bearing capacity - ramcadds.in · 2 bearing capacity - comparison of results from m and dsn 1997-1...

BEARING CAPACITYCOMPARISON OF RESULTS FROM FEM AND DS/EN 1997-1 DK NA 2013Supplementary report to Banedanmark Report 14-07585

Bearing capacity - Comparison of results from FEM and DS/EN 1997-1 DK NA 20132

Ramboll - Consulting Engineers

Hannemanns Allé 53 2300 Copenhagen S Denmark +45 51 61 10 00 [email protected]

Optum Computational Engineering

Thorsgade 59 4. tv 2200 Copemhagen N Denmark +45 32 10 55 32 [email protected]

Supplementary report to Banedanmark Report 14-07585 3

TABLE OF CONTENTS

1 Introduction and summary 4

1.1 Introduction 4

1.2 Summary 4

2 Scope of work 5

3 Results 6

3.1 Undrained Analyses, plane strain 6

3.2 Undrained Analyses, axial symmetry 6

3.3 Drained Analyses, plane strain, q-case, centric loading 6

3.4 Drained Analyses, plane strain, q-case, eccentric loading 7

3.5 Drained Analyses, axial symmetry, q-case 7

3.6 Drained Analyses, plane strain, γ-case, centric loading 8

3.7 Drained Analyses, plane strain, γ-case, eccentric loading 8

3.8 Drained Analyses, axial symmetry, γ-case 9

4 Bearing capacity of surface strip footing located on top of slope – Mohr-Coulomb vs GSK 10

4.1 Geometry of slope and soil parameters 10

4.2 Mohr Coulomb model: 10

4.3 GSK model 11

4.4 NGI triaxial tests 12

4.5 Parameters of the GSK model 13

4.6 Results from slope analysis 15

5 References 15


1 INTRODUCTION AND SUMMARY1.1 Introduction

TheconsultingengineersCowiandnmGeohavebeencontractedbyBanedanmarktoestimatethegeotechnicalbearingcapacityoffoundationsusingtheapproachrequestedinEurocodeDS/EN1997-1DKNA:2014andtocom-parewithresultsobtainedusingthefiniteelementmethod.ThisinvestigationhasresultedinReport14–07585entitled“BearingCapacity,ComparisonofResultsfromFEMandDS/EN1997-1DKNA2013”.Inthefollowingthisreport is referred to as Report 14.

ThereportathandshouldbeseenasasupplementaryworktoReport14focusingexclusivelyonbearingcapacityin the 2D and axisymmetric cases.

ThereporthasbeenpreparedbyRuneChristensen,RambollandSvenKrabbenhøft,Optumce.

1.2 Summary

ThereportpresentstheresultsfromanalysesofthebearingcapacityoffootingsinplanestrainandaxisymmetricconditionsusingthefiniteelementcodesPlaxisandOptumG2.Alsoacomparisonbetweentheresultsproducedbythetwocodeshasbeenmade.

Undrained conditions:

InthecaseofundrainedconditionsPlaxisleadstoresultsthatdeviateabout6%atthemostfromthetheo-reticalvalues,whileOptumG2producesresultswithanaccuracyof±1%.

Drained conditions, the bearing capacity factor Nq :

Bothprogramsproduceresultswhichintheassociatedcaseareveryclosetothetheoreticalvalues.Inthenon-associatedcasetheydeviate fromeachotherbyapproximately6%, withPlaxisproducingthe largervalues.

Drained conditions, the bearing capacity factor Nƴ :

ForcentricloadingPlaxisdeviatesfromthetheoreticalvaluesbyupto6%atafrictionangleof35°.ForlargerfrictionanglesnumericalproblemsoccurwithPlaxis.TheOptumvaluesdeviatefromthetheoreticalvaluesuptoamaximumof2.6%atafrictionangleof50°.Inthenon-associatedcasetheytwoproduceresultswhichdeviatefromeachotherby3.3%.

Foreccentricloadinguptoaneccentricityratioe/Bof0.25,thePlaxisresultsareupto6%greaterthanthetheoreticalvalues.Fore/B>0.30,numericalproblemsoccurwithPlaxis.Forallvaluesofe/Bupto0.45Op-tumproducesresultswhichdeviatebylessthan1.6%fromthetheoreticalvalues.

Footing on slope, drained conditions, Mohr-Coulomb and GSK model :

Inthecaseofacentricallyloadedsurfacestripfootinglocatedonthetopofaslopeinsandofrelativedensity0.60thebearingcapacitiesproducedbyPlaxisandOptumassumingtheMohr-Coulombmodeldeviatefromeachotherbyapproximately3.6to9.5%,thePlaxisvaluesbeingthegreater.TheresultsproducedbyOp-tum’sGSKmodelexceedstheMohr-Coulombvaluesbyupto74%,reflectingthefactthatthefrictionangletendstoincreasewithdecreasingstresslevel.


2 SCOPE OF WORKForthefiniteelementanalysisCowiandnmGeohaveusedthewell-knowngeotechnicalsoftwarePlaxis.Theprima-ryaimofthepresentstudyhasbeentocomparetheresultsobtainedbyEurocodeDS/EN1997-1DKNA:2013andPlaxiswithresultswhenapplyingOptumG2,whichisarathernewFEgeotechnicalsoftware.OptumG2iscapableofperformingelastoplasticanalysisandalsolimitanalysisandstrengthreduction.Forthetwolatteranalyses,itispossibletocalculaterigorousupperandlowerbound,thusbracketingthetruesolutionfromaboveandbelow.IncontrasttoOptumG2,Plaxisonlycomputesasingleestimate,whichusuallyisontheunsafeside,andconsequentlyveryoftenaconvergenceanalysisiscalledfor.

Thefollowingcaseshavebeenconsidered:

a. Undrainedanalysis,planestrain–bearingcapacityfactorNc.

b. Undrainedanalysis,axisymmetric–bearingcapacityfactorNc

c. Drainedanalysis,planestrain–bearingcapacityfactorNq

d. Drainedanalysisaxisymmetric–bearingcapacityfactorNq

e. Drainedanalysis,planestrain–bearingcapacityfactorNγ

f. Drainedanalysis,axisymmetric–bearingcapacityfactorNγ

Forallplanestraincasesbothcentricandeccentricloadhavebeenanalyzed,whilefortheaxisymmetriccasesonlycentricloadwasconsidered.Inalloftheabovecases,associatedplasticityhasbeenassumed,butincasese.andf.onesingleexampleofnon-associatedplasticity(φ = 30, Ψ=0)hasbeeninvestigated.Forassociatedplasticity,thelimitanalysisfeatureofOptumG2findingbothupperandlowerboundofthebearingcapacitywasemployed,whileelastoplasticanalysiswasusedinthenon-associatedcases.

TomakethecomparisonswiththeresultsinReport14asreliableaspossible,boththedimensionsofthefootings,thesoilconditionsandthewaytheloadingisapplied,areexactlythesameastheonesusedinReport14.Intheplanestraincaseastripfootingwithawidthof4.0misconsidered,andintheaxisymmetriccasethediameteris4.0m.

The results of the present study are given in tables and for the convenience of the reader, in every table, reference ismadetotheequivalenttableinReport14.InsometablesreferenceismadetotheABCmanualbyChrisMartin(2004).Intheinternationalgeotechnicalcommunity,thevaluesofthebearingcapacityfactorsfoundbyChrisMar-tinareregardedasbeingthemostaccurateones.

ForeccentricallyloadedfootingsthesocalledMeyerhofs“effectivewidth”approach(inReport14referredtoastheHansenmethod)hasbeenused;thatisB’=B–2ewheree=M/VwithB’beingtheeffectivewidthoverwhichtheverticalloadisuniformlydistributed

All of the above analyses are based on the linear Mohr-Coulomb failure criterion. This criterion ignores the fact, that themagnitudeofthefrictionangleatfailure–atagivendensityindex–isdependentonthestresslevel,althoughthishasbeenknownforatleastthepast40–50years.Thischaracteristicofcohesionlesssoilhasbeentakenintoaccountinanewsoilmodel–theGSKmodel–whichhasbeenimplementedinOptumG2,anditisbelieved,thatitwillleadtoamorecorrectandeconomicdesign.

Toverifythis,anexampledealingwithafoundationonthetopofaslopehasbeenstudiedbothwhenapplyingtheusual Mohr-Coulomb model and the GSK model. A detailed treatment of this example is given in Chapter 4.


3 RESULTS 3.1 Undrained Analyses, plane strain

Table 1. Vertical centric and eccentric load, bearing capacity factors Nc (table2.1page8inReport14)

Eccentricity

e [m]

Eff.Width

B’ [m]e/B

Plaxis Optum

Nc,Plaxis Qf,lower[kN/m] Qf,upper[kN/m] Qf,mean [kN/m] Nc,mean

0.00 4.00 0.000 5.15 203.56 206.82 205.19 5.130.30 3.40 0.075 5.29 174.2 175.9 175.1 5.150.60 2.80 0.150 5.29 143.2 145.0 144.1 5.150.90 2.20 0.225 5.31 112.5 114.1 113.3 5.151.20 1.60 0.300 5.36 81.8 83.2 82.5 5.161.50 1.50 0.375 5.44 51.0 52.3 51.7 5.171.80 0.40 0.450 - 20.3 21.4 20.8 5.20

Comments Table 1 :Foraverticalcentricload,thetheoreticalcorrectbearingcapacityfactorNc has been found equal to π+2=5.14(Prandtl1920).ForeccentricloadingMeyerhofs“effectivewidthmethod”(Meyerhof1953)hasbeenused,andthetableshows,thatforallvaluesofe/BtheOptumvaluesarewithin1%ofthetheoreticalvalue.ThePlaxisvaluesdeviateintherange0to6%,andthegreatertheeccentricitythegreaterthedeviation.

3.2 Undrained Analyses, axial symmetry

Table 2. Vertical, centric load, bearing capacity factors Nc(table2.2page9inReport14)

Interface strength Qf [kPa] Plaxis NcBC Plaxis Nc

0, theoretical Nc0

ABC Nc0 Optum

10 60.64 6.06 6.05 6.05 6.050.10 57.08 5.71 5.67 5.69 5.73

Comments Table 2 : Theroughfootingprovidesagreaterresistancethanthesmoothfooting.BoththePlaxisandOptumvaluesareveryclosetothetheoreticalvalue.

3.3 Drained Analyses, plane strain, q-case, centric loading

Table 3. Vertical centric load, bearing capacity factors Nq (table3.1page14inReport14)

φ’ [°] Ψ [°]Plaxis Prandtl/Reissner OptumNq

BC Nq Nq,lower Nq,upper Nq,mean

15.0 15.0 3.95 3.94 3.90 3.97 3.9430.0 30.0 18.48 18.40 18.12 18.65 18.3945.0 45.0 135.59 134.87 129.57 136.93 133.2530.0 0.0 14.50 - - - 13.58

Comments Table 3 : ThePrandtl/Reissnervaluesareconsideredthetheoreticalcorrectonesforassociatedplastici-ty.BoththePlaxisandOptumvaluesareveryclosetothetheoreticalresults.Inthe-nonassociatedcasethePlaxisandOptumresultsdeviatefromeachotherbyabout6%,whichisconsideredunimportantforpracticaldesign.


3.4 Drained Analyses, plane strain, q-case, eccentric loading

Table 4. Vertical, eccentric load, bearing capacity factors Nq for φ = 30° (table3.2page15inReport14)

Eccentricity

e [m]

Eff.Width

B’ [m]e/B

Plaxis Optum

Nq,Plaxis Qf,lower[kN/m] Qf,upper[kN/m] Qf,mean [kN/m] Nq,mean

0.30 3.40 0.075 19.84 643.2 676.1 659.7 19.400.60 2.80 0.150 19.79 527.7 552.7 540.2 19.290.90 2.20 0.225 19.26 401.3 422.2 411.8 18.721.20 1.60 0.300 16.76 244.0 266.0 255.0 15.94

Comments Table 4 : ForsmallereccentricitiesthebearingcapacityfactorsforbothPlaxis(7.8%)andOptum(5.4%)aregreaterthanthePrandtl/Reissnervalue(18.4).ForgreatereccentricitiesthevalueofNqdrops,andfore/B>0.3thebearingcapacityrapidlytendstowardszeroinlinewiththefailuremechanismdevelopingundertheunloadedpartofthefooting,wheretheeffectivestressesarezeroorclosetozero.ThefailuremechanismfoundbyOptumG2incaseofe/B=0.375isshowninFigure1.

Figure1.Failuremechanism(sheardissipation)intheqcase,planestrainfore/B=0.375

3.5 Drained Analyses, axial symmetry, q-case

Table 5. Vertical, centric load, bearing capacity factors Nq(table3.3page17inReport14)

φ’tr [°]ABC Plaxis OptumNq,ABC Nq,Plaxis Qf,lower/A [kPa] Qf,upper/A[kPa] Qf,mean/A [kPa] Nq,mean

10.0 2.955 - 29.33 29.69 29.51 2.9515.0 5.246 5.28 51.99 52.75 52.37 5.2420.0 9.618 - 94.91 96.75 95.83 9.5825.0 18.40 - 180.90 185.08 182.99 18.3030.0 37.21 37.91 362.65 374.51 368.58 36.8635.0 80.81 - 780.38 814.03 797.21 79.7240.0 192.7 - 1848.88 1943.52 1896.2 189.6245.0 520.6 526.62 4926.27 5259.82 5093.05 509.31

Comments Table 5 : BoththePlaxisandOptumvaluesareingoodagreementwiththeABCvaluesthePlaxisvaluesbeingslightlylarger,andtheOptumvaluesslightlysmallerthantheABCvalues.ThemaximumdeviationforPlaxisis1.9%andforOptum2.2%.


3.6 Drained Analyses, plane strain, γ-case, centric loading

Table 6. Vertical centric load, bearing capacity factors Nƴ (table4.1page24inReport14)

φ’ [°] ᴪ[°]ABC Plaxis OptumNγ,ABC Nγ,Plaxis Nγ,lower Nγ,upper Nγ,mean

15.0 15 1.18 1.26 1.17 1.19 1.1830 30 14.75 15.49 14.36 14.88 14.6235 35 34.48 36.86 33.46 34.79 34.1340 40 85.57 - 82.11 86.44 84.2845 45 234.2 - 222.1 237.2 229.750 50 742.9 - 693.7 754.1 723.930 0 - 12.03 - - 11.63

Comments Table 6 : ForPlaxisthediscrepancyrelativetotheABCvaluesgrowsasthefrictionangleincreasesfrom15 to 35°,whereitreachesamaximumof6.9%.AtthisfrictionangletheOptumvaluedeviatesfromABCby1%.Forgreatervaluesofφ,numericalproblemsoccurwithPlaxis,whiletheOptumvalueatφ = 50° deviates from ABC by2.6%.Inthenon-associatedcasethediscrepancybetweenPlaxisandOptumisabout3.3%,Plaxisproducingthegreatervalue.Incaseofnon-associatedconditionsitiscommontocalculateamodifiedfrictionangleandthuscon-vertthenon-associatedmaterialtoanassociatedmaterialthroughtheDavisequation(Davis1968):

modsin cosa tan( )

1 sin sinϕ ψϕϕ ψ

=−

Inthisequationφmodisthefrictionangleoftheequivalentassociatedmaterialandφ and Ψarethefrictionangleanddilationangleofthenon-associatedmaterial.Insertingφ = 30°andΨ=0° yields φmod = 26.56°whichaccordingto the ABC manual gives Nγ = 8.29. ComparedtobothPlaxisandOptumtheDavisequationprovidessaferesults.

3.7 Drained Analyses, plane strain, γ-case, eccentric loading

Table 7. Vertical, eccentric load, bearing capacity factors Nƴ for φ = 30° (table4.2page26inReport14)

Eccentricity

e [m]

Eff.Width

B’ [m]e/B

Plaxis Optum

Nγ,Plaxis Qf,lower[kN/m] Qf,upper[kN/m] Qf,mean [kN/m] Nγ,mean

0.30 3.40 0.0375 15.51 850.2 875.7 863.0 14.930.60 2.80 0.150 15.08 575.8 594.2 585.0 14.930.90 2.20 0.225 15.60 354.8 367.0 360.9 14.921.20 1.60 0.300 12.27 187.8 194.4 191.1 14.931.50 1.50 0.375 - 73.59 76.13 74.86 14.981.60 0.80 0.400 - 47.08 48.67 47.9 14.931.80 0.40 0.450 - 11.73 12.14 11.94 14.92

Comments Table 7 : Plaxis:Fortherelativeeccentricitye/B<0.25thebearingcapacityisaboutupto6%greaterthantheDS/EN1997DKNAvalues.TheresultsinReport14indicate,thatattheeccentricityratioe/B=0.30failuremaynotbefullydeveloped,andthisexplainsthelowvalueoftheNγ.Fore/B>0.3numericalproblemspreventPlaxisfromreachingasolution.

Optum:Forallvaluesofe/Buptoe/B=0.45thevaluesofNγ deviatelessthan1.6%fromtheDS/EN1997-1DKNA2013 values.


3.8 Drained Analyses, axial symmetry, γ-case

Table 8. Vertical, centric load, bearing capacity factors Nƴ(table4.3page28inReport14)

φ’ [°] ᴪ [°]ABC Plaxis OptumNγ,ABC Nγ,Plaxis Qf,lower/A [kPa] Qf,upper/A[kPa] Qf,mean/A [kPa] Nγ,mean

15.0 15 0.93 1.01 18.43 18.76 18.60 0.9330 30 15.54 16.61 303.9 311.5 307.7 15.3935 35 41.92 44.95 818.6 840.2 829.4 41.4740 40 123.72 - 2393 2480 2437 121.8545 45 417.79 - 7870 8366 8118 405.930 0 - 12.29 - - - 12.15

Comments Table 8 : Forfrictionangleslessthanorequalto35°Plaxisprovidesresultswhichareupto7.2%ontheunsafeside.Forfrictionanglesgreaterthan35°,numericalproblemsoccurwithPlaxis.OptumcalculatesvaluesofNγinthefullrangeandthemaximumdeviationfromtheABCvaluesis2.8%.

Inthenon-associatedcase,thereisagoodagreementbetweenthePlaxisandOptumvalues.


4 BEARING CAPACITY OF SURFACE STRIP FOOTING LOCATED ON TOP OF SLOPE – MOHR-COULOMB VS GSK

4.1 Geometry of slope and soil parameters

Inthefollowingexamplethebearingcapacityofasurfacestripfootinglocatedonthetopofaslopeisdetermined.Theslopeconsistsofsand,andthefootingisplacedatadistanceof1.0mfromthecrestoftheslope.Thebearingcapacityisfoundforwidthsofthefootingequalto1.0m,2.0mand4.0m.

Theinclinationoftheslopeis1:2andtheslopeangle=26.56°.ThegeometryoftheslopeisshowninFigure2.

ThesoilstrengthisbasedontherelativedensityofthesandwhichistakenID=0.60andthesoilunitweightis18kNm-3.

FortheMohr-CoulombmodelthebearingcapacityiscalculatedusingbothPlaxisandOptum,whileonlyOptumisused for the GSK model.

ThePlaxiscalculationshavebeencarriedoutaselastoplasticanalyses,andtheOptumvaluesarebasedonlimitanalysis,wherebothupperandlowerboundsarefound.TheresultsoftheanalysesareshowninTable10attheend of this chapter.

Figure2.Geometryofslopeandfooting.

4.2 Mohr Coulomb model:

TheequationfromtheDanish1984CodeofPractice:

,

,

3 4 3 430 (14 ) 30 (14 )0.6 35.829 (NAF = non associated flow rule)2.1 2.1

Rule of thumb for the magnitude of the angle of dilation :30

35.829 30 5.829

tr NAF D

tr NAF

IU U

ϕ

ψψ ϕ

ψ

= − + − = − + − =

= −

= − =


“TheDavisequation”(Davis1968)isappliedtocalculatetheassociatedangleoffriction:

,,

,

sin cos sin 35.829cos5.829atan( ) atan( ) 31.763 (AF = associated flow rule)1 sin sin 1 sin 35.829sin 5.829

Stakemanns equation (Stakemann 1976) is used to find the plane angle of friction

tr NAFtr AF

tr NAF

ϕ ψϕ

ϕ ψ= = =

− −

,

:(1 0.163 ) (1 0.163 0.6)31.763 34.87pl AF D trAFIϕ ϕ= + = + ⋅ =

4.3 GSK model

TheGSKmodeltakesintoaccountthefact,thatthefrictionangleisstressdependent;thatisthefailureenvelopebecomescurvedinsteadofbeinglinearaswiththeMohrCoulombmodel.TheyieldfunctionissimilartothelinearMohrCoulombandisexpressedbythefollowingequation:τ = σ·tanφswhereφs is the secant angle in σ–τ space. UsingprincipalstressestheyieldfunctionfortheGSKmodelisformulatedinthebelowequations:

It should be noted, that in σ–τspace(Figure4),φ1istheslopeofthetangentatthepoint(σ,τ)=(0,0)andφ2 is the slope of the asymptote τ = c + σtanφ2

Figure3.FailureenvelopeforGSKmaterialin𝛔3-𝛔1space(σt = 0 for sand)

1 21 2 3 3

1 1 2 21 1 2 2

1 1 2 2

2 2

2 2

(1 exp( ))

1 sin 1 1 sin 1sin , sin1 sin 1 1 sin 12 cos (1 sin )1 sin 2cos

a aa kk

a aa aa a

c kk c

σ σ σ

ϕ ϕϕ ϕϕ ϕϕ ϕϕ ϕ

−= + − −

+ − + −= ⇔ = = ⇔ =

− + − +−

= ⇔ =−


Figure4.FailureenvelopeforGSKmaterialin𝛔-τ space

4.4 NGI triaxial tests

The GSK model can be described by the three parameters φ1, φ2 and c, and these have been found on the basis of valuesfromadatabaseofpeakfrictionanglesestablishedatTheNorwegianGeotechnicalInstituteinOslo(Ander-sen and Schjetne 2013).

Thedatabasecontainsresultsfrommorethan500triaxialcompressiontestson54differentsandfrom38differentsites.ThemeanparticlesizeD50=0.23mmandthecoefficientofuniformityCu=1.95.Thequartzcontentwas85%on the average, and for most of the sands the grain shape has been reported and varied from rounded to angular.

TheresultsoftheNGItestsgivingthepeak,triaxialangleareshowninTable9.

Table 9. Results of NGI tests.

TheresultsoftheNGIteststogetherwiththeGSKmodelvaluesfoundbyregressionanalysisareshowninFigure5.TheresultshavebeencomparedwiththeBoltonequation(Bolton1986)forrelativedensities0.40,(thegreengraph)and0.80,(theblackgraph),andascanbeseen,theBoltonresultsconformwiththeNGIandGSKvalues,thoughthefrictionanglesatverysmallvaluesoftheminorprincipalstressaresomewhatoverestimated.


Figure5.Triaxialpeakfrictionanglesversusminorprincipalstressforrelativedensities0.20-1.20.Bolton’smodelisshownbythe green and black lines.

4.5 Parameters of the GSK model

General equations :

Forthethreeparametersφ1, φ2andcthefollowingequationshavebeenestablished:

Triaxial state, non associated flow rule (NAF)

Triaxial state, associated flow rule (AF)

21, 1 1 1 1 1 1,

22, 1 2 2 2 1 2,

22 3 3 2

1

2

( )

( )

( )

= 0.886; = 0.77;

trAF D D trNAF

trAF D D trNAF

trAF D D trNAF

k A I B I C k

k A I B I C k

c k A I B I k c

kk

ϕ ϕ

ϕ ϕ

= + + =

= + + =

= + =

21, 1 1 1

22, 2 2 2

23 3

1 1 1

2 2 2

3 3

2.6; 12.4; 33.3; 6.0; 3.5; 31.4; -8.1; 24.4;

trNAF D D

trNAF D D

trNAF D D

A I B I C

A I B I C

c A I B IA B CA B CA B

ϕ

ϕ

= + +

= + +

= += = == = == =


Plane strain, non-associated flow rule (NAF) :

TriaxialanglesareconvertedtoplanestrainanglesusingtheequationproposedbyStakemann(1976):

(1 0.163 )pl D trIϕ ϕ= + ⋅

ItshouldbementionedthatBonding(1977)suggestedasimilarequation:

(1 0.160 )pl D trIϕ ϕ= + ⋅

1, 1,

2, 2,

(1 0.163 )(1 0.163 )

(1 0.45 )

plNAF D trNAF

plNAF D trNAF

plNAF D trNAF

II

c I c

ϕ ϕ

ϕ ϕ

= +

= +

= +

Plane strain, associated flow rule (AF) :

Actual parameters for ID = 0.60

Figure6.Failuremechanism.GSKmodel,B=2.00m.

1, 1,

2, 2,

(1 0.163 )(1 0.163 )

(1 0.45 )

plAF D trAF

plAF D trAF

plAF D trAF

II

c I c

ϕ ϕ

ϕ ϕ

= +

= +

= +

2 21, 1 1 1

2 22, 2 2 2

Plane strain, associated flow rule (AF) :( 1)(1 0.163 ) 0.8865 (2.6 0.6 12.4 0.6 33.3) (1 0.163 0.6) 40.53

( 2)(1 0.163 ) 0.8865 (6.0 0.6 3.5 0.6 31.4) (1plAF D D D

plAF D D D

k A I B I C I

k A I B I C I

ϕ

ϕ

= + + + = ⋅ ⋅ + ⋅ + ⋅ + ⋅ =

= + + + = ⋅ ⋅ + ⋅ + ⋅ +2 2

3 3

0.163 0.6) 34.70

0.77 ( 8.1 0.6 24.4 0.6)(1 0.45 0.6) 11.46plAF D Dc A I B I

⋅ =

= + = ⋅ − ⋅ + ⋅ + ⋅ =


4.6 Results from slope analysis

Table 10. Results from analysis (bearing capacities in kPa):

Optum PlaxisMohr Coulomb GSK Mohr Coulomb

B [m] Lowerb. Upper b. Mean Lowerb. Upper b. Mean GSKmean/MCmean

1.0 164.4 171.8 168.1 285.4 299.3 292.4 1.74 1842.0 246.1 255.5 250.8 401.2 418.1 409.7 1.63 2664.0 428.1 444.6 436.4 643.3 666.9 655.1 1.50 452

Comments Table 10 :PlaxisproducesgreaterbearingcapacitiesthanOptum’sMohr-Coulombmodel,thedeviationsbeingintherange3.6–9.4%.TheresultsoftheGSKmodelaresubstantiallygreater–upto74%–thanOptum’sMohr-Coulombs values.

5 REFERENCES Andersen,K.HandSchjetne,K.2013.Databaseoffrictionanglesofsandandconsolidationcharacteristicsofsand,siltandclay.JournalofGeotechnicalandGeoenvironmentalEngineering.

Bolton,M.D.1986.Thestrengthanddilatancyofsands.Geotechnique,36(1),65-78.

Bonding, N. 1977. Triaxial state of failure in sand. DGIBuletin26,1977.

Davis,E.H.1968.Theoriesofplasticityandfailureofsoilmasses.In SoilMechanics,selectedTopics.EditedbyI.K.Lee,Butter-worths,London,341–380.

DGI-BulletinNo.36.Codeofpracticeforfoundationengineering.Copenhagen 1985.

DS/EN1997-1DKNA:2013NationaltannekstilEurocode7:Geoteknik–Del1:Generelleregler

Martin,C.H.2004.ABCAnalysisofBearingCapacity,Version1.0DepartmentofEngineeringScience,UniversityofOxford.

Meyerhof,G.G.1953.Thebearingcapacityoffoundationsundereccentricandinclinedloads.In:3rdICSMFEVol.1.Zu-rich:1953:440-45

OptumG2.OptumComputationalEngineering,www.optumce.com,2014.

Reissner,H.1924.Zumerddruckproblem.InProceedingsfirstinternationalcongressofappliedmechanics, Delft,TheNetherlands,pp.295–311.

Prandtl, L. 1920. Über die HärteplastischerKörper. Nachr.D.Ges.D.Wiss.,math-phys.KI. Göttingen1920

Stakemann,O.1976.BrudbetingelseforG12-sandogplanemodelforsøg(FailureconditionsforG12-sandand plane strain modeltests;inDanish).InternalMemoI.M.1976-1,DanishGeotechnicalInstitute.

www.bane.dkwww.optumce.comwww.ramboll.dk

bearing capacity - ramcadds.in · 2 bearing capacity - comparison of results from m and dsn 1997-1...

Documents