The SMP Concept-Based 3D Constitutive Models for Geomaterials

154 Pages·2006·5.747 MB·\154

by  Hajime Matsuoka (Author)

The SMP Concept-based 3D Constitutive
Models for Geomaterials
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BALKEMA-ProceedingsandMonographs
inEngineering,Water,andEarthSciences
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The SMP Concept-based
3D Constitutive Models
for Geomaterials
Hajime Matsuoka
Department of Civil Engineering,
Nagoya Institute ofTechnology,Japan
De’an Sun
Department of Civil Engineering,
Shanghai University,China
LONDON / LEIDEN / NEW YORK / PHILADELPHIA / SINGAPORE
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Matsuoka,Hajime,1943–
TheSMPconcept-based3Dconstitutivemodels
forgeomaterials/HajimeMatsuoka,De’anSun.
p.cm.
Includesbibliographicalreferencesandindex.
ISBN0–415–39504–6(hardcover:alk.paper)1.Soilmechanics–
Mathematicalmodels.I.Sun,De’an,1962–II.Title.
TA710.A1.M372006
(cid:1)
624.15136015118–dc22 2005035141
ISBN100–415–39504–6 ISBN13978–0–415–39504–5
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Contents
Listoffigures vii
Listoftables xiii
Preface xv
1 Spatiallymobilizedplane(SMP)andSMPcriterion 1
1.1 OriginofSMP 1
1.2 Stress–strainrelationbasedoncompositelymobilizedplane(CMP) 1
1.3 Stress–strainrelationbasedonSMP 9
1.4 Failurecriteriaformetalsandgranularmaterials 14
1.5 Failurecriterionforcohesive-frictionalmaterials 20
References 24
2 IntroductiontoCam-claymodel 27
2.1 Introduction 27
2.2 OriginalCam-claymodel 29
2.2.1 Principaldirectionofplasticstrainincrementandadopted
stressandstrainvariables 29
2.2.2 Determinationofplasticpotentialandyieldfunctions 31
2.2.3 Determinationofstrain-hardeningrule 34
2.2.4 Determinationofdεe 37
ij
2.2.5 Detailedderivationofdεp 38
ij
2.3 ModifiedCam-claymodel 48
2.3.1 Principaldirectionofplasticstrainincrementandadopted
stressandstrainvariables 48
2.3.2 Determinationofplasticpotentialandyieldfunctions 48
2.3.3 Determinationofstrain-hardeningrule 51
2.3.4 Determinationofdεe 52
ij
2.3.5 Detailedderivationofdεp 52
ij
References 60
3 TheCam-claymodelrevisedbytheSMPcriterion 61
3.1 Introduction 61
3.2 TheSMPcriterionandatransformedstresstensor 62
3.3 TheCam-claymodelrevisedbytheSMPcriterion 66
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vi Contents
3.4 Comparisonofmodelpredictionswithexperimentaldata 72
3.5 Concludingremarks 76
Appendix1 Derivationof(cid:2) 77
0
Appendix2 DerivationofelastoplasticconstitutivetensorD 78
ijkl
References 80
4 Elastoplasticconstitutivemodelsforgeomaterialsusing
transformedstress 83
4.1 Anelastoplasticmodelforsandsandclays 83
4.1.1 Introduction 83
4.1.2 Aunifiedhardeningparameterforbothclaysandsands 84
4.1.3 Aunifiedelastoplasticmodelforbothclaysandsands 91
4.1.4 Predictionversusexperiment 92
4.1.5 Modelingconfiningpressuredependenceofstrengthand
deformation 93
4.1.6 Conclusions 95
4.2 AnelastoplasticmodelforK -consolidatedsoils 95
0
4.2.1 Introduction 95
4.2.2 TheSekiguchi-Ohtamodelanditsstress–dilatancyrelation 96
4.2.3 Ananisotropichardeningelastoplasticmodelfor
K -consolidatedclaysandsands 98
0
4.2.4 Comparisonofmodelpredictionswithexperimentalresults 102
4.2.4.1 Modelingtriaxialbehavior 102
4.2.4.2 Modelingplanestrainbehavior 104
4.2.5 Elastoplasticconstitutivetensor 107
4.2.6 Conclusions 108
4.3 Anelastoplasticmodelforunsaturatedsoils 109
4.3.1 Introduction 109
4.3.2 Effectivestressforunsaturatedsoils 110
4.3.3 TransformedstresstensorbasedonExtendedSMPcriterion 112
4.3.4 Formulationofmodelforunsaturatedsoils 114
4.3.4.1 Strengthofunsaturatedsoil 114
4.3.4.2 Formulationofmodelinisotropicstressstate 115
4.3.4.3 Formulationofmodelingeneralstress 117
4.3.5 Triaxialtestsonunsaturatedsoils 120
4.3.5.1 Triaxialtestapparatusforunsaturatedsoils 120
4.3.5.2 Unsaturatedsoilspecimen 121
4.3.5.3 Stresspaths 122
4.3.6 Comparisonofmodelpredictionswithexperimentalresults 122
4.3.6.1 Modelparametersandtheirdetermination 122
4.3.6.2 Modelpredictionsversusexperimentalresults 124
4.3.7 Generalstress–strainrelationforunsaturatedsoils 128
4.3.8 Concludingremarks 129
References 129
5 Concludingremarks 133
Index 135
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Figures
1.1 Directsheartestonanassemblyofaluminumrods 2
1.2 Directsheartestonanassemblyofphotoelasticrods 2
1.3 Biaxialcompressiontestonanassemblyofaluminumrods 3
1.4 Biaxialcompressiontestonanassemblyofphotoelasticrods 3
1.5 NormalandshearstressesonmobilizedplanesandSMP 4
1.6 GeometricalrepresentationsofmobilizedplanesandSMPin
three-dimensionalspace 5
1.7 “Two”two-dimensionalmobilizedplanesundertriaxialcompressionand
triaxialextensionconditions 5
1.8 Deformationoftriaxialcompressionandtriaxialextensionspecimens
aftertests 6
1.9 “Two-dimensional”principalstrainincrementsunderrespectivepairsof
principalstresses 6
1.10 Aplanewhereshear–normalstressratioismaximum 8
1.11 Relationbetweenτ/σ and−dε /dγ ononemobilizedplaneobtained
N N
bytriaxialcompressionandextensiontestsonToyourasand 8
1.12 Relationbetweenτ/σ ,γ andε ononemobilizedplaneobtainedby
N N
triaxialcompressionandextensiontestsonToyourasand 9
1.13 Predictedandmeasuredrelationsbetweenσ /σ ,ε andε obtainedby
1 3 1 3
triaxialcompressionandextensiontestsonToyourasand 9
1.14 Amountsofstrainincrementsdε∗ anddγ∗ inprincipalstrain
SMP SMP
incrementspace 11
1.15 Relationbetweenτ /σ and−dε∗ /dγ∗ obtainedbytriaxial
SMP SMP SMP SMP
compressionandextensiontestsonToyourasand 11
1.16 Relationbetweenτ /σ and−dε∗ /dγ∗ obtainedbytrue
SMP SMP SMP SMP
triaxialtestsonToyourasand 12
1.17 Relationbetweenτ /σ and−dε /dγ obtainedbythesametests
oct oct oct oct
asFigure1.15 12
1.18 Relationbetweenτ /σ ,γ∗ ,andε∗ obtainedbytriaxial
SMP SMP SMP SMP
compressionandextensiontestsonToyourasand 13
1.19 Relationbetweenτ /σ ,γ∗ ,andε∗ obtainedbytruetriaxial
SMP SMP SMP SMP
testsonToyourasand 13
1.20 Relationbetweenτ /σ ,γ ,andε obtainedbythesametestsas
oct oct oct oct
Figure1.18 14
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viii Figures
1.21 Predictedandmeasuredrelationsbetweenprincipalstressratioand
principalstrainsobtainedbytruetriaxialtestsonToyourasand 15
1.22 Normalandshearstresseson45◦planesandoctahedralplane 16
1.23 NormalandshearstressesonmobilizedplanesandSMP 16
1.24 Geometricalrepresentationsof45◦planesandoctahedralplanein
three-dimensionalspace 17
1.25 GeometricalrepresentationsofmobilizedplanesandSMPin
three-dimensionalspace 18
1.26 MutualrelationshipsbetweentheTresca,Mises,Mohr-Coulomb,and
Matsuoka-Nakai(SMP)failurecriteriadescribedintheπ-plane 19
1.27 ShapesoftheTresca,Mises,Mohr-Coulomb,andMatsuoka-Nakai
(SMP)failurecriteriainprincipalstressspace 20
1.28 ComparisonoftheMatsuoka-Nakai(SMP)andMohr-Coulombcriteria
withstressstatesatfailureintheπ-planeobtainedbytriaxial
compression,triaxialextensionandtruetriaxialtestsonToyourasand 20
1.29 NormalandshearstressesonmobilizedplanesandExtendedSMPfor
cohesive-frictionalmaterials 21
1.30 ExtendedSMPinthree-dimensionalspaceundertranslatedprincipal
stresses 22
1.31 SchematicdiagramsofExtendedSMPfailurecriterionandgeneral
Mohr-Coulombfailurecriterioninprincipalstressspace 22
1.32 MutualrelationshipsbetweentheTresca,Mises,Mohr-Coulomb,
generalizedMohr-Coulomb,Matsuoka-Nakai(SMP),andExtendedSMP
failurecriteria 23
1.33 ComparisonoftheExtendedSMPcriterionwithstressstatesatfailurein
theπ-planeobtainedbytriaxialcompression,triaxialextension,andtrue
triaxialtestsonacementedsand 24
2.1 Watercontentcontoursfromdrainedtriaxialtestsandstresspathsin
undrainedtriaxialtestsonanormallyconsolidatedclay 28
2.2 Principalstressspaceandprincipalplasticstrainincrementspace 30
2.3 Plasticpotentialandstrainincrementvector 31
2.4 StressratioversusstrainincrementratiorelationadoptedinCam-clay
model 32
2.5 PlasticpotentialandplasticstrainincrementvectorsinCam-claymodel 33
2.6 YieldlocususedinCam-claymodel 34
2.7 Themechanicalmeaningofyieldlocus 34
2.8 Resultsofisotropiccompressionandswellingtests 35
2.9 ThemeaningofyieldlocusinCam-claymodel 36
2.10 Predictionofstressversusstrainrelationindrainedtriaxialcompression
testbyoriginalCam-claymodel 45
2.11 Predictionofstresspathsindrainedtriaxialcompressiontestbyoriginal
Cam-claymodel 45
2.12 Predictionofstressversusstrainrelationinundrainedtriaxialextension
testbyoriginalCam-claymodel 47
2.13 Predictionofstresspathsinundrainedtriaxialextensiontestbyoriginal
Cam-claymodel 48
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Figures ix
2.14 Stressratioversusplasticstrainincrementratioadoptedinmodified
Cam-claymodel 49
2.15 Plasticpotentialandplasticstrainincrementvectorsinmodified
Cam-claymodel 50
2.16 YieldlocusofmodifiedCam-claymodel 51
2.17 ThemeaningofyieldlocusinmodifiedCam-claymodel 52
2.18 Predictionofstressversusstrainrelationindrainedtriaxialtestby
modifiedCam-claymodel 57
2.19 Predictionofstressversusstrainrelationinundrainedtriaxialextension
testbymodifiedCam-claymodel 59
2.20 Predictionofstresspathsinundrainedtriaxialextensiontestsby
modifiedCam-claymodel 59
3.1 ShapesofExtendedTrescaandExtendedMisesfailurecriteriaand
Mohr-CoulombandSMPcriteriainprincipalstressspace 62
3.2 MutualrelationshipsbetweenExtendedTrescaandExtendedMises
failurecriteriaandMohr-CoulombandSMPcriteriainπ-plane 63
3.3 ComparisonofExtendedMises,Mohr-Coulomb,andSMPcriteriawith
stressstatesatfailureinπ-planeobtainedbytriaxialcompression,
triaxialextension,andtruetriaxialtestsonFujinomoriclay 64
3.4 TheSMPcriterioninπ-planeandtransformedπ-plane 65
3.5 ShapesofSMPfailurecriterionexpressedintransformedprincipalstress
space 66
3.6 Stress–dilatancyrelationshipsoftherevisedoriginalCam-claymodel
undertriaxialcompressionandtriaxialextension 68
3.7 Stress–dilatancyrelationshipsforFujinomoriclayundertriaxial
compressionandtriaxialextension 69
3.8 YieldlocioforiginalCam-claymodelgeneralizedbytheSMPcriterion
intriaxialcompressionandtriaxialextension 69
3.9 Yieldsurfaceexpressedintransformedprincipalstressspaceand
ordinaryprincipalstressspace 69
3.10 Stress–dilatancyrelationshipsoftherevisedmodifiedCam-claymodel
undertriaxialcompressionandtriaxialextension 72
3.11 YieldlociofmodifiedCam-claymodelgeneralizedbytheSMPcriterion
intriaxialcompressionandtriaxialextension 72
3.12 Predictedandmeasuredresultsoftriaxialcompressionandtriaxial
extensiontestsonFujinomoriclay 73
3.13 Comparisonbetweenpredictedandmeasuredstress–strainbehavior 74
3.14 Comparisonbetweenpredictedandmeasuredstress–strainbehavior
underthreedifferentprincipalstresses 75
3.15 Comparisonbetweenpredictedandmeasuredstress–strainbehavior
underundrainedtriaxialcompressionandtriaxialextension 76
3.16 Comparisonbetweenpredictedandmeasuredundrainedstresspaths
undertriaxialcompressionandtriaxialextension 76
4.1.1 Directionofplasticstrainincrement 85
4.1.2 Triaxialcompressiontestresultsforclayandsand 87
4.1.3 Stresspathsoftriaxialtestsforexaminingthenewhardeningparameter 89
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