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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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    Rock Mass StrengthRock Mass Strength

    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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    Rock Mass StrengthRock Mass Strength

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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

    New Stress Field Rock Mass Strength

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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

    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?)

    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

    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 failedmaterial (38?)

    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 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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    Limit EquilibriumLimit Equilibrium

    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

    Limit EquilibriumLimit Equilibrium

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    Limit EquilibriumLimit Equilibrium

    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

    New Stress Field Rock Mass Strength

    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