Slope Stability-Examples Verification

Slopestabilityverificationmanual

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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



B.2ResultsMethod:Bishop FactorofSafetyNormalmodel 0.978Reversedmodel 0.994

Note:RefereeFactorofSafety=1.00[Giam]

MeanBishopFOS(18samples)=0.993MeanFOS(33samples)=0.991

FigureB.2Normalmodelsolution

FigureB.3Reversedmodelsolution



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



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



FigureC.4MPNormalmodelsolution

FigureC.5MPReversedmodelsolution



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



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



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



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



FigureE.4BISHOPNormalmodelsolution

FigureE.5BISHOPReversedmodelsolution



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



F.2ResultsMethod:SPENCER FactorofSafetyNormalmodel 1.198Reversedmodel 1.195

Note: RefereeFactorofSafety=1.241.27[Giam]

MeanNoncircularFOS(19samples)=1.293

FigureF.2SPENCERNormalmodelsolution

FigureF.3SPENCERReversedmodelsolution



G.Slopeverificationproblem#6Previousproblemwithpredefinedslipsurface

G.1ProblemDescriptionThisproblemisidenticaltoverificationproblem#5.Theonlydifferenceisthatanoncircularslipsurfaceofknowncoordinatesisanalysed.

TableG.1:MaterialProperties


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)



G.2ResultsMethod:SPENCER FactorofSafetyNormalmodel 1.314Reversedmodel 1.313

Note:RefereeFactorofSafety=1.34[Giam]MeanFOS(30samples)=1.29

FigureG.2SPENCERNormalmodelsolution

FigureG.3SPENCERReversedmodelsolution



H.Slopeverificationproblem#7Externalloading,porepressuredefinedbywatertable

H.1ProblemDescriptionThesoilparametersofthisproblem,theexternalloadingsandthepiezometricsurfaceareshowninTablesG.1,G.2andG.3respectively.Theeffectofthetensioncrackistobeignored.Thefactorofsafetyanditscorrespondingcriticalnoncircularfailuresurfaceisrequired.

TableH.1:MaterialProperties


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



FigureH.1Modeloftheproblem

H.2ResultsMethod:SPENCER FactorofSafetyNormalmodel 0.693Reversedmodel 0.693

Note:RefereeFactorofSafety=0.78[Giam]MeanNoncircularFOS(20samples)=0.808RefereeGLEFactorofSafety=0.6878[Slope2000]



FigureH.2SPENCERNormalmodelsolution

FigureH.3SPENCERReversedmodelsolution



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



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



FigureI.4GLENormalmodelsolution

FigureI.5GLEReversedmodelsolution



FigureI.6BISHOPNormalmodelsolution

FigureI.7BISHOPReversedmodelsolution



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



J.2ResultsMethod:SPENCER FactorofSafetyNormalmodel 0.907Reversedmodel

Note:RefereeFactorofSafety=1.04[Pilot]

FigureJ.2SPENCERNormalmodelsolution



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



k.2ResultsMethod:MP FactorofSafetyNormalmodel 1.92Reversedmodel

Figurek.2ResultswithDeepXcav

Slope Stability-Examples Verification

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