half pit limits

University of AlbertaMINE 325 Mine Planning and Design

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MINE 325Mine Planning

L 15 Pit Li it ILec15 Pit Limits IManual Method

Ultimate or Final Pit Limits (1/5)

Size and shape of mineable reserves and associated waste materials to be excavated

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associated waste materials to be excavated 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) Lec15-3



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Final Pit Limit method (5/5)

Manual methodC t th d (2D 3D)

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Computer methods (2D, 3D) 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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Stripping Ratio

Stripping Ratios (1/6) Overall stripping ratio is the ratio of the total

tonnage of waste divided by the total tonnage of

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tonnage of waste divided by the total tonnage of ore contained in the final pit (SRo)

Incremental stripping ratio (or instantaneous stripping ratio)is the ratio of waste tonnage to ore tonnage as a result of expanding the pit by a unit volume (ISR)

Break-even stripping ratio is the ratio of waste tonnage to ore tonnage where the cost of the waste removal exactly equals the value of the mineral (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 on grades, costs and revenues

Stripping ratio (3/6)The volume of the contained ore is expressed by

2V h

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2V r hwhere r is the ore radius h 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 tancH hR r

213tip

V r h Truncated tip

2 21 13 3m tip c

V V V R H r h

Fully circumscribed cone

213 c

V R HMined volume (ore + waste)

Stripping ratio (5/6) Chapter 4 pages 45 to 49

1 1Mined volume (ore + waste)

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2 21 13 3m tip c

V V V R H r h

2w mV V r h

Volume of waste

( )Waste volumeSR ( )

SROre volume

2

2( )w m

o

V V r hSR overallV r h


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Stripping ratio (6/6)Chapter 4 pages 45 to 49

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Final Pit Limitsa t tsManual Method


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Manual Method Basic Concepts - Sectional Calculation

waste$NV = $GV $TC

Net Value = Gross Value Total Cost

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the density of ore and waste is the

0.6% Cu

ISR = 2:1

1 ton of Ore (0.6% Cu)

3.2 tons of waste

$NV = $GV - $TC

BESR = 3.2:1 the density of ore and waste is the same, the ISR is the ratio of the length in ore to the length in waste. $NV = Cost of Stripping

Manual Method Basic Concepts - Sectional Calculation

waste

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0.6% Cu

ISR = 2:1 BESR = 3.2:1

Actual Stripping Ratios

Allowable Stripping Ratios

Pit Limit is adjusted until: ISR = BESR


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Manual Method Basic Concepts - Both Walls in Waste

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Usually the width of cross section is assigned to each side ( f i fl f ti )(area of influence of section).

Shape is moved vertically and horizontally on section until both sides fit the SR-Grade Curve

Manual Method Sectional Calculation -Variable Grades

Each block or polygon has a grade associated with it

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grade associated with it.

Multiple layers of overburden type material can complicate

Calculation of average grade in the ore is a length weighted average grade.

Each side is done independently.

can complicate the sectional calculation


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Hand Method The 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 1

The volumes are:Strip 1:

31 7.5wV u

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31 5.0oV u

The instantaneous stripping ratio (ISR) is defined as: 1wl

ol

VISRV

1 1.5ISR

Assuming that the net value from selling one unit volume of ore (that money remaining after all expenses have been paid) is $1.90

cost for mining and disposing of the waste is $1/unit volume, the net value for strip I is

1 5.0 x $1.90 - 7.5 x $1 = $2.00NV


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V u238 4= .

Strip 2:

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V uV uISRNV

w

o

2

23

2

2

8 4

5 01 68

=

=

=

.

..

5.0 x $1.90 - 8.4 x $1 = $1..10


Strip 3:

V u339 45= .

For strip 3, the net value is just about zero This pit position is termed

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V uV uISRNV

w

o

3

33

3

3

9 45

5 01 89

=

=

=

.

..

5.0 x $1.90 - 9.45 x $1 = $$0.05 0

zero. This pit position is termed 'breakeven' since the costs involved in mining the strip just equal the revenues.

It is the location of the final pit wall.


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V u310 5=Strip 4:

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V uV uISRNV

w

o

4

43

4

4

10 5

5 02 1

=

=

=

=

.

..

5.0 x $1.90 - 10.5 x $1 = --$1.0

Hand Method Example final pitISR = BESR

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Hand Method the Basic ConceptThe overall stripping ratio (OSR) for this section is calculated as

t A

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waste area AOSRore 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 indetermining pit limits remain the same:

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determining pit limits remain the same:1. A slice is selected.2. The contained value is compared with the

costs.3. If the net value is positive, the pit can be

d d If ti th it t texpanded. If negative, the pit contracts.4. The final pit position is where the net value

of the slice is zero.ISR = BESR

MINE 325

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Mine Planning

M l M th dManual Method Net Value Calculation


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Cutoff Grades

The term cutoff grades refers to grades f hi h th d ti ti f t i l

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for which the destination of materials changes

Cutoff grade is the grade at which the mineral resource can no longer be processed at a profit.processed at a profit.

The break even cutoff grade is defined as the grade for which the net value is zero

Manual Method Example Copper Deposit

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Find the Min and Max grade in the sectionsection


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Net Value Calculationto construct a net value grade curve

1. Compute the amount of saleable product copper (lb/s t of ore)

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copper (lb/s.t of ore)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 TC5. 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 grade curve

9. Presenting the final curves10.Finding the location of pit limits


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Manual Method Creating a Net Value to Grade Curve

Net value must include all recoveries/losses due to processing

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due to processing 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 thatPit l

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Pit slopes: 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 Net Value to Grade Curve

Mine Mill Concentrator Smelter Refinery

Mill recovery = 80%loss = 5 lbs/st ofBlister copper

loss = 10 lbs/stof concen

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0.55%

blister copperconcentrate copperOre1 st = 2000lb weight

grade

lbs cu 11.0

2000lb 20%

8.8 8.58 8.56

2000lb

45.45 tonsCopper price $1 / lb

233.1 tonsCopper price $1 / lbBy product $1.77 / st oreMining cost $1 / ton

Manual Method Creating a Net Value to Grade Curve Mill recovered Quantity of Metal = Contained copper * recovery

0.55% Cu 11 lb/st * recovery = 8.8 lb/st

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y Mill produces 20% concentrate

Conc. Ratio = 400 lb/st conc / 8.8 lb ore = 45.45 tons of ore Means that ~45 tons of ore produces 1 ton conc.

Smelter loses 10 lb/st conc = 0.22 lb/oreSmelter Recovered copper = 8.8 0.22 = 8.58 lb

Refinery recovery = 2000 lb copper/ 8.58 lb copper/st ore= 233.1 tons ore

Refining losses are 5lb/ton copper therefore loss of 0.02 lb of copper

Refinery Recovered copper = 8.56 lb Cu / ton of ore


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Manual method Creating a Net Value to Grade Curve

Copper is $1.00 / lb other recovered $

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ppminerals (Au, Ag etc) total $1.77/ton of ore

Revenue = 8.56lb * $1.00 + $1.77 = $10.33/ ton


Costs:Production costs:

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Production costs:Mining $1.00/ton, Milling $2.80/ton, Administration (15% of m&m) $0.57Total production costs $4.37

Amortization and depreciation costs / ton ore 20% of production costs per ton ore = $0.87Treatment, refining, selling costs = $2.59


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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

4 00

5.00

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y = 1556.1x - 6.064

-1.00

0.00

1.00

2.00

3.00

4.00

0.00% 0.20% 0.40% 0.60% 0.80% 1.00%

Net

Val

ue ($

/ to

n of

ore

)

-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%

Net

Val

ue ($

/ to

n of

ore

)

Net Selling Price of $1.00/lb for the copper

%CU Value

0.55 $2.50

0.37 -$0.31

Break Even Grade

Knowing the cost of waste

-4.00

-3.00

Cu Grade

gremoval, the curve can be

converted to a stripping ratio grade curve

4.00

5.00

Net Value Curve

Cost of stripping is $1 00/ton

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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%

Net

Val

ue ($

/ to

n of

ore

)

Cost of stripping is $1.00/ton

Stripping ratios added to the curve.

BESR =

Net Value/ Stripping costMinimum Value

3:1

2:1

1:10.5:1

-4.00

-3.00

Cu Grade

Minimum value is the cost of moving a ton of waste


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Sectional CalculationVariable Grades-Example

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Manual method

Stripping ratios and average grades are evaluated usually by direct measurement of

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evaluated usually by direct measurement of the lengths of the slope in ore and waste

A final pit slope angle is chosen based on geotechnical considerations


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Sectional Calculation - G1 Variable Grades-Example Contd

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Sectional Calculation G1Variable Grades-Example

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130 296( ) 1.79 :1;238

SR actual ( ) 6.2 :1;SR allowable Conclusion: expand pit

BESRISR


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Sectional Calculation G1Variable Grades-Example

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Sectional Calculation G2 Variable Grades-Example Contd

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Sectional Calculation Line G2Variable Grades-Example

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130 385( ) 3.3 :1156

SR actual ( ) 5.6 :1SR allowable

Conclusion: expand pit

Sectional Calculation Line G3Variable Grades-Example Contd

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130 443( ) 5.51:1104


Conclusion: contract pit

Sectional Calculation - Line G4Variable Grades-Example Contd

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130 435( ) 5.43 :1104


Conclusion: Final Pit

Sectional CalculationsLec15-54

Pit is outlined on each section.

Number of sections required will depend on the complexity and shape of the deposit.

Typically 8-20 sections are used.


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Transfer to Plans

Pit top and bottom are transferred to a plan view and

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pthe surface intersects connected.

The ends must be done separately. At the pit ends a stripping wedge is calculated to complete the design.

Sections

Radial Section at Pit EndLec15-56


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Parallel section

radial section



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Measured SR (for Radial Section)Lec15-59

a

b

a = length in ore

b = length in waste

=slope angle

Plan View

Ba*cos b*cos

includes angle of the wedge

B

A

True SR (for Radial Section)

The angles cancel out in the equationArea A = (a*cos)2 * / 2

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Area A = (a*cos)2 * / 2 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 SRM th SR th ti

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Measure the SR on the section Find the true SR from the graph Use the SR-Grade curve to adjust the

position of the line

True vs Measured SR CurveStripping Ratio

Measured True16 00

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

16.00

True

SR

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

half pit limits

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