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University of AlbertaMINE 325 Mine Planning and Design
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MINE 325
Mine Planning
ec m s
Manual Method
Ultimate or Final Pit Limits (1/5)
Size and shape of mineable reserves and
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based on:
Technical , Economical , Safety constraints
It is used in:
The economic potential of a mineral deposit.
Financing and Taxation.
Short and long term mine plans.
The boundaries outside which mine plant and
structures should be located.
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Pit Limits (2/5)
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Pit Limits (3/5)
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Pit Limits (4/5)
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Final Pit Limit method (5/5)
Manual method
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ompu er me o s ,
Manual methods are based on sections
Involve Stripping Ratios (SR)
Three stripping ratios which can be defined:
Overall Stripping Ratio
Incremental (Instantaneous) Stripping Ratio Break-even or maximum Stripping Ratio
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MINE 325
Mine Planning
Stripping Ratio
Stripping Ratios (1/6)
Overall stripping ratio is the ratio of the totaltonna e of waste divided b the total tonna e of
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ore contained in the final pit (SRo)
Incremental stripping ratio (or instantaneousstripping ratio)is the ratio of waste tonnage toore tonnage as a result of expanding the pit by aunit volume (ISR)
Break-even stripping ratio is the ratio of wastetonnage to ore tonnage where the cost of thewaste removal exactly equals the value of themineral (BESR or SRmax)
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Stripping Ratios (2/6)
SRo and ISR are physical ratios
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BESR is an economic ratio
BESR will change depending ongrades, costs and revenues
Stripping ratio (3/6)The volume of the contained ore is expressed by
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r
whereris the ore radiush is the ore thickness.
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Stripping ratio (4/6)Chapter 4 pages 45 to 49
.tanh r
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tancH h h h r
tan tanc
H hR r
21
3tipV r h
Truncated tip
2 21 1
3 3m tip cV V V R H r h
Fully circumscribed cone
2
1
3 cV R H
Mined volume (ore + waste)
Stripping ratio (5/6)Chapter 4 pages 45 to 49
Mined volume (ore + waste)
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2 2
3 3m tip cV V V R H r h
2
w mV V r h
Volume of waste
( )Waste volume
( )Ore volume
2
2( ) w m
o
V V r hSR overall
V r h
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Stripping ratio (6/6)Chapter 4 pages 45 to 49
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MINE 325
Mine Planning
Final Pit Limits
Manual Method
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Manual MethodBasic Concepts - Sectional Calculation
wasteNet Value = Gross Value Total Cost
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0.6% Cu
ISR = 2:1
1 ton of Ore(0.6% Cu)
3.2 tons ofwaste
= -
BESR = 3.2:1same, the ISR is the ratio of thelength in ore to the length in waste. $NV = Cost of Stripping
Manual MethodBasic Concepts - Sectional Calculation
waste
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0.6% Cu
ISR = 2:1 BESR = 3.2:1
Actual StrippingRatios
AllowableStripping Ratios
Pit Limit is adjusted until:ISR = BESR
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Manual MethodBasic Concepts - Both Walls in Waste
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Usually the width of crosssection is assigned to each sidearea o n uence o sec on .
Shape is moved vertically and
horizontally on section until bothsides fit the SR-Grade Curve
Manual MethodSectional Calculation -Variable Grades
Each block or polygon has a
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.
Multiple layersof overburdentype material
Calculation of average grade in the ore isa length weighted average grade.
Each side is done independently.
the sectionalcalculation
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Hand MethodThe Basic Concept - Example
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Ore Net Value$NV = $GV - $TC = $1.90 / unit volume Cost of stripping waste is $1/unit volume
Hand Method the Basic ConceptExample- Strip 1The volumes are:Strip 1:
3
1 7.5wV u
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3
1 5.0oV u
The instantaneous stripping ratio (ISR) is defined as: 1wl
ol
VISR
V
1 1.5ISR
Assuming that the net value from selling one unit volume of ore (that moneyremaining after all expenses have been paid) is $1.90
cost for mining and disposing of the waste is $1/unit volume, the net valuefor strip I is
1 5.0 x $1.90 - 7.5 x $1 = $2.00NV
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Hand Method the Basic ConceptExample- Strip 2
3=
Strip 2:
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V u
ISR
NV
w
o2
3
2
2
5 0
1 68
=
=
=
.
.
.
5.0 x $1.90 - 8.4 x $1 = $1..10
Hand Method the Basic ConceptExample- Strip 3
Strip 3:
V u3
9 45= .For strip 3, the net value is just about
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V u
ISR
NV
w
o3
3
3
3
5 0
1 89
=
=
=
.
.
.
5.0 x $1.90 - 9.45 x $1 = $$0.05 0
.'breakeven' since the costs involved inmining the strip just equal the revenues.
It is the location of the final pit wall.
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Hand Method the Basic ConceptExample- Strip 4
3=
Strip 4:
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V u
ISR
NV
w
o
4
4
3
4
4
5 0
2 1
=
=
=
.
.
.
5.0 x $1.90 - 10.5 x $1 = --$1.0
Hand MethodExample final pitISR = BESR
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Hand Method the Basic Concept
The overall stripping ratio (OSR) for this section is calculated as
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waste areaOSR
ore area B OSR = 0.8
Hand Method the Basic Concepthow to find the final pit outline?
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Hand Method the Basic ConceptBasic steps in determining pit limits
the following basic steps involved in
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1. A slice is selected.
2. The contained value is compared with thecosts.
3. If the net value is positive, the pit can beexpan e . negat ve, t e p t contracts.
4. The final pit position is where the net valueof the slice is zero.
ISR = BESR
MINE 325
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Mine Planning
anua e oNet Value Calculation
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Cutoff Grades
The term cutoff grades refers to grades
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or w c e es na on o ma er a schanges
Cutoff grade is the grade at which themineral resource can no longer be
rocessed at a rofit.
The break even cutoff grade is definedas the grade for which the net value iszero
Manual MethodExample Copper Deposit
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Find the Min andMax grade in the
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Net Value Calculationto construct a net value grade curve
1. Compute the amount of saleable product
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.
2. Calculate the gross value (GV) for the ore ( $/ s.t)
3. Calculate the associated costs (TC) ($/s.t)
4. Calculate the net value per ton of ore
Net Value = GV TC
5. Calculate the net value per ton of ore for another
ore grade6. Construct a net value grade curve
Net Value Calculationto construct a net value grade curve
7. determine the breakeven cutoff grade
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8. Developing a stripping ratio gradecurve
9. Presenting the final curves
10.Finding the location of pit limits
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Manual MethodCreating a Net Value to Grade Curve
Net value must include all recoveries/losses
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Consider the following example:
Mill recovery = 80%
Mill concentrate grade = 20%
Smelting loss = 10 lbs/st of conc.
Refining loss = 5 lbs/st of copper
Calculations for 0.55% Cu Mining cost $1 / ton
Manual methodCreating a Net Value to Grade Curve
It will be assumed that
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s opes:
Left hand side = 50 degrees
Right hand side = 40 degrees
Minimum width of the pit bottom = 100 ft;
Material densities:
Ore = 165 lb/cu-ft Waste rock = 165 lb/cu-ft
Overburden =165 lb/cu-ft;
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Manual method Creating a Net
Value to Grade Curve
Copper is $1.00 / lb other recovered
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minerals (Au, Ag etc) total $1.77/ton ofore
Revenue =8.56lb * $1.00 + $1.77 = $10.33/ ton
Manual method Creating a Net
Value to Grade Curve
Costs:
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Mining $1.00/ton,
Milling $2.80/ton,
Administration (15% of m&m) $0.57
Total production costs $4.37
Amortization and depreciation costs / ton ore20% of production costs per ton ore = $0.87
Treatment, refining, selling costs = $2.59
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Manual method Creating a Net
Value to Grade Curve
Total costs of $7.83/ ton ore
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For 0.55% grade copper,
Net Value = Revenue Costs =
$10.33 - $7.83 = $2.50
Net Value Curve
5.00
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y = 1556.1x - 6.064
-1.00
0.00
1.00
2.00
3.00
.
0.00% 0.20% 0.40% 0.60% 0.80% 1.00%
NetValue($/tonofore)
-4.00
-3.00
-2.00
Cu Grade
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4.00
5.00
Net Value Curve
Based on total costs of$7.83/ton of ore
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y = 1556.1x -6.064
-2.00
-1.00
0.00
1.00
2.00
3.00
0.00% 0.20% 0.40% 0.60% 0.80% 1.00%NetValue($/tonofore)
Net Selling Price of $1.00/lbfor the copper
%CU Value
0.55 $2.50
0.37 -$0.31
Break EvenGrade
Knowin the cost of waste
-4.00
-3.00
Cu Grade
removal, the curve can beconverted to a stripping ratio
grade curve
4.00
5.00
Net Value Curve
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y = 1556.1x -6.064
-2.00
-1.00
0.00
1.00
2.00
3.00
0.00% 0.20% 0.40% 0.60% 0.80% 1.00%NetValue($/tonofore)
.
Stripping ratios added to thecurve.
BESR =
Net Value/ Stripping costMinimum Value
3:1
2:1
1:1
0.5:1
-4.00
-3.00
Cu Grade
Minimum value is the cost of moving a ton of waste
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Sectional Calculation
Variable Grades-Example
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Manual method
Stripping ratios and average grades are
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the lengths of the slope in ore and waste
A final pit slope angle is chosen based ongeotechnical considerations
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Sectional Calculation - G1
Variable Grades-Example Contd
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Sectional Calculation G1
Variable Grades-Example
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130 296( ) 1.79 :1;
238SR actual
( ) 6.2 :1;SR allowable
Conclusion: expand pit
BESRISR
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Sectional Calculation G1
Variable Grades-Example
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Sectional Calculation G2
Variable Grades-Example Contd
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Sectional Calculation Line G2
Variable Grades-Example
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130 385( ) 3.3:1156
SR actual
( ) 5.6 :1SR allowable
Conclusion: expand pit
Sectional Calculation Line G3
Variable Grades-Example Contd
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Sectional Calculation Line G3
Variable Grades-Example
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130 443
( ) 5.51:1104SR actual
( ) 3.9 :1SR allowable
Conclusion: contract pit
Sectional Calculation - Line G4
Variable Grades-Example Contd
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Sectional Calculation Line G4
Variable Grades-Example
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130 435( ) 5.43 :1104
SR actual
( ) 5.4 :1SR allowable
Conclusion: Final Pit
Sectional Calculations
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Pit is outlined oneach section.
Number of sectionsrequired will dependon the complexity andshape of the deposit.
Typically 8-20
sections are used.
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Transfer to Plans
Pit top and bottom aretransferred to a lan view and
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the surface intersectsconnected.
The ends must be doneseparately. At the pit ends astripping wedge is calculatedto complete the design.
Sections
Radial Section at Pit End
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Radial Section at Pit End
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Parallel section
radial section
Radial Section at Pit End
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Measured SR (for Radial Section)
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a
b
a = length in ore
b = length in waste
=slope angle
Plan View
a*cos b*cos
includes angleof the wedge
A
True SR (for Radial Section)
The angles cancel out in the equation
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rea = a cos
Area B = [((a+b)*cos )2 - (a*cos )2] * / 2
SR (true) = B/A
=[(a+b)2-a2] / a2 = (1 + b/a)2 1
SR (true) = [1 + SR(measured)] 2 - 1
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Pit Ends
Create a graph of Measured vs True SR
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easure e on e sec on
Find the true SR from the graph
Use the SR-Grade curve to adjust theposition of the line
True vs Measured SR Curve
Stripping Ratio
Measured True
True vs Measured
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0.00 0.00
0.25 0.56
0.50 1.25
0.75 2.06
1.00 3.00
1.25 4.06 4.00
6.00
8.00
10.00
12.00
14.00
.
TrueSR
1.50 5.25
2.00 8.00
2.50 11.25
3.00 15.00
0.00
2.00
0.00 1.00 2.00 3.00 4.00
Measured SR