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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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