Pit Limits

8/10/2019 Pit Limits

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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)


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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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


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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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



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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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


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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 Line G2


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130 385( ) 3.3:1156

SR actual

( ) 5.6 :1SR allowable

Conclusion: expand pit



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130 443

( ) 5.51:1104SR actual


Conclusion: contract pit

Sectional Calculation - Line G4


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130 435( ) 5.43 :1104

SR actual


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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Parallel section

radial section


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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

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Pit Limits