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7/30/2019 GEOTECH - OPENPIT

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Introduction toIntroduction toGeomechanicsGeomechanics Applied toApplied to

Open PitOpen Pit

ByByWilliam GibsonWilliam Gibson


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Introduction.sort ofIntroduction.sort of

Area x L x Grade x price = $$$$


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Project has to beeconomical

At the same time

must be safe

Engineering design

must balance bothcomponents


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Nature of the InstabilityNature of the Instability

Any excavation produce aredistribution of stresses

New Stress Field Rock Mass Strength


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Geometric Components to DeliverGeometric Components to Deliver

Bench

Stack

Overall

Slope

Height

Pit Floor

Bench face

angle SBW

Bench

height

Geotechnical

berm or ramp

BSA

IRAPit Floor


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Strength AssessmentStrength Assessment

Rock Mass StrengthRock Mass Strength

Joint StrengthJoint Strength


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Small and Large Scale FailuresSmall and Large Scale Failures


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Mode of FailureMode of Failure


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Scale Define the Rock StrengthScale Define the Rock Strength

and Mode of Failureand Mode of Failure


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Strength defined by Failure EnvelopeStrength defined by Failure Envelope


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Concrete, Steel, Soil

Laboratory Tests

Material Strength

Rock Mass

Laboratory Tests

Rock Mass Strength

Rock Mass

Classification


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LinearLinear Failure EnvelopeFailure Envelope

sin1

sin1

sin1

cos231

++

=

c

tannc +=


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Non Linear Failure EnvelopeNon Linear Failure Envelope

a

c

bc sm

++=

3

31


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RQD Rock Quality DesignationRQD Rock Quality Designation


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Q systemQ system


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Rock Mass Classification RMRRock Mass Classification RMR


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Non Linear Failure EnvelopeNon Linear Failure Envelope

a

c

bc sm

++=

3

31


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Alternative Method to Assess RockAlternative Method to Assess Rock

Mass StrengthMass Strength


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J oint StrengthJ oint Strength


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Half of the J ob doneHalf of the J ob done

Any excavation produce a

redistribution of stresses



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Stress AnalysisStress Analysis

Assessment of the StabilityAssessment of the Stability

(Equilibrium)(Equilibrium)


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Numerical ModelsNumerical Models

The models are function of the modeThe models are function of the mode

of failure analyzed (difficult to have aof failure analyzed (difficult to have amodel that considers all the potentialmodel that considers all the potential

mode of failures)mode of failures)

Failure through joints are differentFailure through joints are different

than failure through rock mass. Inthan failure through rock mass. In

the first one the geometry of thethe first one the geometry of thesurface failure is predefinedsurface failure is predefined


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Mode of FailureMode of Failure

Pl F ilPl F il


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Planar FailurePlanar Failure

l ilPl F il


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Planar FailurePlanar Failure

EquilibriumEquilibrium


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EquilibriumEquilibrium


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Concept ofConcept ofFoSFoS

F>D => Wedge in Equilibrium

Factor of Safety FoS=F/D

Eff t f W t T i C kEffect of Water on Tension Crack


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Effect of Water on Tension CrackEffect of Water on Tension Crack

Change Resistance and Drive Force due to Water

800

900

1000

1100

1200

1300

1400

0 0.2 0.4 0.6 0.8 1

Ratio zw/z

Force

[kN]

0.60

0.70

0.80

0.90

1.00

1.10

1.20

FactorofSafety

F

D

FS


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Wedge AnalysisWedge Analysis

Similar to planar failureSimilar to planar failure

Wedge considered as a rigid blockWedge considered as a rigid block Resistance forces controlled by jointResistance forces controlled by joint

strengthstrength

Actual orientation of the joints isActual orientation of the joints isincluded in the analysisincluded in the analysis

Actual location is not considered atActual location is not considered atbench scale (maximum possiblebench scale (maximum possiblewedge)wedge)

Wedge Stability AnalysisWedge Stability Analysis


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Wedge Stability AnalysisWedge Stability Analysis


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Wedge AnalysisWedge Analysis

In general applied to small scaleIn general applied to small scale

Some times applied to large scaleSome times applied to large scalewhere faults define a wedgewhere faults define a wedge

In mining the main objective isIn mining the main objective is

define the spill berm width (SBW) fordefine the spill berm width (SBW) forfalling rocks and small failuresfalling rocks and small failures

In civil slope design the mainIn civil slope design the mainobjective is identify the unstableobjective is identify the unstablewedge and support itwedge and support it


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Results for Bench Analysis and its useResults for Bench Analysis and its use


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Results for Bench Analysis and its useResults for Bench Analysis and its use

in Open pit Designin Open pit Design In open pit mines some failures atIn open pit mines some failures at

bench scale are acceptablebench scale are acceptable The wedge analysis is used toThe wedge analysis is used to

quantify the spillagequantify the spillage


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Volumes of failed material

Given depthof failure (B)

More spread outMoreconcentrated

Larger length = larger

failure volume

Smaller length =

Smaller failure

volume

Length of wedge (L)

Volumes of failed material

Given depthof failure (B)

More spread outMoreconcentrated

Larger length = larger

failure volume

Smaller length =

Smaller failure

volume

Length of wedge (L)

SBW i d i ill


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SBW required to contain spillageSBW required to contain spillage

Spill Berm

Spill Berm

Symmetrical conicalexpression of volume

of failed material

Radius (R)

3

tantan

tantan6

=KV

R

R

Spill Berm

Spill Berm

Pyramidal (wedge) expression of volumeof failed material

L

tantan

tantan6

=L

KVR

K = 1.5 swelling factor

V = volume of failed material (m3)

L = length of wedge (m)

a = bench face angle (?)

= angle of repose of failed

material (38?)

Spill Berm

Spill Berm


of failed material

Radius (R)

3

tantan

tantan6

=KV

R

R

Spill Berm

Spill Berm


L

tantan

tantan6

=L

KVR





= angle of repose of failed

material (38?)

E lE l


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ExampleExample

E lE l


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ExampleExample

SBW i d t t i illSBW i d t t i ill


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SBW required to contain spillageSBW required to contain spillage

Spill Berm

Spill Berm


of failed material

Radius (R)

3

tantan

tantan6

=KV

R

R

Spill Berm

Spill Berm


L

tantan

tantan6

=L

KVR





= angle of repose of failedmaterial (38?)

Spill Berm

Spill Berm


of failed material

Radius (R)

3

tantan

tantan6

=KV

R

R

Spill Berm

Spill Berm


L

tantan

tantan6

=L

KVR





= angle of repose of failedmaterial (38?)


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Break????Break????

M d f F ilM d f F il < Ki d f A l i> Ki d f A l i


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Mode of Failure Kind of Analysis

Limit EquilibriumLimit Equilibrium


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qq

Problem: more unknowns thanProblem: more unknowns than


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equationsequations

Different Methods based onDifferent Methods based on


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Different SimplificationsDifferent Simplifications



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The method calculates theThe method calculates the FoSFoS for afor a

predefined surfacepredefined surface In general we want the lowestIn general we want the lowest FoSFoS

1000s of trial must be tested to find1000s of trial must be tested to findlowestlowest FoSFoS

In rock mechanics only for largeIn rock mechanics only for large

scale failure can be appliedscale failure can be applied

HoekHoek ChartChart


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ExampleExample


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ExampleExample

Numerical MethodNumerical Method


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Numerical MethodNumerical Method

Numerical Models Numerical Method

Finite ElementsFinite Elements

Finite DifferencesFinite Differences Boundary ElementsBoundary Elements

Discrete ElementsDiscrete Elements Discontinuous Deformation AnalysisDiscontinuous Deformation Analysis

Element 3 nodes,Element 3 nodes,

stresses are constant in the elementstresses are constant in the element


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stresses are constant in the elementstresses are constant in the element0.00000

0.45000

0.90000

1.35000

1.80000

2.25000

2.70000

3.15000

3.60000

15 30 45 60 75 90 105 120 135 150 165 180 195 210 225 240 255

Finite ElementsFinite Elements


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u

v

U=H(x,y)Ui

u

v

1 2

3

Elements 3 or 4 nodes are linearElements 3 or 4 nodes are linear


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Strain and Stresses are constantStrain and Stresses are constant

Triangular Elements 6 nodesTriangular Elements 6 nodes


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-0.02400

-0.01800

-0.01200

-0.00600

0.00000

0.00600

0.01200

0.01800

0.02400

30 45 60 75 90 105 120 135 150 165 180 195 210 225 240 255

Elements 6 or 8 nodes are quadraticElements 6 or 8 nodes are quadratic


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Elements 6 or 8 nodes are quadraticq

Strain and Stresses are linearStrain and Stresses are linear

Finite Difference MethodFinite Difference Method


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FLAC ProgramFLAC Program

u&

v&

Calculation CycleCalculation Cycle


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Calculation CycleCalculation Cycle

Typical FLAC ModelTypical FLAC Model


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Typical FLAC Modelyp


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Factor of Safety using FiniteFactor of Safety using Finite


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Difference or Finite ElementsDifference or Finite Elements

ff ccFoS ==

tantan

f: friction at failure

cf: cohesion at failure

Slope at FailureSlope at Failure


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Discontinuous MethodsDiscontinuous Methods


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Discontinuous MethodsDiscontinuous Methods


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Discontinuous MethodDiscontinuous Method


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Numerical MethodsNumerical Methods


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FoSFoS is calculated with out assuming ais calculated with out assuming a

surface failuresurface failure

More realistic approach to the stressMore realistic approach to the stress

distribution compared with limitdistribution compared with limit

equilibrium methodequilibrium method

Features like faults can be includedFeatures like faults can be included

J ob doneJ ob done


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Any excavation produce a

redistribution of stresses


Sort of, How do we compare stresses andstrength?

Is Fos enough?

ExampleExample


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Combining all the analysisCombining all the analysis

Rock Fall AnalysisRock Fall Analysis


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TypicalTypical FoSFoS Used in MiningUsed in Mining


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IndustryIndustry

Probabilistic AnalysisProbabilistic Analysis


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Reliability IndexReliability Index


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Probabilistic AnalysisProbabilistic Analysis


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Works better than deterministic,Works better than deterministic,

better feeling about the chances tobetter feeling about the chances to

face a failureface a failure

More difficult to calculate, veryMore difficult to calculate, very

demanding in computer power.demanding in computer power.

SummarySummary


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Think the mode of failure of a slopeThink the mode of failure of a slope

is a engineer responsibility not ais a engineer responsibility not a

computer program responsibilitycomputer program responsibility

Choose the right tool for the analysisChoose the right tool for the analysis

Because in mining the slopes areBecause in mining the slopes are

temporary and the access is limitedtemporary and the access is limited

thethe FoSFoS used in design are low.used in design are low.Monitoring is mandatoryMonitoring is mandatory

SummarySummary


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The most common methods toThe most common methods to

improve stability in mining isimprove stability in mining is

dewatering and unloadingdewatering and unloading

Support may be used in some specialSupport may be used in some special

casescases

ReferencesReferences


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HoekHoek, E. and J.W. Bray Rock Slope, E. and J.W. Bray Rock Slope

Engineering, Institution of MiningEngineering, Institution of Mining

and Metallurgy.and Metallurgy.

http://www.rocscience.com/hoek/Prahttp://www.rocscience.com/hoek/Pra

cticalRockEngineering.aspcticalRockEngineering.asp

Contact:Contact: [email protected]@srk.com.au
http://www.rocscience.com/hoek/PracticalRockEngineering.asphttp://www.rocscience.com/hoek/PracticalRockEngineering.asphttp://www.rocscience.com/hoek/PracticalRockEngineering.asphttp://www.rocscience.com/hoek/PracticalRockEngineering.asphttp://www.rocscience.com/hoek/PracticalRockEngineering.asphttp://www.rocscience.com/hoek/PracticalRockEngineering.asp