.

4.5.1. Running FXAN with a Log File and spreadsheet output

Start FXAN and type in the values shown in the following boxes. You will notice that thingsare done a little differently from before.

You start by entering a logging command instead of a print file name. “!LOG tut2.loa” tellsthe program to start logging your responses and to ask the question again. In fact, this canbe shorter: “!LOG” can be shortened to “!L” or “!l”, and “tut2.loa” can be shortened to“tut2”.

Four-X has a list of default file name extensions in fx.ini, and will add the required extensionwhen you do not provide one. For example, when the program asks for a name for the printfile, you only need to type in tut2. FXAN automatically adds .pro.




[exer1.pra] : !L tut2.loa¿¿ NOW LOGGING ALL INPUT

[exer1.pra] : #tut2¿¿


[fxtut.par] : ¿¿


[tut1.res] : ¿¿

Do you want to output data for spreadsheet use (Y/N) [Y] ? ¿¿

Please enter the name of the Spreadsheet Definition File

: tut2¿¿

Please enter a name for a Spreadsheet Output File

: #tut2¿¿

RUN DESCRIPTION

: Multi-element tutorial 2¿¿

Do you wish to enter time/replacement costs explicitly (Y/N) [N] ? ¿¿

Please enter an analysis request

ECONOMIC VARIABLES

Initial capital expenditure

[0] : ¿¿

Reference mining cost

[1.25] : 1¿¿

Price to be obtained for the GOLD

[400.00] : 300-50-450¿¿

Price to be obtained for the SLVR

[5.00] : 5.1¿¿

Select a pit number ( 1 to 48)

: 10-1-20¿¿

Discount percentage per period

[0] : 10¿¿

Maximum TONNES of rock per period

[0] : 4m¿¿

Maximum TONNES per period for method MILL

[0] : 1m¿¿

Maximum units of GOLD per period

[0] : ¿¿

Maximum units of SLVR per period

[0] : ¿¿

OTHER VALUES (* indicates a modified value)

Mining dilution: 1.000 recovery: 1.000

Elements: GOLD SLVR Selling cost: 0 0

Rock types: WTHR OXID SULF Mining CAF: 1.000 1.000 1.000 Rehabilitation cost: 0 0 0 Throughput factor: 1.000 1.000

Processes: MILL.OXID MILL.SULF

Do you want to modify any of these values (Y/N) [N] ? ¿¿



SCHEDULE VARIABLES

Do you want to produce a specified schedule (Y/N) [N] ? ¿¿

Do you want to produce the worst case schedule (Y/N) [Y] ? ¿¿

Do you want to produce the best case schedule (Y/N) [Y] ? ¿¿

Are the values for that request correct (Y/N) ? y¿¿

44 analysis scenarios have been defined so far

Enter another analysis request (Y/N) ? n¿¿

Do you want a full print (Y/N) ? y¿¿

The run will take a minute or two. When it has finished, print out the Log File tut2.loa, andthe Spreadsheet Output File tut2.sso.

4.5.2. Examining the Log File

You will see that the Log File, tut2.loa, contains a list of abbreviated prompts and yourresponses. The run can be repeated exactly by starting up FXAN and then entering “!usetut2.loa”. Again, this can be shortened to “!u tut2”. Indeed, if you want to re-run the sameLog File that you ran with a program the last time, even if you have edited it in between,“!u” is sufficient, because Four-X remembers Log File names as well. All this makes it veryeasy to re-run complicated analyses.

4.5.3. Examining the spreadsheet output

Now examine the Spreadsheet Output File, tut2.sso. You will find that it contains fivecolumns of numbers, each headed by one of the codes from the Spreadsheet Definition File.You will find that the range of pit numbers has been dealt with for each gold price in turn. Agreat deal can be learnt about the economics of the project from this output.

If NPV is your criterion, and you know that the gold price is going to be $450/oz, thenclearly you should use pit 17 as your starting point for design. Similarly, if the price is to be$300/oz, you should use pit 14. Pit 14 is only 70% the size of pit 17, so you probably wouldnot use the same infrastructure and mill size in the two cases. However, let us ignore this forthe moment.

If you do not know what the gold price is going to be, but you are convinced that it will besomewhere between $300 and $450, can you find the best compromise? What you do willdepend on your interpretation of “best”, but let us assume that you want the pit that willdeviate as little as possible from the highest possible NPV for each price in the range.



The following graph is created from the information in the Spreadsheet Output File, tut2.sso,using a spreadsheet program.

NPV for different silver prices

0

5

10

15

20

25

30

35

10 12 14 16 18 20

Pit number

NP

V -

mill

ion

s 7

6

5

4

8

Ten minutes with a calculator will reveal that pit 15 guarantees a deviation of no more than4.7% over the range.

So far we have looked at maximum NPV as the sole criterion for pit evaluation, however,there are many other corporate strategies that can be considered. In general, these otherobjectives will be met at a lower NPV. They can all be evaluated with the aid of aspreadsheet and plotted for ease of display. Other objectives can include:

• Keeping production costs below a certain $/oz or $/gm.• Maximizing mine life.• Providing a certain rate of return on investment.• Balancing mining and production rates.• Keeping the mill fully supplied.• Minimizing risk.• Starting with a small scale operation, followed by upgrade when finances allow.

4.5.4. File Summary

The following diagram gives a summary of the files used by FXAN in this tutorial.


fxtut.partut1.restut2.ssd

FXANtut2.loatut2.pratut2.sso




In working through this tutorial, you have learnt how Log Files and spreadsheet output cangreatly facilitate work with Four-X, and how Four-X will automatically add appropriateextensions to the file names you use.

You have also seen how you can further analyse the data to select appropriate pit outlinesaccording to almost any criterion.

4.6. Exercise 2 – Varying silver prices

In Tutorial 2 we only looked at the effect of variation in gold prices. What happens if silver priceschange?

The easiest way to repeat the analysis run of Tutorial 2 is to first make a copy of the Log Filetut2.loa that you created in that tutorial and name it exer2.loa. Next edit exer2.loa with any texteditor as follows:

1. Change the name of the print file from #tut2 to #exer2.Take care to keep the response lined up with the other responses. The cross hatch (#)ensures that the file is over-written if you run it again.

2. Change the Spreadsheet Output File to #exer2.

3. Change the GOLD price to 380 (default value).

4. Change the SLVR price to 4-1-8.

Run FXAN and enter “!use exer2”.

Print out the Spreadsheet Output File exer2.sso, and study it in the same way as you did in Tutorial2.

NPV for different silver prices

0

5

10

15

20

25

30

35

10 12 14 16 18 20

Pit number

NP

V -

mill

ion

s 7

6

5

4

8



4.7. Tutorial 3 – Improving the value by using contract mining

Up to this point we have concentrated on the over-all value of the pit without concerning ourselvesabout what happens in the individual periods. Let us assume that you want to mine pit 15 in theworst case mining sequence with the economic values and constraints used in the first tutorial.

These are: Reference mining cost $1.00/TPrice of gold $380Price of silver $5.10Discount rate 10%Rock throughput 4,000,000 T/yMill throughput 1,000,000 T/y

In the printout of the periods from Exercise 1, you will see that the mill runs at only 28% of capacityin the first period and at only 92% of capacity in the second period. This may cause operationalproblems, but it is also an economic problem because of the wasted capacity.

If you could organise some contract mining to increase the mining capacity during the first period,you might be able to alleviate the problem, and increase the NPV of the pit. The question, of course,is how much contract mining, and at what price?

The effect that contract mining would have on the rock mining capacity in the first period can easilybe handled in FXAN by increasing the capacity for the first period only. If you want to add onemillion tonnes of contract mining in the first period, then, when the program asks for the maximumtonnes of rock per period, you enter:

5m p2/4m

This sets the maximum tonnes of rock per period to 5,000,000 tonnes for the first period, and then to4,000,000 tonnes thereafter.

To evaluate the effects of a range of capacities in the first period, you enter:

4m-0.5m-8m p2/4m

Since contract mining is usually more expensive than in-house mining, you need to take this intoaccount. You could do this by putting the adjustment in as an initial capital expenditure, but in thiscase it is easier to handle it outside FXAN.

4.7.1. Doing the analysis run

To extract the necessary figures, you will need to prepare a small Spreadsheet Definition Filecontaining the following:

Gra ROCK/LIMIT OPVALUE/DTW

We suggest that you call this file tut3.ssd.

Next run FXAN, using the same figures as in Tutorial 1, except for the period variationshown above for the maximum tonnes of rock.



This should produce a Spreadsheet Output File like the following:

Multi-element tutorial 3

Grand totals:

ROCK OPVALUE /LIMIT /DTW

4000000 12006865 4500000 12222471 5000000 12387104 5500000 12552464 6000000 12740453 6500000 12941871 7000000 13139542 7500000 13286289 8000000 13286289

4.7.2. Further manipulating the output

If you load this data into a spreadsheet program and calculate the adjusted NPVs for a rangeof contract mining cost premiums (from 20 cents to 40 cents per tonne) you should get thefollowing table.

Raw Contract Premiums for contract mining

NPV mining +20c +25c +30c +35c +40c

tonnes Additional profit

12006865 0 0 0 0 0 0

12222471 500000 115606 90606 65606 40606 15606

12387104 1000000 180239 130239 80239 30239 -19761

12552464 1500000 245599 170599 95599 20599 -54401

12740453 2000000 333588 233588 133588 33588 -66412

12941871 2500000 435006 310006 185006 60006 -64994

13139542 3000000 532677 382677 232677 82677 -67323

13286289 3500000 579424 404424 229424 54424 -120576

13286289 4000000 479424 279424 79424 -120576 -320576



If you plot the additional profit versus contract mining rate for the different premiums andadd an overlay showing the mill input in period one, then you will get the following graph,where all the scales are in millions.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 1.0 2.0 3.0 4.0

Contract mining

Mill

in p

erio

d 1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

Ext

ra p

rofi

t Mil l

+20c

+25c

+30c

+35c

+40c

This shows that there can be considerable profit gained by the use of contract mining(depending on the rate). Additional capacity of up to 3.5m tonnes can be utilised.


In working through this tutorial, you have learnt how to vary constraints with time and howto further manipulate output from FXAN.

4.8. Exercise 3 – Improving the value by using two push-backs

The basic problem with mining pit 15 a bench at a time is that initially the stripping ratio is very high.This makes it impossible to maintain mill production at the full rate without spending an amount oncontract mining. This eats severely into the profit.

One way round this is to mine pit 15 in a series of push-backs, or mining phases. As you saw in thefirst tutorial, best case mining suffers from the opposite problem in that initially the stripping ratio islow, but so high later that the mill cannot be fully supplied. This is better than the worst case miningwe have been looking at, because it allows you to use the spare mining capacity that you have in theearly periods to do some preparatory stripping. However, best case mining involves 15 push-backs,which is obviously not feasible, and remember that, when you mine waste early, you reduce the NPVbecause the cost of this mining is not discounted as much as it would otherwise be.

In this exercise, assume that it is feasible to do two preliminary push-backs to pits 11 and 13 beforecompleting pit 15. You may care to check this by examining bench 21 of the plan that you producedin the first tutorial (bench 21 is the first which is entirely below the surface).

You can also run FXUT on the Results File and look at the shell and pit volumes to give you an ideaof the best push packs.

Do an analysis run with the Tutorial 3 figures, but fix the rock throughput at 4,000,000T/y, andanswer “yes” to the question about producing a schedule with specified push-backs. FXAN will thenask you for the push-backs and the lag. You should enter “11 13 15” for the push-backs, but whatlag should you use? Why not try a range of values like “1-1-20”?



You should be able to find a specified push-back schedule that keeps the mill fully supplied. Thisminimizes the amount of stripping you have to do before the period in which it is required, and whichleaves sufficient spare mining capacity in the early periods to do it.

You should be able to find a case where the NPV is about $13.8m, which is a great improvement onthe $12m for worst case mining and almost the same as the best case value of $14m. The addedcomplication of the extra push-backs will cost something, but, on the other hand, mining a small pitto start with allows you to redesign the outer pit if economic conditions change.

Hint: Use spreadsheet output for both period and grand total values.

You will need lag, period, total rock and tonnes input to the mill for each period.

You will need lag and the discounted open pit cash flow for the specified push-back case for eachgrand total.

File exer3.ssd, which is provided, is suitable for this.

Hint: Don’t produce the worst and best case schedules, because you don’t need them.

4.9. Tutorial 4 – Re-arranging a model

In all the preceding tutorials and exercises we have turned a blind eye to a problem with the originaloptimization in Tutorial 1. The problem is that some of the pits, including the pit used in much of thiswork (15), hit the side of the model. That is, they do not continue their correct slope to the surface.In effect they have a vertical wall at the side of the model, and, consequently, they are not reallyoptimal. (See the diagram on page 144).

Since it can be difficult to judge in advance how far the pits will extend, it is not unusual for modelsto be too narrow. When this problem is discovered, the correct solution is to re-create the modelwith the extended topography accurately represented. However, Four-X provides a shortcut thatallows you to extend the model with the topography continuing horizontally from its height at theedge of the existing model. This approximation may be sufficient in many cases.

In this tutorial you will extend fxtut.mod and fxtut.par by five blocks to the east and by three blocksto the west to produce tut4.mod and tut4.par. You will then optimize the new model and checkhow much difference these extensions make.



4.9.1. Extending the model

The following diagram shows the relationship between the two model frameworks.

Start FXRB and enter the responses shown in the following boxes:


: tut4¿¿

With FXRB you can:

1. Read one or more Model Files and write a new Model File. (The normal case)

2. Read one or more Results Files and write a new Results File.

3. Read a single Results File and write a Model File.

4. Read a single Results File and write a Pit List File.

5. Read a single Model File and one or more Pit List Files, and then write a Results File.

Your choice [1] ? ¿¿

How many Model Files (1 - 10) do you want to input [1] ? ¿¿

Please enter the name of the primary input Parameters File

[fxtut.par] : ¿¿

Change the size or position of the model during input (Y/N) [N] ? y¿¿

What is the size of the framework into which the blocks will be loaded:-

in the X direction (1-999) [33] ? 41¿¿ in the Y direction (1-999) [64] ? ¿¿

in the Z direction (1-999) [23] ? ¿¿

Please enter the name of the primary input Model File

[fxtut.mod] : ¿¿

Models can be loaded anywhere in the input framework. They need not lie entirely within the input framework.

Please now enter the position in the input framework of the origin block of the model to be loaded. The origin block is the one with the lowest X, Y and Z, regardless of whether it actually appears in the file.

X direction offset of origin block ( -32 to 40) [0] : 3¿¿ Y direction offset of origin block ( -63 to 63) [0] : ¿¿

Z direction offset of origin block ( -22 to 22) [0] : ¿¿



Do you wish to combine and/or split the blocks (Y/N) [N] ? ¿¿

Max no of parcels (of each rock type) to output for a block [5] ? ¿¿

Calculate positional mining CAFs (Y/N) [N] ? ¿¿

Calculate positional processing CAFs (Y/N) [N] ? ¿¿

Do you want to trim the output with a polygon (Y/N) [N] ? ¿¿

Please enter a name for the new Model File

: tut4¿¿

Write a new Parameters File for the new model (Y/N) [Y] ? ¿¿

Please enter a name for the new Parameters File

: tut4¿¿

Now run FXST, FXOP and FXPR as you did in Tutorial 1, but using tut4 as the name for allthe files you create (the programs will supply the appropriate extensions).

If you examine the print file tut4.prp output by FXPR, you will find that now, none of thepits hit the sides of the model framework. If you compare the pit details included in tut4.prowith those in tut1.pro, you will find that pits 1 to 12 are unchanged, but that the remainingpits are different. In most cases the amount of ore processed has decreased.

Now run FXAN as you did in Tutorial 1, but again using tut4 as the file name base. If youcompare tut4.pra with tut1.pra, you will find that the worst case total cash flow hasdecreased by $28,654. This is a very small reduction, but then pit 19 only just hits the sideof the model framework. Pits that would extend substantially beyond the framework can beaffected much more. To avoid any such problems, it is always a good idea to make sure thatnone of the pits in a Results File hit the side.


In working through this tutorial you have learnt that pits that hit the side of the model haveincorrect values, and you have learnt how to extend a model using FXRB.

4.10. Exercise 4 – Adding positional mining CAFs

Tutorial 4 used only one of the many facilities offered by FXRB, which can be used to extract partsof a Model File, to join Model Files together, to combine blocks into bigger blocks, and to splitblocks.

FXRB can also insert positional mining and/or processing CAFs into a Model or Results File. (Seepage 204 for details of expressions).

Assume that the following table represents the expected mining cost variation with depth in themodel:

Benches Cost ofmining

Positionalmining CAF

18 - 23 1.25 1.00012 - 17 1.47 1.176

7 - 11 1.63 1.3041 - 6 1.97 1.576



The range function, using the bench number IZ as the controlling variable, is the simplest way ofrepresenting this variation:

range (IZ, 1.576, 6.5, 1.304, 11.5, 1.176, 17.5, 1.0)

This translates to 1.576 when IZ is less than 6.5, and to 1.304 when IZ is between 6.5 and 11.5, etc.

Run FXRB using fxtut.par and fxtut.mod as input, and producing exer4.par and exer4.mod. Youwill have to answer Y to the question about calculating positional mining CAFs, and you will have toconfirm that it is OK to write out every block in the framework. Then you can enter the aboveexpression.

The reason that all the blocks have to be output, and thus why the file is much bigger, is that therehas to be a block in each position to carry the mining CAF. This does not apply to a positionalprocessing CAF, which is only required for blocks containing material that might be processed.These blocks are, of course, in the Model File already.

Examine exer4.mod. Check that the positional mining CAFs have been added, and that the valuechanges at the required bench levels.

The only significant difference between exer4.par and fxtut.par is that the positional mining CAFflag has been set to 1 in line type 3, at column 45.

4.11. Tutorial 5 – Dealing with an obstruction

It is not uncommon to have obstructions, such as roads, rivers or lease boundaries, that limit thesideways spread of a pit. “Immovable” objects, such as processing mills, pose similar problems.There is a very simple way of handling obstructions and immovable objects in Four-X.

You add blocks to the model that have a very high rock tonnage and that will be so expensive tomine that they are not included in any optimal pit.

For this tutorial, assume that there is already a processing mill at X/Y block co-ordinates 29/61, inthe north east corner of the model. If you are to continue using the mill, you will need some workingspace around it, so you probably have to exclude an area covering X = 20 to 33 and Y = 59 to 64from optimization.



4.11.1. Preparing the special Model File

First you create a small Model File containing blocks with very high rock tonnages that coverthe area you wish to exclude from optimization. This is easily done with a text editor orword processor, by typing in one block, making copies of it, and editing the co-ordinates asrequired. However, to save you this effort, we have supplied you with the necessary file forthis tutorial. It is called tut5.mil, and it looks like this:

! File used in Tutorial 5 to exclude the area of! the mill from optimization

! Each block contains 100,000,000 tonnes of! waste.

! The blocks cover a range of 20 to 33 in the X! direction and 59 to 64 in the Y direction.

20 ,59,22,0,1,1,10000000021 ,59,22,0,1,1,10000000022 ,59,22,0,1,1,10000000023 ,59,22,0,1,1,10000000024 ,59,22,0,1,1,10000000025 ,59,22,0,1,1,100000000 . . . . . . . . . . . . . . . . . . . . etc.32 ,64,22,0,1,1,10000000033 ,64,22,0,1,1,100000000

Strictly, these blocks should all lie on the surface, which slopes upwards to the right in thisarea, but, for simplicity, we have put the blocks all on one level.

You use FXRB to paste this small Model File over the corresponding blocks in the originalModel File, fxtut.mod, and then to output a new Model File called tut5.mod.

Run FXRB, and enter the responses shown in the following boxes:


[exer4.prr] : tut5¿¿

With FXRB you can:

1. Read one or more Model Files and write a new Model File. (The normal case)




5. Read a single Model File and one or more Pit List Files, and then write a Results File.




How many Model Files (1 - 10) do you want to input [1] ? 2¿¿

Merge element data during input (Y/N) [N] ? ¿¿

Please enter the name of the primary input Parameters File

[exer4.par] : fxtut¿¿

Change the size or position of the model during input (Y/N) [N] ? ¿¿

This model will form the input framework into which the secondary model will be loaded

Please enter the name of the primary input Model File

[exer4.mod] : fxtut¿¿

Please enter the name of secondary input Parameters File 1

[fxtut.par] : ¿¿

Please enter the name of secondary input Model File 1

[fxtut.mod] : tut5.mil¿¿

Do you wish to combine and/or split the blocks (Y/N) [N] ? ¿¿

Max no of parcels (of each rock type) to output for a block [5] ? ¿¿

Calculate positional mining CAFs (Y/N) [N] ? ¿¿

Calculate positional processing CAFs (Y/N) [N] ? ¿¿

Do you want to trim the output with a polygon (Y/N) [N] ? ¿¿

Please enter a name for the new Model File

: tut5¿¿

Write a new Parameters File for the new model (Y/N) [Y] ? n¿¿

4.11.2. Repeating the optimization

Run FXOP and use the following files:


fxtut.partut5.modtut1.stu

FXOPtut5.protut5.wrktut5.res

4.11.3. Examining the output

Use FXPR to print plans and sections of tut5.res with pit 15 (F) emphasised.

If you look at the XY plane for bench 22, you will see that pit 15 sits against the excludedarea.


In working through this tutorial you have learnt how to paste one model over another andhow to exclude the pits from a specific area.



4.12. Exercise 5 – Should the mill be moved?

In Tutorial 5 we regarded the mill as fixed, but it could always be moved, for a price. The questionis: “Do you gain by moving it?”.

This is very easily answered by running the same analysis on Results Files which were produced withand without the exclusion area. If the difference in NPVs for the two cases is more than sufficient topay for moving the mill, then you will gain by doing so.

For example, run the original analysis that you did in Tutorial 1 using tut5.res and compare the NPVfor, say, worst case mining with the NPV that you got in Tutorial 1. What is the maximum amountthat it would be reasonable to spend on moving the mill?

4.13. Tutorial 6 - The basics of mining width control

In working through this tutorial, you will carry out a straightforward application of mining width to aselected series of push-backs in a Results File. You will start from the Tutorial 1 data.

4.13.1. Establishing the push-backs and final pit

To apply the mining width concept you first have to specify a set of initial push-backs. Thefigure on page 29 shows the Results File printout for bench 21, which is the highest benchthat does not contain any air blocks.

For the purpose of this tutorial, the initial push-backs will be 11(B) and 13(D), with 15(F) asthe final pit. This is the same as in Exercise 3.

4.13.2. Running FXMW

Start up program FXMW.

It asks:

For a name for the print fileuse tut6

For the name of the Parameters File- use fxtut

Whether you wish to use a Results or Pit List File- enter 1

For the name of the Results or Pit List File- use tut1

For the name of the Structure File- use tut1



What you see on the screen looks like the following:


: tut6¿¿


[fxtut.par] : ¿¿

With this program you can:

1. Read a Results File 2. Read a Pit List File



[tut5.res] : tut1¿¿

Please enter the name of the Structure File

[tut1.stu] : ¿¿

It then asks:

For a name for the output Results File- use tut6

For the pit number for the final pit- use 15 (as in Exercise 3)

For the pit numbers which identify the required intermediate push-backs and the finalpit- use 11 13 15 (as in Exercise 3)

If the push-backs are correct- enter Y

For a mining width- enter 20

Please enter a name for the output Results File

: tut6¿¿

Select a pit number ( 1 to 48) : 15¿¿

Please enter the pit numbers which identify the required intermediate push-backs and the final pit

: 11 13 15¿¿

The pits used for the push-backs are: 11 13 & 15

Are the values for the push-backs correct (Y/N) ? y¿¿

Mining width [30.0] : 20¿¿

The program will display the current push-back control values. You will note that thetemplate size is 2 x 2 and that the mining tolerance has defaulted to 1.

PUSH-BACK CONTROL VALUES

Mining width 20.0 Mining width in X (in blocks) 2 Mining width in Y (in blocks) 2 Mining tolerance (in blocks) 1

Minimum Additional smoothing options: Blocks Remove small drop cuts No 0 floor 0 elsewhere Remove small walls No 0 Remove small stumps Yes Remove small holes Yes Remove sharp corners Yes Allow expansion of outer pit Yes

Do you want to modify any of these values (Y/N) [Y] ?

For this run we do not want to change any of the default settings, so type in “N”.



The program will process each bench, from the bottom up, and will then write a new ResultsFile. The print file will list the contents of the Parameters File, the names of all the input andoutput files used, the push-back numbers and the number of blocks read, accepted, rejectedand written. You will note that extra blocks have been added to the pit. These are causedby pit expansion to provide mining width. 77 extra blocks have been added, which include14 for which records did not exist in the Results File. These 14 blocks have been written outas pure undefined waste blocks using the default rock tonnage value(s) in the ParametersFile.

A summary report is produced that shows the changes in tonnage for each of the push-backs.The tonnage of the first two push-backs has increased, and the tonnage of the last push-backto the final pit has decreased. The total pit tonnage has increased because of the pitexpansion.

Push-back tonnage summary report

Push Original Revised Back Tonnage Tonnage Variation Percentage

1 4309680 4622000 312320 7.2 2 4481680 4877840 396160 8.8 3 2856080 2311040 -545040 -19.1 ---- ---------- ---------- Total 11647440 11810880 163440 1.4

The modified push-back plans are then displayed in the printout. The push-back numbers arestored as numbers in the Results File but are displayed as alphabetic characters in theprintout. The original push-backs are shown as lower-case, and reassigned blocks are shownin upper-case. In this way it is easy to see what has happened to the push-back and theeffects that various user controls have on the final shape. There are four other symbols used:

“.” denotes an air block, as in FXPR.

“+” shows expansion beyond the ultimate pit into higher numbered pit shells in the ResultsFile. The push-back number can normally be deduced from its neighbours.

“*” shows expansion beyond the last pit shell in the Results File. Since there are no blockdetails available, a block of undefined waste is used. The push-back number can bededuced from its neighbours.

“#” shows a block which has been removed from the floor of the final pit.

The results for bench 21, before and after, are shown on the next page. The changed blocksare shown as capital letters. Here they are also shown in bold type, to make them easier tosee, but that is not normal. Remember that some changes will be the result of changes tolower benches.




Symbols: "." is air, "a-z" denote push-backs, "A-Z" denote revised blocks "+" expansion into another shell, "*" expansion beyond last shell

**********|*********|*********|**** **********|*********|*********|***** * * ** * * ** * * ** c * * *c *- ccc - - *ccc -* aaaac * * *aaaaA ** baaaaaa * * Aaaaaaa ** baaaaaaaa * * Aaaaaaaaa ** baaaaaaaaaa * * Aaaaaaaaaaa ** baaaaaaaaaaaab * * AaaaaaaaaaaaaA ** baaaaaaaaaaaaabb * * Aaaaaaaaaaaaaabb ** baaaaaaaaaaaaaabbb * * Aaaaaaaaaaaaaaabbb ** baaaaaaaaaaaaaabbbb * * AaaaaaaaaaaaaaaAbbb ** bbbaaaaaaaaaaaaaaabbb * * bbAaaaaaaaaaaaaaaaAbb *- bbbbaaaaaaaaaaaaaaabbc - - bbAAaaaaaaaaaaaaaaaAbB -* bbbbaaaaaaaaaaaaaaaaacc * * bbbAaaaaaaaaaaaaaaaaaBB ** bbbbaaaaaaaaaaaaaaaaabc * * bbbbaaaaaaaaaaaaaaaaabB ** bbbbbaaaaaaaaaaaaaaaaabc * * bbbbbaaaaaaaaaaaaaaaaabB ** bbbbbaaaaaaaaaaaaaaaaaabc * * bbbbbaaaaaaaaaaaaaaaaaabB ** bbbbaaaaaaaaaaaaaaaaaabbc * * bbbbaaaaaaaaaaaaaaaaaabbB ** cbbbaaaaaaaaaaaaaaaaaaabcc * * BbbbaaaaaaaaaaaaaaaaaaabBB ** bbbaaaaaaaaaaaaaaaaaaabbcc * * bbbaaaaaaaaaaaaaaaaaaabbBB ** bbbbaaaaaaaaaaaaaaaaaaabbcc * * bbbbaaaaaaaaaaaaaaaaaaabbBB ** bbbbaaaaaaaaaaaaaaaaaabbbcc * * bbbbaaaaaaaaaaaaaaaaaabbbBc *- bbbbaaaaaaaaaaaaaaaaaabbbcc - - bbbbaaaaaaaaaaaaaaaaaabbbcc -* bbbbaaaaaaaaaaaaaaaaabbbbcc * * +bbbbaaaaaaaaaaaaaaaaabbbbcc ** cbbbbaaaaaaaaaaaaaaaaabbbbc * * Bbbbbaaaaaaaaaaaaaaaaabbbbc ** bbbbbaaaaaaaaaaaaaaaaabbbcc * * bbbbbaaaaaaaaaaaaaaaaabbbBB ** bbbbbaaaaaaaaaaaaaaaabbbbc * * bbbbbaaaaaaaaaaaaaaaabbbbB ** cbbbbbaaaaaaaaaaaaaaaabbbcc * * BbbbbbaaaaaaaaaaaaaaaabbbBB ** cbbbbbaaaaaaaaaaaaaaabbbcc * * BbbbbbaaaaaaaaaaaaaaabbbBB * ccbbbbbbaaaaaaaaaaaaabbbcc * cBbbbbbbaaaaaaaaaaaaabbbBB *Yccbbbbbbbaaaaaaaaaaabbbccc * YccbbbbbbbaaaaaaaaaaabbbBBB * ccbbbbbbbbaaaaaaaabbbbccc * ccbbbbbbbbaaaaaaaabbbbBBB *- ccbbbbbbbbaaabbbbbbbccc - - ccbbbbbbbbaaabbbbbbbccc -* cccbbbbbbbbbbbbbbbbccc * * cccbbbbbbbbbbbbbbbbccc ** cccbbbbbbbbbbbbbbccc * * cccbbbbbbbbbbbbbbccc ** cccbbbbbbbbbbbbccc * * cccbbbbbbbbbbbbccc ** ccccbbbbbbccccccc * * ccccbbbbbbccccccc ** ccccbbbccccccccc * * ccccbbbccccccccc ** cccccccccccccc * * cccccccccccccc ** cccccccccccc * * cccccccccccc ** ccccccccc * * ccccccccc ** * * *- - - -* * * ** * * ** * * ** * * ** * * ** * * ** * * ** * * ** * * *- - - -* * * ** * * ** * * ** * * ** * * ** * * ** * * ** * * ** * * ***********|***** X *|*********|**** **********|***** X *|*********|****

Most of the very narrow areas have been removed, but there is a small group of isolatedpush-back 3 (c) blocks at the north end of the pit that could be cleaned up. In fact, if youlook at lower benches, you will see that there are several areas that could be cleaned up.These matters will be explored in Exercise 6.

The ensuing Results File can be used in FXAN to generate new period cash flow andtonnage reports.



We suggest that you do two runs of FXAN using the prices, costs and throughputs fromTutorial 1.

These are: Reference mining cost $1.00/TPrice of gold $380Price of silver $5.10Discount rate 10%Rock throughput 4,000,000 T/yMill throughput 1,000,000 T/y

First, use tut1.res as input, and analyse pit 15. Do a Specified Schedule with push-backs topits 11,13 and 15, and use a lag of 0. This should produce an NPV of $13,823,733

Second, use tut6.res as input, and analyse pit 3. Do a Specified Schedule with push-backsto pits 1, 2 and 3, and again use a lag of 0. This should produce an NPV of $13,428,242.

The difference in NPV, $395,491 or -2.9%, indicates the cost of making the mining morefeasible.

4.14. Exercise 6 - Further tidying up

It was noted earlier that, on many of the benches, there were small areas that could be improved. Ingeneral there is little cost in removing the small stumps, small holes and sharp corners. The cost ofremoving drop cuts and small walls can be greater, as ore bearing rock can be omitted from the finalpit, the processing of ore may be delayed due to blocks being reassigned to a later push-back, orwaste may be mined earlier. Obviously these are areas that need to be investigated by trial and errorfor any Results File.

For example, if you want to try and clean up the small walls, you can re-run the previous tutorial andprovide a minimum number of blocks for small walls. If you are intending to try several values, thenlogging the commands would make sense. The default extension for FXMW logging is “.lom”.

Re-run FXMW using the same values, except, use exer6 for the print file and the output ResultsFile names. Answer Y to the question:

Do you want to modify any of these values (Y/N) [Y] ?

The control values will be re-displayed with a menu.

PUSH-BACK CONTROL VALUES

1. Mining width 20.0 2. Mining width in X (in blocks) 2 3. Mining width in Y (in blocks) 2 4. Mining tolerance (in blocks) 1

Minimum Additional smoothing options: Blocks 5. Remove small drop cuts No 0 floor 0 elsewhere 6. Remove small walls No 0 7. Remove small stumps Yes 8. Remove small holes Yes 9. Remove sharp corners Yes 10. Allow expansion of outer pit Yes

99. Exit

Your choice [99] :



Enter 6 to access the small walls control value and enter 10 as a minimum, so that small walls of 9blocks or less will be removed. Then accept default [99] to exit.

If you look at the printout, you will see that many of the problems have been cleared up.

If you look at the push-backs from the previous examples, you will note also that there are manycases of single isolated blocks. These could be removed by using a floor drop cut minimum of 2.What is the cost of this decision?

The results you should get are tabulated below. Ultimately it is a value judgement as to what is the“better” solution. The ease of mining clean push-backs may translate into cheaper mining costs orlower set-up costs.

Description NPV ChangeBase case as for Exercise 3 $13,823,733With mining width template 2x2 $13,428,242 -2.9%

plus minimum wall = 10 $13,365,970 -0.5%plus minimum internal drop cut = 10 $13,291,328 -0.6%plus minimum pit floor drop cut = 2 $13,118,617 -1.3%

If you spend some time examining the print files output by FXMW from the various runs, you willsee the sort of changes that are made.

Even with all these changes, the outlines are not perfect, and will still require some manualadjustment when the final detailed design is done, but they are a great deal better than those producedwithout the adjustments, and the resultant NPV gives a closer estimate of the true pit value.

___________________________________________________________________________ Data Files 59


5. DATA FILES

5.1. Overview

Four-X uses a wide range of files. Some of these are supplied with the package, some come fromyour GMP, and some are created by Four-X itself. For the latter two categories, you control thenames, and you will find the system easier to use if you establish a consistent way of choosingfile names and extensions. An ounce of planning will prevent pounds of confusion later.

This chapter contains a description of each of the files you will use. The detailed layouts of thosefiles are given in an appendix starting on page 149.

5.2. Additional Arcs Files

Default file name extension – .add

Additional Arcs Files are optional files that contain details of extra structure arcs that you wish to addto those generated for the slopes. Uses of an Additional Arcs File are described in the Techniqueschapter, starting on page 143.

The format of an Additional Arcs File is given on page 149.

5.3. Mining Sequence Files

Default file name extension – .msq

A Mining Sequence File lists the blocks which are mined in each period of a mining sequence,simulated by FXAN. It also gives the particular method used to process each parcel.

Mining Sequence Files allow you to carry out further detailed studies in relation to a miningsimulation.

The format of a Mining Sequence File is given on page 150.

5.4. Model Files

Default file name extension – .mod

Model Files are text files that contain details of the block contents. They come initially from yourGMP.

Each block contains the block co-ordinates within the model framework, a total block tonnage, andzero or more parcels.

Each parcel contains a rock type code, a tonnage and one or more element contents. The rock typecode must match one of the rock type codes in the Parameters File. If the rock type is waste, theelement contents may be zero.

If the block total tonnage is greater than the total of the parcel tonnages in the block, then the excessis treated as undefined waste with a rock type mining CAF of 1.0 and a rehabilitation cost of zero.

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Each block may also include a positional mining CAF and/or a positional processing CAF.

The format of a Model File is given on page 151.

5.4.1. Which blocks to include

Four-X must, in some way, be given the details of every block in its region of interest. Thereare two ways you can provide details of blocks:

1. Through the Model File, and,

2. Through the general and/or sub-region default rock tonnages.

The region of interest depends on the setting of the active blocks indicator. If it is 1, then allblocks within the rectangular model framework are of interest. If it is 2, then only the blocksthat lie within defined sub-regions are of interest. If it is 3, only the blocks you supply are ofinterest, so the default rock tonnages are irrelevant.

If you set the active blocks indicator to 1, you usually provide details of every mineralisedblock and air block in the model framework, as a minimum. Every block that you do notprovide will be assumed to have the appropriate default rock tonnage from the ParametersFile. Alternatively, you can provide all the mineralised and waste blocks, and set the defaultrock tonnage to zero. This will make all missing blocks into air blocks.

If you cannot represent the variations of density through the general or sub-region defaultrock tonnages, then the Model File must include values for all the waste blocks as well as themineralised blocks. You can include them in any case, if you wish, but it will make the filebigger, and some runs will be slightly slower.

If you set the active blocks indicator to 2, then the situation is similar to that where theindicator is set to 1, except that only the blocks within the sub-regions need be considered.Incidentally, with an active blocks indicator of 2, if the Model File contains blocks that lieoutside any sub-region, then programs FXRB and FXOP will reject them and tell you thatthey have done so.

5.5. Opti-Cut Files

Two types of Opti-Cut files can be created by FXAN. These are the Sequence Text File and theEconomic Text File. The default file name extensions for these files are .stx and .etx respectively.

The format of these files is given in the Opti-Cut manual.

If you did not handle time costs explicitly in Four-X, or if you wish to use stockpiles, then theEconomic Text File will require modification before being used in Opti-Cut. Since the philosophiesof the two programs are quite different, it is probably a good idea to check the Economic Text File inany case.

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5.6. Parameters Files

Default file name extension – .par

Parameters Files are small text files that carry general information about the model framework andabout how the optimization is to be done. The section of the program that reads and checks this fileis the same in every program, except for the special program that edits this file (FXED). This sectionexpects and requires a complete and valid copy of the file, even though a particular program may notuse all the data that it contains.

The file can be created and/or edited with program FXED, and you should not need to know thedetails of the formats of the various lines in the file. However these are given in an appendix, startingon page 152, for your reference.

The values included in the Parameters File are:

The dimensions of a blockThe dimensions of the model frameworkThe origin co-ordinatesGlobal values:

The general formatting requirementsThe active blocks indicatorThe restart intervalThe reference mining costThe mining dilution and recovery factorsThe general default rock tonnageControl flags:

The ore selection methodAir flags A and BThe positional mining and processing cost factor flagsThe print unprocessed mineralisation flag

The required Revenue Factor values

For each sub-region:The block limitsThe number of benches for arc generationThe sub-region default rock tonnageFor each slope angle:

The bearingThe slope

For each element:The element type codeThe position in the Model FileThe element formatting requirementsThe selling cost per unitThe price per unit

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For each grade-dependent expression:The expression codeThe expression usageThe expression text

For each rock type:The rock type codeThe rock type mining CAFThe rehabilitation cost per tonneThe processing throughput factor

For each method/type for open pit mining:The processing method codeThe rock type codeThe processing costFor each element:

The element type codeThe cut-off control flagThe element processing cost per unitThe processing recovery fractionThe processing recovery thresholdThe minimumThe maximum

For each method/type for underground mining:As for open pit mining

For each processing method group:A list of method and/or group codes

Each of these values is explained in detail below.

The file can also contain comments, which allow you to keep a record of what the particular file wasused for.

5.6.1. The dimensions of a block

Every block must be the same size and shape. The dimensions are in the X, Y and Zdirections.

We use X, Y and Z as co-ordinates in Four-X because some models are not alignednorth-south. However, in general, the positive X direction corresponds to east, the positiveY direction corresponds to north, and the positive Z direction corresponds to up.

-- Used by FXRB, FXST and FXMW. --

5.6.2. The dimensions of the model framework

The model framework size is expressed as the number of blocks in the X, Y and Z directions.

-- Used by all programs except FXAN. --

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5.6.3. The origin co-ordinates

The origin of the model framework is at the outer corner of the block with co-ordinates1,1,1. Note that it is not at the centre of this block.

The provision of origin co-ordinates is optional, but they can be useful when Results Filesare read back into GMPs, and when reading in a Polygon File. They must be co-ordinates ina system which is aligned parallel to the model framework.

FXRB, the re-blocking program, can change the origin of a model framework and will adjustthe origin co-ordinates when it writes out a new Parameters File.

If the output of FXRB is being limited by a polygon, then the X and Y co-ordinates of theorigin are subtracted from the X and Y co-ordinates of each of the points which define thepolygon. This gives the co-ordinates within the model framework. If the origin co-ordinatesdo not appear in the Parameters File, they are assumed to be zero.

-- Used by FXRB. --

5.6.4. General formatting requirements

These give the number of decimal places to be used for the input and output of variousquantities, other than those associated with elements. Scaling by a power of ten is alsopossible, but this only affects output (e.g. use -3 to show numbers in thousands).

-- Used by all programs except FXPR. --

5.6.5. The active blocks indicator

The active blocks indicator specifies which blocks you want Four-X to work on when doingthe optimizations. There are three possible indicators: 1, 2 and 3.

Active blocks indicator = 1

All the blocks in the model framework are considered for mining.

The sub-region(s) that you define must exactly fill the volume of the model framework.This is because the slopes are defined separately for each sub-region, and, if all blocks areto be considered, then slopes must be defined for all blocks. This is by far the mostcommonly used active blocks indicator.

Refer to page 60 for a discussion of which blocks to include in the Model File.

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Only the blocks within sub-regions are considered for mining.

The sub-regions do not need to fill the model framework, and if blocks occur in the ModelFile in regions not included in a sub-region, they are rejected.

An active blocks indicator of 2 can be useful in certain unusual circumstances. Forexample, if you have very complicated slope requirements that require a large number ofsub-regions to define, you may exceed the number allowed by Four-X. In this case youmay be able to omit some because you know that mining will not take place in these areas.

Refer to page 60 for a discussion of which blocks to include in the Model File.


Only blocks provided in the Model File are considered during optimization. That is, therest of the blocks in the model framework are completely ignored.

With an active blocks indicator of 3, it is your responsibility to ensure that every relevantblock that could be mined is included in the Model File. You must also ensure thatstructure arcs are generated for all these blocks. You can do this by using an activeblocks indicator of 1 for the FXST run, or an active blocks indicator of 2 with sub-regionsthat totally enclose the volume of interest. Any structure arcs in the Structure File, thatdo not apply to blocks in the Model File, are discarded by FXOP.

-- Used by FXRB and FXOP . --

5.6.6. The restart interval

It can be distressing if a long optimization run is terminated after several hours because of,say, a power failure, and you have to start again. FXOP periodically dumps all the data frommemory to its Work File to enable a later restart. Restart dumps do not take long, but itwould be a waste of time to do them too often. The restart interval lets you specify the timebetween these dumps. If it is left blank, restart dumps occur every two hours.

-- Used by FXOP. --

5.6.7. The reference mining cost

This is the cost of mining undefined waste at the Reference Block.

To obtain the cost of mining undefined waste at a particular block, it is multiplied by thepositional mining cost adjustment factor of that block. To obtain the cost of mining definedwaste (i.e. a particular rock type), it is also multiplied by the rock type cost adjustment factorfor that rock type.

-- Used by FXOP and FXAN. --

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5.6.8. The mining dilution factor

When mining at the edge of an ore body, it can be difficult to avoid mining some waste aswell. This waste dilutes the grade of the material that is processed. The mining dilutionfactor allows an overall mining dilution to be applied.

A five percent dilution would be effected by a mining dilution factor of 1.05.

Note that the dilution is applied by increasing the tonnage of mineralised parcels, regardlessof whether there is any waste (non-parcel tonnage or parcels with no elements) in the block.This can lead to an effectively negative waste tonnage for an individual block. Consequently,in regions of the pit that are entirely mineralised, negative stripping ratios are possible.

-- Used by FXOP, FXAN and FXUT. --

5.6.9. The mining recovery factor

When mining at the edge of the ore body, it is possible to miss some of the ore. It is alsopossible to lose some of the ore during transportation to the processing mill. The miningrecovery factor allows an overall mining recovery to be applied.

A five percent mining loss would be effected by a mining recovery factor of 0.95.

Note: do not confuse mining recovery with processing recovery.


5.6.10. The general default rock tonnage

Default rock tonnages are used by FXRB and by FXOP (Active blocks Indicator 1 or 2) forblocks that are not specified in the Model File.

This can be blank (meaning undefined), or a value that is zero, or positive.

If a value is supplied, then that value is used as the default rock tonnage everywhere in themodel, except within sub-regions that have their own default rock tonnage (see page 70).

-- Used by FXRB, FXOP and FXMW. --

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5.6.11. The ore selection method flag

This flag controls how Four-X selects ore for processing from the available parcels. Thereare two possible values: 1 and 2.

Ore selection method flag = 1

Selection by cut-offOre is selected by comparing the grades of the material with pre-calculated processingcut-offs. If it does not satisfy the cut-offs, it is treated as waste.

If more than one processing method is applicable, the grades are compared with thecut-offs of each in turn, in the order in which they are specified in the Parameters File.

Ore selection method flag = 2

Selection by cash flowOre is selected by comparing the cash flow which would be produced by processing it,and the cash flow which would be produced by mining it as waste. If the cash flow fromprocessing it is higher, the material is treated as ore. If not, it is treated as waste.

If more than one processing method is applicable, the one which produces the highestcash flow is used.

Usually, the actions will be the same in both cases, but see page 182 and following, forfurther details.

-- Used by FXOP, FXAN and FXUT. –

5.6.12. Air flag A

The value of this flag controls whether air blocks are included or excluded, duringoptimization.

Air flag A = 1

Air blocks are included in the optimization. This is required if you are going to useFXMW.

Air flag A = 2

Air blocks are not included in the optimization.

It is often quicker to optimize without the air blocks because of the reduction in the numberof blocks the program has to work on. This should only be done if no part of the initialtopography is steeper than the required mining slopes.

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It is important to appreciate that the structure arcs which define the slopes duringoptimization rely on “chaining”. That is, if there is an arc from block P to block Q, and onefrom block Q to block R, then chaining will ensure that, if block P is mined, block R will bemined also. However, this will only happen if block Q is considered during optimization. Ifit is not, then neither the arc P-Q, nor the arc Q-R will be used, and this link between miningP and mining R will be lost.

The above figure shows a situation where, mining block P can only be guaranteed to triggerthe mining of block R if air blocks are included in the optimization. Note that, becauseoptimization is in three dimensions, and because structure arcs vary greatly in length, youcannot assume that, if air is excluded, block R will not be mined. If the topography issteeper than the required slopes, and if air blocks are excluded, then the results areunpredictable.

Air flag A is set to 1 if the active blocks indicator is 3.

-- Used by FXOP and FXMW. --

5.6.13. Air flag B

The value of this flag controls which air blocks from the Model File are included in theResults File.

In the above figure, P, Q and R mark the different air blocks that are discussed below.

Air flag B = 1

No air blocks are included in the Results File regardless of whether air blocks wereincluded or excluded during optimization.

___________________________________________________________________________ Data Files 68


Air flag B = 2

Only those air blocks that would be “mined” as part of the largest pit extended into theair. In the above figure, the blocks in area Q are included in the Results File. This optionis only available if air blocks are included (Air flag A = 1) during optimization.

Air Flag B = 3

All air blocks, the blocks in areas P, Q and R in the above figure, are included in theResults File. This is required if you are going to use FXMW.

Air flag B is set to 2 if the active blocks indicator is 3.

-- Used by FXOP and FXMW. --

5.6.14. The positional mining CAF flag

If this is 1, then positional mining CAFs in the Model File are used by FXOP and FXAN. Ifit is 0, they are not. This flag does not affect the use of rock type mining CAFs.


5.6.15. The positional processing CAF flag

If this is 1, then positional processing CAFs in the Model File are used by FXOP and FXAN.If it is 0, they are not.


5.6.16. The print unprocessed mineralisation flag

If this is 1, then FXOP and FXAN report the total tonnage and element content of anymineralised material that is mined but not processed. If it is 0, they do not. Parcels withzero element content, i.e. defined waste, are never reported by this facility.

These quantities can be useful when reconciling the results of different runs.


5.6.17. The required revenue factor values

Four-X uses a Revenue Factor in FXOP to scale base case prices up or down, in order tocontrol what nested pits are to be produced. Individual values and/or ranges can bespecified, but the resultant sequence of values must be in ascending order.

As a general rule, you should start with a range of Revenue Factor values from 0.3 to 2.0(say 0.3 to 2.0 in steps of 0.02). If the ore body is such that some of the lower values do notproduce a pit at all, the number of pits will be reduced. Also, if successive Revenue Factorvalues are so close together that the change does not add even one block to the pit outline,the number of pits will be reduced. In this case, you may want to re-arrange the values.

___________________________________________________________________________ Data Files 69


The aim is to get 50 or more pits, ranging in size from less than one year’s production tomuch bigger than you expect to mine. These pits will enable you to do realistic sequencingand scheduling during analysis. Note that the fact that you never expect to design a pit withonly a one year life is not relevant. The inner pits are required for sequencing and to guideyou to the best place to start mining.

-- Used by FXOP. --

5.6.18. For each sub-region:

For each sub-region you define, you can specify a set of slopes and a default rock tonnage.Sub-regions are defined on page 178.

When you are using a Parameters File to produce a Structure File with FXST, it is the slopeinformation that is relevant. When you are re-blocking a Model File with FXRB, or doing anoptimization with FXOP, it is the default rock tonnage that is relevant. It is acceptable, andoften useful, to use different Parameters Files with quite different sub-region layouts forthese different purposes.

A Parameters File with no sub-regions is valid, but then FXST will demand an AdditionalArcs File, which will have to contain all the required arcs.

a) The block limits

The size and location of a sub-region is specified by its lowest and highest block numbersin the X, Y and Z directions.

An example of the specification of sub-regions in this way is given in the appendix onpage 178.

-- Used by FXRB, FXST and FXOP. --

b) The number of benches for arc generation

As is explained in the appendix starting on page 69, you can control the accuracy of slopereproduction by controlling the number of benches that are considered when the structurearcs are generated by program FXST.

The larger the number of benches you specify, the greater the accuracy, and the longer theoptimization will take. You may have to do a little experimentation to find the bestcompromise, but as a starting value we suggest using eight times the largest of the twohorizontal dimensions of a block divided by the height of a block. With normalslopes of 40-50 degrees from the horizontal, this will usually give an average slope errorof the order of one degree.

___________________________________________________________________________ Data Files 70


For example, if the blocks are dimensioned 20 by 30 by 10 in the X, Y and Z directions,you would start with 24 (=30x8/10). However, remember that structure arcs aregenerated within sub-regions except for a small overlap into adjacent sub-regions, so thatit is meaningless to specify a number of benches that is more than 2 or 3 greater than thenumber of benches in the sub-region. Even the 2 or 3 extra are only relevant when thereis another sub-region above the one in question.

-- Used by FXST. --

c) The sub-region default rock tonnage

Default rock tonnages are used by FXRB and by FXOP (Active Blocks Indicator 1 or 2)for blocks that are not specified in the Model File.

This can be blank (meaning undefined), or a value that is zero, or positive.

If a value is supplied, then, within this sub-region, that value is used in place of anygeneral default rock tonnage (see page 65).

If the density of rock varies within the model framework, but the variation can besimulated by allocating different default rock tonnages to different sub-regions, thensub-region default rock tonnages can be useful.

It is common for users to simulate variations in density with depth by setting up aParameters File having a number of shallow sub-regions, with each carrying a differentdefault rock tonnage. These sub-regions may be too shallow to adequately reproduce theslopes, but the programs that use the default rock tonnages do not use the slopes and viceversa, so that different Parameters Files can be used for the two purposes.

Remember that the default rock tonnage is only relevant for blocks that are not includedin the Model File.

-- Used by FXRB, FXOP and FXMW. --

d) For each slope angle:

(A discussion of slope handling starts on page 179. Variation of slopes with rock type isdiscussed on page 146).

The bearing

Bearings are expressed in degrees, clockwise from the positive Y direction – usuallynorth.

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It is very important to understand that bearings are given instead of wall positions. Anywalls at right angles to the bearings, in a particular sub-region, will have the given slopeapplied. For example, in the figure below, the slope specified for a bearing of 45degrees would be used by the program in the positions indicated by the arrows.

-- Used by FXST. --

The slope

Slopes are expressed in degrees from horizontal. Thus 50 degrees is steeper than 45degrees.

-- Used by FXST. --

5.6.19. For any grade-dependent expression:

An expression identification code, the expression usage and the definition of the expression.

Expression codes can be used in place of constants to provide user defined grade-dependentvalues for:

Selling costs, *Prices, *Rock type mining CAFs,Rehabilitation costs,Processing costs,Element processing costs, andRecovery fractions.

* Note that it is not usually meaningful to use expressions for selling cost or price, exceptwhen the ore itself is the product (e.g. for iron ore).

Expressions are described on page 204.

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5.6.20. For each element:

a) The element type code

This is an alphanumeric code of from 1 to 4 characters which identifies a particularelement in the model (e.g. GOLD, CU). It is case insensitive.

This code must not contain a period (.) or slash (/), and must not match any spreadsheetcode (e.g. Rock).

If this element is to be recovered, it must be specified in the element processing section ofa method.

-- Used by all programs except FXST. --

b) The Position in Model File

Specify the position of the element data in the Model File (e.g. whether the data is thefirst, second, etc. element value).

-- Used by all programs except FXST. --

c) The element formatting requirements

These give the number of decimal places to be used for the input and output of elementquantities in a parcel, total quantities and grades. Scaling by a power of ten is also possible,but this only affects output (e.g. use -3 to show numbers in thousands).


d) The Selling Cost per Unit

This is the cost involved in selling a unit of the element, where a unit is defined by thevalues used for quantities of the element in the Model File.

The code for a grade-dependent expression can be used instead of a constant, but it wouldonly be meaningful when the ore itself is the product, as in iron ore.


e) The Price per Unit

This is the price for a unit of the element, where a unit is defined by the values used forquantities of the element in the Model File. It is used with the Revenue Factors todetermine element prices for different pit shells.

The code for a grade-dependent expression can be used instead of a constant, but wouldonly be meaningful when the ore itself is the product, as in iron ore.


___________________________________________________________________________ Data Files 73


5.6.21. For each rock type:

a) The rock type code

This is an alphanumeric code of from 1 to 4 characters which identifies a particular rocktype in the model (e.g. OXID, SULF, WTHR). It is case insensitive.

This code must not contain a period (.) or slash (/), and must not match any spreadsheetcode (e.g. ROCK).

If this code does not also appear in a method/type line (see below), this type of rock isknown as defined waste.


b) The rock type mining CAF

This is the ratio between the cost of mining this type of rock as waste, and the cost ofmining undefined waste. Both costs should be the same as they are at the ReferenceBlock (see page 133), regardless of whether there is any of this type of rock in theReference Block.

The cost per tonne of mining a particular parcel as waste, used by FXOP and FXAN, isthe product of the reference mining cost, the rock type mining CAF, and the positionalmining CAF (if used).

If any rock of this type is processed, that is, mined as ore, any extra mining costassociated with this should be included in the processing cost (see below).

The code for a grade-dependent expression can be used instead of a constant.


c) The rehabilitation cost per tonne

There are costs associated with rehabilitating waste dumps chemically, visually andecologically. This cost is applied if the material is treated as waste, but not if it isprocessed.

Note that, during simulation with FXAN, the cost is applied at the time of mining, ratherthan at the actual time of rehabilitation. If these times are very different, you may want tomake some allowance for the discounting which would occur.



___________________________________________________________________________ Data Files 74


d) The processing throughput factor

Some rock types are easier to process than others, so that a processing throughput limitfor one rock type may not be appropriate for another. The situation is furthercomplicated if a mixture of rock types is being processed.

If this factor is set greater than 1.0, then any processing or group throughput limit appliedto this rock type is effectively increased, and vice versa.

This factor has no effect on mining throughput.


5.6.22. For each processing-method/rock-type for open pit mining:

a) The processing method code

This is an alphanumeric code of from one to four characters. It identifies the processingmethod to be used (e.g. MILL, HEAP, CIL). It is case insensitive.

This code must not contain a period (.) or slash (/), and must not match any spreadsheetcode (e.g. ROCK). In addition, it must not be the same as any rock type code.


b) The rock type code

This code, which is case insensitive, must be one of the codes defined for a rock type.

The pairing of the method and type codes indicates that parcels of this rock type may beprocessed by this processing method, if it is economic to do so. If a rock type, even onecontaining elements, occurs in the Model File, but is not paired with a processing methodhere, it will be treated as waste.


c) The processing cost

The effective processing cost used by FXOP and FXAN is the product of the processingcost defined here and the positional processing CAF for the particular block (if used).

The effective processing cost is used not only for calculating cash flows, but also forcalculating cut-offs. Note that, whenever cut-offs are output on the screen, in printedreports or in spreadsheet data, they are shown for a positional processing CAF of 1.0.The cut-offs used in deciding whether to process the parcels of a block may be differentfrom those shown if processing CAFs are being used. Typically they are higher. See page191 for details of how the cut-offs and cut-overs are changed.



___________________________________________________________________________ Data Files 75


d) For each element

The element type code

This code, which is case insensitive, must be one of the codes defined for an elementabove.


The cut-off control flag

Even though an element may be a product, it need not be the subject of a cut-off. Forexample, in a copper/gold mine, you may choose to operate with a cut-off only forcopper.

Note that, when considering any second and subsequent processing methods applicableto a particular rock type:

a) An element cannot be controlled by a cut-off unless it was controlled for theprevious method.

b) All elements which were controlled by a cut-off in the previous method must becontrolled in this method, unless the number of controlled elements is reducedto 1.

This is only relevant when ore selection is by cut-off.


The element processing cost per unit

Costs can be calculated based on the units of each element input into the process, wherea unit is defined by the values used for quantities of the element in the Model File. Thesecosts are in addition to the general processing costs.



The processing recovery fraction

This is the processing recovery (e.g. 0.93) at high grade for this element.



___________________________________________________________________________ Data Files 76


The processing recovery threshold

This is a grade that is subtracted from the actual grade of each parcel before theprocessing recovery fraction is applied.

If it is non-zero, the effective processing recovery will decline with reducing grade. Forfurther details see page 184.


The minimum

This value is used differently, depending on the type of ore selection in use. See page182.

If ore selection is by cut-off:

This value sets a minimum for the cut-off.

When a cut-off or cut-over grade for this element is calculated by FXOP,FXOP or FXUT, it is compared with this minimum. If it is lower than thisminimum, then the minimum is substituted and an asterisk (*) is printed next toit in the printouts.

If ore selection is by cash flow:

This value sets a minimum for the acceptable grade for this element. Parcelswith grades lower than this value are not processed by this method.

Minima can be used to obtain more control over the allocation of parcels in relation toprocessing methods. However, care should be exercised when using them duringoptimization. This is because their value does not change with Revenue Factor,whereas the cut-offs and cash flows calculated by FXOP, FXAN and FXUT do.


___________________________________________________________________________ Data Files 77


The maximum

This value is used differently, depending on the type of ore selection in use. See page182.

If ore selection is by cut-off:

This value sets a maximum for the cut-off used.

When a cut-off or cut-over grade for this element is calculated by FXOP,FXOP or FXUT, it is compared with this maximum. If it is higher than thismaximum, then the maximum is substituted and an asterisk (*) is printed next toit in printouts. This can be used to obtain more control over the allocation ofparcels to processing methods.

If ore selection is by cash flow:

This value sets a maximum for the acceptable grade for this element. Parcelswith grades higher than this value are not processed by this method.

Maxima can be used to obtain more control over the allocation of parcels to processingmethods. However, care should be exercised when using them during optimization.This is because their value does not change with Revenue Factor, whereas the cut-offsand cash flows calculated by FXOP, FXAN and FXUT do.


5.6.23. For each method/type for underground mining:

The codes, values and usages are identical to those for open pit mining, above. See page202 for details of when and how to use them to allow for the effects of underground miningon the open pit.

5.6.24. For each processing method group:

A processing method group is defined by a list of from two to fifteen processing methodcodes, or previous group codes. Group codes are of the form “GR_1”, which refers to thefirst group defined, and “GR_2” which refers to the second, and so forth.

Processing method groups are used by FXAN to allow you to limit the throughput of agroup of processing methods (and/or previous groups). This can be useful, for example, ifyou have two different processing streams but only one crusher. You define a groupconsisting of the two processing codes, and FXAN asks you for a throughput limit for thegroup. Group codes can also be used wherever a method code can be used in spreadsheetcodes.

-- Used by FXAN. --

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5.7. Pit List Files

Default file name extension – .pil

Pit List Files contain a list of block co-ordinates, each with a pit number.

They can be created from a Results File using FXRB, and they can be merged with a Model File,again using FXRB, to create a Results File.

They can be used to simplify the input of pit outlines to your GMP, or you can create them with yoursoftware, so that they describe mining phases that you want to analyse with FXAN. In this case, youmerge them with a Model File, using FXRB, and then run the analysis on the resulting pseudo ResultsFile. By this method you can design your own mining phases and then use the power of FXAN tosimulate the mining of these phases under different conditions.

The format of a Pit List File is given on page 164.

5.8. Polygon Files

Default file name extension – .pol

Polygon files contain a sequence of X,Y co-ordinates that define the vertices of a polygon in theorder that they occur as the edge of the polygon is traversed. The points can be in clockwise oranti-clockwise order.

The output of program FXRB can be limited to blocks whose centres lie within such a polygon.

The format of a Polygon File is given on page 164.

5.9. Results Files

Default file name extension – .res

Following a specialised header that contains details of what optimizations were done, Results Filescontain the block details of all blocks within the optimized pit for an infinite Revenue Factor. Inaddition to the information carried for a Model File block, each block carries the number of thesmallest pit that it forms part of.

The Results File is produced by FXOP from a Parameters File, a Model File, and a Structure File.FXRB can also construct a pseudo Results File, by merging a Pit List File with a Model File.

The format of a Results File is given on page 165.

___________________________________________________________________________ Data Files 79


5.10. Spreadsheet Files

Spreadsheet Definition Files control the data that FXAN outputs to Spreadsheet Output Files.

The default file name extension for a Spreadsheet Definition File is .ssd

The default file name extension for a Spreadsheet Output File is .sso

Each value that can appear in the FXAN printed output has been given an alphabetic code that isused to identify it. For example “ROCK/TG” represents the tonnes of rock in the ground,“ROCK/CP” represents the cash flow associated with the mining of rock in a period, and“ROCK/DP” represents the discounted cash flow associated with the mining of rock in a period.Similarly “PIT/FI” represents the final pit number for the scenario and “PRICE” represents theproduct price. There are also codes for a wide range of values that do not appear in the printedoutput. See pages 167 to 173 for a complete list of the codes. All the codes are case insensitive.

Three classes of values can be output:

1. Period data such as period tonnages, grades, cash flows and start/end benches and pits.

2. Grand-total values such as those that appear at the end of each schedule report.

3. Common values, such as mining cost, product price, discount rate and tonnage limits, thatapply to both periods and grand totals. Most of these are values used to specify an economicscenario.

One or both of two tables of values can be output:

1. A period table that can include any of the period or common values.

2. A grand total table that can include any of the grand total or common values.

Each table consists of columns of numeric values, and each column has its code as a heading. Codesmay appear more than once.

The format of a Spreadsheet Definition File is given on page 166.

The format of a Spreadsheet Output File is given on page 177.

5.11. Structure Files

Default file name extension – .stu

Structure Files are binary files containing the structure arcs necessary to ensure that the requiredslopes are obeyed during optimization. The arcs are calculated from the block proportions, thesub-region limits and the bearings and slopes for each sub-region, as defined in the Parameters File.Structure Files may also contain arcs defined in an Additional Arcs File.

___________________________________________________________________________ Data Files 80


If you optimize with an active blocks indicator of 1, you must create the Structure File with an activeblocks indicator of 1. If you optimize with an active blocks indicator of 2 or 3, you must ensure thatthe sub-regions you use when creating the Structure File include the whole of your volume ofinterest. If not, some part of the region you wish to optimize will have no slope constraints, andFXOP may mine mineralised blocks without taking out the waste above them. FXOP “knows”nothing about slopes, nor indeed about mining. It uses a mathematical method that takes note only ofarcs and block values.

The Structure File is created by FXST, and read by FXOP and FXMW, which do not themselves usethe slope definitions from the Parameters File. It usually requires about one byte for each arc perblock for each block, although this can vary depending on the particular slope requirements, and thesize of the model framework.

Structure Files are created and used only by Four-X. You should never attempt to alter them in anyway.

5.12. Work Files

Default file name extension – .wrk

Work Files are binary files used by program FXOP during optimization.

They contain all the intermediate information generated during optimization. They also hold all thedetails recorded during the last restart dump, and can therefore be used to restart an optimization runthat was terminated by power failure or hardware malfunction.

A Work File grows in size during the optimization run until the start of the first pass of the firstoptimization. After that, its size stays constant.

Work Files are created and used only by Four-X. You should never attempt to alter them in any way.

5.13. Auxiliary Files

5.13.1. The Initialization File

This text file is updated every time you run one of the Four-X programs. It keeps a recordof the file names you are using, and enables the programs to offer a likely name as a defaultwhen they ask you for a file name.

Also included in this file are the number of lines to print on a page, controls for output fileformats, and details of your license entitlement.

The Initialization File is called fx.ini and a copy of it must exist in your working directorywhenever you run any of the Four-X programs. You can have different copies of it fordifferent directories.

___________________________________________________________________________ Data Files 81


5.13.2. The Language File

This file allows the programs to translate their screen prompts, screen messages and printeroutput into a language other than English.

The Language File is always called fx.lng, no matter what language is involved. If you aresupplied with such a file, and you wish to use the translation facilities, make sure that there isa copy of it in your working directory. If a copy of fx.lng is not present in your workingdirectory, all output text will be in English.

5.13.3. Log Files

Although it is not necessary to do so, you will probably find it convenient to use Log Files.These record the responses you give when running any of the programs, and can be used tore-run the programs later. These files can be edited with a text editor or a word processor inpure text mode.

Details of how to use Log Files can be found on page 85.

____________________________________________________________ Program Operation - General 82


6. PROGRAM OPERATION – GENERAL

6.1. At the keyboard

6.1.1. Prompts and answers

All user interaction with Four-X programs takes the form of prompts for information thatyou respond to by keying in an answer. In some cases the prompt requests a decision, avalue or a file name. In other cases, the prompt takes the form of a menu and a request thatyou make your choice from the options offered.

In many cases Four-X will include a suggested answer in the prompt. The suggested answeris always enclosed in square brackets (“[…]”), and, if that is the answer you want to give,you merely have to press “Enter”. These suggested answers are called “defaults”.

An example could be:

How many Model Files do you want to input [1] ?

If you press “Enter”, 1 will be used. Alternatively you can type in a different answer.

6.1.2. Editing the defaults

On PC compatibles and some other systems, it is possible to edit default answers rather thanjust accepting them as they are, or keying in a completely new answer.

If a default is given and the first key you press is “backspace” or the “left arrow”, then thedefault answer will appear on the screen as though you had typed it. You will then be ableto edit it in the usual way.

Specifically, the effects of the various special keys are as follows:

End moves the cursor to the end of the text.Home moves the cursor to the start of the text.Left arrow moves the cursor one character to the left.Right arrow moves the cursor one character to the right.DEL deletes the character at the cursor position.Backspace deletes the character to the left of the cursor.INS toggles between insert and over-type mode.<ctrl>Y deletes all the text.ESC restores the text to the original default.



6.1.3. File names

a) Default

At the end of every successful run Four-X takes note (in the Initialization File fx.ini) ofthe file names that you have used. In a subsequent run, usually of a different program, itwill use this information to provide the names for files as defaults.

b) Extensions

The Initialization File also includes default extensions for the various files. These are asfollows:

File type Extension

Additional Arcs Files .addMining Sequence Files .msqModel Files .modOpti-Cut Economics Text Files .etxOpti-Cut Sequence Text Files .stxParameters Files .parPit List Files .pilResults Files .resSpreadsheet Definition Files .ssdSpreadsheet Output Files .ssoStructure Files .stuWork Files .wrk

Print Files for FXRB .prrPrint Files for FXST .prsPrint Files for FXOP .proPrint Files for FXPR .prpPrint Files for FXAN .praPrint Files for FXUT .pruPrint Files for FXMW .prm

Log Files for FXED .loeLog Files for FXRB .lorLog Files for FXST .losLog Files for FXOP .looLog Files for FXPR .lopLog Files for FXAN .loaLog Files for FXUT .louLog Files for FXMW .lom

If you type in a file name without an extension, it will add the default extension for a fileof that type. If you want to insist that the file name has no extension, you should end itwith a period (.).



If you use EXCEL™, you may find it convenient, in fx.ini, to change SSOutput=.sso toSSOutput=.csv under [Extensions] andStoreSpread=Fixed to StoreSpread=Quote under [System]. You will then find that it isvery easy to read spreadsheet data.

c) Upper and lower case

Four-X distinguishes between upper and lower case alphabetic characters in file names.This has no effect on the files when running the programs on PCs, but can be significanton other machines, particularly under UNIX. If Four-X adds an extension to a file nameas described above, it will match the alphabetic case of the extension to the case of the lastalphabetic character in the name.

Even on a PC, it is a good idea to be consistent in your use of alphabetic case, becausethis enables Four-X to check that you do not accidentally use the same file name fordifferent files, in the same run.

d) Overwriting files with the same name

Four-X will not allow you to overwrite an existing data file with a new file of the samename, unless you take specific action to do so. The action required is that you type thecross-hatch character (“#”) in front of the file name (with no space in between). If asuggested file name is the one you want to re-use, you merely have to type in the #character. In neither case does the # appear in any subsequent suggested file name.

(On some UNIX systems # is set up as the erase key. If this is true on your system, pleaseredirect erase to some other key).

Please be warned that you should think very carefully before using this facility tooverwrite a Work File, because, if you get into the habit of doing so, there is always thepossibility that you will overwrite a Work File that you want for the restart of a longoptimization run. In particular, only if the optimization runs are very short should youinclude the # character in front of a Work File name in a Log File (see below).

e) Length

Four-X can handle long file names of up to 50 characters, including any path. However, ifyou use any of the DOS utilities such as EDIT, you may prefer to restrict your usage to aname of eight characters and an extension of three characters.



6.2. Log Files

Everything you type into a Four-X program can be recorded and replayed later, in another run. Youcontrol this logging facility by the use of special logging commands, which you enter in response toany prompt. Each of these special command starts with an exclamation mark (“!”).

For example, if you type in !LOG myrun.log in response to any prompt, the program will issue thesame prompt again, and all subsequent answers that you type in will be written into file myrun.loguntil the end of the run, or until you terminate logging by typing an !END, in response to a prompt.Naturally, you can use any file name in place of myrun.log, or you can give a file name without anextension. In this case, Four-X will add the default extension for a Log File for the program you arerunning. Note that Log Files are not regarded as data files, and any file of the same name will beoverwritten.

The logging commands can all be abbreviated to their first two characters (e.g. !L), and can be ineither upper or lower case.

A full description of the logging commands follows.

!LOG <file name>The !LOG command starts the writing of answers to the Log File, and repeats the prompt.

If you do not provide a file name, the last one used as a Log File for the program you arerunning will be used.

With each answer, the program writes a shortened version of the prompt.

You cannot use the !LOG command if you are already logging.

!ENDThe !END command stops the logging of answers and repeats the prompt.

You cannot use the !END command unless you are logging.

!USE <file name>The !USE command causes the program to start reading answers from the named file, asthough you had typed them in. The program then replays the prompts and answers on thescreen.




Reading of a Log File can stop if/when:

1. The program run finishes.

2. The end of the Log File is reached. In this case the program reverts to waiting foranswers from the keyboard.

3. The program prompts and the Log File get out of step, usually because a mistake hasbeen made when editing the Log File (see below). The program issues a warning.Then, as in 2 above, it reverts to waiting for answers from the keyboard.

You cannot use the !USE command if you are logging.

!DEMO <file name>The !DEMO command has exactly the same effect as the !USE command, except that theprogram pauses after displaying each answer. It is used for demonstration purposes.


You cannot use the !DEMO command if you are logging.

!ASKThe !ASK command puts !ASK in the Log File in place of your answer and asks the questionagain. When the Log File is replayed, the program asks for an answer to the particularprompt interactively before continuing to read the Log File. This is useful if you want to doa series of similar runs while varying just one or two answers.

The !ASK command can only be used at the keyboard when you are logging.

The !ASK command is the only logging command that is valid in a Log File.

PrintFile #tut4Restart_run? nParametersFile tut4ModelFile tut4StructureFile tut4WorkFile #tut4ResultsFile #tut4

The above is an example of a Log File for running program FXOP. In the left hand column areshortened versions of the screen prompts. In the right hand column are the responses. (Anexplanation of the responses required for each program is given under Program Details below).

Log Files can be edited with any text editor, or with a word processor operating in pure text mode.It is quite common to edit an existing Log File to produce a new one, but care must be taken not tochange anything in the left hand column, and to ensure that responses all start in the same column(column 26).



6.3. Running the programs in batch mode

Two things make Four-X easy to use in batch mode.

If a Log File with the name auto????.log exists in the current directory when a program is run,where ???? is the name of the program, then this file will automatically be used as a Log File withoutyou giving it a !USE or !DEMO command.

When each program starts, it looks in the current directory for a file called ????.ok, where ???? isthe program name. If it finds one, it deletes it. Each program, except FXED, writes another copy of????.ok if the run completes successfully. Therefore the presence of this file indicates a successfulrun, and its presence or absence can be used to control subsequent action by a batch or macro file.

___________________________________________________________________ Operation of FXED 88


7. OPERATION OF THE EDIT PROGRAM – FXED

7.1. Purpose

FXED is an editor for Parameters Files.

There are facilities for changing all the different types of information in a Parameters File, with simplerange checking of the values that you input. There is also a facility for validating the data as a whole;that is, for checking all the inter-relationships between the different parts of the file. This checking isidentical to that done when any of the other programs reads a Parameters File.

FXED is different from the other programs in the package in that it uses a series of menus. Thesefollow the structure of the data. For example, to edit the slopes within a sub-region, you first choosethe menu options that select that sub-region. One of the menu options then offered to you is to editthe bearings and slopes.

7.2. Menu operation

When you run FXED, the first screen that you see is the one shown below.

Whittle Four-X PARAMETERS FILE EDITOR Rev 1.00 Licensed for use by -Your Company name will appear here- ------------------------------------------------------------------------------

Press "Enter" to continue...

Once the “Enter” key has been pressed the main menu comes up. This has the same structure as all ofthe other menus in FXED, so we will explain its various features.

Whittle Four-X PARAMETERS FILE EDITOR The Main Menu

O. Open an old file for editing C. Create a new file . cHange to a new file name

. Edit the data . . .

. Validate the data . Save the data

X. eXit the program

Your choice [X] :

FXED menus start with two lines that identify the program, followed by the title of the menu. Thismenu is “The Main Menu”.

After the title are a number of options that you can choose, and a prompt for you to enter “Yourchoice”.

Some of the options have a single letter to the left of them, and this is what you type in to choose thatparticular option. You can use either upper or lower case letters when you do this. (You will noticethat the letter to the left of the option is always capitalised in the option itself).



If an option does not have a letter to the left of it, it means that the option is not currently availablefor some reason, and you cannot choose it. For example, in the menu shown above, you cannotvalidate the data because you have not yet given the program the name of the file you want to edit.

Most options cause the program to prompt you for more information. For example, if you choose to“Open an old file for editing” by typing in an “O”, the program will prompt you for the name of thefile. On the right of the option “Edit the data”, you will notice an ellipsis (. . .). This indicates thatthe option leads to another menu, possibly after prompting you for some information.

Finally, the last option always gets you out of the menu back to a higher level, except in “The MainMenu”, where it terminates the program. This last option, “X”, is always given as the default choice,so that it is easy to get back up to higher levels.

After you have opened an old file for editing or created a new file, the menu changes.

Whittle Four-X PARAMETERS FILE EDITOR The Main Menu +----------------------------------------------------------------------------+ | Current Parameters File: fxtut.par | +----------------------------------------------------------------------------+

O. Open an old file for editing C. Create a new file H. cHange to a new file name

E. Edit the data . . .

V. Validate the data S. Save the data

X. eXit the program

Your choice [X] :

You will now see that, not only are there letters to the left of all the options, but there is also aninformation box under the menu title. This particular box shows the name of the file you arecurrently editing. Menus normally have an information box showing values that are relevant to thechoices offered by the menu.



7.3. Menu navigation

Once you start to use FXED, you will probably find it easy and intuitive to move around the variousmenus and make the changes you require. However, if you have difficulty visualising therelationships between the menus, the following chart will help:

The Header Comment Edit Menu and The Trailer Comment Edit Menu, as their names imply,allow the editing of comment lines at the start and end of the Parameters File. FXED does notsupport comments embedded in the file, although they are allowed by the other programs. If it findssuch comments in an input file, it moves them to the end.

Note: when comment lines are typed into FXED, all leading and multiple spaces are usually removed.If you really want leading or multiple spaces in a comment, use the tilde character (~) in place of therequired spaces. The tildes will be changed to spaces.

The Dimension Edit Menu handles the block size, the framework size and the origin co-ordinates.



The Global Value Edit Menu handles the active blocks indicator, the restart interval, the air flags,the reference mining cost, the mining dilution and recovery factors, and the general default rocktonnage. This menu also leads to menus for editing the formats, the control flags and the RevenueFactor values.

The Sub-region Edit Menu handles the sub-regions and, via another menu, the bearings and slopesfor each sub-region.

The Element Type Edit Menu handles element type codes and their related values.

The Expressions Edit Menu handles user definable expressions. The codes for these expressionscan be used in place of constants in the Parameters File.

The Rock Type Edit Menu handles rock type codes and their related values.

The Processing Method/Rock Type Edit Menu handles processing path definitions and theirrelated values.

The Processing Method Group Menu handles groups of processing methods for which a combinedproduction limit is required.

7.4. Operation

The normal sequence of operations when using FXED is as follows:

Open the Parameters File you want to change, or create a new file. If you are creating a newfile, FXED asks you if you want to use an existing file as a starting point.

Edit the data in the file.

Validate the data, and correct it by further editing if necessary.

Save the data.

Exit the program.

Any time, from the main menu, you can save the data, change to a new file name (Create a new file),and edit the data again before saving, so as to produce different versions of the file.

___________________________________________________________________ Operation of FXRB 92


8. OPERATION THE RE-BLOCKING PROGRAM – FXRB

8.1. Purpose

FXRB allows you to manipulate Model and Results Files in various ways.

Depending on its operating mode, which you determine, FXRB can do any of the following fileoperations:

1. Read one or more Model Files and write a new Model File.(The normal case).




5. Read a single Model File and one or more Pit List Files,and then write a Results File.

There are facilities for extending and truncating model frameworks, in any direction.

There are facilities for merging element data from multiple models into one multi-element model.

There are facilities for combining blocks into bigger blocks and/or for splitting blocks into smallerblocks, along each of the three axes independently.

There are facilities for “mining out” some of the inner pits and/or stripping off some of the outer pitsfound in a Results File.

There are facilities for calculating positional mining and processing CAFs.

The output blocks can be limited to those whose centres lie within a polygon specified by the user.

A new Parameters File, that reflects changes to the model framework, can be produced.



8.2. Explanation

Terminology:

We use the term “model” to denote a rectangular co-ordinate framework containing a collection ofblocks. A model is defined by a Parameters File together with a Model File, a Results File or a PitList File.

In FXRB the first model to be read into the program is called the “primary” model. The primarymodel, together with the required input framework size and the position of the model within thatframework, is used to set up the framework and to establish any air or waste extensions. Theposition of the model within the framework is defined by the offset of the model origin from theframework origin. When the two origins coincide, the offset is zero.

Any subsequent models that are read in are merely pasted over this initial arrangement. These modelsare referred to as “secondary” models.

We use the term primary for the first model, even when there are no secondary models.

The type of operation that is carried out is controlled by your choice from the mode numbers.

With mode 1, when reading one or more Model Files and writing a new Model File, you can:

Make the input framework any sizeLoad the Model Files(s) into the framework in any position(s)Combine and/or split blocksMerge element dataCalculate positional mining and/or processing CAFs

If a mining CAF is calculated, all blocks in the frameworkwill be output

Limit the output with a polygonWrite a new Parameters File

Each Parameters File stipulates the order of the element data. The re-blocking program can mergefiles with different element orders and different element names. The total number of elements cannotexceed the system limit. If there are different numbers of elements, then a new Parameters File mustbe written to update the names and location information. See page 209 for details of how elementsare merged.

With mode 2, when reading one or more Results Files and writing a new Results File, you can:

Make the input framework any sizeMine out or trim off pitsLoad the Results Files(s) into the framework in any position(s)Split blocks (note: you cannot combine blocks)Calculate positional mining and/or processing CAFsLimit the output with a polygonWrite a new Parameters File



With mode 3, when reading a Results File and writing a Model File, you can:

Make the input framework any sizeMine out or trim off pitsLoad the Results File into the framework in any positionCombine and/or split blocksCalculate positional mining and/or processing CAFsLimit the output with a polygonWrite a new Parameters File

With mode 4, when reading a Results File and writing a Pit List File, you can:

Make the input framework any sizeMine out or trim off pitsLoad the Results File into the framework in any positionSplit blocks (note: you cannot combine blocks)Limit the output with a polygonWrite a new Parameters File

With mode 5, when reading a Model File together with one or more Pit List Files and writing aResults File, you can:

Make the input framework any sizeLoad the Model File and Pit List File(s) into the framework in any position(s)Split blocks (note: you cannot combine blocks)Calculate positional mining and/or processing CAFsLimit the output with a polygonWrite a new Parameters File



Thus all modes support changing the framework size, splitting blocks, limiting the output with apolygon, and writing a new Parameters File. The limitations on the other features are summarised inthe following table in which “M”, “R”, and “P” represent Model, Results, and Pit List Filesrespectively:

Input file type(s) andoutput file type foreach mode

Mine outor trim off

pits

Combineblocks

CalculateCAFs

All blockswith mining

CAF1. M[+M...] → M - 4 4 Y2. R[+R...] → R 4 - 4 N3. R → M 4 4 4 N4. R → P 4 - - -5. M+P[+P...] → R - - 4 N

Explanation:You can only mine out, or trim off pits when a Results File is input.Only blocks without pit numbers can be combined.CAFs can only be stored in Model and Results Files.Only Model Files are optimized, and so require all blocks to be present if a mining CAF is

included.

8.2.1. Framework extension and truncation

Since FXRB allows you to extend and truncate model frameworks, the size of the space intowhich block values are loaded may be different from that of the primary model framework.The space it uses is called the input framework, and one or more files can be loaded into it inany position.

Extension and truncation are relative to the primary model framework.



Truncation is obvious, in that blocks are removed and sub-regions are reduced in size oreven deleted. For extensions, on the other hand, we need to define clearly what rules are tobe used by FXRB to determine the values of the new blocks:

• First, the sub-regions are extended as required. The new blocks are assigned thedefault rock tonnage of the sub-region that they are now in, and any upwardsextension is filled with air blocks.

• After the blocks of the primary Model or Results File have been loaded into theprimary model framework, any block on the side or bottom of that framework isreplicated into the nearest blocks in any adjacent extension. (Any element content ofthese replicated blocks is removed but the rock type and the tonnage of the parcels isretained). One effect of this replication is to extend any topographic surfacehorizontally outwards to the limits of the input model framework.

The above figure shows, in section, a primary model framework that has been extended bothsideways and vertically.

8.2.2. Multiple input models

For mode 1, normally, and for mode 2, if second and subsequent files are read in, and a blockgoes into the same position as a block read from a previous file, then the new blockinformation replaces whatever was there before. In other words, if more than one block isread into a particular block position, the last block read in is retained.

However, in mode 1, if the merge option is selected, different elements from different modelsall appear in the new model. See page 209 for details of this facility.

For Mode 5, pit numbers from the Pit List File(s) are attached to the blocks in the inputframework. Again, if there is more than one Pit List File, and more than one pit number isread for a particular block, then the last pit number read is the one that is retained.

Blocks should not be repeated within a particular file. If they are, the program detects thefact, warns you, and rejects the second version.

No extension of the blocks in second and subsequent files is carried out.



Note that, if more than one Model or Results File is to be input, then the primary ParametersFile must have an active blocks indicator of 1, that is the sub-region(s) must fill the primarymodel framework space. Otherwise, there may be no default rock tonnage available wherethe program needs it.

If there is more than one input model, the dimensions of a block must be the same in eachmodel.

Hints: If you are reading multiple files into different positions, draw a sketch with the blockpositions of each of the model frameworks on it before you run FXRB. You can also add adummy waste block with a recognisable tonnage (e.g. 10001, 10002) to each file in blockposition 1,1,1, and then check that the special blocks are correctly placed in the output file.

8.2.3. Combining and splitting blocks

When the program asks you for the combining/splitting factor for a particular direction, youcan answer with an integer such as 3, in which case the blocks are combined by that factor inthat direction. Alternatively you can answer with a fraction such as “1/2”. In this case theblocks are split by that factor. Note than an integer fraction must be used. The value 0.5cannot be used in place of the fraction “1/2”.

It is even possible to answer with, say, “3/2”. In this case the blocks are combined in threesand then split in two.

When blocks are combined, the resultant block is given a tonnage equal to the sum of thetonnages of the component blocks. If the number of parcels of any rock type is greater thanthe limit you have specified when running the program, the pair of parcels with the elementgrades having the smallest sum of squares of grade differences is combined into one parcel,by summing the tonnage and element contents. If necessary, this combining process isrepeated until the number of parcels of each rock type complies with your limit.

A reasonable limit to set for the number of parcels for a particular rock type is discussed onpage 140.

When merging models, if two blocks have the same co-ordinates, then, if they containdifferent element information, they are merged, otherwise the second overrides the values ofthe first.

When blocks are split, the tonnage and element content is shared equally between the outputblocks; the number of parcels in each output block is the same as in the original block.

The usual reason for splitting blocks is to improve the slope modelling when blocks are wide,in relation to the depth of the pit. The optimizer can only mine whole blocks, so that wideblocks sometimes make it difficult to model the slopes accurately.



When blocks are combined along a particular direction, it may be that the combining factordoes not divide evenly into the number of blocks along the corresponding axis of the inputframework. In this case, the input framework is (further) extended until it does divideevenly. The rules for extension are just the same as those described above. This extensionis, in fact, carried out at the same time. The input framework is not affected by splittingfactors.

When it writes out a new file, FXRB writes out every new block that contains one or moreblocks read from an input file, plus any extension air blocks. Where a new block isincomplete, it uses the appropriate default rock tonnage to fill in the gaps. For example, ifyou are re-blocking by a factor of two in all three directions, and it finds an output block intowhich only five sub-blocks have been read rather than eight, it adds three times the defaultrock tonnage for that sub-region. If the output block straddles two sub-regions, theappropriate default rock tonnages are used for each sub-block.

8.3. Information required

FXRB is very flexible and has many options and, inevitably, it must ask a lot of questions todetermine exactly what you want to do. This makes the following lists of required information lookrather daunting. Do not worry. Providing you know what it is you want to do, the program will leadyou through the necessary questions.

The following information is requested at the terminal:

A name for the print fileWhich mode you want to run in (see table on page 95 for a list of the possibilities)



If the mode is 1 (Input one or more Model Files, output a Model File):

How many Model Files you want to inputIf only one Model File is to be input:

The name of the Parameters FileWhether you want to change the size or position of the model frameworkIf you are changing the model framework:

The size, in each directionThe name of the Model FileIf you are changing the model framework:

The offset, in each directionIf more than one Model File is to be input:

Whether you want to merge element data during inputThe name of the primary Parameters FileWhether you want to change the size or position of the model frameworkIf you are changing the model framework:

The size, in each directionThe name of the primary Model FileIf you are changing the model framework:

The offset, in each directionFor each secondary Model File:

The name of the Parameters FileThe name of the Model FileThe offset, in each direction

If you want to combine and/or split the blocks:The re-blocking factor, in each direction

A maximum for the number of parcels of each rock typeIf you want to calculate positional mining CAFs:

If it is OK to write all blocks in the framework:The required expression *

If you want to calculate positional processing CAFs:The required expression *

If you want to limit the output with a polygon:The name of the Polygon File

A name for the new Model FileIf you want to write a new Parameters File:

A name for the new Parameters File

* Expressions are described on page 204.



If the mode is 2 (Input one or more Results Files, output a Results File):

How many Results Files you want to inputIf only one Results File is to be input:

The name of the Parameters FileWhether you want to change the size or position of the model frameworkIf you are changing the model framework:

The size, in each directionThe name of the Results FileIf you are changing the model framework:

The offset, in each directionIf more than one Results File is to be input:

The name of the primary Parameters FileWhether you want to change the size or position of the model frameworkIf you are changing the model framework:

The size, in each directionThe name of the Primary Results FileIf you are changing the model framework:

The offset, in each directionFor each secondary Results File:

The name of the Parameters FileThe name of the Results FileThe offset, in each direction

If you want to split the blocks:The splitting factor, in each direction


If it is OK to write all blocks in the framework:The required expression *

If you want to calculate positional processing CAFs:The required expression *

If you want to limit the output with a polygon:The name of the Polygon File

A name for the new Results FileIf you want to write a new Parameters File:





If the mode is 3 (Input a Results File, output a Model File):

The name of the Parameters FileWhether you want to change the size or

position of the model frameworkIf you are changing the model framework:

The size, in each directionThe name of the Results FileIf you want to mine out any of the pits:

The number of the pit to be mined outIf you want to strip off any of the pits:

The number of the biggest pit you want to keepIf you are changing the model framework:

The offset, in each directionIf you want to split the blocks:

The splitting factor, in each directionA maximum for the number of parcels of each rock typeIf you want to calculate positional mining CAFs:

The required expression *If you want to calculate positional processing CAFs:

The required expression *If you want to limit the output with a polygon:

The name of the Polygon FileA name for the new Results FileIf you want to write a new Parameters File:





If the mode is 4 (Input a Results File, output a Pit List File):

The name of the Parameters FileWhether you want to change the size or


The size, in each directionThe name of the Results FileIf you want to mine out any of the pits:

The number of the pit to be mined outIf you want to strip off any of the pits:

The number of the biggest pit you want to keepIf you are changing the model framework:

The offset, in each directionIf you want to split the blocks:

The splitting factor, in each directionIf you want to limit the output with a polygon:

The name of the Polygon FileA name for the new Pit List FileIf you want to write a new Parameters File:




If the mode is 5 (Input a Model File and one or more Pit List Files, output a Results File):

How many Pit List Files you want to inputThe name of the Parameters File associated with the Model FileWhether you want to change the size or


The size, in each directionThe name of the Model FileIf you are changing the model framework:

The offset, in each directionFor each Pit List File:

The name of the corresponding Parameters FileThe name of the Pit List FileThe offset, in each direction

If you want to split the blocks:The splitting factor, in each direction


The required expression *If you want to calculate positional processing CAFs:

The required expression *If you want to limit the output with a polygon:

The name of the Polygon FileA name for a new Results FileIf you want to write a new Parameters File:



The following information is used from the first Parameters File read in each run:

The dimensions of a blockThe dimensions of the model frameworkThe model framework originThe active blocks indicatorThe general default rock tonnageFor each sub-region:

The block limits in the X, Y, and Z directionsThe sub-region default rock tonnage

If you are using mode 1 and merging element data:The element type codes and positions



The following information is used from any other Parameters Files read in each run:

The dimensions of a blockThe dimensions of the model frameworkIf you are using mode 1 and merging element data:

The element type codes and positions

8.4. Operation

If you have requested a new Parameters File, the program writes it out.

The program then sets up its data structures, and reads in the primary model. If the modelframework has been extended, it carries out any necessary block extensions.

It then reads in any secondary models and stores the blocks, or pit numbers for mode 5, in theappropriate positions.

Finally, FXRB writes out the new file, carrying out any re-blocking and CAF calculations as it doesso.

____________________________________________________________________Operation of FXST 105


9. OPERATION OF THE STRUCTURE ARCS PROGRAM – FXST

9.1. Purpose

FXST prepares a file of “structure arcs” that describes the slopes you require in a form that is suitablefor use in optimization.

Structure arcs are like arrows pointing from one block to another. If a particular block is to bemined, then the structure arcs from that block point to blocks which must be removed first. Ingenerating these structure arcs, FXST takes into account the dimensions of the blocks and therequired pit slopes. It can also include in the file arcs which are specified by the user in an AdditionalArcs File.

Details of the slope generation process can be found in the appendix, starting on page 179.



A name for the print fileThe name of the Parameters FileIf you have an Additional Arcs File:

The name of the Additional Arcs FileA name for the new Structure File

The following information is used from the Parameters File:

The dimensions of a blockThe dimensions of the model frameworkFor each sub-region:

The block limits in the X, Y and Z directionsThe number of benches for arc generationFor each slope angle:

The bearingThe slope

9.3. Operation

For each sub-region, the program generates a generic set of arcs suitable for blocks in thatsub-region. It reports on the number of arcs, the slope errors at each bearing specified, the minimumslope error, the average slope error and the maximum slope error. This information appears on thescreen and in the print file. In addition, the print file shows a plan of the blocks that would be minedto expose a one-block ore body.

You should examine this information carefully to make sure that the accuracy is sufficient for yourpurposes.

____________________________________________________________________Operation of FXST 106


The program then generates the actual arcs for each block to create the Structure File. If anAdditional Arcs File was supplied, the arcs from it are included at the end of the Structure File. Theformat of Additional Arcs Files can be found on page 149.

___________________________________________________________________ Operation of FXOP 107


10. OPERATION OF THE OPTIMIZATION PROGRAM – FXOP

10.1. Purpose

FXOP carries out the optimizations, and produces a Results File containing many different pitoutlines.



A name for the print fileWhether this is a normal run or a restart runIf it is a normal run:

The name of the Parameters FileThe name of the Model FileThe name of the Structure FileA name for the Work FileA name for the new Results File

If it is a restart run:The name of the Work File to restart fromA name for the new Results File


The dimensions of the model frameworkThe active blocks indicatorAir flag AAir flag BThe restart intervalThe general default rock tonnageFor each sub-region:

The block limits in the X, Y, and Z directionsThe sub-region default rock tonnage

For each rock type:The rock type codeThe rock type mining CAFThe rehabilitation cost

cont./



Information used from the Parameters File (continued):

For each element:The priceThe selling cost

Any grade-dependent expressionsFor each method/type for open pit mining:

The processing method codeThe rock type codeThe processing costFor each element

The element processing costThe processing recovery fractionThe processing recovery thresholdThe minimumThe maximum

For each method/type for underground mining:As for open pit mining

The Revenue Factor values

10.3. Operation

The operation of FXOP goes through a number of different stages:

Stage 1The initial data structures are set up and the Model File is read in.

Stage 2 – Active blocks indicators 1 and 2 only.One or more preliminary scans of the Structure File are carried out to identify those blocksthat would have to be mined if every block containing any product were mined. (This isequivalent to setting the Revenue Factor to infinity).

These blocks, which usually constitute only 20 to 30 percent of the total blocks in the modelframework, are the only blocks of interest, because they are the only ones that could possiblybe mined in an optimal pit. The other blocks are therefore discarded so as to reduce the sizeof the problem. This allows the program to change the active blocks indicator to 3internally, and the run continues on that basis.

Stage 3The Structure File is read (again, if stage 2 was done). The arcs that do not begin and endon a block that is to be considered, are discarded. The remaining arcs are stored in the WorkFile. At this point, the Work File is complete, and it will not get any bigger as the runproceeds. Only after this can restart dumps take place.

Stage 4An optimization is carried out for each value of Revenue Factor that you have defined in theParameters File. The order in which the Revenue Factor values are dealt with is such thatthe number of blocks to be considered in each optimization is less each time. For this reason,and for other more technical reasons, the time taken for each optimization falls rapidly afterthe first three or four have been done.



During each optimization the program repeatedly carries out a pass through the blocks,during which it adds structure arcs to create links between blocks, according to the rulesdescribed by Lerchs and Grossmann. The number of arcs added at each pass is generally, butnot always, less than for the previous pass. When a pass takes place in which no arcs areadded, the optimization is complete.

It is not possible to predict how many passes will be required for an optimization. This isbecause it depends on the details of the block values, but you will quickly get a feel for thenumber required for your block values. The optimization process is explained in more detailin the appendix on the Lerchs-Grossmann method, starting on page 223.

If the blocks under consideration during this stage will not fit into physical memory, theprogram is forced to use its virtual memory system, and optimization is much slower. Youcan find out how many blocks will fit into memory by using program FXUT. See page 125.

Stage 5The Results File is written out, and the pit details are printed.

Note that the largest pit in the Results File is always for an infinite Revenue Factor. If youhave included fake blocks with large tonnages to mimic immovable objects, you shouldalways exclude this pit from any analysis you do. FXPR will only display it if the highestRevenue Factor you specify mines all possible ore.

If you restart a previous run, the new run will recommence with the first pass after the last restartdump was done. If the run is terminated again after further restart dumps, it can be restarted againfrom the latest dump. Note that the run-time shown at the end of a restarted run is the time thewhole run would have taken if done without restarts.

See page 26 for examples of the pit details given by FXOP.

____________________________________________________________________Operation of FXPR 110


11. OPERATION OF THE PRINT PROGRAM – FXPR

11.1. Purpose

FXPR reads a Results File, a Model File or a Mining Sequence File, and prints simple plans andsections of the blocks.

The plans and sections show each block as a single character that can indicate the pit number in aResults File, the zone number in a Model File or the period in a Mining Sequence File. Alternatively,the character can show whether the block contains one or more elements, is entirely waste, or is air.

If desired, a particular pit number can be outlined with asterisks (*) to make it easier to see.



A name for the print fileThe name of the Parameters FileThe type of file you want to readIf you are reading a Results File:

The name of the Results FileHow you want to display the blocksIf you want to display pit numbers:

Whether you want to emphasise a pit numberIf you do:

The pit number to be emphasisedIf you want to display block contents:

If you want to display all elements or selected elementsThe pit to be displayed

If you are reading a Model File:The Model File NameHow you want to display the blocks

If you are reading a Mining Sequence File:The Mining Sequence File Name

Which planes you want to display


The dimensions of the model framework

____________________________________________________________________Operation of FXPR 111


11.3. Operation

The program sets up some data structures and reads in the relevant file.

It then prints the required plans and/or sections, using one character for each block. Air blocks,defined as having exactly zero tonnage, are always printed as a period (.). Other blocks are eitherprinted as their pit, zone or period, or as a + or - sign, as shown below, to indicate the presence orabsence of elements in the block, according to the choice you made when running the program.

The following is a section of the model in fxtut.mod. The plus signs indicate ore and the minus signsindicate weathered waste, which is the only waste included in the Model File. All other waste isundefined and automatically assumes the default rock tonnage.

Whittle Four-X BLOCK PRINT OF PIT OPTIMIZATION Page 16 Rev 1.00 18:22 Licensed for use by -Your Company name will appear here- 19-NOV-97 ------------------------------------------------------------------------------

XZ plane for Y = 29 facing in the direction of +ve Y

Symbols: "." is air, "+" could be processed, "-" is waste

Elements selected: GOLD

**********|*********|*********|**** *...........................------* *.............--------------------* *---------------------------------* ----------------------------------- *---------------------- * * * * * * +++ * * +++ * * +++++ * ++++++ * Z +++++++ * +++++++++ * - ++++++++ - * ++++++++ * * +++++++++ * * +++++++++ * * ++++++++ * * +++++++ * * ++++ * * * * * * * **********|***** X *|*********|****

When pit numbers are being displayed, for pit numbers higher than 9, the characters A-Z and then a-zare used, as is shown in the following table:

pit char pit char pit char pit char

1 1 11 B 21 L 31 V2 2 12 C 22 M 32 W3 3 13 D 23 N 33 X4 4 14 E 24 O 34 Y5 5 15 F 25 P 35 Z6 6 16 G 26 Q 36 a7 7 17 H 27 R 37 b8 8 18 I 28 S 38 c9 9 19 J 29 T 39 d10 A 20 K 30 U 40 e

etc.

An example of a pit number print can be found in the tutorial section on page 29.

___________________________________________________________________ Operation of FXAN 112


12. OPERATION OF THE ANALYSIS PROGRAM – FXAN

12.1. Purpose

FXAN allows you to analyse the contents of a Results File by simulating the operation of the mineover its lifetime, under a wide range of throughputs and economic circumstances. This allows you toselect the best pit outline and the best way of operating the mine long-term, according to almost anycriteria.

You specify the final pit, prices, costs, discount rate and throughput limits, and the program simulatesthe operation of the mine, through to the end of production. It then prints period-by-periodtonnages, grades, cash flows and discounted cash flows for the life of the mine.

The prices, costs, and throughput limits for mining, processing and production can be varied fromperiod to period.

One to three different mining sequences can be used during simulation. One of these sequences isunder your control.

Selected values from the print output, and many other values, can be passed to a spreadsheetprogram for graphing and/or further manipulation.

An unlimited number of different simulations can be carried out in one run.

12.2. Explanation

Program FXAN analyses the Results File output by FXOP according to a number of analysis requestsinput by the user. Each analysis request details one or more economic scenarios. For each scenario,FXAN simulates the mining of the pit in various sequences, and prints out mining schedules withtonnages, grades and cash flow figures.

The mining sequences used by FXAN consist of two extreme sequences, “worst case” and “bestcase”, which it supplies. In addition, there is a sequence that you can control, called the usersequence. The best case and the user sequence make use of the pit outlines that lie inside the onebeing studied.

The intersections between the various pit outlines and the benches divide the benches into nestedmining units, and it is the sequence of these units that is controlled.

The “worst case” sequence, and hence the worst case schedule, consists of mining each benchcompletely before starting on the next bench. This sequence, or something very close to it, is usuallyfeasible. It also sets a lower limit to the Net Present Value. Unless you mine waste to the exclusionof ore, it is difficult to achieve a lower Net Present Value.

The “best case” sequence consists of mining out pit 1, the smallest pit, and then mining out eachsubsequent pit shell from the top down before starting the next pit shell. In other words, we do asmany intermediate mining push-backs as there are pit outlines within the one we are mining. Thissequence is seldom feasible because the push-backs are usually much too narrow. Its usefulness liesin setting an upper limit to the achievable Net Present Value.



If, as is sometimes the case, worst case and best case Net Present Values differ by only a percent ortwo, then you know that, for that pit, mining sequence is unimportant from an economic point ofview.

If, as is more common, the difference is significant, you can approximate a more realistic miningsequence, between the two extremes, by specifying the sequence of pit outlines to push back to. Youcan also specify a number of benches by which the mining of each push-back is to lag behind theprevious one. With care, this option can be used to model real cash flows very accurately.

When these schedules are combined with careful economic forecasting, they allow you to makeinformed strategic decisions that will minimize corporate exposure to economic changes, whilstmaximizing the likely return.

When carrying out a study using Four-X, most of the time is spent in running FXAN and studying itsoutput.



A name for the print fileThe name of the Parameters FileThe name of the Results FileIf you want to output data for spreadsheet use:

The name of the Spreadsheet Definition FileA name for the Spreadsheet Output File

A run description for use in printed and spreadsheet outputWhether you want to enter time and/or replacement costs explicitly

(This is a very advanced technique – see page 136)For each analysis request:

The details of the request - see belowWhether you want a full print


The dimensions of the model frameworkThe mining and processing cost adjustment flagsThe print unprocessed mineralisation flagThe formatting requirementsThe mining dilution and recovery factorsThe reference mining costThe element informationThe rock type informationThe processing data for both open pit and underground miningThe processing method groups



Each analysis request includes the following:

The initial capital expenditureIf entering time and/or replacement costs explicitly:

Time costsReplacement capital expenditure

The reference mining costIf entering time and/or replacement costs explicitly:

Time/Replacement costs factored into mining costFor each method/type:

Time/Replacement costs factored into thismethod and type

The price to be obtained for each productThe pit numberThe discount percentage per periodThe maximum tonnes of rock per periodFor each processing method:

The maximum tonnes per periodFor each processing method group (if any):

The maximum tonnes per periodThe maximum units of each product per periodIf you want to override any of the Parameters File values:

You can change one or more of the following:The mining dilution factorThe mining recovery factorThe mining CAF(s)The rehabilitation cost(s)The processing cost(s)The element processing cost(s)The element recovery fraction(s)The element recovery threshold(s)The selling cost(s)The minimaThe maxima

If you want a specified schedule (see page 119):The push-backsThe benches by which each must lead the next

Whether you want to produce a worst case scheduleWhether you want to produce a best case schedule

At the end of each analysis request, you are asked to confirm that the values you have entered arecorrect. If they are not, the request is started again, but the default values given are what you havejust entered. It is therefore easy to skip down to a value that you want to change.

When the request is correct, the program indicates how many analyses are set up so far, and asks ifyou want to enter another request.

If you request only one analysis, and only one sequence for that analysis, you are asked if you want tooutput Opti-Cut sequence and economic files and/or a Mining Sequence File.



12.4. Entering request values

There are a number of facilities available in FXAN that make it easier to enter analysis requests.

12.4.1. Error correction

If you make a mistake when entering an analysis request, typing in a caret “^” will take youback to the previous question. Also, before accepting a complete scenario, the system willcheck whether you are satisfied. If you respond “N” you can subsequently change any of thevalues you have entered.

12.4.2. Default values

A default value is given, in square brackets, for each value requested. If that value issuitable, you merely have to press the Enter key to input it into the program. If you gothrough the analysis request questions a second time, either to make a correction or to enteranother request, the default values will be the ones you entered previously. It is thereforeeasy to input multiple requests with small changes for each request. You merely have topress the Enter key for most of the questions.

12.4.3. Large values

The entry of large values is facilitated by the use of “k” or “K” to indicate thousands and “m”or “M” to indicate millions. Consequently, 200000, 200K, and 0.2m represent the samevalue, as do 2M and 2000k.

12.4.4. Value ranges

If you want to change one or more values in an ascending series, from request to request,there is a mechanism for doing this automatically. Instead of entering a single number, youcan enter a range, in the form of “LOW-STEP-HIGH”. This has the effect of generating aseries of numbers starting with LOW, followed by LOW+STEP, then LOW+2xSTEP, etc.until a value higher than HIGH is obtained (this last value is not used). A series of analysisrequests is generated, using each of these values, and leaving all other values in the requestconstant. Note that the hyphens connecting the numbers together are required. Underscores(“_”) will not do.

Example: if you enter 300-25-400 for the price, and normal values for everything else, it is asthough you had entered analysis requests for 300, 325, 350, 375 and 400. Similarly, youcould enter 20-1-40 for the pit number so as to carry out the same analysis on a range ofdifferent pit sizes.



If you enter a range for more than one value, then each range is expanded within each valueof the preceding range. For example, if price is given as 300-50-400, and pit number is givenas 35-2-41, then the requests for the following cases will be generated, in the order shownbelow, with all other values being constant.

Price Pit

300 35300 37300 39300 41350 35350 37350 39350 41400 35400 37400 39400 41

Ranges cannot be used with push-back pit numbers, when setting up specified push-backs.

If you want two values to change together, you cannot use ranges. For example, if you wantto vary the price of gold and silver, in step, you could enter:

Price to be obtained for the GOLD [400] : 350-10-450Price to be obtained for the SLVR [5] : 4.5-0.1-5.5

However this would generate 121 scenarios. These would contain the data that you want,but it would be buried in a lot of data that you do not want.

What you have to do is enter each pair of values separately as follows:

Other questions ….Price to be obtained for the GOLD [400] : 350Price to be obtained for the SLVR [5] : 4.5Other questions ….Enter another analysis request (Y/N) ? Y

Other questions …. just press enter to repeat the previous valuesPrice to be obtained for the GOLD [350] : 360Price to be obtained for the SLVR [4.5] : 4.6Other questions …. just press enter to repeat the previous valuesEnter another analysis request (Y/N) ? Y

Other questions …. just press enter to repeat the previous valuesPrice to be obtained for the GOLD [360] : 370Price to be obtained for the SLVR [4.6] : 4.7etc.



12.4.5. Values that change with time

If you currently operate a processing mill with a maximum throughput of 200k tonnes perperiod, but are constructing a second mill with a throughput of 150k, which you expect tobring on stream after 2 periods, you can enter the throughput limit of the mill as200k p3/350k.

During simulation, FXAN will use a limit of 200k for the first two periods, and will then use350k for the remainder of the life of the mine.

The construct P<n>/<value> can be used repeatedly for the same entry. If you wish to entermore than will fit on one line of input, terminate the first line with an ampersand (“&”). Theprogram will then request a continuation line, and will repeatedly do this until you end a linewithout an ampersand.

The following rules apply:

1. Period indicators cannot be used when specifying initial capital expenditure, pitnumbers, or lags between specified push-backs. In these cases they would bemeaningless.

2. Period 1 is assumed for the first value, so P1/ should never be used.

3. Period indicators must be in ascending order.

4. With the exception of values entered for replacement capital expenditure, valuesremain the same until the end of scheduling, or until the next period indicator isreached.

Amounts entered for replacement capital expenditure apply only to the specifiedperiod, or to period 1 if no period is specified.

5. The values in the headings are always for period 1. Changes to values, and anyconsequent changes to cut-offs, are announced between periods in the listing.

6. If ranges are used with period changes, then all the ranges for a particular entry musthave the same number of steps, or have a single step (i.e. one value). An example ofthis is given below.



7. Ranges within an entry do not multiply with each other.

e.g. 20-1-25 p7/30-1-35

will produce 6 requests, not 36. It is the equivalent of entering:

20 p7/30 the first time,21 p7/31 the second time,22 p7/32 etc.

and 20 P5/30-1-32 is the equivalent of entering:

20 P5/30,20 P5/31, and20 P5/32.

8. All currency amounts should be in today’s currency, even when they come into effectat a future date. You should never use inflated dollars when working with Four-X.

12.4.6. Period length

In Four-X the period length is defined implicitly by the throughput limits, time costs anddiscount rate that you specify, rather than explicitly as a number of, say, months.

Since these values can change with period number, the period length can change. It isentirely under your control.

Note, however, that when FXAN calculates the Internal Rate of Return, it assumes that allperiods are of one year.

12.4.7. Discount percentage

Any discount percentage that you set should be for the length of period you have decided on.Thus, if a period is three months, the discount percentage will be less than if the period is ayear. If the period length varies, then the discount percentages should vary as well.

The fraction by which cash flows for a period are multiplied to produce discounted cashflows is worked out by multiplying the factor for the previous period (or 1.0 if this is the firstperiod) by either (1-D/100) or 1/(1+D/100). We refer to the first as method A, and thesecond as method B.

Method A is the default used by Four-D and Four-X because it was the method originallyused in earlier versions of the software. It is consistent with the common understanding ofthe term “discount”.

Method B is now known by Whittle to be the conventional way to calculate NPV and isconsistent with the “generalised cost of capital model”2.

2 For example, see Gentry, D.W. and O’Neil, T.J., Mine Feasibility Studies, in Hartman, H.L., et al (Eds.), SME MiningEngineering Handbook, 2nd Editions, Society for Mining, Metallurgy, and Exploration, Inc., Littleton, Colorado, 1992, p.p. 393-404.



You control which type of discounting you use through the fx.ini file, where the entryappears under the [System] heading. Use a text editor to change the value as required.

[System]Discount=MethodA

or Discount=MethodB

12.4.8. Throughput limits

Throughput limits for mining, processing and product all work on the same principle. If apositive value is supplied, that value is taken as the limit and is honoured absolutely. That is,if, during a simulation, any limit is reached, then the current period is terminated, and a newperiod is started. For example, there is no provision for balancing ore and waste mining.

Any throughput limit that you set should be for the length of period that you have decidedon. Thus, if the period is a quarter, its throughput limits will be less than if the period is ayear.

If the limit is set to zero, then it is ignored, and has no effect on scheduling. At least onelimit should be non-zero, otherwise scheduling cannot take place, and everything is mined inthe first period.

12.4.9. Varying the period length

You may want the period lengths at the start of a simulation to be different from those at theend. For example, you may be interested in scheduling four quarters and then yearly periods.To do this, set the discount rate and the production limits to reflect the period lengths:

Discount rate: 2.5 p5/10Mill throughput: 250k p5/1m

Note that, when calculating Internal Rate of Return, FXAN assumes that the period cashflows are for periods of one year, regardless of the discount rate and throughput settings.

12.4.10.Schedules with specified push-backs

If you wish to specify your own mining sequence, then you must provide a list of the pitnumbers that you wish to push back to, in ascending order, separated by spaces.

These will normally be chosen after examination of the shapes of the pits, shown by a run ofFXPR. Also the list will normally end with the number of the final pit.

If the list goes beyond the final pit, it will be truncated. For example, if the final pit is 40,“15 25 42” becomes “15 25 40”.

If the list does not reach the final pit, the last change of pit number is repeated, as required.For example, if the final pit is 40, “15 25” becomes “15 25 35 40”.



You must also provide the number of benches by which each push-back is to “lag” behindthe previous one. For example, if the lag is 3, bench (n+3) of the second push-back will bemined at the same time as bench (n) of the first push-back, etc. If the lag is set to zero, eachpush-back is completed before the next is started.

12.5. Spreadsheet output

FXAN can generate a large quantity of information very quickly, particularly when ranges are used,and users frequently want to manipulate the data further, or to plot graphs from it. Manipulationand/or plotting can most easily be done by using a spreadsheet program. FXAN offers a facility thatallows you to output selected values to a text file, which can then be read into a spreadsheet (or anyother) program.

When you use this facility, you need to create a Spreadsheet Definition File that lists the items thatyou want to output for spreadsheet use. FXAN then outputs the values you have indicated in aSpreadsheet Output File.

A description of the spreadsheet files can be found on page 79. The detailed formats can be foundon pages 166 and 177 respectively.

If you are reading this manual for the first time, we suggest that you ignore the details of this facilityuntil you are familiar with using FXAN.



12.6. Operation

The program sets up some data structures and scans the Results File.

It then produces the print output, and any required spreadsheet output.

If you have requested it, a Mining Sequence File is output.

If you have requested it, Opti-Cut Sequence and Economic Files are output.

The following is a sample of FXAN print file output.

Whittle Four-X ANALYSIS OF PIT OPTIMIZATION RESULTS FILE Page 6 Rev 1.00 17:29 Licensed for use by -Your Company name will appear here- 19-NOV-97 ------------------------------------------------------------------------------ Multi-element tutorial 1

General cost of mining ($/TONNE) : 1.00 GOLD price ($/UNIT) : 380.00 SLVR price ($/UNIT) : 5.10 Pit number : 19 (J) Discount rate (% per period) : 10.00 Calculation based on selection by : Cut-off Maximum mining per period (TONNES) : 4000000 Maximum MILL per period (TONNES) : 1000000 Results File : tut1.res

Rock Proc Meth Proc T/R Recov Thresh Minimum Maximum Cut-off Type Element Cost adj Ratio Grade cut-off cut-off /over

OXID MILL 21.25 GOLD 0.950 0.0589 SLVR 0.800 5.2083 SULF MILL 18.75 GOLD 0.900 0.0548 SLVR 0.800 4.5956 ==============================================================================

BEST CASE SCHEDULE : with inner pits always mined out first


1 Rock MILL 3773714 2.77 -3773714 -3396343 MILL OXID 272320 -5786800 -5208120 GOLD 18375 0.0675 6633194 5969875 SLVR 306157 1.1243 1249122 1124210 MILL SULF 727680 -13644000 -12279600 GOLD 30282 0.0416 10356582 9320924 SLVR 2588940 3.5578 10562876 9506589 Rejected 692107 GOLD 21560 0.0312 SLVR 736596 1.0643 ---------- ---------- Pit 1 at bench 22 to pit 11 at bench 15 5597260 5037534

An example of part of a small Spreadsheet Output File, with commas and quotes to make it easy toimport into a spreadsheet program, is shown below.

"Multi-element tutorial 2"

"Grand totals:"

" "," "," "," "," "" "," "," "," "," "" GOLD"," Pit"," Rock"," Mill"," OPVALUE"" /Price"," /FI"," /tgw"," /tiw"," /DTW"" "," "," "," "," " 300.00 , 10 , 2094480 , 559920 , 2573027 300.00 , 11 , 4309680 , 1097440 , 4225424 300.00 , 12 , 6658000 , 1624480 , 5090110 300.00 , 13 , 8791360 , 2086400 , 5534342 300.00 , 14 , 10276800 , 2362560 , 5565635 300.00 , 15 , 11647440 , 2587200 , 5304338 300.00 , 16 , 14420160 , 2976000 , 4727464

___________________________________________________________________ Operation of FXUT 122


13. OPERATION OF THE UTILITY PROGRAM – FXUT

13.1. Purpose

FXUT is effectively four utility programs in one. It can:Summarise a data fileShow block value calculationsShow cut-off variation with processing CAFShow Four-X or Four-X system limits



A name for the print file.Your choice from:

Summarise a data fileShow block value calculationsShow cut-off variation with processing CAFShow Four-X system limits

If you choose to summarise a data file:

Whether you want to use a Parameters FileIf you do:

The name of the Parameters FileIf you don’t:

The number of elementsYour choice from:

Use Model FileUse Results FileUse Mining Sequence File

The name of the fileYour choice from:

Counts onlyDistribution graphs onlyBoth counts and graphs

If distribution graphs are to be produced:Decisions on which elements you wish to plotDecisions on which graphs to produce(The options depend on the input file type)Decisions on which elements you wish to plotWhether you want fixed scaling for all graphs(The alternative is to have each scaled separately)

The codes of any rock types that you want to exclude

cont./



If you choose to summarise a data file (continued):

Whether you want to specify cut-off gradesIf you do:

A cut-off grade for each elementIf counts are to be produced:

Whether you want to output spreadsheet dataIf you do:

A name for the Spreadsheet Output File

If you choose to show block value calculations:

The name of a Parameters FileYour choice from:

Model FileResults FileMining Sequence File

The name of the fileThe X, Y and Z block co-ordinates of the block(s) that you want to calculate block values for (They can be single values or ranges)The Revenue Factor value to use

In this case, the following information is used from the Parameters File:

The dimensions of the model frameworkThe mining dilution and recovery factorsFor each rock type:

The rock type codeThe rock type mining CAFThe rehabilitation cost

For each method/type for both open pit and underground mining:All details

If you choose to show cut-off variation with processing CAF:

The name of a Parameters FileThe processing cost adjustment factors to useThe Revenue Factor value to use



In this case, the following information is used from the Parameters File:

The mining dilution and recovery factorsFor each rock type:

The rock type codeThe rehabilitation cost

For each method/type for both open pit and underground mining:All details

If you choose to show Four-X system limits:

Whether you want to print config.sys, autoexec.bat and fx.ini files.

13.3. Operation

13.3.1. Summarising a data file

If you are summarising a data file, the program reads through the file once, and then, ifdistribution graphs are required, a second time. It outputs the counts and/or graphs to theprint file, as shown below.

Whittle Four-X UTILITY PROGRAM Page 2 Rev 1.00 18:22 Licensed for use by -Your Company name will appear here- 19-NOV-97 ------------------------------------------------------------------------------

Input Model File - fxtut.mod

File count information -

12840 Blocks were read: 2587 were air (no rock) 10253 contained parcels: 10253 parcels might be processed

Total ROCK in file 18762480 tonnes Total GOLD in file 265244 units Total SLVR in file 18345620 units

WASTE is calculated from ROCK minus ORE above user specified cut-off

------------------------------------------------------------------------------

Summary by rock type -

Rock No of Mine Proc Total Total ---- Grade distribution --- Type Parcels CAF CAF Tonnes Element Minimum Average Maximum

-------------- ------ ------ --------- --------- -------- -------- --------

WASTE 6818 1.000 1.000 11454240 OXID 348 1.000 1.000 640320 GOLD 32338 0.0185 0.0505 0.1144 SLVR 549736 0.1709 0.8585 2.1434 SULF 3087 1.000 1.000 6667920 GOLD 232906 0.0090 0.0349 0.1102 SLVR 17795885 0.5833 2.6689 7.5412 -------------- ------ ------ --------- --------- -------- -------- --------

TOT 10253 1.000 1.000 18762480 GOLD 265244 0.0090 0.0363 0.1144 SLVR 18345620 0.1709 2.5103 7.5412



Element GOLD: Grade distribution for all parcels -

x 1000 Tonnes Tonnes of material in grade range Grade range material 0 500 1000 1500 2000 2500 --------------------------|---------|---------|---------|---------|---------| 0.005 0.010 2160 | 0.010 0.015 73440 |# 0.015 0.020 449840 |######### 0.020 0.025 856800 |################# 0.025 0.030 1334880 |########################### 0.030 0.035 1307920 |########################## 0.035 0.040 902480 |################## 0.040 0.045 807280 |################ 0.045 0.050 476720 |########## 0.050 0.055 382880 |######## 0.055 0.060 252080 |##### 0.060 0.065 160480 |### 0.065 0.070 102560 |## 0.070 0.075 68640 |# 0.075 0.080 50160 |# 0.080 0.085 21520 | 0.085 0.090 20000 | 0.090 0.095 8000 | 0.095 0.100 13520 | 0.100 0.105 7360 | 0.105 0.110 3680 | 0.110 0.115 5840 | ---------- 7308240

13.3.2. Showing block value calculations

If you are showing block value calculations, the program reads through the file and outputsto the print file a full explanation of the block value calculation for each block that youselected.

Input Model File - fxtut.mod

Calculations based on selection by cut-off

Rock Proc Proc Recov Thresh Minimum Maximum Cut-off Type Meth Element Cost Ratio Grade cut-off cut-off /over

OXID MILL 21.25 GOLD 0.950 0.0358 SLVR 0.800 3.4000 SULF MILL 18.75 GOLD 0.900 0.0333 SLVR 0.800 3.0000 ----------------------------------------------------------------------------- Block value calculation for 19,36,1 1,1,2160 with REVFAC = 1.5625 Set BLOCKAG, BLOCKUG and TMPADJ to zero === Parcel 1 SULF,2160 Add 2160x(1-1) to TMPADJ to give 0 Set REHVAL to 2160x0 = 0 Try Method MILL For GOLD: GRADE = 0.0368, CUTOFF = 0.0333 --- Method MILL used to process this parcel (Mode 1) Set PARVAL to 2160x1x1x1x18.75 = -40500 For GOLD,79.5 Set AVAILMET to maximum of zero and 79.5-2160x0 = 79.5 Set REVENUE to 79.5x1x0.9x1.5625x400 = 44718.7 Set SELLVAL to 79.5x1x0.9x0 = 0 Set ELEMVAL to 79.5x1x0 = 0 Set PARVAL to PARVAL + REVENUE-SELLVAL-ELEMVAL = 4218.75 For SLVR,3086.77 Set AVAILMET to maximum of zero and 3086.77-2160x0 = 3086.77 Set REVENUE to 3086.77x1x0.8x1.5625x5 = 19292.3 Set SELLVAL to 3086.77x1x0.8x0 = 0 Set ELEMVAL to 3086.77x1x0 = 0 Set PARVAL to PARVAL + REVENUE-SELLVAL-ELEMVAL = 23511.1 Add PARVAL to BLKAG to give 23511.1 Subtract (2160+0)x1x1.25 from BLOCKAG to give 20811.1 Subtract BLOCKUG from BLOCKAG to give BLOCKVAL = 20811.1 -----------------------------------------------------------------------------

This can be read alongside the explanation of how Four-X calculates block values, on page199.



13.3.3. Showing cut-off variation with processing CAF

If you are showing cut-off variation with processing CAF, the program lists the theoreticalcut-offs calculated by using the full formulae, given on pages 188 and 190. These are subjectto any minima or maxima in the Parameters File. It also calculates the cut-offs obtained bycut-off scaling (see page 191), and shows these values, if they are different from thetheoretical ones by more than 1 in the last digit.

Whittle Four-X UTILITY PROGRAM Page 2 Rev 1.00 12:22 Licensed for use by -Your Company name will appear here- 20-NOV-97 ------------------------------------------------------------------------------

Cut-offs at the reference block with a Revenue Factor of 1.00000:

Rock Proc Proc Recov Thresh Minimum Maximum Cut-off Type Meth Element Cost Ratio Grade cut-off cut-off /over

ORE MILL 6.00 GOLD 0.860 0.478 SLVR 0.700 4.250

Cut-offs for specific positional processing CAFs:

Processing Rock Process Cut-off Scaled cut-offs which CAF Type Method Element /over are different ---------------------------------------------------------------------------

0.800 ORE MILL GOLD 0.382 SLVR 3.393





1.300 ORE MILL GOLD 0.623 SLVR 5.536 5.525



Differences will occur between the theoretical cut-offs and those applied in FXOP and FXAN. Please review these differences to determine whether they are significant.



13.3.4. Showing Four-X system limits

If you are showing Four-X system limits, these appear immediately on the screen, as well asin the print file. For the PC version of the programs, the display is as follows:

The following maxima apply to the programs:

MODELS Parcels in a block 99 Dimension in blocks in X,Y and Z direction 999 Sub-regions 20 Slopes within a sub-region 8 Number of elements 10 Number of expressions 20 Rock types 50 Processing-method/rock-type combinations 50 Processing method groups 9 Total items in all processing method groups 50

COMPUTER MEMORY & FILE NAMES Data buffers 8192 Characters in a buffer 2048 Blocks without using software virtual memory 1048575 Characters in a file name 50

RE-BLOCKING (FXRB) Input models in FXRB 10 Parcels in a block during re-blocking 3000 Characters in a positional factor expression 20 Points in a polygon definition 100

STRUCTURE ARCS (FXST) Arcs per block 500

OPTIMIZATION (FXOP) Optimal pits per run 101

ANALYSIS (FXAN) Periods in a simulation 999 Columns for spreadsheet output 50

PRINTING (FXPR) Characters in a printed line 1001

The actual numbers that you will see will be the limits that apply to your particular copy ofFour-X. For example, the number of data buffers may be different on different workstations.

The number of blocks that can be held in memory, without using the software virtualmemory system, is particularly important during optimization. Each block requires 16 bytes(characters) of memory, and if, after the preliminary scan(s) the blocks will fit into memory,then the program will run a lot faster. This is because FXOP does not have to spend timecopying block details back and forth, between memory and disk. Note that the program willalways run, no matter how many blocks you have (up to 2 billion), but if you try to optimize,say, a one hundred million block model on a PC, not only will you need a great deal of diskspace, but you will have to wait a long time for the result. Fortunately, you should neverneed to optimize such a big model. This is explained in the section on block sizes whichstarts on page 137.

Whenever you work with more blocks than will fit into memory, the programs automaticallyswitch into virtual memory mode, and this is when the buffers are used. In this mode, theprogram keeps data which it has not needed recently on disk rather than in memory. When itdoes need it, something else has to be written to disk before the required data can be readinto memory. This disk reading and writing slows things down, but the alternative is to beunable to run with so many blocks.

The program offers to print your system files (config.sys, autoexec.bat (PC systems only),and fx.ini). This can be useful when reporting problems to Whittle Programming.

__________________________________________________________________ Operation of FXMW 128


14. OPERATION OF THE MINING WIDTH PROGRAM - FXMW

14.1. Purpose

FXMW modifies a set of push-back outlines and a final pit based on specified pit numbers. It adjuststhe shapes of the outlines, so as to produce practical push-backs that satisfy mining width conditions.

Input is usually provided in the form of a Results File, and the corresponding Parameters andStructure Files. The user specifies which pit numbers to use as push-back outlines and for the finalpit outline, and a set of mining width conditions. The output is a new Results File with the push-backnumbers in place of pit numbers, and a print file showing the push-backs after modification.

A Pit List File can be used in place of the input Results File. In this case a new Pit List File is output,and FXRB can then be used to merge it with a Model File to produce a Results File.

The analysis program can be used on the new Results File in the normal way, except that referencesto pit numbers will then be to push-back numbers, and “specified case” with the push-back numbers1, 2, 3 etc. will be your specified push-backs case. It is therefore easy to measure any changes inNPV caused by the modifications made by FXMW to the push-backs.



A name for the print fileThe name of the Parameters FileWhether you wish to use a Results or Pit List FileThe name of the Results or Pit List FileThe name of the Structure FileA name for the new Results or Pit List FileThe pit number to use for the final pit outlineThe pit numbers for the intermediate push-back outlines and the final pit outlineThe required mining width

cont./



Information is requested at the terminal (continued):

If you want to override any of the push-back control flags or values :You can change one or more of the following:Mining width in X (in blocks) Mining width in Y (in blocks)Mining tolerance (in blocks)Remove small drop cuts Y/N

if yes, then minimum blocks for floor and intermediate drop cutRemove small walls Y/N

if yes, then minimum blocks for small wallRemove small stumps Y/NRemove small holes Y/NRemove sharp cornersY/NAllow expansion of outer pitY/N

14.3. Operation

FXMW reads in the Results File or Pit List File and converts the pit numbers to push-back numbers(i.e. 1, 2 ,3). Working from the bottom up, it then applies a series of tests and adjustments to eachbench, in turn.

If the user has specified a value for small drop cuts, the program will check to see if any blocks needto be reallocated. The program then deals with the pit outline to ensure that all blocks are accessible(within tolerance). If pit expansion is allowed, it will expand the pit to make the blocks accessible insuch a way as to minimize the number of blocks affected.

The program then deals with each push-back in turn, starting from the outside. In each case it carriesout a series of actions. It:

a) Checks that all blocks can be accessed within the specified tolerance. If necessary it allowsthe previous push-back to extend into the current push-back in such a way as to minimize thenumber of blocks affected.

b) Removes small walls.

c) Removes small stumps.

d) Removes small holes.

e) Removes sharp corners.

More details of the program operation, and definitions of the above terms, can be found in theAppendices on page 211.



14.4. The FXMW print file

Below is a description of the contents of the print file in the case where a Results File is used as input.If a Pit List File is used as input, then the print file reports on blocks rather than tonnages.

The print file consists of several sections:

1. A summary of the Parameters File.

2. A summary of the file names and the values used in the push-back adjustment.

3. A summary of the blocks read, accepted and rejected on input and a summary of the blockswritten to the new file.

4. A summary of any material added to or omitted from the final pit.

5. A push-back tonnage summary report showing changes in tonnages of each push-back.

6. A printout of the push-backs.

The final push-backs are displayed bench by bench. The push-backs are labelled a to z, ratherthan 1 to 9, to allow blocks that have been moved to a new push-back to be highlighted withcapital A to Z. There are two symbols used to highlight, where the final pit has been expandedto accommodate mining width. A “+” is used to show where a block has been added to thefinal pit for which a record exists in the input Results File and a “*” is used where no recordexists in the Results File. In the latter case the block is assumed to be waste. If blocks areremoved from the final pit, they are shown as “#”.

14.5. Air blocks in the input Results File

The input Results File must contain all of the air blocks. Specifically, this means that when theResults File was produced with FXOP, the Active Blocks Indicator should have been set to 1 or 3and Air flag B should have been set to 3. When air is included in the Results File, the program cancorrectly handle sloping terrain and the application of structure arcs, without generating erroneouswaste blocks.

The Parameters File you use with FXMW should be the same Parameters File you used to producethe Results File. FXMW checks the Air Flag B in the Parameters File, and if it is not set to 2 or 3 therun terminates with an error message.

Regardless of the setting of Air Flag A in the Parameters File, FXMW considers all air blocks whenworking out the slopes. In effect, it temporarily sets Air Flag A to 1. If the optimization has beendone with the flag set to 2, and some part of the topography is steeper than the specified slopes,FXMW may be forced to add extra blocks to the pit. In this case, if the user has requested that therebe no pit expansion, the blocks are still added, but a warning is issued at the end of the run.

14.6. Additional Arcs

If you are using additional arcs, see page 216 for details of the effect this may have on FXMW.



14.7. Initial push-back printouts

If you want to get a printout of the push-backs without any other modifications, you can use FXMWwith a mining width of zero (or a template of one block by one block) and no other changes. This willjust change the pit numbers to push-back numbers and print out the push-backs, bench by bench.

__________________________________________________________________________ Techniques 132


15. TECHNIQUES

It cannot be too greatly emphasised that the use of any optimizer in pit design is an iterative process. Evenwith Four-X, which makes some of the iterations easier, you do not just create a block model, do anoptimization run and some analysis, and then complete a detailed final design. There can be many reasonsfor this. For example, until you have done one optimization, you may not know where the haul roads will be.Until you know this, you do not know where to lay back the slopes to allow for the haul roads.

15.1. Calculating costs for use with Four-X

When preparing for a Four-X optimization, you have to calculate the expected mining, processing,rehabilitation and selling costs. However, Four-X has very specific requirements with regard to thecalculation of these costs and the way they are input, and it is important that these be fullyunderstood.

Costs must be expressed as “mining cost per tonne”, as “processing cost per tonne”, as “rehabilitationcost per tonne”, or as “selling cost per unit of product produced”.

To reduce costs to a per tonne or a per unit basis, you have to make assumptions about theproduction rate. If the size of the pit, produced by the optimization, makes these assumptionsinappropriate, then the costs should be re-calculated and the optimization done again. Many users setup all their cost calculations in a computer spreadsheet. This makes re-calculation much easier.

15.1.1. What costs to include

Incremental costs, such as wages and fuel costs, must obviously be included in thecalculation of the cost of the activity with which they are associated.

Expenditures that are related to time, rather than to tonnage or production require carefulthought, but there is a clear rule that allows you to decide which should be included:

Any expenditure that would stop if mining stopped must be included in one of the costs inputto Four-X, and conversely, any expenditure that would not stop if mining stopped must beexcluded.

The reasoning behind this is that, when the optimizer adds a block to the pit outline, it mayeffectively extend the life of the mine. If it does, the extra costs that would occur as a resultof this extended life must be paid for. Otherwise the optimizer will add blocks to the pit thatreduce, rather than increase its real value. Examples of what to include and not to includeare given later.

__________________________________________________________________________ Techniques 133


Since the optimizer can only take note of costs expressed through the block values, it isnecessary to share time-related costs between the blocks in some way. How they should beshared depends on whether production is limited by mining, by processing or by the market.Usually it is limited by processing, and, in this case, only the mining of an ore block extendsthe life of the mine. The ore block values should therefore include an allowance for timecosts. This is done by adding an appropriate amount to the processing cost per tonne. Ifproduction is limited by mining, as in some heap leach operations, every block that is minedextends the life of the mine, so that time costs should be added to the mining cost. A marketlimit means that time costs should be added to the selling cost. In each case, the amountadded is the time costs per year, divided by the throughput limit per year.

During analysis, using program FXAN, it is possible to handle time costs explicitly, ratherthan factoring them into other costs as described above, and this is discussed on page 136.

15.1.2. The reference block

Four-X assumes that all costs that you give it are calculated for a particular block in themodel. This block, called the “Reference Block”, is usually at the surface, but it can beanywhere you nominate. The concept of a Reference Block is very important in Four-X.

Waste mining and processing costs should be worked out for the Reference Block even ifthere is no appropriate material in that block. That is, the Reference Block may consistentirely of barren material, but you should still work out the processing cost as though thematerial to be processed was in that block.

Four-X deals with any variation of these costs, such as the increase of mining cost withdepth, by the use of CAFs. There can be adjustment factors for the waste mining cost andfor the processing cost for each block in the Model File. There can be a second adjustmentfor the waste mining cost that depends on rock type, and that appears in the Parameters File.

15.1.3. Extra ore mining costs

Because different equipment may be used, it is not uncommon for the cost per tonne ofmining ore to be greater than the cost per tonne of mining waste. For Four-X purposes, thisextra cost should be added to the processing cost.

For example, if the costs of mining and processing ore are $1.54 and $7.37 respectively, andthe cost of mining waste is $0.82, then, for Four-X, we use a processing cost of $8.09(=1.54+7.37-0.82).

Remember that it is important to calculate these figures initially as though mining weretaking place at the Reference Block, even if there is no mineralised material in the ReferenceBlock. If the costs are different in other parts of the model, then the differences should behandled by including positional mining and/or processing CAFs in the Model File.

15.1.4. Examples

The following examples cover most types of cost.

__________________________________________________________________________ Techniques 134


a) Processing mill

Consider a processing mill that costs $10m to build and commission.

If the mine were to be shut down, for whatever reason, on day 2 of operations, the millwould have a certain salvage value, say $6m. In this case $4m has gone for ever. It is an“up-front” or “sunk” cost that must be subtracted from any optimized value of the pititself, or entered during analysis as an initial capital expenditure. It is not a cost foroptimization purposes.

We can deal with the remaining $6m in one of two ways.

1. If we assume that there will be an on-going program of maintenance and capitalreplacement that will keep the salvage value of the mill close to $6m in today’sdollars, then the $6m is theoretically recoverable when the mine is closed, and so isnot a cost. However the maintenance and periodic capital replacement expenses arecosts for these purposes, because they would stop if mining stopped. They shouldbe averaged and treated as a time cost.

2. Alternatively, we can assume that only essential maintenance will be done, and thatthe salvage value of the mill will progressively decline. In this case, the expectedrate of this decline should be treated as a time cost. Note that the rate of decline isnot necessarily the same as the depreciation rate that is used by accountants. Inmost cases the depreciation rate is set by taxation considerations, and may reducethe book value to zero when the salvage value is clearly not zero.

We discuss the interest on the salvage value below.

b) Trucks

If the expected life of the mine is shorter than the operating life of a truck, then truckpurchases can be treated in the same way as the cost of the mill.

If the life of the mine is much longer than the life of a truck, then trucks will have to bepurchased progressively to maintain the fleet, and such purchases will stop if mining isstopped. Consequently the cost of purchasing trucks should be averaged out over the lifeof the mine and treated as a time cost.

Unless the life of the mine is expected to be very long, some compromise between theabove two approaches is usually required.

Contract mining companies must take these factors into account when quoting for a job,and it is sometimes useful to think as they do when you are working out the costs for yourown fleet. You should include every cost that they do, but there should be no allowancefor profit.

__________________________________________________________________________ Techniques 135


c) Administration costs

On-site administration costs will usually stop if mining is stopped. They must therefore betreated as a time cost.

Head office administration costs may, or may not, stop if mining stops at this particularmine, and thus may, or may not, be included.

d) Bank loans for initial costs

Repayment (principal and interest) of a bank loan taken out to cover initial set-up costswill have to continue whether mining continues or not. It should therefore not beincluded in the costs used when calculating block values.

Of course, these repayments will have to come from the cash flow of the mine. If themine is not going to produce enough cash flow to cover them, the project should notproceed. You should not introduce these repayments as costs in an attempt to “improve”the optimization. The result will be quite the opposite. You will get a smaller pit with asmaller total cash flow.

Although bank loan repayments themselves are not included, some of the items that theloan was used to pay for may be included, as you will see below.

e) Bank loans for recoverable costs

If you borrow money from the bank for day-to-day working capital or for items, such asthe $6m discussed in the mill example above, then you can reasonably expect to repay theloan if mining stops. Consequently the interest paid on such a loan is a cost that stops ifmining stops. It should therefore be treated as a time cost. Note that Four-X worksthroughout in today’s currency, so the interest rate used should not include an allowancefor inflation.

f) Grade control costs

It is often necessary to do grade control work on waste as well as ore. In this case, gradecontrol costs apply to waste costs too. If only some of the waste is grade controlled, thenthe correct way to handle it is to increase the cost of those particular waste blocks.However, many users make an estimate of the tonnes of such waste per tonne of ore, andload the cost of mining ore.

g) Support – cable bolts

If the permitted pit wall slope is to be increased by the use of cable bolts or some othersimilar technique, the cost per tonne is related to pit size, which has to be estimated. Thena cost per square foot of wall can be transformed into a cost per tonne of waste. This isan iterative estimate, but fortunately costs per tonne are usually low.

__________________________________________________________________________ Techniques 136


15.1.5. Sample cost calculation

The following spreadsheet shows how time costs would be handled in the two different casesof an operation that could be milling or mining limited.

Tim e c o st c a lc u la tions:

Time costs per year 980000Expected yearly mill throughput 1000000

Time cost per tonne milled 0.98Expected yearly mining capacity 4000000

Time cost per tonne mined 0.24

Incremental costs per tonne:

Extra forMining Mining Mining Milling

Bench Waste Ore Ore Ore

5 1.05 1.87 0.82 8.254 1.17 2.15 0.98 8.253 1.29 2.47 1.18 8.252 1.41 2.84 1.43 8.251 1.53 3.26 1.73 8.25

With throughput limit on milling:

Mining Extra for Milling MillingMining cost Milling Mining Time cost for cost

Bench Waste adj. Ore Ore costs Four-D adj.

5 1.05 1.00 8.25 0.82 0.98 10.05 1.004 1.17 1.11 8.25 0.98 0.98 10.21 1.023 1.29 1.23 8.25 1.18 0.98 10.41 1.042 1.41 1.34 8.25 1.43 0.98 10.66 1.061 1.53 1.46 8.25 1.73 0.98 10.96 1.09

Cost of mining: 1.05 Processing cost: 10.05

With throughput limit on mining:

Mining Mining Extra for Milling MillingMining Time cost for cost Milling Mining cost for cost

Bench Waste costs Four-D adj. ore Ore Four-D adj.

5 1.05 0.24 1.29 1.00 8.25 0.82 9.07 1.004 1.17 0.24 1.41 1.09 8.25 0.98 9.23 1.023 1.29 0.24 1.53 1.19 8.25 1.18 9.43 1.042 1.41 0.24 1.65 1.28 8.25 1.43 9.68 1.071 1.53 0.24 1.77 1.37 8.25 1.73 9.98 1.10

Cost of mining: 1.29 Processing cost: 9.07

15.1.6. Time cost handling during analysis

During optimization with FXOP, time costs and replacement capital costs must be factoredinto the mining, processing or selling cost, because the Lerchs-Grossmann optimizationmethod can only take account of block values and slope requirements. In effect, time isignored.

During analysis with FXAN, the situation is different because time is explicitly dealt with.

__________________________________________________________________________ Techniques 137


If there is only one production limit, and the amounts factored in are correct, then the cashflows will include the correct allowance in each period for the time costs, and there is noneed to take any special action unless you need the time costs to be reported separately.

However, if two limits are applied (e.g. mining and processing), and one limit controls thethroughput during some of the periods and the other during the other periods, it is notpossible to allow correctly for the required time costs through the factored amounts.

In this case you can set up the time costs and replacement capital expenditures as explicitamounts per period, but it is essential also to remove the amounts that you factored into themining, processing or selling cost for optimization purposes. If you do not remove them,then some costs will be paid for twice in the FXAN simulation. The problem is that if youdo this by changing the costs directly, the cut-offs calculated by Four-X will also be changed,and you probably do not want this to happen.

To deal with this, FXAN has a special facility that allows you to enter the factored amountsthemselves. FXAN can then use the original costs for calculating the cut-offs and cancorrect the costs when calculating the cash flows. This special facility is invoked byanswering “Yes” to the question:

Do you wish to enter time and/or replacement costs explicitly?

You will then be prompted, in each analysis request, for the time costs and the replacementcapital costs. You will also be prompted, after you have entered the reference mining cost,for the “Time/Replacement costs factored into” the mining cost, the processing cost(s)and, if a selling cost exists, the selling cost.

15.2. Reagent costs

If a certain element, not necessarily a product, uses up reagent and thus increases the cost ofprocessing, you can use an element processing cost to simulate it.

If the extra cost is not directly proportional to the amount of the element input to the mill, set up agrade-dependent expression for the processing cost per tonne, and then use the expression code inplace of the processing cost.

15.3. Block sizes

There are four different block sizes that are relevant in optimization.

15.3.1. For outlining the ore body

The size of block that you need for outlining the ore body depends on the shape and size ofthe ore body, and on your GMP. The size of the block may be quite small, which can lead toa model framework consisting of millions of blocks.

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15.3.2. For calculating values

The values of blocks should be calculated for a block size that is similar to the selectivemining size. That is, a block should not be so small that it could not be mined separately, norso large that grades are artificially smoothed.

A block size calculated in this way is sometimes bigger than is required for outlining the orebody.

If the block size in the model passed to Four-X is less than this, then FXRB should be usedto re-block it, and the number of parcels (per rock type) in each block should be reduced toone. This has the effect of averaging the grade within the block. If you do not do this, youwill be simulating the mining of the ore body with a selectivity that you cannot achieve inpractice. This will produce an optimistic result.

15.3.3. For designing a pit

There is now considerable experience in pit design using optimization techniques, and,assuming that the pit occupies most of the model framework, and is not too convoluted, then100,000 to 200,000 blocks for the model framework is usually sufficient for pit designpurposes.

The main reasons for this are that the smoothed optimal outline discussed earlier is quiteinsensitive to block size, and that the pit value is quite insensitive to pit tonnage changes nearthe optimal (maximum) value.

The above figure shows the sort of curve you get if you plot total pit value against pittonnage.

Note that the graph goes through a smooth maximum. Such a smooth maximum is normalfor real ore bodies, and, indeed it is possible to prove that the curve cannot have a sharppeak. This has a profound effect on the process of designing pits.

Small deviations from a design that is not optimal (A) can have significant effects on the pitvalue. Thus generations of mining engineers have experimented with small changes to try toimprove their designs. This is quite unnecessary if you start from the optimal outline (B),which Four-X provides, where small deviations have only a second order effect on the valueof the pit.

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These considerations can lead to a block size that may be bigger than is required forcalculating values.

If it is, you should combine blocks by using FXRB, but, in this case, you should not reducethe parcels to one per rock type per block. See page 140 for a discussion on limiting theparcels to a reasonable number.

15.3.4. For sensitivity work

If you want to do sensitivity work to examine the effects of different prices, for example, wefind that, assuming the pit fills most of the model framework, a framework of 25,000 to50,000 blocks will usually give just the same shape of graph with a very small shift ofabsolute value.

When you work with a model of this size, sensitivity work can be done very quickly, and thisapproach generally leads to a much more thorough sensitivity analysis. Time spent onsensitivity work is almost always rewarded by an increase in the value of the project that isout of all proportion to the cost of the sensitivity work itself.

The general strategy to follow is to first create a block model with a suitable block size fordelineating the ore body. Then re-block, if necessary, within your GMP to a size that is ofthe same order as your selective mining tonnage, before outputting it from your GMP as aFour-X Model File. Alternatively you can output it in its original form, and then re-block itwith FXRB, as mentioned above.

Next, re-block this initial Model File with FXRB so as to reduce the number of blocks in themodel framework to 25,000-50,000. Again, see page 140 for a discussion on limiting theparcels to a reasonable number.

Do the sensitivity work using this model, and establish the Revenue Factor, costs and slopeswhich give you the outline that you want to use for design purposes.

Re-block the initial Model File again, but this time produce a model framework havingaround 200,000 blocks. Optimize this using the required economics and slopes. You maythen want to use FXAN to do a few quick checks on your sensitivity work conclusions,before importing the Results File back into your GMP for final detailed design.

15.4. Re-blocking and bias

When someone has put a great deal of effort into creating a very detailed block model of amineralised body, it may seem almost sacrilegious to combine the small blocks into larger blocks.However, the fact remains that, provided the parcels are retained when the blocks are combined, itusually has very little effect on the optimized result. This is because, for any price and costs, thevalue of the new block is exactly the sum of the values of the component blocks. All that has beenlost is a little positional accuracy with respect to the parcels.

It is easy to see that there is no effect at all when a combined block happens to be completely insideor completely outside an optimal outline, even if mineralised blocks are combined with waste blocks.The total value is unchanged.

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When combined blocks lie on the side boundaries of a pit in a waste region, there is randomgive-and-take that produces very little overall change.

When combined blocks include ore inside a pit and waste outside it, there can be a bias due to theexcess waste carried. However, in most cases, this bias is small and, in others, the bias can beremoved by careful modelling in the first place.

For example, in the above figure we show a high-grade, shallow dipping reef, the footwall of whichwill obviously form one wall of the pit. The squares represent blocks created by combining severalsmaller blocks, and the shaded areas show waste that would never be mined in practice, but whichre-blocking might attach to the ore, thus biasing the optimization. However, if the region under themain reef is modelled with a very low density (say 0.01 or even zero), then the cost of mining it willhave negligible effect on the optimization. The detailed pit design will, of course, exclude theunwanted waste.

Tests on a wide range of ore bodies have given changes in total pit value of around only one percentwhen model frameworks are re-blocked from, say, 200,000 blocks to 25,000 blocks. Sincere-blocking of this order reduces optimization time by a large factor, this makes the runs required forsensitivity work very quick.

15.5. Restricting the number of parcels in a block

Four-X currently allows up to 99 parcels per block. Since most GMPs export only one parcel perblock, this limit is seldom a restriction, even when models are severely re-blocked.

However, some GMPs do subdivide their blocks in order to more fully delineate the ore body, andsome of them export the pieces as separate parcels. Also, multiple parcels are sometimes used tomodel the results of indicator kriging.

In either case, re-blocking can lead to a number of parcels which exceeds the limit of 99.

FXRB allows you to set a limit on the number of parcels for each rock type per block. If, whencombining blocks, the program finds an output block which contains more parcels than this limit for aparticular rock type, it reduces the number by a mechanism which is described on page 97.

If you are producing a model where the block size is similar to the selective mining size, you shouldlimit the number of parcels to one for each rock type, as is discussed in the section on block sizes,starting on page 137. If you are producing a model for use in design or sensitivity work, you have toconsider how many parcels you need.

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Assuming that the grades are different in the different parcels, what is important is to retain a gooddescription of the grade distribution in the model as a whole, so that the tonnage processed will reactrealistically to changes in cut-off. It does not have to be too detailed in a particular block . This isbecause the over all mine behaviour is dependent on the grade distribution of groups of blocks ratherthan that of individual blocks.

With a single element, five or ten parcels per rock type in a block is probably enough. With twoelements, one might expect to have to square this, but five or ten is still probably enough. This isbecause the tonnage discrimination is the same as for one element.

15.6. From optimized outline to design

Even when you have done all the necessary sensitivity work, and have settled on a particular optimalpit that you want to use for the design, you still have to do the detailed design. However, the optimaloutline makes this very easy.

Since Four-X uses a block model and mines each block completely or not at all, the optimal outline ispresented initially as a jagged line defined by block edges. However, it is important to remember thatthe blocks themselves are artefacts. The ore body itself does not consist of neat rectangular blocks.It is therefore not relevant to try to follow the jagged outline in detail, or to mine the individualblocks as though they were significant entities.

The first step in design is to get rid of the jagged outline.

The precise method by which you do this depends on the tools that are available to you in your GMP.You may do it entirely by hand, or with varying degrees of computer assistance.

In plan, it is only necessary to draw a smooth line through the zigzag, as is shown in the above figure.

In section, the simplest method is to join the centre points of the bottom of each column of blocksthat is to be mined, as is shown in the above figure.

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Having done this, you then add the details of the haul roads and safety berms, etc.

If haul roads and safety berms are to be incorporated correctly, it is essential that the slopes usedduring optimization be laid back to allow for them. Given this, there should be no particulardifficulty, as is illustrated by the following figure.

The aim is to produce a detailed design that deviates as little as possible from the general outlineprovided by optimization. Where deviation is unavoidable, you should try to balance extra tonnage inone place with reduced tonnage in another.

The final design should, in most cases, have ore and waste tonnages very similar to those for theoptimal outline that you are using. If you cannot achieve this, you may need to re-optimize withdifferent slopes that make better allowance for haul roads, etc.

Sometimes you may find that the bottom of the optimal pit is too narrow to allow sufficient room tomanoeuvre the equipment. This situation is discussed in the following section.

15.7. Minimum mining width

If the ore body is large, achieving the necessary minimum mining width at the bottom of the pitusually involves only minor adjustments to the optimal outline.

However, if you have a steeply dipping, narrow, high-grade reef, or the mineralisation is very spotty,the problem may be more significant.

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There are four ways of dealing with these situations:

1. You can exclude a small amount of ore when you do the design, thus deviating slightly fromthe outline. The viability of this approach depends on how much you have to exclude. TheFour-X mining width program FXMW can do this for you.

2. You can lay the slopes back slightly during optimization, widen the bottom of the pit, and getback the extra waste further up the walls, as is shown in the following exaggerated diagram:

3. If only small parts of the bottom of the pit are too narrow, you can check that the miningwidth is maintained on the bench above, and then plan to dig out the blocks containing ore atthe end of mining.

4. You can, in some cases, use a file of additional arcs, as is explained below.

If you know where, in a horizontal sense, the base of the pit will be, you can link strings of blockstogether with additional arcs to ensure that the required mining width is achieved.

The above figure shows a steeply dipping reef, where it is obvious that the footwall of the reef willform one wall of the pit. It also shows strings of four blocks, each that could be linked to ensure aminimum width of four blocks at the bottom of the pit. Strings like this would have to be providedalong the whole strike and depth of the reef, but you should take care not to link them along strike aswell as across strike. This would have the effect of linking planes of blocks together, which wouldspecify the length of the pit floor and force it to be horizontal. Such a constraint could easily distortthe optimization so much that it would hardly be worth doing.

The sheer number of additional arcs required for this technique would almost certainly make itnecessary to write a program to create them. The program would have to be given, or would have toobtain from the model, details of the line where the footwall of the reef intersects each bench. Itwould then be a simple matter to identify the positions of the blocks which have to be linked.

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To link together four blocks (A, B, C & D), you should include the following arcs in the AdditionalArcs File, in the order shown:

A → BB → CC → DD → CC → BB → A

Other arcs and sequences will produce the same pit outline, but this approach gives the quickestoptimization. For similar reasons, it is best to include the arcs for the lowest bench first, and thenwork upwards.

Hint: Always optimize without additional arcs first. The problem may not turn out to be as bad asyou expect.

15.8. Pits that hit the side of the model framework

If the active blocks indicator is 1 and any of the nested pits reaches the extreme edge of the modelframework, as is shown in the above figure, then that pit has effectively got a vertical wall. Noallowance has been made for the cost of mining the dashed area. This result is certainly not optimal,and, in normal circumstances, would be undesirable. Consequently, it is always a good idea to do aquick check for this with FXPR, after doing an optimization. If you find that any of the pits do hitthe side of the model framework, consider using FXRB to extend the model and the topologysideways before running FXST and FXOP again.

However, in some circumstances it might actually be useful to have a pit reach the side. For example,it might be useful when a lease boundary divides a single ore body that is being mined by twodifferent companies, and you want to explore the consequences for your company of joining the pits.

If the active blocks indicator is 2, and the sub-regions do not fill the whole model framework, thesame ideas apply if a pit hits a sub-region wall that is not at the side of the model framework, but thatdoes not have another sub-region adjacent to it.

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15.9. Immovable objects

It is not uncommon in open pit design to have things, such as a crusher, road or lease boundary, thatthe pit must not encroach upon.

It is quite easy to deal with these situations when using Four-X, and a detailed example is given inTutorial 5, starting on page 50.

15.10. Extending the ore body

Sometimes when you optimize, the pit reaches the bottom of the model framework, and the questionarises as to whether it could go deeper.

If drilling has already been done below the model framework, then you can create a new, deeperblock model in your GMP, re-create the Model File and repeat the optimization and sensitivity work.

If the model framework goes as deep as the drilling, there is still something you can usefully dowithin Four-X. You can extend the mineralised body downwards by repeating the bottom level ofblocks downwards to see if further drilling is warranted.

The steps required for this are as follows:

1. Using the existing Parameters File and Model File, do a run of FXRB in which you reduce theheight of the model framework to 1 bench, but change nothing else. This will create a ModelFile containing just the blocks from the bottom bench. You should create a new ParametersFile to go with it, in the same run.

2. You can then effectively paste this single bench model under your original model framework,say, an extra five times. Run FXRB and tell it you want to input 6 Model Files. Use theoriginal Parameters File as the primary Parameters File and extend the framework downwardsby five benches. You do this by increasing the height of the model by 5 and by loading theprimary Model File with an offset of 5 in the Z direction only. When FXRB asks for details ofthe secondary files, use the single bench Parameters File and Model File for each of them, andload each with a different Z offset in the range 0 to 4.

The Parameters File and Model File created in this way are based on the assumption that themineralisation continues downwards with the same width and grade, as in the blocks in the bottombench of the original model framework. If the pit goes no deeper than it did before when youre-optimize, then there is not much point in drilling deeper unless you have reason to believe that thegrades or the mineralisation width may increase with depth.

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15.11. Slopes that vary with rock type

Each rectangular sub-region in the model framework has a set of bearings and slopes associated withit. Thus the slopes can vary with direction within a single sub-region, as is illustrated on page 71.However, due to different rock types, you may require the slopes to vary with position as well.

The following diagram shows a model with two rock types, separated by an irregular boundary. Ifwe assume that rock type A will support 40 degree slopes and rock type B will support 55 degreeslopes, then an approximation to this can be achieved by setting up sub-regions 1 to 4 as shown.Sub-regions 1 and 2 would have 40 degree slopes, and 3 and 4 would have 55 degree slopes. Abetter approximation could be achieved by using more sub-regions, but some reasonable compromisehas to be reached.

Care should be taken not to use sub-regions that contain only a few benches, because this can makethe slope modelling for that sub-region very poor.

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15.12. Sensitivity example

An important aspect of Four-X is its ability to provide information about thesensitivity of the project to the various processing and cost factors. One way of presenting this data iscalled a “spider” diagram. Plot the distribution of NPV for each of the factors involved in theoptimization when the factors are varied by, say, plus or minus 10% from the base case. The itemwith the most potential impact on the project is the one with the maximum gradient.

SENSITIVITY TO CHANGE

0

5

10

15

20

25

30

35

-10% Base 10%

NP

V in

mill

ion

s

Cost of mining

Process cost

Gold price

Silver price

+25% NPV

-25% NPV

Items that affect the NPV by more than ± 25% are highly significant. In the above example both theprocessing cost and the gold price are highly significant.

15.13. Complex processing methods

When there are multiple products, it is common for processing streams to have different sectionswhich are used to extract different products. Here are some examples, with some suggestions onhow to model them in Four-X.

15.13.1.Element extraction at different stages

Sometimes different products are extracted at different stages in the processing, as is shownbelow.

This can simply be treated as a single method with a recovery of 0.6+0.4x0.1=0.64 for EL1and of 0.70 for EL2.

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15.13.2.Separation

If, for example, after crushing, the material is divided into two streams which each extract adifferent product, we might have the following.

This can be treated as one processing method, with recoveries of 0.9x0.7=0.63 for EL1 and0.7x0.6=0.42 for EL2.

If the percentage split of the ore is fixed, then the sum of the costs of crushing and separationof Method A (x0.2) and Method B (x0.8) gives the processing cost.

If the costs of any of the stages vary with the element quantities processed, this can probablybe handled with the use of element processing costs.

If the split of the ore depends on the relative grades of EL1 and EL2, the situation is morecomplicated, and can probably only be modelled with the use of a grade-dependentexpression for the processing cost.

15.13.3.Different selling costs

In the above example, there are two types of ore with each ore type going to a separateprocess.

If there are different selling costs or prices associated with EL1 in the two streams, then itmay be better to treat it as two separate elements (e.g. EL1 and EL4).

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16. APPENDICES

16.1. Detailed file formats

Four-X uses and/or creates ten different types of text data files plus three auxiliary files. The layoutsof the two Opti-Cut files are given in the Opti-Cut manual. This section details the layout of theremaining eight data files and the three auxiliary files.

Apart from the formats given, those that have fixed widths and column positions for the values canalso be arranged in “comma delimited format”, by using commas to separate the different items. Inthis case the width and column positions are immaterial, but every field, even if it is blank, mustappear with a comma after it.

You will find a more general discussion of the significance of the various data items in the DATAFILES chapter on page 59.

16.1.1. The Additional Arcs File format

The file consists of lines of text that each contain two sets of block co-ordinates. The tablebelow details where the X, Y and Z co-ordinates are to be shown in the Additional Arcs File.

Cols Type Contents

2-4 I X co-ordinate in blocks for block A5-7 I Y co-ordinate in blocks for block A8-10 I Z co-ordinate in blocks for block A

12-14 I X co-ordinate in blocks for block B15-17 I Y co-ordinate in blocks for block B18-20 I Z co-ordinate in blocks for block B

Each line specifies that, if block “A” is to be mined, then block “B” must be removed as well,to uncover “A”.

Blank lines, or comment lines starting with any of the characters shown in parentheses (*'!"),can appear anywhere in the file.

As an alternative to the fixed column layout given above, Additional Arcs Files can be incomma delimited format, with the values on each line separated by commas.

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16.1.2. The Mining Sequence File format

The format of the Mining Sequence File is identical to that of the Model File, except that aperiod and fraction is added to each block header, and a processing method is added to eachparcel.

Columns 50-59 of the block header line are formatted as follows:

Cols Type Contents

50-52 I Period in which the following fraction of this block was mined

53-58 R Fraction of the block mined in the period

The processing method is added to each parcel after all the element details are listed. Thereis a one character space followed by the four character method code. If the parcel was notprocessed, the code “-np-” appears.

The file is written in period order, and, if any of the blocks for a period have a fraction of lessthan 1.0, then the same blocks will appear again in the next period.

Note that the economic conditions can be different in different periods so that, if a block ismined partly in one period and partly in another, it is theoretically possible for the processingmethod code to be different in the two periods for the same parcel.


As an alternative to the fixed column layout, Mining Sequence Files can be produced incomma delimited format, with the values on each line separated by commas.

FXAN writes Mining Sequence Files in fixed or comma delimited format, depending onwhether the “StoreMinSeq” field is set to “Fixed” or “Comma”, in file fx.ini.

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16.1.3. The Model File format

The Model File consists of lines of text that describe a series of blocks. A block descriptionincludes the following information:

The block X, Y and Z co-ordinatesA positional mining CAFA positional processing CAFThe block tonnageA zone number (optional)For each parcel (if any):

The rock type codeThe parcel tonnage

For each elementThe units of element in the parcel(Note that this is a quantity, not a grade).

The optional zone number can be used to indicate the source of the block in the originalmodel. Zone numbers can be displayed for checking by using FXPR.

The format is as follows:

Block header line

Cols Type Contents

2-4 I Block index in the X or East direction5-7 I Block index in the Y or North direction8-10 I Block index in the Z or up direction

(Note that the vertical index increases upwards, not downwards).

12-13 I Number of parcel lines to follow this line(May be zero)

17-26 R Positional mining CAF28-37 R Positional processing CAF

39-48 R Total tonnage of the block(Zero if the block is entirely air)

50-59 I Zone number (optional)

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Parcel line

Cols Type Contents


12-15 C Rock type code

17-26 R Parcel tonnes (Must be positive)

28-37 R Units of element 1in the parcel39-48 R Units of element 2in the parcel50-59 R Units of element 3in the parcel61-70 R Units of element 4in the parcel72-81 R Units of element 5in the parcel83-92 R Units of element 6in the parcel94-103 R Units of element 7in the parcel105-114 R Units of element 8in the parcel116-125 R Units of element 9in the parcel127-136 R Units of element 10in the parcel

Data is only required for the number of elements in the model.

The blocks can be in any order in the file.


As an alternative to the fixed column layout given above, Model Files can be in commadelimited format, with the values on each line separated by commas.

FXRB writes Model Files in fixed or comma delimited format, depending on whether the“StoreModel” field is set to “Fixed” or “Comma”, in file fx.ini. You will find this field underthe “[System]” heading.

16.1.4. The Parameters File format

The Parameters File is a small file containing a wide range of information needed by Four-X.It is read by each of the Four-X programs, although each does not use all of the informationit contains. The actual information used by each program is detailed in the section thatexplains how to use the program.

The Parameters File is a text file with 16 different types of line identified by a line typenumber (detailed below). Program FXED can be used to prepare, modify and validate it. Itautomatically enters the line codes.

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The line types must be arranged in the following sequence:

Type 1Type 2Type 3For each sub-region:

Type 4Type 5For each bearing and slope in the sub-region:

Type 6Type 12Type 13One or more:

Type 14For each element type:

Type 18For each grade-dependent expression:

Type 19For each element type:

Type 20For each rock type:

Type 21For each method/type combination for above ground:

Type 25For each element:

Type 26For each method/type combination for below ground:

Type 30For each element:

Type 31For each processing method group:

Type 35

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The following is one of the Parameters Files used in the Tutorials and Exercises:

1 10.00 10.00 8.00 2 33 64 23 3 1 2 1 1 1 2.00 4 1 33 1 64 19 23 5 1 5 6 0.00 37.00 4 1 33 1 64 1 18 5 2 10 6 0.00 50.00 6 180.00 55.00 12 2 0 5 2 0 $ 13 2160 1.00 1.00 2 3 1.25 1

14 0.20 0.030 2.00

18 GOLD 2 3 0 4 18 SLVR 1 3 0 4 20 GOLD 0.000 400.000 20 SLVR 0.000 5.000

21 WTHR 1.000 0.000 1.000 21 OXID 1.000 0.000 1.000 21 SULF 1.000 0.000 1.000

25 MILL OXID 21.250 26 GOLD C 0.950 26 SLVR C 0.800 25 MILL SULF 18.750 26 GOLD C 0.900 26 SLVR C 0.800

There are maxima to the numbers of items of various types that can be included. Themaxima for your installation can be found by running program FXUT.

Most values in the file are real (R), integer (I) or character (C). Real values should include adecimal point. Real and integer values can be positioned anywhere within the range ofcolumns indicated. Character values should be left-justified. Some values can be either aconstant or a code for a grade-dependent expression which the user has defined (see linetype 19 on page 160). In this case the field is marked R/C.

Line type 1 – The dimensions of a block and the origin co-ordinates

Cols Type Contents

3 I “1”

6-15 R Block size in the “X” or east-west direction16-25 R Block size in the “Y” or north-south direction26-35 R Block size in the “Z” or vertical direction

36-45 R Model framework origin co-ordinate in the “X” or east-west direction(optional) (See P.63 for detailed description)

46-55 R Model framework origin co-ordinate in the “Y” or north-south direction(optional)

56-65 R Model framework origin co-ordinate in the “Z” or vertical direction(optional)

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Line type 2 – The dimensions of the model framework

Cols Type Contents

3 I “2”

11-15 I Number of blocks in the X direction21-25 I Number of blocks in the Y direction31-35 I Number of blocks in the Z direction

Line type 3 – General information – see also line type 13

Cols Type Contents

3 I “3”

15 I The active blocks indicator –1 = All blocks in the model framework are considered.2 = Only blocks within the defined sub-regions are considered.3 = Only blocks that appear in the Model File are considered.

21-25 I The number of sub-regions in the model.

45 I The positional mining CAF flag –0 = Mining CAFs are not used.1 = Mining CAFs are used.

55 I The positional processing CAF flag –0 = Processing CAFs are not used.1 = Processing CAFs are used.

59 I The print unprocessed mineralisation flag –0 = Quantities of unprocessed material are not printed by FXOP and

FXAN.1 = Quantities of unprocessed material are printed by FXOP and

FXAN.

66-75 R The restart interval in hours2.0 is used if this is blank.

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Line type 4 – The sub-region block limits

Cols Type Contents

3 I “4”

11-15 I The lowest X co-ordinate in terms of blocks21-25 I The highest X co-ordinate in terms of blocks31-35 I The lowest Y co-ordinate in terms of blocks41-45 I The highest Y co-ordinate in terms of blocks51-55 I The lowest Z co-ordinate in terms of blocks61-65 I The highest Z co-ordinate in terms of blocks

Note that, for FXST only, a minimum of three benches is required forany sub-region which is at the top of the model framework.

Line type 5 – Slopes, benches and default rock tonnage

Cols Type Contents

3 I “5”

11-15 I The number of slope angles for this sub-region.

21-25 I The number of benches to consider when generating the structure arcs.This must be 2 or greater.

26-35 R The sub-region default rock tonnage.

Line type 6 – Slope bearing and angle

Cols Type Contents

3 I “6”

6-15 R Bearing (0-360) clockwise in degrees from the positive Y direction –any bearing if only one slope.

16-25 R Required pit slope (0.01-89.99) in degrees from the horizontal.

(Line types 7 to 11 are not used. )

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Line type 12 – The general formatting requirements

Cols Type Contents

2-3 I “12”

Decimal places for:6-10 I tonnes in a block (≤ 8)

11-15 I totals of tonnes (≤ 8)26-30 I Revenue Factor values (≤ 8)36-40 I small amounts of currency (≤ 4)41-45 I currency totals (≤ 8)

(A negative number will scale the output bythat power of ten (e.g. -3 for thousands)).

67-70 C Any characters in these columns, other than blank, will become thecurrency characters in the FXAN listings. Blank implies “$”.

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Line type 13 – General information – see also line type 3

Cols Type Contents

2-3 I “13”

6-15 R The general default rock tonnage

16-25 R The mining dilution factor

26-35 R The mining recovery factor

36-45 R Not used

50 I Air flag A –1 = Air blocks are considered in the optimization.2 = Air blocks are not considered in the optimization.

55 I Air flag B –1 = Air blocks are not included in the Results File.2 = Those air blocks that would fall within the pit wall if it were

extended into the air, are included in the Results File. Air flag Amust be 1.

3 = All air blocks in the Model File are included in the Results File.

56-65 R The reference mining cost

70 I Ore selection method1 = By cut-off2 = By cash flow

There are two different formats for line type 14. Successive line types 14 can have eitherformat in any order, provided that the resulting Revenue Factor values form an ascendingsequence.

Four-X uses Revenue Factor as a means of varying the pit shells. With Four-X, it is moreappropriate to talk of a base case revenue, and then scale the revenue up or down to createthe inner and outer pit shells. The factor varies, typically, from .25 to 2 in 40 to 100 steps.

Line type 14A – Single Revenue Factor value

Cols Type Contents

2-3 I “14”

6-15 R Single Revenue Factor value.Must be greater than or equal to zero, or any to any previousRevenue Factor.

__________________________________________________________________________ Appendices 159


Line type 14B – Revenue Factor value range

Cols Type Contents

2-3 I “14”

6-15 R Start of Revenue Factor range.Must be greater than or equal to zero, or any to previous RevenueFactor.

16-25 R Step size of Revenue Factor range.Must be positive.

26-35 R End of Revenue Factor range.Must be greater than the start of the range.

The start value is stored, then repeatedly increased by the step value andstored, until it is greater than the end value. The last value stored isless than or equal to the end value.

(Line types 15 to 17 are used in Four-D Parameters Files. You can use FXED toconvert a Four-D Parameters File to the Four-X format).

Line type 18 – Elements

Cols Type Contents

2-3 I “20”

6-9 C The element type codeThis code must start with an alphabetic character. It is caseinsensitive.

21-25 I The position in the Model File

26-30 I Decimal places for units of this element in a block (≤ 8)

31-35 I Decimal places for totals of units of this element (≤ 8)A negative number will scale the output by that power of ten - e.g. “-3” for thousands

36-40 I Decimal places for grades and cut-offs for this element (≤ 4)

__________________________________________________________________________ Appendices 160


Line type 19 – Grade-dependent Expressions

Cols Type Contents

2-3 I “19”

6-9 C Expression code (1-4 characters)An alphabetic code which can be used in later lines to represent thegrade expression which follows.

15 C Expression usage

M = Expression is for a rock type mining CAF, in which case gradesMined will be used,

W = Expression is for a rehabilitation cost, in which case grades inthe Waste will be used, and,

I = Expression is for a processing cost or a recovery, in which casegrades Input to the mill will be used.

Note that grades here are for individual parcels. Contrast this withexpressions for positional CAFs in FXRB, which are average grades forthe whole block.

17-80 C Expression textAn expression as described on page 204.

Line type 20 – Element prices

Cols Type Contents

2-3 I “20”

6-9 C The element type code

16-25 R/C The selling cost per unit

26-35 R/C The price per unit

It is not usually meaningful to use expressions for selling cost or price, except when the oreitself is the product (e.g. for iron ore).

__________________________________________________________________________ Appendices 161


Line type 21 – Rock types

Cols Type Contents

2-3 I “21”

6-9 C The rock type codeThis code is case insensitive.

16-25 R/C The rock type mining CAF

26-35 R/C The rehabilitation cost per tonne

36-45 R The processing throughput factor


Line type 25 – Processing data for open pit mining

Cols Type Contents

2-3 I “25”

6-9 C The processing method code(This code is case insensitive).

11-14 C The rock type codeMust appear in a line type 21.

16-25 R/C The processing cost per tonne

Note: if more than one processing method is available for a particular rock type and oreselection is by cut-off, then the methods must be specified in the order they are to be applied.

For example, for a mill and heap leach operation, it is important to describe the mill first.Four-X would first check to see if a parcel was at, or above, the cut-off(s) for the mill. If itwas, the parcel would be sent to the mill. Only if the parcel is not good enough for the millwould it be checked against the heap leach cut-offs.

__________________________________________________________________________ Appendices 162


Line type 26 – Element data for open pit mining

Cols Type Contents

2-3 I “26”

6-9 C The element type codeMust appear in a line type 20.This code is case insensitive.

15 C Cut-off control flagC = cut-off controlledN = not controlledNote that, when considering any second and subsequent processingmethods applicable to a particular rock type:

An element cannot be controlled by a cut-off, unless it wascontrolled for the previous method.

All elements which were controlled by a cut-off in the previousmethod must be controlled in this method, unless the number ofcontrolled elements is reduced to 1.

This is not relevant if ore selection is by cash flow.

16-25 R/C The element processing cost per unit

26-35 R/C The processing recovery fraction

36-45 R The processing recovery threshold

46-55 R The minimum

56-65 R The maximum


Line type 30 – Processing data for underground mining

Cols Type Contents

2-3 I “30”

The remainder of the line is identical to that of line type 25.

__________________________________________________________________________ Appendices 163


Line type 31 – Element data for underground mining

Cols Type Contents

2-3 I “31”

The remainder of the line is identical to that of line type 26.


Line type 35 – Processing method group

Cols Type Contents

2-3 I “35”

6-9 C Processing method or previous group code 111-14 C Processing method or previous group code 216-19 C Processing method or previous group code 3

. . . . . . . . .

. . . . . . . . .76-79 C Processing method or previous group code 15

All codes are case insensitive, and should be left-justified within thecolumns indicated.

To include a group inside another group, use a group code. Forexample, “GR_1” refers to the first group defined, “GR_2” to thesecond, etc. Group codes cannot be used until after the group hasbeen defined.

Comment lines starting with any of the characters shown in parentheses (*'!") can appearanywhere in the file. However, only comments at the beginning and end of the file can beedited by FXED, which moves comments in other positions to the end. Blank lines aretreated as comments.

Parameters Files can be in comma delimited format with the items on each line separated bycommas, but the file is so small that there is little point. FXED always writes ParametersFiles in fixed format.

__________________________________________________________________________ Appendices 164


16.1.5. The Pit List File format

The Pit List File is a text file that is produced by FXRB, FXMW or by user software, and itcan be read by FXRB and FXMW. It lists the smallest numbered pit that each block is partof. It is thus like a Results File without the details of the block contents.

Pit List line

Cols Type Contents


(Note that the vertical index increases upwards, not downwards).

13-15 I Number of the smallest pit that the block is part of

If you create a Pit List File outside Four-X to describe mining phases, you must ensure thatphase 1 can be completely mined out, before starting phase 2 etc. This is because FXAN willassume that this sequence will honour the slope requirements.

Blank lines, or comment lines, starting with any of the characters shown in parentheses (*'!"),can appear anywhere in the file.

As an alternative to the fixed column layout, Pit List Files can be in comma delimited format,with the values on each line, separated by commas.

FXRB and FXMW write Pit List Files in fixed or comma delimited format, depending onwhether the “StorePitList” field is set to “Fixed” or “Comma”, in file fx.ini. You will findthis field under the “[System]” heading.

16.1.6. The Polygon File format

The file consists of lines of text that each contain a set of X,Y co-ordinates. X and Y areexpressed as distances, not blocks, in the co-ordinate system in which the origin inParameters File is expressed. If no origin is given in the Parameters File, the co-ordinatesystem is assumed to start at the lower left hand corner of the lower left hand column ofblocks in the model framework.

All X,Y points must lie within the model framework.

For example, assuming the following values:

Origin in the Parameters File 9000,3400,340Block dimensions 10M,12M,8MModel framework dimensions in blocks 78,47,30

Each X value must lie between 9000 and 9000+78x10=9780.

Each Y value must lie between 3400 and 3400+47x12=3964.

__________________________________________________________________________ Appendices 165


Cols Type Contents

1-10 R X co-ordinate11-20 R Y co-ordinate

The points must lie in sequence around the polygon, but can be ordered either clockwise oranti-clockwise. There is no need for the last point to be the same as the first point becauseFXRB automatically joins the last to the first.

FXRB selects blocks with centres which lie within the polygon.

Blank lines or comment lines, starting with any of the characters shown in parentheses (*'!"),can appear anywhere in the file.

As an alternative to the fixed column layout given above, Polygon Files can be in commadelimited format, with the values on each line separated by commas.

16.1.7. The Results File format

The format of the Results File is identical to that of the Model File, except that columns50-59 of the block header line are formatted as follows:

Cols Type Contents

50-59 I Number of the smallest pit that the block is part of

Any air blocks have a zero in this field.

The Results File is output in ascending order of X within Y within Z. Only those blocks,including waste blocks, that are to be mined in the largest pit, are output. Air blocks may ormay not be included, depending on the value of Air flag B in the Parameters File.

The first several “blocks” in a Results File are dummy blocks that carry information aboutthe optimizations that have been done. They are distinguished by having a block index in theX direction (columns 2-4) of -1. If you read a Results File into another package, theseblocks should be ignored.


As an alternative to the fixed column layout, Results Files can be in comma delimited format,with the values on each line separated by commas.

FXRB, FXOP and FXMW write Results Files in fixed or comma delimited format,depending on whether the “StoreResults” field is set to “Fixed” or “Comma”, in file fx.ini.You will find this field under the “[System]” heading.

__________________________________________________________________________ Appendices 166


16.1.8. The Spreadsheet Definition File format

The Spreadsheet Definition File is a text file. Any editor or word processing program thatcan write files without including special characters can be used to prepare and modify it. Thedata is not in fixed field positions. Only its sequence is important.

Each line consists of a line type, followed by one or more spreadsheet codes, separated byspaces. Each value that can be output has been given a code that is used to specify it.

Most codes are quite easy to remember once you are used to using them. For example“ROCK/TG” represents Tonnes of ROCK in the Ground for the period table, and“ROCK/LIMIT” represents the throughput limit you have set on the amount of rock to bemined in a period. Similarly “MIL1.OXID.GOLD/UOW” would represent the grand total ofUnits Output in Worst case scheduling (/UOW) when we extract GOLD from OXID ore inthe MIL1.

Each line starts with the line type “PER” or “GRA”. Codes in lines starting with “PER”specify which values should appear in the periods table, and the order in which they appear.Similarly, codes in lines starting with “GRA” specify which values should appear in the grandtotals table. Codes can appear more than once, if required.


As an example, we show below the contents of a Spreadsheet Definition File that is used inthe tutorials:

Gra GOLD/Price Pit/FI Rock/tgw Mill/tiw OPVALUE/DTW

As you can see, codes can be in upper or lower case, or a mixture of the two.

Codes can also be continued on second and subsequent lines. The following would be theexact equivalent of the example above:

Gra GOLD/Price Pit/FI Rock/tgwGRA Mill/tiw OPVALUE/DTW

The maximum length of a line in the Definitions File is 80 characters.

The maximum number of codes/columns that can appear in a period or grand total table isset when the program is compiled. Run program FXUT to find out what your limit is.

The user must ensure that enough values are output to identify the source of the values. Forexample, period data will normally include CASE and PERIOD.

As was illustrated above, some spreadsheet codes consist of a text part followed by an“attribute” in the form of a slash (/) and further letters. Other codes merely consist of a textpart.

__________________________________________________________________________ Appendices 167


The spreadsheet codes are divided into two lists. Codes in the first list return values that theuser specifies, such as prices, recoveries etc. Codes in the second list return amounts thatFXAN derives. Most of the codes in the second list are made up of a text part and anattribute consisting of a slash (/) and two or more letters.

Capital expenditure could be in either list. It has been included arbitrarily in the second list.

a) Values set by the user

In all codes for values which are set by the user, the inclusion of an exclamation mark (!)indicates that the insertion of a “U” at that point will cause the code to return theunderground value.

Codes for values set by the userCode Type of valueCAPEXINI Initial capital expenditureDISCOUNT Discount percentage per

periodLAG Bench lag between the

mining in specificpush-backs

MINDIL Mining dilution factorMINREC Mining recovery factorPUSH<n> Pit number for the nth

push-back in thespecified push-backsschedule

ROCK/LIMIT Throughput limitUNDEF/TIME_CM Time cost factored into

reference mining costUNDEF/UNIT_CM Reference mining cost<element>/LIMIT Throughput limit<element>/PRICE Price<element>/TIME_CS Time cost factored into

unit cost of selling<element>/UNIT_CS Unit cost of selling<GR_n>/LIMIT Throughput limit<method>/LIMIT Throughput limit<method>.<type>/TIME_CP Time cost factored into

unit cost of processing<method>.<type>/UNIT_CP! Unit cost of processing<method>.<type>.<element>/MAX! Maximum<method>.<type>.<element>/MIN! Minimum<method>.<type>.<element>/RECPER!

Recovery percentage

<method>.<type>.<element>/RECTHR!

Recovery threshold

__________________________________________________________________________ Appendices 168


Codes for values set by the user - continuedCode Type of value<method>.<type>.<element>/UNIT_CE!

Unit cost of processingdue to an element

<type>/CAF Rock type costadjustment factor

<type>/THRFACT Throughput factor<type>/TIME_CM Time cost factored into

unit cost of mining for arock type(Derived value)

<type>/UNIT_CM Unit cost of mining for arock type(Derived value)

<type>/UNIT_CR Unit cost of rehabilitation

Note: when any of the codes for values set by the user is requested in a grand total, and thevalue is changed during the life of the mine, it returns the value applicable in the first period.

b) Derived values

Codes for derived values use a common set of attributes, which it is convenient to describeseparately.

All attributes, except for /OFU, start with a two character base which indicates the type ofvalue.

All cash flow and cost attributes start with /C, with the second letter indicating the type ofcash flow or cost. The discounted equivalent of each attribute is obtained by changing the Cto D.

Similarly, all tonnages start with /T, all units of elements start with /U and all grades startwith /G.

__________________________________________________________________________ Appendices 169


In the following two tables, an asterisk (*) after an attribute indicates that, for grand totalcodes, another letter must be added to the Attribute to indicate the scheduling option. Theextra letter will either be “B” for the best case, “S” for the specified case and “W” for theworst case.

Attributes for codes for derived valuesAttribute(s) Type of value/CE* /DE* Cost of processing due to Elements/CI* /DI* Cash Income (Revenue)/CM* /DM* Cost of Mining/CP* /DP* Cost of Processing/CR* /DR* Cost of Rehabilitation/CS* /DS* Cost of Selling/CT* /DT* Cash flow - Total of the other cash flows in the

category/EN ENd pit or bench for a period/FI FInish pit or bench for a grand total/GG* Grade in the Ground before processing/GI* Grade Input to processing/GP* Grade in Place/GR* Grade Rejected/OF cut-OFf/OFU cut-OFf for Underground methods/ST STart pit or bench for a period/TG* Tonnes in the Ground before processing/TI* Tonnes Input to processing/TP* Tonnes in Place/TR* Tonnes Rejected/UG* Units of an element in the Ground before

processing/UI* Units of an element Input to processing/UO* Units of an element Output from processing/UP* Units of an element in Place/UR* Units of an element Rejected

__________________________________________________________________________ Appendices 170


In this second table, there are some instances where no attribute is required for periodvalues, but a slash and B, S or W is required for grand total values. This is shown as /*.

Codes for derived valuesText Allowed

attributesType of value

AVMINCAF Average positionalmining cost adjustmentfactor

AVPROCAF Average positionalprocessing costadjustment factor

BENCH Period/EN /STGrand totals/FI

The bench being mined

BLANK Special – produces ablank column betweendata columns

CAPEXREP /CT* /DT* Replacement capitalexpenditure

CASE Special – 1 for worstcase, 2 for specifiedpush-backs, 3 for bestcase

COVALUE /CT* /DT* The extra cash flow forthe company thatresults from operatingthe open pit, as distinctfrom not operating theopen pit, and miningany suitable ore byunderground methods

INTERNAL Grand totalsonly/*

The percentage InternalRate of Return,calculated on theassumption that allperiods are one yearlong

LIFE Grand totalsonly/*

The life of the pits, inperiods

__________________________________________________________________________ Appendices 171


Codes for derived values - continuedText Allowed


OPVALUE /CT* /DT* The cash flow from theopen pit

OUTSIDE /TP The mineralisedmaterial in the modelbut outside the final pit(Not available if theResults File is producedby FXRB).

OUTSIDE.<element> /GP /UP The element grade andunits in the model butoutside the final pit(Not available if theResults File is producedby FXRB).

PERIOD The period number

PIT Periods/EN /STGrand totals/FI

The pit numberFor /EN and /ST, if theschedule is for specifiedpush-backs and the lagis greater than zero, thisrefers to the push-backwhich is currentlyleading.

ROCK /CM* /DM*/CR* /DR*/TG* /TP*/TR*

Total material

STRIP /* The stripping ratio -unprocessed material /processed material

TIMECOST /CT* /DT* Fixed costsUGVALUE /CT* /DT* The cash flow that

would have resulted ifany suitable ore in theregion mined had beenmined by undergroundmethods

WASTE /* Tonnage mined but notprocessed

__________________________________________________________________________ Appendices 172




<element>

(CT = CI - CE - CS)

/CE* /DE*/CI* /DI*/CS* /DS*/CT* /DT*/GG* /GI*/GP* /GR*/UG* /UI*/UP* /UR*/UO*

Element

<GR_n>

(CT = CI - CE - CP -CS)

/CE* /DE*/CI* /DI*/CP* /DP*/CS* /DS*/CT* /DT*/TG* /TI*

Processing methodgroup

<GR_n>.<element>

(CT = CI - CE - CS)

/CE* /DE*/CI* /DI*/CS* /DS*/CT* /DT*/GG* /GI*/UG* /UI*/UO*

Group ‘n’/elementcombination

<method>



Processing method

<method>.<element>

(CT = CI - CE - CS)

/CE* /DE*/CI* /DI*/CS* /DS*/CT* /DT*/GG* /GI*/UG* /UI*/UO*

Processingmethod/elementcombination

<method>.<type>



Processingmethod/rock typecombination

__________________________________________________________________________ Appendices 173




<method>.<type>.<element>

(CT = CI - CE - CS)

/CE* /DE*/CI* /DI*/CS* /DS*/CT* /DT*/GG* /GI*/UG* /UI*/UO*Periods only/OF /OFU

Processingmethod/rocktype/elementcombination

<type>

(CT = CI - CE - CM -CP - CS)

/CE* /DE*/CI* /DI*/CM* /DM*/CP* /DP*/CR* /DR*/CS* /DS*/CT* /DT*/TG* /TI*/TP* /TR*

Rock type

<type>.<element>

(CT = CI - CE - CS)

/CE* /DE*/CI* /DI*/CS* /DS*/CT* /DT*/GG* /GI*/GP* /GR*/UG* /UI*/UP* /UR*/UO*

Rock type/elementcombination

These codes give you access to almost every value you could want in order to best assess adesign. If you find their sheer number confusing, you may find it helpful to refer to thediagrams in the following section.

__________________________________________________________________________ Appendices 174


c) Spreadsheet code overview

There are many spreadsheet codes available to the user. The following diagrams may make itclearer where the codes are applied.

First there is a “map” showing the relationships between the other diagrams. Material whichis mined is either mined as waste, because it has no processing path or is not processed, or ismined as ore. Material mined as ore is processed and produces output.

Material Mined

Output

Processing Details

Material Mined as Waste Material Mined as Ore

Material Mined

Set by the user:Unit cost of mining waste - /UNIT_CM, /TIME_CM

UNDEF <t>Rock type mining CAF - /CAF

<t>Mining limit - /LIMIT

ROCKPush-back definition

PUSH<n>Lag between push-backs

LAG

Produced by FXAN:Tonnage - /TP*

<t> ROCKElement quantity - /UP*

<e> <t>.<e>Grade - /GP*

<e> <t>.<e>Average Mining CAF

AVMINCAFBench - /ST, /EN, /FI

PIT BENCHMining Cost - /CM*, /DM*

<t> ROCKStripping Ratio - /*

STRIP

__________________________________________________________________________ Appendices 175


Material Mined as Waste

Set by the user:Unit rehabilitation cost - /UNIT_CR

<t>

Produced by FXAN:Total waste tonnage - /*

WASTERehabilitation cost - /CR*, /DR*

<t> ROCKRejected tonnage - /TR*

<t> ROCKRejected element quantity - /UR*

<e> <t>.<e>Rejected material grade - /GR*

<e> <t>.<e>

Material Mined as Ore

Set by the user:Mining dilution

MINDILMining recovery

MINREC

Produced by FXAN:Tonnage in the ground - /TG*

<t> <m> <m>.<t>ROCK <GR_n>

Element quantity in the ground - /UG*<e> <m>.<e> <t>.<e><m>.<t>.<e> <GR_n>.<e>

Grade in the ground - /GG*<e> <m>.<e> <t>.<e><m>.<t>.<e> <GR_n>.<e>

Tonnage input to processing - /TI*<t> <m> <m>.<t>ROCK <GR_n>

Element quantity input to processing - /UI*<e> <m>.<e> <t>.<e><m>.<t>.<e> <GR_n>.<e>

Grade input to processing - /GI*<e> <m>.<e> <t>.<e><m>.<t>.<e> <GR_n>.<e>

Mining dilution and mining recovery can affect thequantities input to processing. This leads to thefollowing relations between the above attributes for thesame code:

TI = TGxMINDILxMINRECUI = UGxMINRECGI = GG/MINDIL

__________________________________________________________________________ Appendices 176


Processing Details

Set by the user:Cut-offs - /MIN_OF!, MAX_OF!

<m>.<t>.<e>Product prices - /PRICE

<e>Processing limits - /LIMIT

<m> <GR_n>Recoveries - /RECPER!, /RECTHR!

<m>.<t>.<e>Throughput factors - /THRFACT

<t>Unit costs of processing - /UNIT_CP!, /TIME_CP

<m>.<t>Unit cost of element processing - /UNIT_CE!

<m>.<t>.<e>

Produced by FXAN:Costs of processing - /CP*, /DP*

<m> <t> <m>.<t><GR_n>

Average processing CAFAVPROCAF

Costs of element processing - /CE*, /DE*<e> <m> <t><m>.<e> <m>.<t> <t>.<e><m>.<t>.<e> <GR_n> <GR_n>.<e>

Cut-offs - /OF, /OFU<m>.<t>.<e>

Output

Set by the user:Production limit - /LIMIT

<e>Unit selling cost - /UNIT_CS, /TIME_CS

<e>

Produced by FXAN:Product - /UO*

<e> <m>.<e> <GR_n>.<e><t>.<e> <m>.<t>.<e>

Selling costs - /CS*, /DS*<e> <m> <t><m>.<e> <m>.<t> <t>.<e><m>.<t>.<e> <GR_n> <GR_n>.<e>

Revenue - /CI*, /DI*<e> <m> <t><m>.<e> <m>.<t> <t>.<e><m>.<t>.<e> <GR_n> <GR_n>.<e>

Net cash flow - CT*, DT*<e> <m> <t><m>.<e> <m>,<t> <t>.<e><m>.<t>.<e> <GR_n> <GR_n>.<e>CAPEXREP TIMECOSTOPVALUE COVALUE UGVALUE

Internal rate of return - /*INTERNAL

__________________________________________________________________________ Appendices 177


16.1.9. The Spreadsheet Output File format

A Spreadsheet Output File is a text file, and it is quite simple. It contains a period tableand/or a grand totals table.

Each table consists of columns of numbers, with each column headed by the correspondingcode.

If both a period table and a grand totals table are included, the periods table appears first.

By default the columns are separated by spaces. This format can be read into mostspreadsheet packages, although in some cases it may be necessary to “parse” the text afterinput in order to get the numbers into their corresponding columns. If this is inconvenient,two other formats are available to you. These are obtained by changing the “StoreSpread”field in your fx.ini file from “StoreSpread=Fixed” to “StoreSpread=Comma” or“StoreSpread=Quote” using a text editor. You will find this field under the “[System]”heading.

If StoreSpread is set to “Comma”, the columns are separated by commas. If StoreSpread isset to “Quote”, the columns are separated by commas, and the headings are enclosed indouble quotes.

An example of a small Spreadsheet Output File is shown on page 121.

16.2. The block model

A block model is a collection of data that contains estimates of things such as element grade anddensity for a set of blocks that include the ore body and its surrounds. This is usually prepared withyour Generalised Mining Package (GMP). Details of the precise data requirements for a Four-XModel File start on page 151.

We use the term “model framework” to denote a rectangular region of space that is divided into anumber of such blocks, all rectangular and of the same size.

The above figure shows such a region with one of the blocks outlined. The only restriction set byFour-X on the size and proportions of a block is that an exact number of them must fit into the modelalong each side. That is, the size of the model framework in any direction must be a multiple of theblock size in that direction.

__________________________________________________________________________ Appendices 178


The position of each block in the model framework is defined by the block indices IX, IY and IZ.These are counts of block positions along each of the axes, starting from 1. We use X, Y and Zrather than Easting, Northing and Elevation because not all models are aligned by the compass. Notethat blocks are numbered from the bottom up in the Z direction.

16.3. Sub-regions

For certain purposes, we divide the model region into two or more sub-regions. Each sub-region isrectangular, and is defined in the Parameters File by the minimum and maximum block co-ordinates inthe X, Y and Z directions.

The above figure shows a model framework divided into four sub-regions, and the table below showsthe block limits used to define these sub-regions. The numbers represent block positions along eachaxis.

Sub-region MinX

MaxX

MinY

MaxY

MinZ

MaxZ

1 1 35 1 40 1 102 1 35 1 40 11 203 1 35 41 55 1 204 36 60 1 55 1 20

Sub-regions carry the slope definitions and the sub-region default rock tonnage. Consequently, theslope definitions and the default rock tonnage can vary with position in the model. The order inwhich sub-regions are declared in the Parameters File is immaterial.

It is possible to have a different sub-region layout for slopes and for default rock tonnages. Youwould set these up in two different Parameters Files, and use one for structure arc generation, and theother for re-blocking and optimization.

__________________________________________________________________________ Appendices 179


16.4. Slope handling

You must specify slopes for each sub-region. The required bearings and slopes are included in aParameters File, from where they are read by program FXST when it creates a Structure File.

These slopes set maxima to the slopes of the final pit outline. If the outline is following the ore body(e.g. along an ore footwall), the slopes may be shallower.

16.4.1. The slope cone

For each sub-region, FXST first converts the slope requirements into an inverted “cone” thatdefines the rock that must be mined to expose a point at the tip of the cone. At each bearingspecified in the Parameters File, this cone has the required slope. Between these bearings theslope is interpolated. If only one bearing and slope is specified, the slope is the same allround, and the bearing is ignored.

If we consider bearings BA and BB, with BB greater than BA, and corresponding slopes SAand SB, then the interpolation formula for the slope at a bearing B, between BA and BB, isas follows:

( ) ( )arctan min

tan tan,tan cos

,tan cos

−

−−

+−

− −

1

1 1 1BB BA

BB BSA

B BASB SA B BA SB BB B

If you find the formula somewhat daunting, consider the following figure:

This is a horizontal section through part of the inverted “cone” with slopes specified asabove, and with SA being steeper than SB. The curved line PQR is the initial interpolationline, but note that between P and Q it curves outside the tangent to the slope SA. Thiswould rarely be what the engineer would want, so FXST uses the tangent (straight line PQ)until it reaches Q, and then follows the curve QR. This explains why the formula abovecontains a minimum function.

__________________________________________________________________________ Appendices 180


In a more extreme situation with, say, a steep slope to the north and a shallow one to thesouth, without the limitation to the tangent, a single block ore body would produce a heartshaped pit, as shown below.

Under such circumstances, FXST uses the straight line PQR, rather than the curve PQR.

This use of tangents to the slope wall sets a minimum bearing difference for a particularchange of slope. This is because neither slope radius can go beyond a right-angle to theother slope radius.

For two slopes SA and SB, where SA is greater than SB, as in the example above, theminimum bearing difference is:

arccostan

tan

SBSA

If you have slopes that change quicker than this, then any program except FXED will detectit when it reads the Parameters File, and will show on the screen and in the print file theminimum bearing difference required. FXED only detects the problem when you “validate”the data you are editing.

16.4.2. Generating the possible arcs for a block

Having created the inverted cone for a particular sub-region, Four-X then works out theminimum set of arcs that will ensure that the necessary blocks will be removed, if these arcsare applied to all blocks. The procedure is complicated and works in three dimensions, butan example in two dimensions will illustrate it.

__________________________________________________________________________ Appendices 181


In the above case, the desired slope can be achieved by using just the three arcs shown bydashed lines with arrow heads for each block. This is because, when we apply these threearcs to all the blocks, chaining of the block dependencies results in every block with a centreabove the line of the desired slope being mined, if the bottom left-hand block is mined.

In this case we have considered 8 benches. If we had only considered 3 benches, we wouldonly have found two of the arcs, and the slopes would have been steeper. Clearly, the morebenches we examine, the more accurately we can reproduce the slopes. For Four-X, youspecify the number to be examined, by supplying a number of “benches for arc generation”for each sub-region in the Parameters File.

In practice, when working in three dimensions, it typically requires between 50 and 100 arcsper block to ensure an average slope accuracy of 1 degree, which is sufficient for mostpurposes. The number of benches required for this depends on the proportions of theblocks. We suggest a way of calculating a starting number in the section on the ParametersFile, on page 69. However, remember that there is an inherent limitation to the accuracy,which is the fact that the optimizer can only “mine” whole blocks.

Some models that are shallow and/or have wide blocks can present slope modellingdifficulties. In these cases FXRB can be used to split the blocks so as to make themnarrower.

16.4.3. Generating the Structure File

When these generic lists of arcs per block have been generated for each sub-region, FXSTexamines each block in the model and writes out to the Structure File those arcs appropriateto it. During this operation, it checks for and rejects arcs that go outside the model, or thatpenetrate too far into another sub-region.

The definition of “too far” is complicated, but takes into account the block-stepping up andout required by the particular block proportions and slopes. For example, if the slopes stepup one block and out two blocks, the arcs will be allowed to penetrate further into anadjoining sub-region than if the stepping was up one and out one. Similar considerationsapply when crossing up into another sub-region.

The arcs are stored as lists towards each block from below, and consequently no arcs aregenerated for the bottom bench. The lists are stored in a compressed binary format.

If an Additional Arcs File is supplied, FXST adds the arcs from it to the end of the StructureFile.

__________________________________________________________________________ Appendices 182


16.5. Ore selection methods

Four-X has two methods of selecting parcels for processing. It can use cut-offs or cash flow.

A parcel has a rock type and one or more element grades. Zero or more processing methods will beapplicable to that rock type. If there are zero methods for the rock type, the parcel is automaticallymined as waste.

16.5.1. Ore selection by cut-off

Ore is selected by comparing the grades of the material with pre-calculated processingcut-offs. If it does not satisfy the cut-offs, it is treated as waste. See page 190 for anexplanation of how multiple cut-offs are handled.

If more than one processing method is applicable, the grades are compared with the cut-offsof each in turn, in the order in which they are specified in the Parameters File.

16.5.2. Ore selection by cash flow

Ore is selected by comparing the cash flow which would be produced by processing it andthe cash flow which would be produced by mining it as waste. If the cash flow fromprocessing it is higher, the material is treated as ore. If not it is treated as waste.

If more than one processing method is applicable, the one which produces the highest cashflow is used.

In straightforward cases this produces a similar result to that of ore selection by cut-off(except for rounding effects), but there are significant exceptions, and an example is given onpage 192.

16.6. Cut-off calculation

This section explains how cut-offs are calculated for a single element, when ore selection is bycut-off. We start with a simple case and progressively introduce more complexity.

16.6.1. The simple case

If only one element is involved and only one processing method is applicable to a particularrock type, the cut-off used to decide whether to process material or not is that grade atwhich the product recovered just pays for the processing of the material (plus any extramining and hauling cost for ore).

That is:

Cut-off x Recovery x Price = Cost of “processing”or:

Cut-off = PROCOST/(RECOVERYxPRICE)

__________________________________________________________________________ Appendices 183


This is illustrated below.

We refer to the thick line as the processing line. If the processing recovery or the priceincreases, the line gets steeper and the cut-off grade decreases.

We assume that the decision to process or not to process is made while the material is still inthe ground. Thus, material that is not processed incurs only the cost of mining it as waste.Material that is to be processed will often be handled with different equipment at a greatercost, and this extra cost should be added to the cost of processing. This is not the usualdefinition of processing cost, so we have put the word “processing” in quotes to remind youof this.

16.6.2. Mining dilution and recovery

Allowing for mining dilution and mining recovery, the cost and revenue can be expressed as:

Processing cost/T = MINDILxMINRECxPROCOST

Revenue/T = MINRECxGRADExRECOVERYxPRICE

and hence

Cut-off = (MINDILxPROCOST) / (RECOVERYxPRICE)

Note that mining recovery has no effect on cut-off.

__________________________________________________________________________ Appendices 184


16.6.3. Positional processing cost adjustment factor

The processing cost at the Reference Block is multiplied by the Positional Processing CAFfor each block. This leads to a cut-off for a parcel within a particular block of:

Cut-off = (PROCOSTxPROADJ) / (RECOVERYxPRICE)

Note that this means that the cut-offs applied by Four-X may be different in different parts ofthe pit. However, see page 191 for details of how the cut-offs are scaled in Four-X.

16.6.4. Element processing cost

Four-X provides for an extra processing cost which is proportional to the grade of anelement. This gives:

Cut-off = PROCOST / (RECOVERYxPRICE-ELCOST)

16.6.5. Non-linear processing recovery

Four-X has a facility whereby you can simulate non-linear recovery by subtracting a“threshold” grade from the actual grade of the material before applying the recovery fraction.The amount of product per tonne that we get is:

(GRADE-THRESHOLD)xRECOVERY

This gives an effective recovery of:

(GRADE-THRESHOLD)xRECOVERY/GRADE

The sort of effective recovery fraction curves that result from this are illustrated below.

Non-linear recovery gives:

Cut-off = THRESHOLD + PROCOST / (RECOVERYxPRICE)

__________________________________________________________________________ Appendices 185



If a processing mill has a constant tailings grade, regardless of head grade, and all the otherproduct is recovered, this is easily simulated by setting the recovery threshold to theexpected tailings grade, and the recovery to 100%.

16.6.6. Selling cost

If there is a cost which is proportional to the amount of a product sold, then it can effectivelybe subtracted from the price.

This gives:

Cut-off = PROCOST / [RECOVERYx(PRICE-SELCOST)]

16.6.7. Rehabilitation cost

If there are rehabilitation costs incurred when a particular type of rock is mined as waste anddumped, this can make it more economic to process some material at a loss, rather thanmining it as waste.

This has the effect of reducing the calculated cut-off.

Cut-off = (PROCOST-REHCOST) / (RECOVERYxPRICE)

__________________________________________________________________________ Appendices 186



In the extreme case where the rehabilitation cost is greater than the processing cost, thecut-off will fall to zero, and all mineralised material will be processed.

16.6.8. Derivation of the formula for a cut-off

In this section we derive a formula for the marginal cut-off, taking into account all theoptional values. Four-X uses this cut-off for each element when a single processing methodis applicable to a particular rock type.

The tonnage into the mill per tonne mined is:

MINDILxMINREC

The amount of product into the mill per tonne mined is:

GRADExMINREC

where GRADE is the grade in the ground.

The grade input to the mill is:

(GRADExMINREC)/(MINDILxMINREC)

= GRADE/MINDIL

The mill recovery is:

[(GRADE/MINDIL-THRESHOLD)/(GRADE/MINDIL)]xRECOVERY

= [(GRADE-THRESHOLDxMINDIL)/GRADE]xRECOVERY

__________________________________________________________________________ Appendices 187


The amount of product produced per tonne mined is:

GRADExMINRECx[(GRADE-THRESHOLDxMINDIL)/GRADE]xRECOVERY

= (GRADE-THRESHOLDxMINDIL)xMINRECxRECOVERY

The revenue per tonne mined is:

(GRADE-THRESHOLDxMINDIL)xMINRECxRECOVERYxPRICE

The main processing cost per tonne mined is:

MINDILxMINRECxPROCOSTxPROADJ

The element processing cost per tonne mined is:

GRADExMINRECxELCOST

The selling cost per tonne mined is:

(GRADE-THRESHOLDxMINDIL)xMINRECxRECOVERYxSELCOST

If the material is processed, the cash flow per tonne is therefore:

(GRADE-THRESHOLDxMINDIL)xMINRECxRECOVERYxPRICE-MINDILxMINRECxPROCOSTxPROADJ-GRADExMINRECxELCOST-(GRADE-THRESHOLDxMINDIL)xMINRECxRECOVERYxSELCOST

=(GRADE-THRESHOLDxMINDIL)xMINRECxRECOVERY

x(PRICE-SELCOST)-MINDILxMINRECxPROCOSTxPROADJ-GRADExMINRECxELCOST

If the material is rejected, the rehabilitation cost per tonne mined is:

REHCOST

Note that, because the decision to process or not is made while the material is still in theground, MINDIL and MINREC do not affect rehabilitation cost.

In order to calculate the marginal cut-off, we equate the cash flow per tonne calculatedabove, plus the rehabilitation cost per tonne to zero.

(GRADE-THRESHOLDxMINDIL)xMINRECxRECOVERYx(PRICE-SELCOST)

-MINDILxMINRECxPROCOSTxPROADJ-GRADExMINRECxELCOST+REHCOST

=ZERO

__________________________________________________________________________ Appendices 188


We then take the necessary steps to solve this equation for GRADE.

Bring the GRADE items together on one side of the equation:

GRADExMINRECxRECOVERYx(PRICE-SELCOST)-GRADExMINRECxELCOST

=THRESHOLDxMINDILxMINRECxRECOVERYx(PRICE-SELCOST)+MINDILxMINRECxPROCOSTxPROADJ-REHCOST

Divide through by MINREC:

GRADExRECOVERYx(PRICE-SELCOST)-GRADExELCOST

=THRESHOLDxMINDILxRECOVERYx(PRICE-SELCOST)+MINDILxPROCOSTxPROADJ-REHCOST/MINREC

Give GRADE a single multiplier:

GRADEx[RECOVERYx(PRICE-SELCOST)-ELCOST]=

MINDILxPROCOSTxPROADJ+THRESHOLDxMINDILxRECOVERYx(PRICE-SELCOST)-REHCOST/MINREC

Divide through by the GRADE multiplier:

Cut-Off =[MINDILxPROCOSTxPROADJ+THRESHOLDxMINDILxRECOVERYx(PRICE-SELCOST)-REHCOST/MINREC]/[RECOVERYx(PRICE-SELCOST)-ELCOST]

Or:Cut-Off =

[THRESHOLDxMINDILxRECOVERYx(PRICE-SELCOST)]/[RECOVERYx(PRICE-SELCOST)-ELCOST]

+[MINDILxPROCOSTxPROADJ-REHCOST/MINREC]/[RECOVERYx(PRICE-SELCOST)-ELCOST]

If we remove the optional values MINDIL, MINREC, THRESHOLD, SELCOST,REHCOST and ELCOST, this simplifies to:

Cut-Off = (PROCOSTxPROADJ)/(RECOVERYxPRICE)

__________________________________________________________________________ Appendices 189


16.6.9. Multiple processing methods

If more than one processing method is applicable to a particular rock type then, when oreselection is by cut-off, Four-X looks at them in the order in which they are specified in theParameters File and selects the first method that passes the cut-off criteria. Thus the order inwhich methods are described in the Parameters File can be important. For example, for amill and heap leach operation, it is important to describe the mill first.

Graphically, the “processing lines” are laid on top of each other and the highest at each pointis used. Where this process leads to a grade at which we change from one processingmethod to another, we refer to this grade as a cut-over, rather than a cut-off.

The figure below shows the effect for a mill and heap leach operation, where it is cheaper toheap leach material, but the recovery fraction is less.

With this arrangement, Four-X will put material that is above the cut-over through the mill.It will heap leach material that is between the cut-over and the cut-off, and it will minematerial that is below the cut-off as waste. The thick combined processing line reflects this.

__________________________________________________________________________ Appendices 190


16.6.10.The formula for a cut-over

If we use techniques similar to those shown in the derivation of the formula for a cut-off onpage 186, we get the following formula for a cut-over between two processing methods “a”and “b”:

Cut-Over =[MINDILx(PRICE-SELCOST)x(THRESHOLDAxRECOVERYA-THRESHOLDBxRECOVERYB)

-MINDILxPROADJx(PROCOSTA-PROCOSTB)]/[RECOVERYAx(PRICE-SELCOST)-ELCOSTA-RECOVERYBx(PRICE-SELCOST)-ELCOSTB]

If we remove the optional values MINDIL, MINREC, THRESHOLD, SELCOST andELCOST, this simplifies to:

Cut-Over =[(PROCOSTB-PROCOSTA)xPROADJ]/[(RECOVERYA-RECOVERYB)xPRICE]

16.6.11.Multiple elements

When there are two or more elements with cut-offs, Four-X uses an approach which has thesame effect as using an equivalent metal. This is illustrated below for the case where thereare two elements P and Q with cut-offs as shown. Note that any grade combination can berepresented by a point in the plane of the graph.

If the sum of the grades divided by the corresponding cut-offs is greater than one, then thematerial is processed.

__________________________________________________________________________ Appendices 191


Note that this can lead to an apparently strange situation where the average grade of anelement processed is below the cut-off for that element. The material in the shaded area inthe next diagram is below both cut-offs, but still gives a positive cash flow when processed,because both elements make a contribution.

Note that, if non-linear grade-dependent expressions are used for the prices or costs, theexact line which divides positive and negative cash flow grade combinations may not bestraight. Nevertheless, if Four-X is using ore selection by cut-off, a straight line is used tojoin the cut-offs. If this discrepancy is important to you, consider using ore selection by cashflow (see page 192).

16.6.12.Display of cut-offs and cut-overs

The cut-offs and cut-overs produced by the optimization program FXOP, the analysisprogram FXAN and the utility program FXUT are rounded to the number of decimal placesthat you specify for cut-offs. These rounded values are then used in ore selection.

It is important to realise that cut-offs and cut-overs reported by FXOP and FXAN are alwaysfor processing material at the Reference Block (see page 133). If positional processingCAFs in the Model File are in effect, then the cut-offs and cut-overs calculated for theparcels of a particular block are affected by the processing CAF for that block, as isexplained below.

16.6.13.Cut-off scaling

When the processing cost adjustment factor in a block is other than 1.0, Four-X scales thecut-offs and cut-overs as follows:

Cut-Off = (CUTREF-THRESHOLD)xPROADJ + THRESHOLD

where CUTREF is the cut-off at the reference block.

If you examine the formulae given for cut-offs and cut-overs on pages 188 and 190respectively, you will realise that, when optional values are in use, the above simplifiedadjustment may not always be exactly correct. We have used this approach in the belief thatit is better to do something that the user can understand easily and can use on the pit floor,than to be technically exact.

__________________________________________________________________________ Appendices 192


Note that this approximation can only affect the ore selection. It does not affect the cashflow calculations, which are always exact.

If you wish to know the cut-offs to use on the pit floor for different processing CAFs, thereis an option in FXUT which will enable you to print them out. This option also gives awarning if the scaling approximation used by FXOP and FXAN is significantly different fromthe correct cut-off.

16.7. Ore selection by cash flow example

In most cases ore selection by cash flow will produce the same result as that produced by the use ofmarginal cut-offs. However, there are some cases where this is not true. An example will make thisclear.

Consider products P and Q with mills A and B.

Price of P = $100/TPrice of Q = $100/T

Mill AProcessing cost = $18/TRecovery of P = 90%Recovery of Q = 60%Cut-off for P alone = 0.2Cut-off for Q alone = 0.3

Mill BProcessing cost = $18/TRecovery of P = 60%Recovery of Q = 90%Cut-off for P alone = 0.3Cut-off for Q alone = 0.2

For mill A we can draw a line on the plane of all grade combinations which divides those gradecombinations for which it is profitable to send material to mill A from those for which it is not.

__________________________________________________________________________ Appendices 193


When we add mill B, we get:

Clearly, it is not possible here to use cut-offs to select material for each mill so as to give the highestcash flow in all cases. The only option is to adopt a grade control system which is based on cashflows.

Whilst this case is artificial, real cases do occur which are just as complicated, particularly wheredeleterious elements are involved.

16.8. The effects of minima and maxima

When ore selection is by cut-off, any minima or maxima you include in the Parameters File are usedas minimum or maximum cut-offs. When ore selection is by cash flow, they are used as minimum ormaximum parcel grades. The difference may appear subtle, but it is important.

16.8.1. Minimum and maximum cut-offs

When ore selection is by cut-off, Four-X initially calculates its cut-offs so as to maximize thecash flow. Minimum and maximum cut-offs can over-ride these calculated cut-offs.

If the minimum cut-off for a particular rock type and processing method combination is lessthan the calculated cut-off, it has no effect.

__________________________________________________________________________ Appendices 194


If the minimum cut-off is higher than the calculated cut-off, then it forces the cut-off higher,as is shown below. This may cause material that could have been processed at a profit to berejected.

A maximum cut-off works in exactly the opposite way to a minimum cut-off.

If it is higher than the calculated cut-off, it has no effect.

If it is lower than the calculated cut-off, it forces the cut-off down, as is shown below. Thismay cause material to be processed at a loss.

If both a minimum and a maximum are used, then the minimum will come into play when thegradient of the line increases with increasing price, and the maximum will come into playwhen the gradient decreases with decreasing price. If the minimum and maximum are equal,then the cut-off will be fixed, regardless of price.

__________________________________________________________________________ Appendices 195


Minimum and maximum cut-offs can be specified for eachprocessing-method/rock-type/element combination. They apply to both cut-offs andcut-overs.

The example below shows the effect of a minimum cut-off that applies to the mill, when bothmill and heap leach processing is available. If the minimum were below the calculatedcut-over at the intersection of the two sloping lines, it would have no effect.

The example below shows the effect of a maximum cut-off that applies to the mill.

Note that Four-X differs from Four-D in that a maximum cut-off is effective on cut-overs.

The initial cut-offs, which are calculated so as to maximize cash flow, change if the RevenueFactor changes, and thus they are different for each pit in a set of nested pits produced byFour-X. Remember that any minima or maxima that you specify do not change with theRevenue Factor and they should therefore be used with care for optimization.

__________________________________________________________________________ Appendices 196


16.8.2. Minimum and maximum parcel grades

When ore selection is by cash flow, Four-X usually treats each parcel in the way which willmaximize cash flow. Minimum and maximum parcel grades can over-ride this.

A parcel with any of its grades outside the range specified by a minimum and/or maximumparcel grade for a particular processing method is excluded from that method.

When there is only one element involved, the minimum has the same effect regardless of theore selection method. That is, a minimum cut-off and a minimum parcel grade are the same.However, if two or more elements are involved, the effects are very different.

The following diagram illustrates ore selection by cut-off. A minimum cut-off for element Qcould affect the position of that cut-off, but parcels with Q grades below that cut-off wouldstill be acceptable if their P grade was sufficiently high.

Contrast this with ore selection by cash flow, illustrated below.

Here material with a Q grade less than the minimum will not be processed regardless of the Pgrade and regardless of the cash flow.

__________________________________________________________________________ Appendices 197


If there is more than one element and any of the parcel’s grades is below the minimum, it willbe rejected.

The maximum has a very different effect with the two different ore selection methods, evenwhen there is only one element involved.

If ore selection is by cut-off, the cut-off cannot be above the maximum, so material withgrades above the cut-off will always be processed.

If ore selection is by cash flow, material with grades above the maximum will never beprocessed. If there is more than one element, and any of the parcel’s grades is above themaximum, it will be rejected.

16.9. The concepts behind Four-X nested pits

Four-X uses a Model File containing details of the content of each block, but, for optimizationpurposes, we need a single value for each block. This value is the cash flow (positive or negative)that would result from mining the block.

For optimization purposes it is important to assume that the block has been uncovered. It is incorrectto allow for stripping costs, because the optimizer does this.

If we calculate the block values for a particular model we will get a certain set of block values that,when used in an optimization, will lead to a particular pit outline. Let this outline be “A” in thefollowing diagram.

On page 10 we explained that, within an optimal outline, every block is “worth mining”.

Now, each block consists of zero or more parcels and, possibly some undefined waste which can beregarded as another parcel. The cash flow which results from mining a block consists of the sum ofthe cash flows which result from mining its parcels.

The cash flow which results from mining a particular parcel depends on the way we treat the parcel,and on the prices and costs associated with it. What happens if we increase all the prices used byFour-X and keep the costs the same?

Although the increase in prices may cause the parcel to be treated differently (e.g. it may now beprocessed rather than treated as waste), the cash flow will always stay the same or increase.Increasing the prices will not decrease the cash flow which results from mining any parcel.

__________________________________________________________________________ Appendices 198


Thus, if we increase the prices, the value of every block within outline A will increase or stay thesame. No block value will go down. Consequently, every block within outline A is still worthmining, and, if we do another optimization using the new values, the new outline, shown as B below,is certain to include the whole of A. It may also include extra blocks that were not worth miningbefore, but which now are worth mining.

Consequently, if we step the prices through a series of values, doing an optimization for each, weobtain a set of nested pit outlines, and this is, in effect, what the optimization program in Four-Xdoes. It multiplies all of the prices by a series of 50 to 100 “Revenue Factors” ranging, typically,from 0.3 to 2.0, and produces a pit outline for each.

The reason for producing outlines for the smaller values of Revenue Factor is that we want toproduce inner pit shells to highlight the best positions to start mining and to assist with thesequencing. The outlines are usually very close together and form an almost continuous “spectrum”,where the change in tonnage from one outline to the next is quite small. However, if the gradeincreases sharply with depth, or the ore body is discontinuous, large tonnage differences betweenadjacent pits can occur.

Since all the outlines obey the pit slope requirements, it is simple to determine what sequences arepermissible when mining out a particular pit.

In the schematic of nested pits above, if pit 5 is the ultimate pit, we can clearly mine in the sequencea, b, c, d, f, g, h, etc. If the pits are sufficiently far apart to give working space, another possiblesequence is a, f, b, g, k, c, etc. The point is that, given a set of nested pits, these sequences areclearly defined and easy for the computer to trace, and thus to simulate various mining schedules inorder to obtain projected tonnages, grades and cash flows.

__________________________________________________________________________ Appendices 199


Although each set of outlines is only strictly optimal for a particular set of costs, their usefulness goesfar beyond this. Provided that the costs used are of the same order, another optimization run withdifferent costs will usually produce a set of pits of very similar shape, but which are shifted relative tothose from the first run. For example, pit number 20 from one run may be very similar to pit number25 from the other run. It is therefore reasonable to simulate mining with wide ranges of prices andcosts using the same set of nested pits. Once a set of costs has been settled on, a final optimizationwith those costs and a repeated simulation can be run as a check.

16.10. How Four-X calculates a block value

In calculating a block value, Four-X uses information from the Model File and from the ParametersFile. We have given the different items code names and have listed them, below. Those marked withan asterisk (*) are optional and can be ignored at the first reading.

16.10.1.Definition of terms

The values from the Model File are:

ROCK The total tonnage of the block

MINADJ* The ratio between the cost of mining waste, where this block is, and thecost of mining waste at the Reference Block

PROADJ* The ratio between the processing cost, where this block is, and theprocessing cost at the Reference Block

For each parcel within the block, if any:

TYPE The rock type of the parcel

PAR The tonnage of the parcel

For each element:

ELEM The quantity of the element, if any

The values from the Parameters File are:

MINCOST The reference mining cost

MINDIL* The mining dilution factor

MINREC* The mining recovery factor

REVFAC The fraction of the base case revenue to use in this optimization

For each element:

PRICE The price for a unit of product

SELCOST* The cost of selling a unit of product

__________________________________________________________________________ Appendices 200


For each rock type:

REHCOST* The cost per tonne of rehabilitating this rock type if it is mined anddumped

TYPADJ* The mining CAF for this rock type

For each allowed processing-method/rock-type combination:

PROCOST The cost per tonne of processing this rock type, by this method

For each element within a method/type combination:

ELCOST* The extra cost per input unit of this element, when processingthis rock type by this method

RECOVERY The fraction of the element recovered at high grade, whenprocessing this rock type by this method.

THRESHOLD* The threshold below which no product at all is recovered, whenprocessing this rock type by this method.

MINCUT* The minimum cut-off that can be used when processing this rocktype, by this method.

MAXCUT* The maximum cut-off that can be used when processing thisrock type by this method.

16.10.2.Procedure

Four-X calculates the value of a block by adding together the cash flows associated witheach parcel, and subtracting the cost of mining the whole block as waste.

If the optional values (*) are ignored, there is no underground option, and ore selection is bycut-off. In this case, the procedure for calculating the value of a block, is as follows:

Set BLOCKAG to zeroÚÄ For each parcel in the block, if any:³ ÚÄ For each processing method suitable for this parcel, if any:³ ³ ÚÄ If the parcel passes the cut-off criteria³ ³ ³ Set PARVAL to -PARxPROCOST³ ³ ³ ÚÄ For each element in this parcel, if any:³ ³ ³ ³ Set REVENUE to³ ³ ³ ³ ELEMxRECOVERYxPRICExREVFAC³ ³ ³ ³ Set PARVAL³ ³ ³ ³ to PARVAL + REVENUE³ ³ ³ ÀÄ Next element³ ³ ³ Add PARVAL to BLOCKAG³ ³ ³ Go to the next parcel³ ³ ÀÄ End If³ ÀÄ Next processing methodÀÄ Next parcel

Subtract ROCKxMINCOST from BLOCKAGSet BLOCKVAL to BLOCKAG

__________________________________________________________________________ Appendices 201


where BLOCKAG is the value of the block if it is mined above ground,BLOCKVAL is the value of the block (in this simple case equal to BLOCKAG),REVENUE is the value of the element recovered from the parcel,

and PARVAL is the cash flow from processing the parcel.

The procedure is very similar if ore selection is by cash flow, except that parcel values arecalculated for all processing methods and the best is used, provided that it produces a bettercash flow than treating the parcel as waste.

If all the optional values are taken into account, the procedure for calculating the value of ablock is as follows:

Set BLOCKAG, BLOCKUG and TMPADJ to zeroÚÄ For each parcel in the block, if any:³ Add the PARx(TYPADJ-1.0) to TMPADJ³ Set REHVAL to PARxREHCOST³ ÚÄ For each above ground processing method suitable for this parcel, if any:³ ³ ÚÄ If the parcel passes the cut-off criteria³ ³ ³ Set PARVAL to -PARxMINDILxMINRECxPROADJxPROCOST³ ³ ³ ÚÄ For each element in this parcel, if any:³ ³ ³ ³ Set AVAILMET to the maximum of zero and³ ³ ³ ³ (ELEMi - PARxTHRESHOLD)³ ³ ³ ³ Set REVENUE to³ ³ ³ ³ AVAILMETxMINRECxRECOVERYxPRICExREVFAC³ ³ ³ ³ Set SELLVAL to³ ³ ³ ³ AVAILMETxMINRECxRECOVERYxSELCOST³ ³ ³ ³ Set ELEMVAL to³ ³ ³ ³ AVAILMETxMINRECxELCOST³ ³ ³ ³ Set PARVAL³ ³ ³ ³ to PARVAL + REVENUE-SELLVAL-ELEMVAL³ ³ ³ ÀÄ Next element³ ³ ³ Add PARVAL to BLOCKAG³ ³ ³ Go to check underground processing methods³ ³ ÀÄ End If³ ÀÄ Next processing method³ (The parcel is not worth processing)³ Subtract REHVAL from BLOCKAG³ ÚÄ For each underground processing method suitable for this parcel, if any:³ ³ ÚÄ If the parcel passes the cut-off criteria³ ³ ³ Set PARVAL to -PARxPROCOST³ ³ ³ ÚÄ For each element in this parcel, if any:³ ³ ³ ³ Set AVAILMET to the maximum of zero and³ ³ ³ ³ (ELEMi - PARxTHRESHOLD)³ ³ ³ ³ Set REVENUE to³ ³ ³ ³ AVAILMETxRECOVERYxPRICExREVFAC³ ³ ³ ³ Set SELLVAL to³ ³ ³ ³ AVAILMETxRECOVERYxSELCOST³ ³ ³ ³ Set ELEMVAL to³ ³ ³ ³ AVAILMETxELCOST³ ³ ³ ³ Set PARVAL³ ³ ³ ³ to PARVAL + REVENUE-SELLVAL-ELEMVAL³ ³ ³ ÀÄ Next element³ ³ ³ Add PARVAL to BLOCKUG³ ³ ³ Go to next parcel³ ³ ÀÄ End If³ ÀÄ Next processing methodÀÄ Next parcel

Subtract (ROCK+TMPADJ)xMINADJxMINCOST from BLOCKAGBLOCKVAL = BLOCKAG - BLOCKUG

where BLOCKUG is the value of the block if it is mined underground,REHVAL is the total rehabilitation cost for the parcel,AVAILMET is the element content of the parcel above the processing recovery

threshold,SELLVAL is the cost of selling the recovered element,

and ELEMVAL is the cost of processing the element.

__________________________________________________________________________ Appendices 202


Again, the procedure is very similar if ore selection is by cash flow, except that parcel valuesare calculated for all processing methods and the best is used, provided that it produces abetter cash flow than treating the parcel as waste.

Program FXUT has facilities for printing out details, like those shown above, of actual blockvalue calculations using your data.

16.10.3.Allowing for underground mining

Four-X is concerned with designing open pits and has no direct relevance to undergroundmining. However, if both above-ground and underground methods are to be used, this canaffect the design of the open pit, and Four-X can take account of this.

When considering this issue, it must first be understood that, if a particular block can bemined by either above-ground methods or underground methods, then the correct value togive it during open pit optimization is the difference between its value when minedabove-ground and its value when mined underground.

For example, consider a block that is worth $1,000 if mined by above-ground methods and$800 if mined by underground methods.

If underground mining is not to take place, then the correct value to use during open pitoptimization is $1,000. If the decision to go underground below the open pit has been taken,then the correct value to use for open pit optimization is $200. This is because theadvantage to the company obtained by mining the block by above-ground methods is only$200, since the company will still make $800 if the block is omitted from the open pit.

However, if the block is included in the open pit, then $1,000 is made from it, so there is adifference between the profit gained from mining the block and the advantage gained fromchoosing to mine it by above-ground methods. It is this advantage which is relevant to openpit optimization.

If you wish to use this facility of Four-X, you should take the following steps:

a) If only some of the blocks in the model are being considered for underground mining,say a particular reef, then identify the relevant parcels by giving them a different rocktype code.

b) For those rock types that could be mined underground, provide lines of line-type 30and 31 indicating how they will be processed if mined underground.

Note that the underground value of a block is calculated without any reference to the totalROCK in the block. The processing cost, PROCOST, you supply must cover all miningcosts, which are assumed to be proportional to the amount of ore mined.

A further difference in the way values are calculated for above-ground mining andunderground mining is that the positional mining, the rock type mining and the positionalprocessing CAFs are not applied to underground calculations. Similarly, mining dilution andrecovery are ignored.

__________________________________________________________________________ Appendices 203


If you want to generate just one pit and have thus set the minimum and maximum RevenueFactor to the same value, then there are no restrictions on the methods and values you supplyfor underground value calculations.

However, if you want to produce multiple nested pits, then there are certain restrictionsrequired to ensure that the pits do nest correctly. For each rock type these are:

a) If one or more underground processing method(s) is defined, at least oneabove-ground processing method must be defined.

And for each element in the rock type:

b) All above-ground processing recovery fractions must be greater than, or equal to, anyunderground processing recovery fractions.

c) The ratio of RECOVERY/(PROCOST-REHCOST) for all above-ground methodsmust be greater than, or equal to, the ratio of RECOVERY/(PROCOST-REHCOST)for any underground methods.

d) All above-ground recovery thresholds must be less than, or equal to, anyunderground recovery thresholds.

e) All above-ground minimum cut-offs must be less than, or equal to, any undergroundminimum cut-offs.

f) All above-ground maximum cut-offs must be less than, or equal to, any undergroundmaximum cut-offs.

These restrictions are normally complied with naturally, and will only come into effect if yousupply unusual values in the Parameters File.

If you are using positional processing CAFs (which only apply to above-ground mining) oryou are using grade-dependent expressions, even the above restrictions do not ensure thatthe pits are correctly generated in all cases. If such a possibility is detected, the optimizingprogram does extra checks when it is reading in the Model File. If nesting could fail, theoptimization continues, but a warning message is issued. In this case the pits will be nested,but each may not be strictly optimal.

__________________________________________________________________________ Appendices 204


16.11. Expressions

Expressions are used for two different purposes, but operate the same way in both, except for thevariables which can be used in them.

Positional CAF expressions can be used with FXRB to calculate values for the positional miningand processing cost adjustment factors. They are entered at the keyboard or via a Log File.

Grade-dependent expressions can be included in a Parameters File, each with a 1-4 character codewhich identifies the expression. These codes can then be used in place of certain constants in theParameters File.

Specifically they can be used for:

Selling costs, *Prices, *Rock type mining CAFs,Rehabilitation costs,Processing costs,Element processing costs, and,Recovery fractions.

* Note that it is not usually meaningful to use expressions for selling cost or price, except when theore itself is the product (e.g. for iron ore).

Also note that grade-dependent expressions should be used sparingly. Their effect on cash flow canusually be foreseen fairly easily, but they can have some unexpected effects on cut-offs. You shouldbe particularly careful when using the grade of one element in an expression for the recovery ofanother element. When working out the cut-off(s) for an element, Four-X assumes that the grades ofall other elements are zero. When working out the cash flows, the actual grades of the parcel areused.

Each expression takes the form of a normal algebraic expression containing constants (e.g. 3.47),variables, arithmetic operators (e.g. +), functions (e.g. LOG(x)) and parentheses. Some specialfunctions have been provided that are particularly useful for this purpose.

Upper and lower case are equivalent throughout, and spaces can occur anywhere.

16.11.1.Constants

Constants can be included in an expression. These can have zero or more decimal placesand, optionally, a decimal exponent.

Examples:51.376256.1e+3 (=256100)

__________________________________________________________________________ Appendices 205


16.11.2.Variables

When grade dependent expressions are used in a Parameters File, the only variables whichcan be used are grades:

element.G the grade of “element” in the parcel under consideration. Grades may begrades mined, grades sent to the waste dump or grades input to themill, depending on the usage of the expression. The usage is definedby the expression “type” on the same line as the expression.

When expressions are used for positional mining or processing cost adjustment factors,seventeen variables are provided. Note that all except OLDCAF refer to the output modeland block size. They are as follows:

BX, BY, BZ the output block size in units of distance

NX, NY, NZ the output model size in blocks

MX, MY, MZ the output model size in units of distance

IX, IY, IZ the co-ordinates in blocks of the output block

X, Y, Z the co-ordinates of the centre of the current output block relative to themodel origin, in units, of distance

element.G the average grade of all mineralised material, for the designated element, inthe current output block. Contrast this grade with the grade used ingrade-dependent expressions.

OLDCAF the CAF from the input file. When blocks are combined, this is a weightedaverage of the CAFs from the input blocks.

16.11.3.Operators

The following operators are provided:

+ and - perform addition and subtraction,

* and / perform multiplication and division,

** raises a value to a power, and

parentheses ( ) can be used to any depth.

Subject to the effects of parentheses, powers are evaluated first, followed by multiplicationand division, then addition and subtraction. In each of the three cases, evaluation proceedsfrom left to right. If you are uncertain about what will happen, use more parentheses. Theyhave no effect on evaluation speed.

__________________________________________________________________________ Appendices 206


If a divisor in an expression is zero when the expression is evaluated, the result of theexpression is set to zero. For this reason, you should consider carefully before including adivision by a grade.

16.11.4.Functions

A number of useful functions are provided. In each case, their name can be truncated to theminimum number of letters that is still unique. In each case, any argument of a function canbe a constant or an expression, that may in turn include functions to any depth.

Seven normal functions are provided. These are as follows:

Square root (X) (SQ) the square root of X

Integral part of (X) (I) the largest integer that is not greater than X

Log(X) (LOG) the natural logarithm of X

Log10(X) (LOG1) the log to the base 10 of X

Exponential(X) (E) the exponential (base “e”) of X

Minimum(X1,X2,X3....) (MI) the minimum of a list of values

Maximum(X1,X2,X3....) (MA) the maximum of a list of values

Three special functions are provided. These are:

Select(X, Y1, Y2, Y3, Y4,......Yn) (SE)Distance(X1, Y1, Z1, X2, Y2, Z2) (D)Ranges(X, Y1, Z1, Y2, Z2, Y3, Z3,.....Yn) (R)

Details of these functions are as follows.

Select(X, Y1, Y2, Y3, Y4,......Yn)

This takes the integral part of X and uses it to select from the Y values. That is, if X is 3.6,Select will have the value Y3. If X is less than 1, Y1 is used. If the integral part of X isgreater than the number of Y values, the last Y value is used.

Example:

se(iz, 1.4, 1.35, 1.32, 1.3, 1.27,...)

could be used to generate a positional mining CAF that varies irregularly with depth.

Distance(X1, Y1, Z1, X2, Y2, Z2)

This calculates the straight line distance between a point at co-ordinates (X1,Y1,Z1) and apoint at (X2,Y2,Z2).

__________________________________________________________________________ Appendices 207


Example:

d(x, y, 0, mx, my, 0)

could be used to find the horizontal distance of the current block from the North Westcorner of the model (note: zero has been used for both Z values).

Ranges(X, Y1, Z1, Y2, Z2, Y3, Z3,.....Yn)

Ranges selects one of the Y values according to the value of X in relation to the Z values.The Z values should be in ascending order (no check is made on this). The value of X iscompared with each Z value in turn, until a Z value higher than the X value is found. The Yvalue prior to the Z value is then used.

In other words, the function finds the pair of Z values between which the X value lies, andoutputs the Y value that is also between these two Z values.

If X is greater than or equal to the last Z value, the last Y value is used.

Note that the second value and the last value should be Y values, so there should be an evennumber of arguments.

Example:

R(gold.G, 1, 3.6, 1.2)

could be used to set a factor 20% higher if the gold grade was greater than or equal to3.6.

16.11.5.Example expression

The following expression would return an effective recovery exactly like the one obtained byhaving a threshold of 0.2 and a recovery fraction of 0.95:

max(0,Au.g-0.2)*0.95/max(Au.g,0.2)

16.11.6.Input

a) Positional CAF expressions

Positional CAF expressions are input to FXRB interactively or via a Log File. If you typean ampersand (“&”) at the end of a line, the program will repeat the prompt and you cancontinue typing in the expression. This can continue for many lines. The maximumdepends on a number of factors such as the maximum number of characters in anexpression etc.

If you have to input a long expression, it is easiest to enter a simple expression brokeninto two lines and use a Log File to record the prompts and responses. The longexpression can then easily be edited into the log file, using as many lines as required, andthe program re-run with the Log File.

__________________________________________________________________________ Appendices 208


b) Grade-dependent expressions

Grade-dependent expressions are limited to 64 characters in the Parameters File. If anexpression is longer than this, it must be split into sub-expressions and then combined in asubsequent expression.

The following shows an example of how a long select function can be split into two.Usually, splitting is much simpler than this.

Original expression:

Select(Au.g,1,2,3,5,6,7,8,9,10)

Partial expressions:

EX1 - Select(Au.g,1,2,3,4,5,0)EX2 - Select(Au.g-4,0,6,7,8,9,10)

Combined expression:

EX3 - EX1 + EX2

If Au.g is 5 or less EX1 evaluates correctly, otherwise it returns zero. Similarly, if Au.g is6 or more, it evaluates correctly, otherwise it return zero.

EX3, the sum of the two, therefore returns the same value as the original expression.

__________________________________________________________________________ Appendices 209


16.12. Merging elements from different Model Files

Some GMPs have facilities for outputting Four-D Model Files, but not Four-X Model Files. To dealwith this situation, FXRB has a facility whereby two or more Four-D Model Files, each with differentelements, can be merged to create a Four-X Model File containing all the elements.

Note: this merge facility is provided purely as an interim solution to the problem. It relies heavily onthe models which are merged being very similar, except for the elements they contain, and canproduce unexpected results if they are not. Encourage you GMP supplier to provide a Four-Xinterface which outputs all the elements at once.

If you wish to merge two Model Files containing, say, elements A and B, you should do thefollowing:

1. Export a Four-D Model File, containing element A, from your GMP.

2. Export a Four-D Model File, containing element B, from your GMP. This should be assimilar as possible to the first Model File, except for containing element B rather than elementA.

3. Create the Four-D Parameters Files which correspond to the two models. These may havebeen produced by your GMP when it produced the Model Files.

4. Change each Four-D Parameters File into the corresponding Four-X Parameters File. You dothis by reading each Four-D Parameters File into FXED, fixing the mining default waste cost,changing the single element name (EL1) to “A” or “B”, and saving the file.

Note that elements “A” and “B” should both be shown as occupying the first position in theModel File in their respective Parameters File. When they are merged they will be positionedin the order that the files are read.

5. Run FXRB and use mode 1 with two input files. When asked, choose the merge option.Make sure that you take the option to create a new Parameters File.

Note: always use the original Model Files from your GMP as inputs to this merge operation.Do not re-block them first, as this may interfere with the element merging.

6. Use FXED to check and correct any inappropriate values in the new Parameters File.

Before the merge starts, FXRB first sets the positions of the elements in the merged Model File. Inthis simple case, element “A” would go in position 1 and element “B” would go in position 2.

More generally, the element positions for the first model are retained and any new elements fromsubsequent models are allocated successive positions as required.

The first Model file is then read in and stored. The second and any subsequent files are then read inand merged, block by block, with the stored model.

__________________________________________________________________________ Appendices 210


During merging, where the same block occurs in the stored model and in the new Model File, theinformation is merged according to the following rules:

1. If the two blocks have exactly the same number of parcels and all parcels match in relation torock type and tonnage, then, for each parcel, the element quantities are copied from the newblock into the appropriate positions in the stored block. Note that, where the same elementappears in both blocks, the element quantity from the new block replaces that in the storedblock.

2. If the blocks have different numbers of parcels or different parcel rock type, tonnage or orderthen the system searches for the first parcel that matches the rock type and tonnage that hasnot yet been used in this merge. If it cannot find a match, it adds the material as a new parcel.

ÚÄ For each parcel in the new block:³ ÚÄ For each parcel in the stored block:³ ³ If the parcel has not been used:³ ³ If the stored and new parcels have the same rock type and tonnage:³ ³ Copy the element quantities from the new parcel to the stored parcel³ ³ Deal with the next new parcel³ ³ End If³ ³ End If³ ÀÄ Next stored parcel³ If a match was not found:³ Add the new parcel to the stored block with the elements repositioned as required³ End IfÀÄ Next new parcel

3. If any blocks have different numbers of parcels, the system will report the first 50 differenceswith the message:

*** WARNING: MODEL BLOCK X,Y,Z DOES NOT HAVE THE SAME NUMBER OFPARCELS FOR MERGE

where X,Y,Z are the block co-ordinates of the block.

__________________________________________________________________________ Appendices 211


16.13. How FXMW works

FXOP takes no account of mining width in the generation of pits. Consequently, an optimized pitwhich is used as a starting point for the design of a final pit can have a floor that is too narrow, orirregularities in the pit wall that cannot be followed easily in practice. Optimized pits that are used asthe starting points for the designs of push-backs can have the same problems as the final pit. Othermining width problems can arise if the wall of a push-back is too close to that of a subsequentpush-back or the final pit.

FXMW starts from a series of pits that the user has selected as push-back walls and the final pit wall.It then checks for certain conditions and makes adjustments to each bench in turn, from the bottom ofthe pit to the top. Adjustments can result in four types of change:

• Blocks at the bottom of the pit can be excluded from the pit

• Blocks at the bottom of a push-back can be included in a later push-back

• Blocks can be included in an earlier push-back

• Blocks can extend the final pit

After each bench is adjusted, blocks in higher benches which, as a result, must be removed earlierbecause of the slope constraints, are also adjusted.

The possible conditions and adjustments are described below.

16.13.1.Mining width

“Mining width” is defined as the minimum width necessary for the extraction of the oreregardless of the actual width of ore-bearing rock (Dictionary of Mining Terms - UnitedStated Department of the Interior, Bureau of Mines, 1968).

Mining width is represented in FXMW by a template. The template is a rectangle defined bynumbers of blocks in the X and Y directions. Blocks in a particular push-back, which cannotbe covered by the template without part of the template lying outside the push-back areregarded as inaccessible and requiring correction.

To cater for practical mining situations, a tolerance can be specified to control precisely howstrictly the template must be applied. If the tolerance is set by the user to zero, then thecomplete template must be able to cover every block in every push-back without extendingoutside the push-back. If the tolerance is set to one, then it is permissible for one block to lieoutside the push-back, etc.

It is recommended that the mining tolerance be set to one less than the largest templatedimension in blocks (i.e. a 3 x 3 template would have a tolerance of 2), although ultimatelythe most appropriate setting will vary from case to case.

__________________________________________________________________________ Appendices 212


For example, if the template was three blocks by three blocks and the tolerance was zero,then the highlighted blocks in push-back 2 below, would be regarded as inaccessible. If, onthe other hand, the tolerance was 2, then all of the blocks in push-back 2 would be regardedas accessible.

22222 2222222222222 2222222222222222222 222222111111112222222 2222211111111112222222 222221111111111112222222 222221111111111112222222 222221111111111112222222 222221111111111112222222

Inaccessible blocks are dealt with either by extending the push-back that they belong to, orby extending an earlier push-back to cover them.

16.13.2.Small drop cuts

The floor of the final pit or of push-backs can be smoothed by eliminating small drop cuts. Adrop cut is eliminated by reassigning those blocks within it to a later push-back, or, in thecase of the final pit, by removing the blocks from the design.

Drop cuts are defined in FXMW as regions of contiguous blocks, within a push-back, thatare surrounded by blocks of later push-backs or by the final pit limit. Contiguous blocks aredefined as blocks that share a common boundary:

Diagram a) shows a group of 4 contiguous blocks while b) shows two blocks which are notcontiguous.

The user specifies the minimum number of blocks that must be in a drop cut for it to remain.If FXMW finds a drop cut which has less than the minimum number, then the drop cut willbe eliminated.

There are two cases to consider: drop cuts at the final pit floor and drop cuts elsewhere. Atthe final pit floor, blocks in drop cuts that are eliminated are excluded from the pit and theyare no longer available for mining. Elsewhere, the blocks within small drop cut arereassigned to the next push-back. In other words, access to the blocks is delayed.

__________________________________________________________________________ Appendices 213


There are two drop cut control values that may be set by the user: the minimum number ofblocks for drop cuts in the final pit floor, and the minimum number of blocks for drop cutselsewhere.

If the user-specified value for final pit floor drop cuts is 4, then in the final pit, any drop cutthat contains 3 or less contiguous blocks will be excluded from the pit design. The user willbe informed of the position and value of any blocks removed. Any blocks that are removedwill be flagged in the diagrams in the print file with a #.

Original push-back Modified push-back

11 1 11 1 11

11 # single 11 # ## 3 contiguous

In the above example, which is a plan view, the right hand group of blocks will be changedbecause it consists of a single block and a group of 3 contiguous blocks.

If the user-specified value for drop cuts elsewhere is 4, then any area with 3 or lesscontiguous blocks will be affected:


22222222222222222222222222222212222222222221222222222221222111122222212222222222222211112222211222222222222222222222222222222

22222222222222222222222222222222222222222222222222222222222111122222222222222222222211112222222222222222222222222222222222222

The small drop cuts to the left and right would be changed, while the centre drop cut wouldremain.

16.13.3.Small walls

Small walls are defined as small groups of contiguous blocks that are surrounded by blocksbelonging to both earlier and later push-backs, or by earlier push-backs and by the edge ofthe final pit. If the number of contiguous blocks is less than a user-specified minimum, thenthe blocks will be included in the earlier push-back.

__________________________________________________________________________ Appendices 214


The small walls may occur at the edge of the final pit:


33 3333 211133 2111113 1111111111

11 1111 111111 1111111 1111111111

Or they may occur within the pit:


33333333333333333333333333333333333333332223333333333333333333322222222111111111111111111111111111111111111111111111111111111

33333333333333333333333333333333333333331113333333333333333333311111111111111111111111111111111111111111111111111111111111111

In both these cases the blocks in the small walls would be reassigned to push-back 1.

16.13.4.Small stumps

A “stump” is a row of blocks belonging to a later push-back sticking out of an otherwisestraight wall of blocks. It may be inconvenient to work around these blocks and easier tomine as a straight wall.

The following plan illustrates a stump 3 blocks long:


111111111111111111111111111111111222111111111111112222222222222222222222222

111111111111111111111111111111111111111111111111112222222222222222222222222

A stump is small if its length is less than or equal to the template width or template heightalong the wall. Stumps are removed by including them in the earlier push-back. In the caseabove, if the template was four or more blocks wide, the blocks within the stump would bereassigned to push-back 1, as is shown.

16.13.5.Small holes

A “hole” is a row of blocks belonging to an earlier push-back sticking into an otherwisestraight wall of blocks. It may be easier to mine as a straight wall.

The following plan illustrates a hole 3 blocks long:

__________________________________________________________________________ Appendices 215



222222222222222222222222222222222111222222222222221111111111111111111111111

222222222222222222222222222222222222222222222222221111111111111111111111111

A hole is small if its length is less than or equal to the template width or template height asappropriate. Small holes are removed by assigning the blocks within them to a laterpush-back. In this case, the blocks within the hole may be reassigned to push-back 2.However, since FXMW works by extending earlier push-backs into later ones, the removalof small holes can only take place if a previous adjustment to the bench has extended the firstpush-back into the area.

16.13.6.Sharp corners

Sharp corners can be difficult to deal with, and it may be easier to work with roundedcorners. This option can be turned on or off by the user.


11111111111111111111111111111111111111111111111111222222222222111111111111122222222222211111111111112222222222221111111111111

11111111111111111111111111111111111111111111111111222222222221111111111111122222222222211111111111112222222222221111111111111

The corner block will be included in the earlier push-back. The final pit outline will not bemodified.

Similarly, a corner where an earlier push-back protrudes into a later one may be trimmed.However, since FXMW works by extending earlier push-backs into later ones, suchtrimming can only take place if a previous adjustment to the bench has extended the firstpush-back.

16.13.7.Slopes

The final pit and push-backs contained in the input Results File all comply to the required pitslope constraints, with the possible exception of slopes defined by additional arcs (see nextsection). In order to ensure that the modified pit and push-backs produced by FXMWcontinue to comply with pit slope constraints, the program refers to the input Structure Filethroughout processing. In other words, if a block is reassigned to an earlier push-back, thenall the blocks in higher benches that need to be removed to gain access to this block will alsobe reassigned to the earlier push-back.

__________________________________________________________________________ Appendices 216


16.13.8.Additional arcs

If the Structure File contains additional arcs from an Additional Arcs File, then these arcswill be obeyed in almost all cases. In general, additional arcs either point to a block on thesame bench or a block on a higher bench. However, it is possible to include a downwardpointing arc in an Additional Arcs File. The program cannot guarantee to obey thedependencies defined by downward pointing arcs, however FXMW issues a warning if thistype of arc is found.

If you don’t want the additional arcs to be applied during push-back adjustment, then createanother Structure File without the additional arcs.

__________________________________________________________________________ Appendices 217


16.14. Interfacing with Opti-Cut

Opti-Cut files can be generated any time a user runs a single economic scenario and a single miningsequence in FXAN. The user merely has to answer “yes” to the option, and nominate the file andelement names.

The interface option can be turned on or off in the fx.ini file. The default option is for a file to beproduced. The entry appears under the [System] heading. Use a text editor to change the value asrequired.

[System]Opti-Cut=Yes Allows Opti-Cut file generationOpti-Cut=No Prevents Opti-Cut file generation

Physically producing an interface file is easy, however, there a few issues that need to be consideredwhen setting up a Four-X run to produce Opti-Cut data.

a) Opti-Cut deals with capital costs and time costs. The Four-X run should have capital costsand take the option to input explicit time costs (and remove them from the unit costs). If thisis not done then it will have to be done later by editing the economic interface file.

b) Four-X can have throughput adjustment factors for one or more rock types. This factor is notdirectly available in Opti-Cut, however, it can be simulated. You may need to adjust thethroughput limit in the economic interface file if the processing is the limiting factor.

For example if a MILL can handle rock types OREA and OREB and OREB has a throughputfactor of 1.15. Then you could specify a throughput group

TG PROC OREA.Q + OREB.Q/1.15TL PROC USER_DEFINED_LIMIT

c) Expressions are treated slightly differently in Four-X and Opti-Cut. In Four-X for example,the recovery can be expressed as a period variation of the form:REC1 P3/REC2where REC1 and REC2 are grade dependent expressions.

In Opti-Cut the expression would be set up to vary by period and then the recovery would beassigned to that expression. You may need to adjust the economic interface file if expressionshave been used.

__________________________________________________________________________ Appendices 218


16.15. Precision within Four-X

Line type 12 in the Parameters File gives the user control over the number of decimal places in thereport outputs for the following fields:

Tonnes in a block Totals of tonnesRevenue Factor valuesSmall currency Currency totals

Line type 20 gives the user control over the decimal places used for element quantities in a block, forelement totals and for grades.

Other variables are rounded to a precision specified by Whittle, as listed below.

VariableNumber of

decimal places.Block dimensions 2Bearings 2Cost adjustment factors 3Discount percentage 2Hours between restarts 2Recovery fraction 3Rock throughput factor 3Slopes 2

16.16. Four-X / Four-D comparison

Experienced Four-D users may find the following summary useful when coming to grips with thechanges in Four-X. In general, the major changes have been to the Parameters File, the Model andResults File, and the Spreadsheet codes.

16.16.1.Data files

The Parameters File has new records for expressions and elements. The processing methodsnow have recovery and cut-offs defined at an element level. MCOSTM ratios have beenreplaced with a Revenue Factor which scales revenues up and down, to provide the pitshells. Data is entered into the Parameters File as actual costs rather than as cost ratios.

The Model File can now carry more than one element. Model Files based on individualelement details can be merged using FXRB.

The Results File can now carry more than one element. The header records contain the basevalue and Revenue Factors, rather than the MCOSTM values.

This manual and the programs now refer to element or element quantity rather than “metal”.

__________________________________________________________________________ Appendices 219


16.16.2.FXED

The operation of FXED is the same, however, it now allows the user to define expressionswhich can be used in place of constants. There is a new menu item for elements andprocessing methods has been revised to allow for the allocation of elements.

Existing Four-D Parameters Files can be converted to Four-X files using this program.

16.16.3.FXRB

FXRB has a new option when processing models that allows the user to merge models whichcontain different elements.

The use of GRADE in CAF expressions is replaced by <element>.G to be more specific.

16.16.4.FXST

FXST is exactly the same as the Four-D version.

16.16.5.FXOP

In FXOP, the pit shell increments are controlled by the Revenue Factors rather than theMCOSTM values.

16.16.6.FXPR

FXPR allows the selection of specific elements when displaying element distributions.

16.16.7.FXAN

In FXAN, prices must be given for each product. The Parameters File change screen hasbeen revised to allow for increased complexity in processing methods.

Four-X does not use cost ratios, so that the reference mining cost can be changed in anyperiod without affecting other costs.

The spreadsheet codes have changed and have been extended. Refer to the section below.

16.16.8.FXUT

In FXUT, data is provided by element.

__________________________________________________________________________ Appendices 220


16.16.9.Spreadsheet codes

The spreadsheet codes for Four-X are similar to those for Four-D, but because Four-X is amulti-element package, codes such as METAL are now element based, and Method andType codes must be extended to include Method.Element, Type.Element andMethod.Type.Element.

Codes that no longer apply (Period and Grand total)Text Allowed attributesCOSTMuse UNDEF/UNIT-CMGR_<n>use GR_<n>.<element>

/GG /GI /UG /UI /UO

METALuse <element>

/UG /UI /UO

<method>use <method>.<element>

/GG /GI /UG /UI /UO

<method>.<type>use <method>.<type>.<element>

/GG /GI /UG /UI /UO

OUTSIDEuse OUTSIDE.<element>

/GG /UG

PRICEuse <element>/PRICEREJECTEDuse <type>.<element>/GR /UR

/GG /UG

SELLCOSTuse /CS* DS* on <e>, <m>.<e> etc.<type>use <type>.<element>

/GG /GI /UG /UI /UO

New attributes for Four-X

There have been additional dissections provided. The codes for periods and grand totals arethe same, except that the grand totals have a B, S or W to distinguish best, specified or worstcase scenarios. The * shows that a grand total extension is required.

In general CP,CB,CS,CW has been replaced by CT* and DP,DB,DS,DW by DT*.

GM, TM and UM have been changed to GP, TP and UP

__________________________________________________________________________ Appendices 221


New AttributesAttribute(s) Type of value/CE* /DE* Cost of processing due to Elements/CI* /DI* Cash Income (Revenue)/CM* /DM* Cost of Mining/CP* /DP* Cost of Processing/CR* /DR* Cost of Rehabilitation/CS* /DS* Cost of Selling/CT* /DT* Cash flow - Total of the other cash flows in the

category/GP* Grade in Place/GR* Grade Rejected/LIMIT Throughput LIMIT/OF cut-OFf/OFU cut-OFf for underground mining/TIME_CM Time cost rate factored into unit cost of processing/TIME_CS Time cost rate factored into unit cost of selling/TP* Tonnes in Place/TR* Tonnes Rejected/UNIT_CE! Unit cost of processing due to an element/UNIT_CM Unit cost of mining/UNIT_CP! Unit cost of processing/UNIT_CR Unit cost of rehabilitation/UNIT_CS Unit cost of selling/UP* Units of an element in Place/UR* Units of an element Rejected

Refer to page 174 for an overview of in-ground, in-place and rejected codes.

Revised codes for Four-XFour-D Four-XROCK C* D* ROCK CM* DM*ROCK L ROCK LIMITMETAL LI <e> LIMITGR_<n> C*D* GR_<n> CE*DE*GR_<n> L GR_<n> LIMIT<m> C* D* <m> CE* DE*<m> L <m> LIMIT<m>.<t> C* D* <m>.<t> CE* DE*<m>.<t> CO <m>.<t>.<e> OF<m>.<t> MA <m>.<t>.<e> MAX!<m>.<t> MI <m>.<t>.<e> MIN!<m>.<t> RF <m>.<t>.<e> RECPER<m>.<t> RT <m>.<t>.<e> RECTHR<t> C* D* <t> CM* DM*<t> MF <t> UNIT-CM<t> RC <t> UNIT-CR<t> TF <t> THRFACT<t> TM* <t> TP*

__________________________________________________________________________ Appendices 222


16.17. Error messages

A package such as Four-X, that runs on a wide range of machines, can produce a wide range of errormessages if things go wrong.

The error messages produced by Four-X fall into three broad categories. These are data checks,problem traps and system error messages.

16.17.1.Four-X data checks

Four-X never assumes that the data that it is given is correct, and it does whatever checks itcan as soon as it can. For example, when you give any of the programs, except FXED, thename of the Parameters File, it immediately reads it and checks it. Any errors it detects arereported on the screen and in the print file.

All the error messages produced by Four-X start with three asterisks (***) and are in capitalletters. We have tried to make the meaning of these messages self-explanatory, so there islittle point in listing them here.

Remember that there is a limit to the power of data checking. If you inadvertently give itwrong data that is still valid, Four-X cannot detect the error.

16.17.2.Four-X problem traps

The programming of Four-X is defensive to the point that it does not even trust itself to dothe right thing! There are nearly four hundred points in the code where the programmer’sunderstanding of the problem and the integrity of the program itself are checked.

If any of the programs ever stop and show the message

“PROGRAM ERROR ? IN ??????”

on the screen, where the question marks are replaced by various letters, you should informWhittle Programming immediately, giving the details of the message and the circumstancesunder which it appeared.

16.17.3.System error Messages

Four-X, like all application packages, uses the facilities of the computer operating systemwhen starting up, when reading input, producing output, and when stopping. It also uses thefacilities of a FORTRAN compiler. When either the operating system or the compilerdetects an error, it usually issues a message and stops the run, without giving the Four-Xcode the opportunity to take any action. Consequently their error message is all you get.

Since Four-X can run on a variety of operating systems and compilers, there is not a greatdeal that can be said to help you deal with these messages, which can sometimes be verycryptic, except to suggest that you take their wording very literally. If you report one ofthese system messages to Whittle Programming, please be sure to include details of anycomputer gobbledegook that accompanies them.

__________________________________________________________________________ Appendices 223


However, we can say that the most common problem is to run out of disk space. Themessage this produces can be anything from “Out of disk space” to the less helpful “Unableto write file”, and you will have to clear something off your disk before you can runsuccessfully.

If, after getting one of these messages, you find that there appears to be ample free diskspace, the important thing to remember is that the Four-X programs often use temporaryfiles, which the system automatically deletes when the program stops. In consequence, it isquite possible for there to be free disk space after the run, even though the message indicatedthat there was none left.

On UNIX systems it can be even more confusing. This is because the systems sometimes puttemporary files in a special directory which may have space restrictions, and this is notapparent in your working directory.

On a PC, another confusing error arises with the message “Unable to open file”. This isusually caused by the “Files=” line in the CONFIG.SYS file being omitted or set to too low anumber.

On a PC, when a program is started, you may get one of these error messages:

*** WARNING - AVAILABLE MEMORY IS RESTRICTED SEE NOTES IN READ.ME FILE THAT CAME WITH THIS SOFTWARE

*** NOT ENOUGH MEMORY AVAILABLE TO RUN SEE NOTES IN READ.ME FILE THAT CAME WITH THIS SOFTWARE

The READ.ME file contains a discussion of how available memory might be increased.

16.18. The Lerchs-Grossmann method

There is absolutely no need for you to know the details of how the Lerchs-Grossmann optimizationmethod works. It is well established and well regarded in the industry. However, in case you areinterested, we have included an explanation here. It is certainly simplified, but it contains examples ofall the essentials of the method.

The Lerchs-Grossmann three-dimensional optimization method achieves its aim by manipulating theblock values, and the structure arcs, which are explained in the appendix on slope handling, startingon page 179. It uses no other information. In other words, except for the information given by thearcs, it “knows” nothing about the positions of the blocks – nor indeed about mining.

Therefore, in order to demonstrate how the method works, it is merely necessary to work with a listof blocks and a list of arcs. Whether these are laid out in one, two or three dimensions and howmany arcs per block are used is immaterial to the logic of the method, which is purely mathematical.

In order to demonstrate how the method works, we will choose to work in two dimensions, becausethat is much easier to visualise. Also for simplicity, we will choose square blocks and slopes of 45degrees, although this is not a requirement for Lerchs-Grossmann.

__________________________________________________________________________ Appendices 224


This allows us to work with only three arcs per block. These three arcs go from a block to thehorizontal row of three blocks immediately above it, as shown in the following figure:

This ensures that, whenever a block is mined, the three immediately above it are mined. Since thethree arcs are applied to each of the blocks, a chaining effect ensures that, whenever any block ismined, the whole 45 degree cone above it is also mined.

The method flags each block that we currently intend to mine. During the optimization process,these flags can be turned on and off many times. A block is flagged to be mined if it currentlybelongs to a linked group of blocks that have a total value that is positive. These groups are called“branches”.

The method repeatedly scans through the blocks looking for blocks that are flagged to be mined andthat have an arc pointing to a block that is not flagged to be mined. Whenever it finds such asituation it has to do something about it, because we are planning to mine a block without mining allthe blocks above it. The way it resolves these situations forms the core of the Lerchs-Grossmannmethod.

The following figures take you through such a search.

We start with a two dimensional model, 17 blocks long and 5 blocks high. Only three blocks contain potential ore, and they have the valuesshown.

All other blocks are waste and have the value -1.0.

We search along the bottom bench, starting at the left, and the first arc from a “flagged” block that we find is to a block which is not flagged.

__________________________________________________________________________ Appendices 225


To resolve this, we link the two blocks together.The total value of the two-block branch is 22.9.

We deal with the other two arcs from this block in the same way.The total value of the four-block branch is 20.9.

We continue in the same way along the bottom bench,and then along the next bench.

(Note that even waste blocks are flagged if they belong to a positive branch).

The next flagged block has an arc to a block which is also flagged.We don’t create a link for this arc or for the vertical one from the same block, because nothing has to be resolved.

The next arc from a flagged to another flagged block is between two branches.The procedure is unchanged - we do not insert a link.

We continue adding links until we reach the one shown. When we add this link, the branch total will become -0.1, and ALL the blocks in thebranch have their flags turned off.

__________________________________________________________________________ Appendices 226


The next arc of interest is from a flagged block to a block which is part of a branch which is not flagged. Effectively the centre and theright-hand branches can co-operate in paying for the mining of the circled common waste block.

The Lerchs-Grossmann method includes a procedure for combining the two linked branches into one branch, with only one total value.(Note that there is no requirement to always branch upwards from the root).

The next arc of interest is from a flagged block to a waste block. Lerchs-Grossmann detects that this extra waste will remove the ability of thecentre branch to co-operate with the right-hand branch in paying for the mining of the circled block.

Lerchs-Grossmann includes a procedure for breaking the single branch into two branches by REMOVING a link.

We continue adding links and, eventually, the total value of the left-hand branch becomes negative. The next arc after this is again between apositive and a negative branch.

__________________________________________________________________________ Appendices 227


This is dealt with in the same way as before, and the left and right-hand branches are combined into one, with one total value.

We continue adding arcs until we reach the situation shown above. The program would then do another scan for arcs from blocks which areflagged to blocks which are not flagged. However, we can see that it will find none, and the optimization is complete.

Lerchs and Grossmann showed that, when no further arcs can be found that are from a flagged blockto a block that is not flagged, then the flagged blocks constitute the optimal pit. In this case, we havea W shaped pit that is worth 0.8, and we can see that this is indeed the pit with the maximum possiblevalue. Note that the centre branch has a negative value, so that none of its blocks are flagged andnone of them are mined.

In real three-dimensional optimizations, there will usually be many scans of the blocks, checking forarcs that have to be resolved. These continue until a scan occurs in which none have to be resolved,and we know that the optimization is complete.

__________________________________________________________________________ Appendices 228


16.19. Request for program enhancement

From time to time, users may feel that additional features or functions would make their life easier.We are responsive to users’ needs, and all requests will be considered, and implemented whereverpossible. If you wish to submit a request for an enhancement, the more detail or explanation you cangive, the better our chances of implementing it. Please photocopy this page and fax it to WhittleProgramming on one of the following facsimile numbers:

International Facsimile (61.3) 9899 3755USA Facsimile 1 800 942 2460Canada Facsimile 1 800 665 4312

Name :

Company :

Suggestion :

____________________________________________________________________________ Glossary 229


GLOSSARY

Additional Arcs File A Text file containing details of Arcs that are in addition to thoserequired to maintain the slopes specified in the Parameters File.

Air block A block that is entirely above the earth’s surface. It has exactly zerotonnage, no parcels, and is given a value of zero during optimization.

Analysis In Four-X, the term analysis refers to carrying out runs of programFXAN and considering its output. The runs simulate the operationof the mine with different pit sizes, Throughput limits and economiccircumstances. Most of the time in a Four-X study is spent onanalysis.

Arc An ordered association between two blocks which indicates that, ifthe first block is to be mined, then the second must also be mined,but not vice versa. These are used during optimization to indicatethe required slopes.

Bench A horizontal layer of blocks.

Binary file A disk file containing information that is purely for computer use,and that cannot be displayed on the screen, printed, or edited as text.

Block A rectangular volume of space for which density and grade estimatesare made by interpolation from drill-hole and other data.

Block model A regular set of blocks covering the ore body and its surrounds.

CAF The cost of mining and the cost of processing can vary with bothposition in the pit and with rock type. Four-X deals with this byusing “cost adjustment factors” (CAFs). See Positional CAFs andRock type CAFs.

Cash flow The net cash income generated by the operation of a mine or somecomponent of it.

“Cost of mining” In this manual, unless the context indicates otherwise, “cost ofmining” means the cost of blasting, loading and hauling a tonne ofrock as waste. See also Reference Mining Cost.

____________________________________________________________________________ Glossary 230


“Cost of processing” This is the difference between the total cost of blasting, loading,hauling and processing a tonne of material as ore, and the cost ofblasting, loading and hauling the same material in the same positionas waste.

If the cost of processing varies with the type of rock processed,and/or the processing method, then different costs are used for eachcombination.

If the cost of processing varies with position in the pit, thenpositional processing CAFs are used.

Cut-off A grade below which we choose not to process material.

Cut-over A grade below which we choose to process material by one methodrather than another. For example, there will often be a cut-overgrade below which it is more profitable to heap leach gold ore thanto mill it.

Defined waste Parcels with a rock type for which there is no processing method.

Deleterious element An element whose presence causes an increase in costs, or areduction in recovery.

Dilution See Mining dilution.

Discounting A dollar that we get today is more valuable to us than a dollar thatwe expect to get next year. When estimating the value of a project,it is common to reduce expected future cash flows by a certainpercentage per year, to allow for interest and risk, etc. This processis called discounting. The sum of all expected discounted cash flowsis called the Net Present Value or NPV.

Drop cut Drop cuts are defined in FXMW as regions of contiguous blocks,within a push-back, that are surrounded by blocks of laterpush-backs or by the final pit limit. See page 212 for moreinformation.

Element A substance of interest in the mineralised material. It need not be aproduct.

Element Processing Cost An addition to the processing cost which is proportional to thequantity of an element which is input to the process.

Expression A user-defined expression. See page 204.

Footwall The rock surface exposed after a layer of ore has been removed.

Four-D™ A Whittle computer package which is similar to Four-X but whichcan only handle one element.

____________________________________________________________________________ Glossary 231


G&A costs See Time costs.

Generalised Mining Package This is used to prepare the Model File for Four-X and, probably, tocomplete the details of the design after the final optimization.

GMP Generalised Mining Package – see above.

Haul road A roadway leading into the open pit that gives trucks access to theregion to be mined.

Initial capital expenditure The amount spent before the first day of operation of the mine.

Initialization File A small Text file that is used to retain a record of the most recentlyused file names and extensions, so that the programs can offersensible default file names. It also contains license information. Thisfile is named fx.ini.

Input framework A rectangular region in space into which blocks are loaded prior tore-blocking.

Lag The number of benches by which the mining of one specifiedpush-back is to lag behind the previous one.

Language File A Binary file which contains the necessary information for translatingthe English text that appears on the screen into another language.The file, if present, is named fx.lng.

Log File A Text file of abbreviated prompts and keyboard responses that canbe used to re-run a program.

Maximum cut-off A cut-off specified by the user, above which FXOP, FXAN andFXUT will not raise a cut-off or cut-over that they use.

Maximum parcel grade A parcel with a grade greater than this will not be processed.

Minimum cut-off A cut-off specified by the user, below which FXOP, FXAN andFXUT will not lower the cut-off or cut-over that they use.

Minimum parcel grade A parcel with a grade less than this will not be processed.

Mining dilution When mining ore, it is common to inadvertently also mine somewaste. If possible this dilution of the ore should be dealt with in theconstruction of the Model File. If this is not possible, or has notbeen done, Four-X can apply an over-all dilution factor thatincreases the tonnage of each Parcel processed, but leaves theelement content of the Parcel unchanged. A five percent dilutionwould require a mining dilution factor of 1.05. This factor affectsCut-offs and Cut-overs.

____________________________________________________________________________ Glossary 232


Mining recovery Not all of the ore that you intend to mine actually reaches theprocessing mill. If five percent is lost, then the mining recoveryfactor is 0.95. Both the tonnage and the element contents of eachParcel processed are multiplied by this factor. This does not affectCut-offs and Cut-overs.

Mining Sequence File A Text file containing details of the blocks mined in each period ofan analysis simulation.

Mining Width The minimum width required for access and equipment operation ona working bench.

Model framework The whole rectangular region of a Block model. This contains NX xNY x NZ blocks. The term is used in this manual when we wish toemphasise that we are referring to the whole region.

Model File A Text file containing details of the contents of the blocks in a Blockmodel.

Modelling The process of creating a Block model from drill-hole and otherdata. The term “slope modelling” is used for the process ofconverting slope requirements into Structure arcs.

Net Present Value See Discounting.

Opti-Cut™ A Whittle Programming package which optimizes cut-offs over timeso as to maximize Net Present Value.

Ore body A solid and fairly continuous mass of mineralised material that can bedistinguished from the surrounding waste.

Ore selection by cash flow Ore is selected by comparing the cash flow which would beproduced by processing it and the cash flow which would beproduced by mining it as waste. If the cash flow from processing itis higher, the material is treated as ore. If not it is treated as waste.

If more than one processing method is applicable, the one whichproduces the highest cash flow is used.

Ore selection by cut-off Ore is selected by comparing the grades of the material withpre-calculated processing cut-offs. If it does not satisfy the cut-offs,it is treated as waste.

If more than one processing method is applicable, the grades arecompared with the cut-offs of each in turn, in the order in which theyare specified in the Parameters File.

Overheads See Time costs.

____________________________________________________________________________ Glossary 233


Parameters File A small Text file containing general information about the projectand how it is to be handled.

Parcel This is part of a block for which the rock type, tonnage and elementcontent (if any) are known. A block may contain zero or moreparcels. The total tonnage of the parcels may be the same as thetonnage of the block, or it may be less. If it is less, the difference iscalled undefined waste, that is, it is waste of unknown rock type. Ifa block has no parcels, the total tonnage of the block is undefinedwaste.

Neither the position of a parcel within a block, nor its shape, aredefined.

PC IBM Personal Computer or compatible clone.

Period In Four-X, a period is a time interval to which particular economicsand Throughput limits apply, and for which tonnages and grades,etc. are reported. The period length is arbitrary, but the discountrate, Throughput limits and any Time costs supplied must be for thatlength of time.

Pit List File A Text file containing the block co-ordinates of each block in thepits produced in an optimization run.

Polygon File A Text file containing the co-ordinates of a polygon, that can beused to limit the blocks output by the re-blocking program FXRB.

Positional CAFs Four-X allows for the variation of mining and processing cost withposition in the pit by the use of positional mining and processing“cost adjustment factors” (CAFs) which are part of the descriptionof a block. These factors should be 1.0 in the Reference block, butcan have any value in other blocks.

The mining cost per tonne, which applies to a particular rock type atthe Reference block, is multiplied by the positional mining CAF ofeach block to obtain the mining cost for that block.

Processing costs in a block are obtained in a similar manner by usingthe positional processing CAF.

Processing cost See Cost of processing.

Processing recovery fraction The fraction of product that is extracted by a particular processingmethod. See also Processing recovery threshold.

Processing recovery threshold A grade that is subtracted from the ore grade before the Processingrecovery fraction is applied.

____________________________________________________________________________ Glossary 234


Product An “element” which may be extracted for sale.

Examples are gold, copper, diamonds, etc.

Push-back An intermediate pit outline that is mined to before mining to anotherpush-back or to the final pit outline.

Reference Block A particular block in the model, chosen by the user, for which allmining and processing costs are calculated. If the costs are differentin other parts of the model, this is handled by positional CAFs formining and/or processing.

Reference Mining Cost The cost of mining a tonne of undefined waste, at the ReferenceBlock.

The cost of mining a defined rock type as waste at the ReferenceBlock is obtained by multiplying the Reference mining cost by therock type mining CAF.

The cost of mining any type of rock as waste at another block isobtained by multiplying the cost of mining the same rock as waste atthe Reference Block by the positional mining CAF for the block inquestion.

Rehabilitation cost The cost per tonne of rehabilitating material of a particular Rocktype, after it has been dumped as waste.

Rejected material Material for which there is a processing path (i.e. amethod/rock-type combination) but which is not processed becauseit grades are not good enough.

Replacement capitalexpenditure

From time to time in the operation of a mine it is necessary torefurbish major pieces of equipment, and this often involvesexpenditure that is well in excess of normal maintenance costs. Werefer to this as replacement capital expenditure.

For optimization purposes, it must be handled implicitly by averagingit out over the expected mine life and factoring it into the mining,processing or selling cost.

During Analysis, it is possible to handle replacement capitalexpenditure explicitly, as is explained on page 136.

Results File A Text file containing details of each block that is contained in thepits produced in an optimization run.

____________________________________________________________________________ Glossary 235


Revenue Factor This is the factor by which the revenue for each block is scaled inorder to produce one of the nested pits. Different Revenue Factorsproduce different pits, unless the change is so small that not even asingle block is added or removed.

Refer to page 197 for the theory behind the use of Revenue Factors.

Rock This refers to all material, not just waste.

Rock type Different rock types are identified in Four-X by the four-letter codeswhich appear in each Parcel. The same codes appear in theParameters File.

Rock type mining CAFs The cost of mining can vary with Rock type, and this is handled inFour-X by the use of rock type mining “cost adjustment factors”(CAFs) in the Parameters File.

Any variation of processing cost with rock type is dealt with throughthe processing costs.

Safety berm A horizontal strip along the wall of an open pit inserted to improveslope.

Selective mining size The minimum tonnage of ore that can be extracted from a minewithout extracting adjacent waste. This is usually determined by thetype of equipment used for mining the ore.

Spreadsheet Definition File A small Text file that lists the items which are to be output during arun of FXAN as a Spreadsheet Output File.

Spreadsheet Output File A small Text file containing columns of selected values from a run ofFXAN. The items that are to be included are listed in a SpreadsheetDefinition File.

Structure arc The term used in Four-X for an Arc.

Structure File A Binary file containing the Structure arcs required for anoptimization.

Sub-region A rectangular volume of blocks that forms part (or all) of a Modelframework.

Text file A disk file containing alphanumeric characters that can be displayedon the screen, printed, and edited as text.

Throughput factor The relative speed of processing for a particular rock type. (i.e. arock type which is easy to crush might have a throughput factor of1.2, and this would be allowed for when applying milling throughputlimits.

____________________________________________________________________________ Glossary 236


Throughput limits During analysis, Four-X accepts limits on total mining, totalprocessing (by processing method or group of methods) and totalproduction (by product). When simulating the mine operation, aperiod is terminated when any of these limits is reached.

Time costs Costs that continue during mining regardless of the amount mined,processed or sold. These are often called Overheads or G&A(General & Administration) costs.

For optimization purposes, they must be handled implicitly byfactoring them into the mining, processing or selling cost.

During analysis, it is possible to handle time costs explicitly, as isexplained on page 136.

Undefined waste Any part of the total tonnage of a block which is not included in aParcel in that Block is called undefined waste.

Units In Four-X, the units used for quantities of rock, elements andcurrency are arbitrary, and it is possible to have different units foreach element.

The units for rock and elements are set by the units used in theModel File, and grades are expressed throughout as the ratio ofquantities measured in these units. For example, if the Model Filecontains rock quantities measured in metric tonnes, gold quantitiesmeasured grams and copper in pounds, then the grades and cut-offswill be expressed in grams per tonne and pounds per tonnerespectively. (This manual and Four-X refer to tonnes, but noparticular scaling is implied by this).

Four-X makes no assumptions about the units of distance except thatthey must be the same for the block dimensions and the originco-ordinates in the Parameters File.

The symbol for the unit of currency, which appears in the printedoutput from program FXAN, can be controlled by the user.

Virtual memory A system that uses the computer’s hard disk as temporary storage inplace of high-speed memory, to enable data that will not fit intomemory to be processed. Four-X uses this system only if thenumber of blocks or analyses being processed cannot be fitted intophysical memory.

Waste Material that contains no product, or so little that it is not worthprocessing.

Work File A Binary file containing working information for the optimizationprogram FXOP.

_______________________________________________________________________________Index 237


INDEX

Special characters and keys! - for logging commands 85# - for a block removed 130# - for block which has been removed 55# - for file overwriting 22, 84& - for extending input lines 117* - for an added waste block 130*'! and double quote - for comments 149, 150, 152, 163, 164, 165, 166. - for air blocks 111/ - for changes with period 117[] - for defaults 22, 82^ - to go to previous question 30+ - for an added block 130k - to indicate thousands 115m - to indicate millions 115Special keys - for keyboard editing 82

AActive blocks indicator

description 63–64position in file 155reference 60, 61, 65, 67, 68, 70, 80, 91, 97, 103, 107, 108, 144

Additional Arcs Filedescription 59format 149reference 24, 69, 79, 83, 105, 106, 143, 144, 181, 216

Air blockdescription 229reference 28, 60, 66–67, 96, 98, 110, 111, 151, 165

Air flag Adescription 66–67position in file 158reference 61, 91, 107

Air flag Bdescription 67–68position in file 158reference 61, 91, 107, 165

Arc see Structure arcArc generation see Benches for arc generation

_______________________________________________________________________________Index 238


BBatch operation 87Benches for arc generation

description 69–70, 180–81formula 69position in file 156reference 61, 105

Blank lines see Comment linesBlock

definition 229Block model

description 149–78reference 132, 139, 141, 229

Block sizesdescription 62discussion 137–39position in file 154reference 18, 90, 93, 94, 99, 100, 101, 102, 103, 177, 205

Block value calculation 199–202

CCAF see Cost adjustment factorCapital expenditure 44, 114, 117, 134Comma delimited format 149, 150, 152, 163, 164, 165, 177Comment lines 90, 149, 150, 152, 163, 164, 165, 166Co-ordinates of the origin see Model framework/originCorner see Sharp cornerCost adjustment factor

description 12positional mining

calculation 204flag 61, 68

position in file 155position in file 151reference 13, 49–50, 60, 92, 93, 94, 99, 100, 101, 103, 133, 151, 170, 202, 233,

234positional processing

calculation 204effect on cut-offs 74, 191flag 61, 68

position in file 155position in file 151reference 13, 49, 60, 74, 92, 93, 94, 99, 100, 101, 103, 133, 151, 170, 191, 233,

234rock type mining

description 73position in file 161reference 13, 59, 62, 114, 123, 133, 234

_______________________________________________________________________________Index 239


Cost of miningdescription 12, 229ore 135reference 32, 73, 183, 229, 235undefined waste 57, 133

Cost of processingdescription 13, 230

Costs 132–37Currency characters

position in file 157Cut-off see also Minimum and Maximum cut-off grades

description 230display 191effect of processing CAFs 74, 191reference 26, 117, 137, 218

Cut-off control flagdescription 75position in file 162reference 62

Cut-off scalingdescription 191

Cut-overdescription 189, 230display 191reference 77, 195

DDecimal places see Formatting control of output values and element decimalsDefault rock tonnage

generaldescription 65position in file 158reference 60, 61, 91, 103, 107

sub-regiondescription 70position in file 156reference 60, 61, 69, 103, 107, 178

Defined waste see also Undefined wastedescription 230reference 13, 73, 234

Deleterious elements 230Dilution see Mining dilutionDimensions of a block see Block sizesDimensions of the model framework see Model framework/dimensions

_______________________________________________________________________________Index 240


Discountingdescription 230methods 118reference 32, 73, 79, 112, 114, 118, 119, 167, 168, 233

Drop cut see Small drop cut

EElement

codedescription 72position in file 159, 160reference 61, 75

description 13formatting

description 72position in file 159reference 61

position in Model Filedescription 72position in file 159reference 61

processing costdescription 75position in file 162reference 108, 114

Element processing costcode

reference 62description 230

Element typecode

reference 62Error messages 222–23Expansion see Pit expansionExpression

codedescription 71position in file 160reference 62, 91, 154

definitiondescription 71

reference 91, 218, 219text

position in file 160reference 62

usageposition in file 160reference 62

_______________________________________________________________________________Index 241


Expressionsdescription 204

Extensions 83

FFile names 83–84Formatting control of output values

description 63, 218position in file 157reference 61, 113

Four-D 10Four-D comparison 218–21Free format see Comma delimited format

HHole see Small hole

IImmovable objects

reference 50, 109, 145Initial capital expenditure 231Initialization file

description 80reference 83, 231

Input framework 93, 94, 95, 96, 98, 231Internal Rate of Return

reference 118, 119, 170

LLag

description 120, 231reference 46, 113, 170, 171

Language Filedescription 81reference 231

Lerchs-Grossmann methodreference 10

Lerchs-Grossmann methoddescription 223–27reference 109, 136

License entitlement 80Lines per page 80Log File

description 85–86in batch mode 87reference 38, 39, 41, 81, 83, 231

_______________________________________________________________________________Index 242


MMaximum

position in file 162reference 62, 108, 114

Maximum cut-off gradedescription 193–95

Maximum parcel gradedescription 196

Menudescription 16

Milling throughput factordescription 74position in file 161reference 62

Minimumposition in file 162reference 62, 76, 108, 114

Minimum cut-off gradedescription 193–95

Minimum parcel gradedescription 196

Mining cost see Reference mining costMining cost adjustment factor see Cost adjustment factor/positional mining and Cost adjustment

factor/rock type miningMining dilution

description 65position in file 158reference 61, 91, 113, 114, 123, 124, 167, 202, 231

Mining recoverydescription 65position in file 158reference 61, 65, 91, 113, 114, 123, 124, 167, 202, 232

Mining Sequence Filedescription 59format 150reference 83, 110, 114, 121, 122, 123, 232

Mining tolerancedefinition 211reference 129

Mining widthdefinition 211reference 53, 55, 128, 130, 131, 211

Model Filedescription 59–60format 151–52reference 14, 18, 20, 49, 64, 74, 78, 82, 83, 92, 93, 94, 96, 99, 103, 107, 108,

110, 122, 123, 133, 139, 150, 165, 191, 232

_______________________________________________________________________________Index 243


Model framework 144description 93, 149–78, 232dimensions

description 62position in file 155reference 61, 90, 103, 104, 105, 107, 110, 113, 123

origindescription 63position in file 154reference 61, 90

reference 59, 64, 92, 95, 97, 99, 100, 101, 102, 103, 108, 137, 138, 139, 140,145, 164

Multi-element concepts 148

NNested pits

theory 197

OObstructions see Immovable objectsOffset

definition 93reference 99, 100, 101, 102, 103, 145

Opti-Cut interface 114, 217Ore selection by cash flow

description 66, 232example 192

Ore selection by cut-offdescription 66, 232

Ore selection methodreference 61

Ore selection method flagdescription 66

Pparameters file

description 61–77format 152–63reference 20, 24, 78, 79, 80, 83, 88, 90, 91, 92, 93, 94, 99, 100, 101, 102, 103,

104, 105, 107, 108, 110, 113, 114, 123, 124, 130, 133, 164, 165, 178,179, 180, 181

Parceldescription 13

Parcelscombining 97, 139, 140description 233format 152limit 99, 100, 101, 103, 138, 139reference 59, 65, 68, 73, 74, 76, 77, 96, 150, 151, 191, 210splitting 97

_______________________________________________________________________________Index 244


Pit expansiondefinition 129reference 55, 129, 130

Pit List Filedescription 78format 164reference 83, 92, 93, 94, 96, 102, 103, 128, 129, 130, 233

Pit shellreference 55

Polygon Filedescription 78format 164–65reference 63, 99, 100, 101, 102, 103, 233

Precision 218Price

description 72position in file 160reference 61, 108

Print unprocessed mineralisation flagdescription 68position in file 155reference 61, 113

Processing costdescription 74position in file 161reference 148

Processing cost adjustment factor see Cost adjustment factor/positional processingProcessing method code

description 74position in file 161reference 62, 77, 108, 150, 163, 172, 220

Processing method groupdescription 77position in file 163reference 62, 74, 91, 113, 114, 153, 172, 220

Processing recoveryreference 62

Processing recovery fractiondescription 75, 184–85position in file 162reference 65, 76, 108, 114, 182, 183, 184, 185, 189, 233

Processing recovery thresholddescription 76position in file 162reference 62, 108, 114, 233

Productdescription 13

Push-backreference 53, 128, 129, 130, 131, 211, 212, 213, 214, 215

_______________________________________________________________________________Index 245


RReagent costs 137Re-blocking

description 92format 152reference 63, 139

Recovery see Mining recoveryReference block

description 13Reference Mining Cost

description 13, 64position in file 158reference 61, 91, 113, 114

Rehabilitation cost 59, 114, 132, 234description 73effect on cut-offs 185–86, 185–86position in file 161reference 62, 123, 124

Rejected material see Unprocessed mineralisationReplacement capital expenditure 234

reference 114Restart

dump 64, 80, 108, 109interval 61, 64, 91, 107, 155run 25, 80, 84, 107, 109

Results Filedescription 78format 165reference 18, 30, 38, 53, 67, 78, 83, 92, 93, 94, 96, 100, 101, 102, 103, 107,

109, 110, 111, 112, 113, 121, 122, 123, 128, 129, 130, 158, 164, 234Revenue Factor

description 13position in file 158–59reference 26, 61, 68, 76, 77, 91, 108, 123, 139, 235theory 197

Rockdescription 13

Rock type 235code

description 73position in file 152, 161, 162reference 62, 74, 91, 107, 108, 122, 123, 124, 151, 172, 173, 220

rehabilitation cost see Rehabilitation cost

_______________________________________________________________________________Index 246


SSelling cost

description 72position in file 160reference 61, 108, 114, 132, 133, 136, 137, 148

Sensitivity workdescription 18–19example 147reference 139, 141, 145

Sharp cornerdefinition 215reference 57, 129

Slopesdescription 70–71, 179–81errors 105position in file 156reference 18, 24, 61, 69, 79, 91, 97, 105, 132, 135, 142, 143, 178techniques 146usage 71

Small drop cutdefinition 212reference 57, 129

Small holedefinition 214reference 57, 129

Small stumpdefinition 214reference 57, 129

Small walldefinition 213reference 57, 129

Spider diagram 147Spreadsheet Definition File

description 79format 166–76reference 20, 38, 41, 83, 113, 120, 235

Spreadsheet Output Filedescription 79format 177reference 39, 41, 83, 113, 120, 235

Stripping rationegative 65reference 26, 32, 35, 46, 171

Structure arc 64, 79, 105, 109, 178, 223, 235. see Benches for arc generationStructure File

description 79–80reference 18, 24, 64, 78, 83, 105, 106, 107, 108, 128, 179, 181, 235

Stump see Small stump

_______________________________________________________________________________Index 247


Sub-region block limitsdescription 69position in file 156reference 61, 103, 105, 107, 178

Sub-region default rock tonnage see Default rock tonnage/sub-regionSub-regions 178System Limits 126, 127

TThree-D 10Time costs

description 13reference 11, 60, 114, 118, 133, 136

UUndefined waste see also Defined waste. see also Defined waste

description 236reference 59, 73, 233

Underground miningdescription 202–3position in file 162, 163reference 62, 77, 108, 113, 123, 124, 170spreadsheet code 172, 220

Unitsdescription 14, 236

Unprocessed mineralisation 26

VVirtual memory

description 127, 236reference 109

WWall see Small wallWork File

description 80reference 64, 83, 84, 107, 108, 236

ZZone number 110, 151

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