Computer Aided Mine DesignComputer Aided Mine Design(Part I – Ultimate Pits)(Part I – Ultimate Pits)

Mnge 315Mnge 315

©Dr. B. C. Paul spring 2003©Dr. B. C. Paul spring 2003

Computer Aided Mine Computer Aided Mine DesignDesign• Many surface mines (especially Many surface mines (especially

metal/industrial mineral) are metal/industrial mineral) are designed with computer packagesdesigned with computer packages– Mintec ExampleMintec Example– Packages are comprehensive from Packages are comprehensive from

exploration to operationexploration to operation

• Many more limited packages that do Many more limited packages that do parts of designparts of design– Autocad and some of add-onsAutocad and some of add-ons

Our ScopeOur Scope

• We are not going to learn a packageWe are not going to learn a package– (They change anyway and companies have (They change anyway and companies have

specific preferences)specific preferences)

• We will look at what the basic steps are We will look at what the basic steps are and an overview of how they workand an overview of how they work– Will be explained at a conceptual Will be explained at a conceptual

understanding levelunderstanding level– Will not attempt to teach how to do or Will not attempt to teach how to do or

program the calculationsprogram the calculations

How Does Computer Aided How Does Computer Aided Design WorkDesign Work

• First - geology of the mineralization is First - geology of the mineralization is worked outworked out– Exploration data working with geologistsExploration data working with geologists– Really same step as traditional methodsReally same step as traditional methods

• Second – The data is converted into a 3D Second – The data is converted into a 3D block model of the mineralizationblock model of the mineralization– A crude model is 100 X 100 X 100 blocks (ie. A crude model is 100 X 100 X 100 blocks (ie.

100,000) – detailed over 1,000,000100,000) – detailed over 1,000,000– Mineral character and other properties of each Mineral character and other properties of each

block are assigned to the block (computers block are assigned to the block (computers process as array)process as array)

How are Block Models BuiltHow are Block Models Built

• Sampling programs obtain specimens of Sampling programs obtain specimens of the mineralization and rockthe mineralization and rock– Often done with core drillingOften done with core drilling

• Geologic and preliminary exploration Geologic and preliminary exploration normally identifies the structure and normally identifies the structure and basic mineral zones likely presentbasic mineral zones likely present– Computer package is used to help determine Computer package is used to help determine

where to sample to obtain the most useful where to sample to obtain the most useful information with the least expenseinformation with the least expense

The Building of Block The Building of Block ModelsModels

• Samples are analyzed for the key Samples are analyzed for the key parameters that will determine the parameters that will determine the value of the mineralizationvalue of the mineralization– Put into a sample Data BasePut into a sample Data Base

• Computer then interpolates the Computer then interpolates the sample data to a grid of blocks using sample data to a grid of blocks using KrigingKriging

What is KrigingWhat is Kriging

• Basic idea is that a sample from near by Basic idea is that a sample from near by is likely to be more similar than one that is likely to be more similar than one that is distantis distant– Kriging compares samples for their similarity Kriging compares samples for their similarity

to each other at different distancesto each other at different distances– The similarity as a function of distance is The similarity as a function of distance is

plotted graphically as a “Semi-Variogram”plotted graphically as a “Semi-Variogram”– A curve is fitted to the similarity as a A curve is fitted to the similarity as a

function of distance graphfunction of distance graph

Distance

Variance

More KrigingMore Kriging

• The blocks of the block model are then The blocks of the block model are then “Kriged” using the mathematical function “Kriged” using the mathematical function fitted to the “Semi-Variogram” (also called the fitted to the “Semi-Variogram” (also called the Variogram by people who don’t know better)Variogram by people who don’t know better)

• Block Values are assigned a weighted average Block Values are assigned a weighted average of the values of the samples around themof the values of the samples around them– Advance calculus techniques are used to give the Advance calculus techniques are used to give the

most weight to the samples most likely to be most weight to the samples most likely to be similar as determined by the mathematical function similar as determined by the mathematical function fitted to the “Semi-Variogram”fitted to the “Semi-Variogram”

• (There is a “Geostatistics” Class available as (There is a “Geostatistics” Class available as one of your electives that will get down to one of your electives that will get down to detail)detail)

At the End of the DayAt the End of the Day

• You have a series of blocksYou have a series of blocks– Often separate rock formations are made Often separate rock formations are made

separate sets of blocksseparate sets of blocks

• The blocks are each assigned geologic The blocks are each assigned geologic parameters that define the value of the parameters that define the value of the “ore”“ore”– For metal mines this will most likely be ore For metal mines this will most likely be ore

grade (percentage of the rock that is the grade (percentage of the rock that is the mineral of interest)mineral of interest)

Metal/Industrial Minerals Metal/Industrial Minerals DilemmaDilemma• Coal and Quarry people had similar value in all pay Coal and Quarry people had similar value in all pay

materialmaterial– Minable/ Non-Minable or get first is largely based on cheapest Minable/ Non-Minable or get first is largely based on cheapest

material to getmaterial to get• Usually means avoid things that screw you upUsually means avoid things that screw you up

• Metal/ Industrial MineralsMetal/ Industrial Minerals– Mineral of interest is usually only part of the rock to be minedMineral of interest is usually only part of the rock to be mined– Disseminated deposits have no clear boundariesDisseminated deposits have no clear boundaries

• Grade of mineralization just decreases and fades outGrade of mineralization just decreases and fades out

• Result – Metals and Industrial Minerals usually need Result – Metals and Industrial Minerals usually need multiple parameters in their block models to explain multiple parameters in their block models to explain what a block of ground really iswhat a block of ground really is– Still quite doable with a computer todayStill quite doable with a computer today

Using the Block ModelUsing the Block Model

• You have a Geologic Block ModelYou have a Geologic Block Model– Collections of blocks each assigned one or more geologic Collections of blocks each assigned one or more geologic

parameters that define its economic valueparameters that define its economic value• Computer Aided Packages today relay this Computer Aided Packages today relay this

information to mining machineryinformation to mining machinery– Blocks are just cubes with imaginary boundariesBlocks are just cubes with imaginary boundaries– Shovels get location of the “blocks” with satellite or radio Shovels get location of the “blocks” with satellite or radio

relaysrelays– Sensors on the digging motion help position the buckets to Sensors on the digging motion help position the buckets to

line up and take controlled material from block modelline up and take controlled material from block model– Keep track of what material is in each truckKeep track of what material is in each truck– Data sent to the processing plant to help adjust the Data sent to the processing plant to help adjust the

process to exactly what has been takenprocess to exactly what has been taken– Blocks are continuously updated and refined using data Blocks are continuously updated and refined using data

from drill holes made for blastingfrom drill holes made for blasting

Adapting Block Models for Mine Adapting Block Models for Mine PlanningPlanning

• Geologic parameters of each block Geologic parameters of each block provide information on potential value of provide information on potential value of blockblock– Also have an X, Y, Z coordinate location on the blockAlso have an X, Y, Z coordinate location on the block

• Take the mining and processing costs Take the mining and processing costs most likely for the type of mine you are most likely for the type of mine you are thinking aboutthinking about– Estimate the $ value of each blockEstimate the $ value of each block

• Obviously done by giving functions to the computerObviously done by giving functions to the computer

• Result is called an Economic Block ModelResult is called an Economic Block Model

Economic Block ModelsEconomic Block Models

• Economic Block Model assigns each Economic Block Model assigns each block only one numberblock only one number– The dollar value (or cost) of mining that The dollar value (or cost) of mining that

blockblock

$

The Cut-Off Grade IssueThe Cut-Off Grade Issue

• Value of the mineral in the block is Value of the mineral in the block is determined by the marketdetermined by the market

• Cost of mining and processing a block is Cost of mining and processing a block is determined by what is done with itdetermined by what is done with it– It would cost more to grind a block to power and It would cost more to grind a block to power and

put it through a flotation mill than to dump it.put it through a flotation mill than to dump it.– Decided on whether the extra expense of ore Decided on whether the extra expense of ore

treatment is recouped from the materialtreatment is recouped from the material

• Need to Determine a “Cut-Off-Grade”Need to Determine a “Cut-Off-Grade”– Only material above a certain grade is processed Only material above a certain grade is processed

as oreas ore

More Cut-Off Grade IssuesMore Cut-Off Grade Issues

• May be more than one type of processingMay be more than one type of processing– Cu ore can be ground and put through floatationCu ore can be ground and put through floatation– Cu ore can be leached in vats or pilesCu ore can be leached in vats or piles– Cu ore can be dumpedCu ore can be dumped– May have more than one Cut-Off GradeMay have more than one Cut-Off Grade

• Polymetallic deposits contain more than one Polymetallic deposits contain more than one mineral of interestmineral of interest– Lead Zinc and Silver often togetherLead Zinc and Silver often together– Cut-Off may be based on sales value of several Cut-Off may be based on sales value of several

mineralsminerals

Cut-Off Grades and Block Cut-Off Grades and Block ModelsModels

• In translating Geologic Block Model to In translating Geologic Block Model to Economic you have to determine COV Economic you have to determine COV before you can assign costsbefore you can assign costs

• Common COV is the “Break Even Cut-Common COV is the “Break Even Cut-Off Grade”Off Grade”– Take cost of processing rockTake cost of processing rock

•Calculate the minimum mineral content that Calculate the minimum mineral content that will pay the costwill pay the cost

•That is your break-even cut-off gradeThat is your break-even cut-off grade

What the ##@@!!*What the ##@@!!*

• ““Break-Even Stripping Ratio” determines the Break-Even Stripping Ratio” determines the maximum OB that can be movedmaximum OB that can be moved– Cost to recover ore depends on OBCost to recover ore depends on OB

• How can you calculate a COV then?How can you calculate a COV then?• When Converting a Geologic to Economic Block When Converting a Geologic to Economic Block

Model determine each block value individuallyModel determine each block value individually– Ie. Break-Even COV is based only on direct mining Ie. Break-Even COV is based only on direct mining

and processing costand processing cost• What would you do with the block if it were right on the What would you do with the block if it were right on the

surfacesurface

• Other Routines will deal with the OB issueOther Routines will deal with the OB issue

The Surface IssueThe Surface Issue

• Classroom drawing have level surfacesClassroom drawing have level surfaces– Real life does notReal life does not

• How do you deal with the shape of the How do you deal with the shape of the surface?surface?

• Air BlocksAir Blocks– Blocks located above the mine surface Blocks located above the mine surface

provide no profit and have no cost to moveprovide no profit and have no cost to move– Blocks are assigned zero value and called Blocks are assigned zero value and called

“Air Blocks”“Air Blocks”

The Next StepThe Next Step

• We have an Economic Block ModelWe have an Economic Block Model– Millions of blocks with assigned dollar valuesMillions of blocks with assigned dollar values

•The OB has negative valuesThe OB has negative values•The Air Blocks have zero valuesThe Air Blocks have zero values

• Computer Routines Will Examine the Computer Routines Will Examine the Model to determine what the largest Model to determine what the largest profitable group of blocks is that can be profitable group of blocks is that can be minedmined– That group of blocks will define the “Ultimate That group of blocks will define the “Ultimate

Pit” – how large the surface mine will becomePit” – how large the surface mine will become

How Do You Do That?How Do You Do That?

• Simplest Method to explain called Simplest Method to explain called “Floating Cone Miner”“Floating Cone Miner”

• Computer begins examining the top Computer begins examining the top blocks one at a timeblocks one at a time– Looking for a block with a positive valueLooking for a block with a positive value– If it finds a positive block it will move the If it finds a positive block it will move the

block to its “mined” blocks recordblock to its “mined” blocks record•Replace the block with an air blockReplace the block with an air block

– It just cybermined a block of oreIt just cybermined a block of ore

Floating Cones ContinueFloating Cones Continue

• Often top level of blocks are nothing but air or Often top level of blocks are nothing but air or overburdenoverburden– Usually finds nothingUsually finds nothing

• Computer then examines next row downComputer then examines next row down– Looks for a block with positive valueLooks for a block with positive value

• If it finds a block it will look at the blocks aboveIf it finds a block it will look at the blocks above– Blocks above are usually air or OBBlocks above are usually air or OB

• (because if it were ore it probably already got cybermined)(because if it were ore it probably already got cybermined)– Blocks above are added with the ore blockBlocks above are added with the ore block

• If the added total is positive the computer puts all the If the added total is positive the computer puts all the ore blocks in the ore mined column and all the OB ore blocks in the ore mined column and all the OB blocks in the OB column and replaced them with “air blocks in the OB column and replaced them with “air blocks in the block modelblocks in the block model

• They were just cyberminedThey were just cybermined

Whats Above Me?Whats Above Me?

-$5.40 -$5.40 -$5.40 -$5.40 $0 $0

-$5.50 -$5.50 $45 -$5.50 -$5.50 -$5.50

$0

-$5.50

This one – of courseHow About This?Can you reallyMine straight upAnd down?

Computer is programmed with a “Cone Angle” – Tells it how toLook at the blocks above and determine if they need to be mined

As you see this cone floating around on the model in search of minable ore beginTo understand why it is called a floating cone miner.

Adding Things UpAdding Things Up

-$5.40 -$5.40 -$5.40 -$5.40 $0 $0

-$5.50 -$5.50 $45 -$5.50 -$5.50 -$5.50

$0

-$5.50

$45-$5.40-$5.40=$34.20

$34.20 > 0

ActionAction

-$5.40 -$5.40 $0 $0 $0 $0

-$5.50 -$5.50 $0 -$5.50 -$5.50 -$5.50

$0

-$5.50

Now we are ready to move on to the next block

Cone AnglesCone Angles

• Routines differ in how pit slope angles are handledRoutines differ in how pit slope angles are handled• Some use a single input put angleSome use a single input put angle

– Go up with a coneGo up with a cone– Any block that gets hit or nicked is included in the Any block that gets hit or nicked is included in the

calculation of block group valuecalculation of block group value

• Some routines keep a maximum slope in each blockSome routines keep a maximum slope in each block– Ie they did not completely convert the geologic block model Ie they did not completely convert the geologic block model

to an economic block modelto an economic block model– They may allow partially mining a blockThey may allow partially mining a block

• These cone angles come out of your rock mechanics These cone angles come out of your rock mechanics work on slope stabilitywork on slope stability

What Happened to Working What Happened to Working Slope?Slope?

• You may remember that need a You may remember that need a certain amount of bench room for certain amount of bench room for equipment to workequipment to work– Usually made slope less steep than a Usually made slope less steep than a

final pit slope based on geologyfinal pit slope based on geology

• We are working on “Ultimate Pit” We are working on “Ultimate Pit” after every slope and ton of ore than after every slope and ton of ore than can be mined has been minedcan be mined has been mined

Routine ContinuesRoutine Continues

• Computer moves down to the 3Computer moves down to the 3rdrd level level looking for positive value blockslooking for positive value blocks– If it finds one it cones up to the surface and adds If it finds one it cones up to the surface and adds

up the valueup the value• Cybermines the whole thing if value is positiveCybermines the whole thing if value is positive

• Moves on looking more if the cone comes up negativeMoves on looking more if the cone comes up negative

• Computer keeps dropping one level after Computer keeps dropping one level after another till it is doneanother till it is done– ““Ultimate Pit” is the set of Air Blocks in the modelUltimate Pit” is the set of Air Blocks in the model

Woops FactorsWoops Factors

-$5 -$5 -$5 -$5 -$5 -$5 -$5 -$5 -$5

$10 -$5 -$5 -$5 -$5 -$5 -$5

-$5

-$5 -$5

-$5 -$5 $70 -$5 -$5 -$5 -$5

-$5

$25 $25 -$5

--$15 + $10 = -$5

Working on WoopsWorking on Woops

-$5 -$5 -$5 -$5 -$5 -$5 -$5 -$5 -$5

$10 -$5 -$5 -$5 -$5 -$5 -$5

-$5

-$5 -$5

-$5 -$5 $70 -$5 -$5 -$5 -$5

-$5

$25 $25 -$5

-$40 + $70 = $30

CyberminingCybermining

-$5 -$5 -$5 $0 $0 $0 $0 -$5

$10 $0 $0 -$0 -$5 -$5 -$5

-$5

-$5 -$5

-$5 -$5 $0 -$5 -$5 -$5 -$5

-$5

$25 $25 -$5

$0

Now the Cone Is Profitable

To catch situations like this, most floating coneMiners will start searching from the top of theModel every time they cybermine a cone to lookFor ore on the edge.

Harder to FixHarder to Fix

-$5 -$5 -$5

-$5 -$5 -$5

-$5

-$5 -$5

-$5 -$5 -$5 -$5 -$5 -$5

-$5

$25 $25 -$5-$5

-$5

-$5

-$5

-$5

-$5 $0

$0 $0 $0

$0

$0$0$0

$0

$0$0

TThis Pit is Not Profitable

Weaknesses of Floating Weaknesses of Floating ConesCones

-$5 -$5 -$5

-$5 -$5 -$5

-$5

-$5 -$5

-$5 -$5 -$5 -$5 -$5 -$5

-$5

$25 $25 -$5-$5

-$5

-$5

-$5

-$5

-$5 $0

$0 $0 $0

$0

$0$0$0

$0

$0$0

This Pit is Profitable

Unfortunately Floating Cones will never see thisSince they look at only one block at a time andSometimes profitability requires looking at groups

SolutionsSolutions

• Floating Cone Miners are in a class called Floating Cone Miners are in a class called Heuristic RoutinesHeuristic Routines– Based on a guess a plug approachBased on a guess a plug approach

• Is an analytical solution called method of Is an analytical solution called method of convex-hullsconvex-hulls– Don’t ask about the math (you don’t want to know)Don’t ask about the math (you don’t want to know)– Will cut through a block model and get the largest Will cut through a block model and get the largest

block of ground that still keeps increasing profitblock of ground that still keeps increasing profit– Routine is called “Learch Grossman”Routine is called “Learch Grossman”

• Requires fairly powerful computer (which we easily have Requires fairly powerful computer (which we easily have today)today)

Choices and LimitationsChoices and Limitations

• Learch Grossman includes some fairly restrictive Learch Grossman includes some fairly restrictive assumption about uniform slopesassumption about uniform slopes– Real pit slopes that are stable may vary by direction Real pit slopes that are stable may vary by direction

and rock typeand rock type

• Heuristic Routines can handle lot of flexibility, Heuristic Routines can handle lot of flexibility, but are subject to errorsbut are subject to errors

• Whittle Programming has tried to impose of few Whittle Programming has tried to impose of few Heuristic variations on a true Learch GrossmanHeuristic variations on a true Learch Grossman

• Bottle-Line - In the end you will have an ultimate Bottle-Line - In the end you will have an ultimate pit that is somewhat close to the true optimumpit that is somewhat close to the true optimum

Things Not IncludedThings Not Included

• Ultimate Pit generated by computer is Ultimate Pit generated by computer is generally a smooth walled thinggenerally a smooth walled thing– Ultimately you will have to deal with benches Ultimately you will have to deal with benches

which are added in as part of the human which are added in as part of the human guided planningguided planning

• Usually not done at this time – ultimate pit Usually not done at this time – ultimate pit is what is left over when mining is doneis what is left over when mining is done– Stands to reason that most road and bench Stands to reason that most road and bench

networks are whats left over – not an end you networks are whats left over – not an end you worked towardworked toward