geotech  openpit
TRANSCRIPT

7/30/2019 GEOTECH  OPENPIT
1/82
Introduction toIntroduction toGeomechanicsGeomechanics Applied toApplied to
Open PitOpen Pit
ByByWilliam GibsonWilliam Gibson

7/30/2019 GEOTECH  OPENPIT
2/82
Introduction.sort ofIntroduction.sort of
Area x L x Grade x price = $$$$

7/30/2019 GEOTECH  OPENPIT
3/82
Project has to beeconomical
At the same time
must be safe
Engineering design
must balance bothcomponents

7/30/2019 GEOTECH  OPENPIT
4/82
Nature of the InstabilityNature of the Instability
Any excavation produce aredistribution of stresses
New Stress Field Rock Mass Strength

7/30/2019 GEOTECH  OPENPIT
5/82
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

7/30/2019 GEOTECH  OPENPIT
6/82

7/30/2019 GEOTECH  OPENPIT
7/82

7/30/2019 GEOTECH  OPENPIT
8/82
Strength AssessmentStrength Assessment
Rock Mass StrengthRock Mass Strength
Joint StrengthJoint Strength

7/30/2019 GEOTECH  OPENPIT
9/82
Small and Large Scale FailuresSmall and Large Scale Failures

7/30/2019 GEOTECH  OPENPIT
10/82
Mode of FailureMode of Failure

7/30/2019 GEOTECH  OPENPIT
11/82
Scale Define the Rock StrengthScale Define the Rock Strength
and Mode of Failureand Mode of Failure

7/30/2019 GEOTECH  OPENPIT
12/82
Strength defined by Failure EnvelopeStrength defined by Failure Envelope

7/30/2019 GEOTECH  OPENPIT
13/82
Rock Mass StrengthRock Mass Strength
Concrete, Steel, Soil
Laboratory Tests
Material Strength
Rock Mass
Laboratory Tests
Rock Mass Strength
Rock Mass
Classification

7/30/2019 GEOTECH  OPENPIT
14/82
LinearLinear Failure EnvelopeFailure Envelope
sin1
sin1
sin1
cos231
++
=
c
tannc +=

7/30/2019 GEOTECH  OPENPIT
15/82
Non Linear Failure EnvelopeNon Linear Failure Envelope
a
c
bc sm
++=
3
31

7/30/2019 GEOTECH  OPENPIT
16/82
RQD Rock Quality DesignationRQD Rock Quality Designation

7/30/2019 GEOTECH  OPENPIT
17/82
Q systemQ system

7/30/2019 GEOTECH  OPENPIT
18/82
Rock Mass Classification RMRRock Mass Classification RMR

7/30/2019 GEOTECH  OPENPIT
19/82
Non Linear Failure EnvelopeNon Linear Failure Envelope
a
c
bc sm
++=
3
31

7/30/2019 GEOTECH  OPENPIT
20/82
Rock Mass StrengthRock Mass Strength

7/30/2019 GEOTECH  OPENPIT
21/82
Alternative Method to Assess RockAlternative Method to Assess Rock
Mass StrengthMass Strength

7/30/2019 GEOTECH  OPENPIT
22/82
J oint StrengthJ oint Strength

7/30/2019 GEOTECH  OPENPIT
23/82
Half of the J ob doneHalf of the J ob done
Any excavation produce a
redistribution of stresses
New Stress Field Rock Mass Strength

7/30/2019 GEOTECH  OPENPIT
24/82
Stress AnalysisStress Analysis
Assessment of the StabilityAssessment of the Stability
(Equilibrium)(Equilibrium)

7/30/2019 GEOTECH  OPENPIT
25/82
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

7/30/2019 GEOTECH  OPENPIT
26/82
Mode of FailureMode of Failure
Pl F ilPl F il

7/30/2019 GEOTECH  OPENPIT
27/82
Planar FailurePlanar Failure
l ilPl F il

7/30/2019 GEOTECH  OPENPIT
28/82
Planar FailurePlanar Failure
EquilibriumEquilibrium

7/30/2019 GEOTECH  OPENPIT
29/82
EquilibriumEquilibrium

7/30/2019 GEOTECH  OPENPIT
30/82
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

7/30/2019 GEOTECH  OPENPIT
31/82
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

7/30/2019 GEOTECH  OPENPIT
32/82
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

7/30/2019 GEOTECH  OPENPIT
33/82
Wedge Stability AnalysisWedge Stability Analysis

7/30/2019 GEOTECH  OPENPIT
34/82

7/30/2019 GEOTECH  OPENPIT
35/82
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

7/30/2019 GEOTECH  OPENPIT
36/82

7/30/2019 GEOTECH  OPENPIT
37/82
Results for Bench Analysis and its useResults for Bench Analysis and its use

7/30/2019 GEOTECH  OPENPIT
38/82
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

7/30/2019 GEOTECH  OPENPIT
39/82
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

7/30/2019 GEOTECH  OPENPIT
40/82
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

7/30/2019 GEOTECH  OPENPIT
41/82
ExampleExample
E lE l

7/30/2019 GEOTECH  OPENPIT
42/82
ExampleExample
SBW i d t t i illSBW i d t t i ill

7/30/2019 GEOTECH  OPENPIT
43/82
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?)

7/30/2019 GEOTECH  OPENPIT
44/82
Break????Break????
M d f F ilM d f F il < Ki d f A l i> Ki d f A l i

7/30/2019 GEOTECH  OPENPIT
45/82
Mode of Failure Kind of Analysis
Limit EquilibriumLimit Equilibrium

7/30/2019 GEOTECH  OPENPIT
46/82
Limit EquilibriumLimit Equilibrium
Limit EquilibriumLimit Equilibrium

7/30/2019 GEOTECH  OPENPIT
47/82
qq
Problem: more unknowns thanProblem: more unknowns than

7/30/2019 GEOTECH  OPENPIT
48/82
equationsequations
Different Methods based onDifferent Methods based on

7/30/2019 GEOTECH  OPENPIT
49/82
Different SimplificationsDifferent Simplifications
Limit EquilibriumLimit Equilibrium

7/30/2019 GEOTECH  OPENPIT
50/82
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

7/30/2019 GEOTECH  OPENPIT
51/82

7/30/2019 GEOTECH  OPENPIT
52/82

7/30/2019 GEOTECH  OPENPIT
53/82
ExampleExample

7/30/2019 GEOTECH  OPENPIT
54/82
ExampleExample
Numerical MethodNumerical Method

7/30/2019 GEOTECH  OPENPIT
55/82
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

7/30/2019 GEOTECH  OPENPIT
56/82
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

7/30/2019 GEOTECH  OPENPIT
57/82
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

7/30/2019 GEOTECH  OPENPIT
58/82
Strain and Stresses are constantStrain and Stresses are constant
Triangular Elements 6 nodesTriangular Elements 6 nodes

7/30/2019 GEOTECH  OPENPIT
59/82
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

7/30/2019 GEOTECH  OPENPIT
60/82
Elements 6 or 8 nodes are quadraticq
Strain and Stresses are linearStrain and Stresses are linear
Finite Difference MethodFinite Difference Method

7/30/2019 GEOTECH  OPENPIT
61/82
FLAC ProgramFLAC Program
u&
v&
Calculation CycleCalculation Cycle

7/30/2019 GEOTECH  OPENPIT
62/82
Calculation CycleCalculation Cycle
Typical FLAC ModelTypical FLAC Model

7/30/2019 GEOTECH  OPENPIT
63/82
Typical FLAC Modelyp

7/30/2019 GEOTECH  OPENPIT
64/82
Factor of Safety using FiniteFactor of Safety using Finite

7/30/2019 GEOTECH  OPENPIT
65/82
Difference or Finite ElementsDifference or Finite Elements
ff ccFoS ==
tantan
f: friction at failure
cf: cohesion at failure
Slope at FailureSlope at Failure

7/30/2019 GEOTECH  OPENPIT
66/82
Discontinuous MethodsDiscontinuous Methods

7/30/2019 GEOTECH  OPENPIT
67/82
Discontinuous MethodsDiscontinuous Methods

7/30/2019 GEOTECH  OPENPIT
68/82

7/30/2019 GEOTECH  OPENPIT
69/82
Discontinuous MethodDiscontinuous Method

7/30/2019 GEOTECH  OPENPIT
70/82
Numerical MethodsNumerical Methods

7/30/2019 GEOTECH  OPENPIT
71/82
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

7/30/2019 GEOTECH  OPENPIT
72/82
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

7/30/2019 GEOTECH  OPENPIT
73/82
Combining all the analysisCombining all the analysis
Rock Fall AnalysisRock Fall Analysis

7/30/2019 GEOTECH  OPENPIT
74/82
TypicalTypical FoSFoS Used in MiningUsed in Mining

7/30/2019 GEOTECH  OPENPIT
75/82
IndustryIndustry
Probabilistic AnalysisProbabilistic Analysis

7/30/2019 GEOTECH  OPENPIT
76/82

7/30/2019 GEOTECH  OPENPIT
77/82
Reliability IndexReliability Index

7/30/2019 GEOTECH  OPENPIT
78/82
Probabilistic AnalysisProbabilistic Analysis

7/30/2019 GEOTECH  OPENPIT
79/82
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

7/30/2019 GEOTECH  OPENPIT
80/82
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

7/30/2019 GEOTECH  OPENPIT
81/82
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

7/30/2019 GEOTECH  OPENPIT
82/82
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