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B.Slopeverificationproblem#1SimpleSlope
B.1ProblemDescriptionThefirstproblemisthesimplecaseofatotalstressanalysiswithoutconsideringporewaterpressures.ThesoilpropertiesarepresentedinTable1andthemodeloftheproblemisshowninFigure1.Thefactorofsafetyanditscorrespondingcriticalcircularfailureisrequired.
TableB.1:MaterialProperties
c(kN/m2) (deg.) (kN/m3)3.0 19.6 20.0
FigureB.1Modeloftheproblem
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B.2ResultsMethod:Bishop FactorofSafetyNormalmodel 0.978Reversedmodel 0.994
Note:RefereeFactorofSafety=1.00[Giam]
MeanBishopFOS(18samples)=0.993MeanFOS(33samples)=0.991
FigureB.2Normalmodelsolution
FigureB.3Reversedmodelsolution
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C.Slopeverificationproblem#2Tensioncrack
C.1ProblemDescriptionThisproblemhastheexactslopegeometryastheVerificationproblem#2,withtheadditionofatensioncrackzone.A suitable tension crack depth D is required and it can be estimated from the following equations [Craig (1997)]:
D=2*c/(),=(1sin)/(1+sin)
TableC.1:MaterialProperties
c(kN/m2) (deg.) (kN/m3)3.0 10.0 20.0
FigureC.1Modeloftheproblem
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C.2ResultsMethod:Bishop FactorofSafety Method:MP FactorofSafetyNormalmodel 1.618 Normalmodel 1.555Reversedmodel 1.614 Reversedmodel 1.536
Note:RefereeFactorofSafety=1.65[Giam]
FigureC.2BISHOPNormalmodelsolution
FigureC.3BISHOPReversedmodelsolution
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FigureC.4MPNormalmodelsolution
FigureC.5MPReversedmodelsolution
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D.Slopeverificationproblem#3Nonhomogeneous
D.1ProblemDescriptionThisproblemisa nonhomogeneous,threelayerslope.Thefactorofsafetyanditscorrespondingcriticalcircularfailuresurfaceisrequired.
TableD.1:MaterialProperties
c(kN/m2) (deg.) (kN/m3)Soil 1 0.0 38.0 19.5Soil 2 5.3 23.0 19.5 Soil 3 7.2 20.0 19.5
FigureD.1Modeloftheproblem
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D.2ResultsMethod:GLE FactorofSafetyNormalmodel 1.378Reversedmodel 1.384
Note: RefereeFactorofSafety=1.39[Giam] Mean Bishop FOS (16 samples) = 1.406
Mean FOS (31 samples) = 1.381
FigureD.2GLENormalmodelsolution
FigureD.3GLEReversedmodelsolution
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E.Slopeverificationproblem#4Nonhomogeneouswithseismicload
E.1ProblemDescriptionVerificationproblem#4isidenticaltoproblem#3,butwithahorizontalseismicallyinducedaccelerationof0.15gincludedintheanalysis.Thefactorofsafetyanditscorrespondingcriticalcircularfailuresurfaceisrequired.
TableE.1:MaterialProperties
c(kN/m2) (deg.) (kN/m3)Soil 1 0.0 38.0 19.5Soil 2 5.3 23.0 19.5 Soil 3 7.2 20.0 19.5
FigureE.1Modeloftheproblem
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E.2ResultsMethod:GLE FactorofSafety Method:BISHOP FactorofSafetyNormalmodel 0.985 Normalmodel 0.984Reversedmodel 0.993 Reversedmodel 1.015
Note: RefereeFactorofSafety=1.00[Giam] Mean Bishop FOS (15 samples) = 0.973
FigureE.2GLENormalmodelsolution
FigureE.3GLEReversedmodelsolution
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FigureE.4BISHOPNormalmodelsolution
FigureE.5BISHOPReversedmodelsolution
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F.Slopeverificationproblem#5Watertablemodeledwithweakseam
F.1ProblemDescriptionInthisproblem,thewatertableisassumedtocoincidewiththebaseoftheweaklayer.Theeffectofnegativeporewaterpressureabovethewatertableandtheeffectofthetensioncrackistobeignored.Thefactorofsafetyanditscorrespondingcriticalnoncircularfailuresurfaceisrequired.
TableF.1:MaterialProperties
c(kN/m2) (deg.) (kN/m3)Soil 1 28.5 20.0 18.84Soil 2 0.0 10.0 18.84
FigureF.1Modeloftheproblem
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F.2ResultsMethod:SPENCER FactorofSafetyNormalmodel 1.198Reversedmodel 1.195
Note: RefereeFactorofSafety=1.241.27[Giam]
MeanNoncircularFOS(19samples)=1.293
FigureF.2SPENCERNormalmodelsolution
FigureF.3SPENCERReversedmodelsolution
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G.Slopeverificationproblem#6Previousproblemwithpredefinedslipsurface
G.1ProblemDescriptionThisproblemisidenticaltoverificationproblem#5.Theonlydifferenceisthatanoncircularslipsurfaceofknowncoordinatesisanalysed.
TableG.1:MaterialProperties
c(kN/m2) (deg.) (kN/m3)Soil 1 28.5 20.0 18.84Soil 2 0.0 10.0 18.84
FigureG.1Modeloftheproblem
TableG.2:FailureSurfaceCoordinates
X(m) Y(m)41.85 27.7544.00 26.5063.50 27.0073.31 40.00
AxisofRotation:(53.3,45)
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G.2ResultsMethod:SPENCER FactorofSafetyNormalmodel 1.314Reversedmodel 1.313
Note:RefereeFactorofSafety=1.34[Giam]MeanFOS(30samples)=1.29
FigureG.2SPENCERNormalmodelsolution
FigureG.3SPENCERReversedmodelsolution
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H.Slopeverificationproblem#7Externalloading,porepressuredefinedbywatertable
H.1ProblemDescriptionThesoilparametersofthisproblem,theexternalloadingsandthepiezometricsurfaceareshowninTablesG.1,G.2andG.3respectively.Theeffectofthetensioncrackistobeignored.Thefactorofsafetyanditscorrespondingcriticalnoncircularfailuresurfaceisrequired.
TableH.1:MaterialProperties
c(kN/m2) (deg.) (kN/m3)Soil 1 28.5 20.0 18.84Soil 2 0.0 10.0 18.84
TableH.2:externalLoadings
X(m) Y(m) NormalStress(kN/m2)23.00 27.75 20.0043.00 27.75 20.0070.00 40.00 20.0080.00 40.00 40.00
TableH.3:DataforPiezometricsurface
Xc(m) Yc(m)20.00 27.7543.00 27.7549.00 29.860.00 34.0066.00 35.8074.00 37.6080.00 38.4084.00 38.40
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FigureH.1Modeloftheproblem
H.2ResultsMethod:SPENCER FactorofSafetyNormalmodel 0.693Reversedmodel 0.693
Note:RefereeFactorofSafety=0.78[Giam]MeanNoncircularFOS(20samples)=0.808RefereeGLEFactorofSafety=0.6878[Slope2000]
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FigureH.2SPENCERNormalmodelsolution
FigureH.3SPENCERReversedmodelsolution
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I.Slopeverificationproblem#8Porepressuredefinedbydigitizedtotalheadgrid
I.1ProblemDescription
Thisslopehasbeenexcavatedataslopeof1:2(=26.56)belowaninitiallyhorizontalgroundsurface.Thepositionofthecriticalslipsurfaceandthecorrespondingfactorofsafetyarerequiredforthelongtermcondition,i.e.afterthegroundwaterconditionshavestabilized.GridinterpolationisdonewithTINtriangulation.Thecriticalslipsurface(circular)andthecorrespondingfactorofsafetyarerequired.
TableI.1:MaterialProperties
c(kN/m2) (deg.) (kN/m3)
11.0 28.0 20.00
FigureI.1Modeloftheproblem
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I.2Results
Method:SPENCER FactorofSafety Method:GLEFactorofSafety Method:BISHOP
FactorofSafety
Normalmodel 1.468 Normalmodel 1.441 Normalmodel 1.495Reversedmodel 1.462 Reversedmodel 1.439 Reversedmodel 1.417
Note:RefereeFactorofSafety=1.53[Giam]MeanFOS(23samples)=1.464
FigureI.2SPENCERNormalmodelsolution
FigureI.3SPENCERReversedmodelsolution
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FigureI.4GLENormalmodelsolution
FigureI.5GLEReversedmodelsolution
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FigureI.6BISHOPNormalmodelsolution
FigureI.7BISHOPReversedmodelsolution
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J.Slopeverificationproblem#9Porepressuredefinedbyporepressuregrid
J.1ProblemDescriptionThematerialpropertiesofthisproblemaregiveninTableJ.1.Thepositionofthecriticalslipsurfaceandthecorrespondingfactorofsafetyarerequired.PorewaterpressureswerederivedfromthegivenequalporepressurelinesonFigure11.usingtheThinPlateSplineinterpolationmethod.
TableJ.1:MaterialProperties
c(kN/m2) (deg.) (kN/m3)Embankment 0.0 44.0 18.8
Clay foundation 2.0 28.0 16.68
FigureJ.1Modeloftheproblem
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J.2ResultsMethod:SPENCER FactorofSafetyNormalmodel 0.907Reversedmodel
Note:RefereeFactorofSafety=1.04[Pilot]
FigureJ.2SPENCERNormalmodelsolution
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k.Slopeverificationproblem#10VerificationexamplewithsoilnailsfromFHWAsoilnailingmanual
k.1ProblemDescriptionThematerialpropertiesofthisproblemaregiveninTablek.1.Thepositionofthecriticalslipsurfaceandthe corresponding factor of safety are required. A safety factor of 2 is used in the soil nail skinresistance.
Tablek.1:MaterialProperties
c(ksf) (deg.) (pcf) qSkinUlt(psi)Sand 0.1 32 120 50
AllsoilnailshaveFy=60ksiandanareaof1in2.Thehorizontalspacingisassumedat5ft.
Figurek.1Modeloftheproblem
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k.2ResultsMethod:MP FactorofSafetyNormalmodel 1.92Reversedmodel
Figurek.2ResultswithDeepXcav