lecture 03 - 2 - hs model 2
DESCRIPTION
geotechnical finite element lecture noteTRANSCRIPT
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Hardening Soil Model (HS)
Constitutive Model in FE Analysis
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Constitutive Model - PlasticityYield SurfaceFlow RuleHardening RuleExpansion or shrinkage of the loading or yield surface.
Predicts change in the yield surface due to plastic strains.
Link changes in stresses and strains to the size of the Loading Surface
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Constitutive Model - PlasticityM-C model has a fixed yield surface, a yield surface fully defined by model parameters and not affected by strainVariation of yield surface
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2k1k
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Hardening Soil Model (HS)
strain or displacement)
(stress) Real soil response
Idealised soil model – MC model
Hardening Soil Model
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Hardening Soil Model (HS)
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Yield Surface of HS Model
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p’
qMC Model Failure Line
With increasing hardening parameter
Shear Hardening
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Yield Surface
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q
p
3
2
1
q
p
3
2
1
q
p
3
2
1
Shear hardening
Compression hardening
2 yield surface
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Yield Surface Cap in HS Model
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p’
q
cc cot
Elastic Zone
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Yield Surface Cap in HS Model
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Dilatancy Cut-off in HS Model
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Dilatancy cut-off on emax
1
v
HS Model
MC Model
2 sin1 - sin
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Strain-Hardening Types
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Strain-hardening has two types:
Shear hardening: plastic strain is primarily due to deviatoric loading
Compression hardening: plastic strain is primarily due to compression (oedometer) and isotropic loading
y
x= z
zTriaxial Test
y
Oedometer Test
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Features of HS ModelAllows for non-linearity of the stress-strain curve (Hyperbolic)Differentiate between first loading and unloadingStiffness depends on stressesYield surface expands (harden) in the space due to plastic strainThe yield surface has a cap to allow for hardening due to volumetric strain
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Input Parameters of HS ModelStress-dependent stiffness according to a power law [input parameter: m]
Plastic straining due to primary deviatoric loading [input parameter: ( )]
Plastic straining due to primary compression loading [input parameter ( )]
Elastic unloading/reloading [input parameter: ( , )]
Failure according to the Mohr-Coulomb model [input parameter: (c, and )]
refE50
refoedE
refurE
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From triaxial test
From oedometer test
Unloading/reloading test
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Stress Dependent E50
qaqf
qf/2
150E
AsymptoteFailure line
1urE
Axial strain
Deviator stress
m
refref
pccEE
sincos'sin'cos' 3
5050
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y
x= z
z
Triaxial Test
’3 = x = z
f
fa
f
Rq
q
cq
and
sin1
sin2)'cot'( 3
refE50 When ’ = pref = 100 kPa
Rf = 0.9 qf = 0.9qa
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Stress Dependent Eur
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qaqf
qf/2
150E
AsymptoteFailure line
1urE
Axial strain
Deviator stress
m
refrefurur pc
cEEsincos'sin'cos' 3
y
x= z
z
Triaxial Test
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Stress Dependent Eoed
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v’
Axial strain
pref
1
refoedE
m
refrefoedoed p
EE 1
Oedometer Test
v
1 = v
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Application of HS Model
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When shearing is dominant (more than compression)
When the problem involves substantial unloading
When the stiffness varies with stress
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Selection of Parameters in HS Model
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: Secant modulus in standard drained triaxial test
: Tangent stiffness for primary oedometer loading
: unloading/reloading modulus ( 3 )
ur : Poisson’s ratio for unloading/reloading (default ur = 0.2 )
pref : Reference stress for stiffness (default pref = 100 kPa)
: K0-value for normally consolidation (default = 1-sin )
m 1 for clays and m 0.5 for sands
refE50refoedErefurE ref
urE refE50
NCK0NCK0
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Hardening Soil ModelAdvantages
Better nonlinear formulation of soil behaviour in general (both soft soil and harder soil types)Distinction between primary loading and unloadingMemory of preconsolidation stressesDifferent stiffness for different stress paths based on standard testsWell suited for unloading situations with simultaneous deviatoric loading
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Hardening Soil ModelLimitation
No peak strength and softeningNo secondary compressionNo anisotropyE50/Eoed > 2 difficult to inputStiffness at small strain is underestimated
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Hardening Soil ModelThe hardening soil model is completely defined in effective stresses and therefore need both effective strength parameters and effective stiffness parameters in order to take advantages of the modelA total stress analysis maybe performed with both undrained strength (Cu and friction angle=0). However, no stress dependent stiffness and no compression hardening.
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Remarks* on Finite Element Analysis
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The ability of the Finite Element Method to accurately reflect field conditions essentially depends on the ability of the constitutive models to represent real soil behaviour and the ability of the geotechnical engineer to assign appropriate boundary conditions to the various stages of construction.
Advantages over the conventional methods are the effects of time on the development of pore water pressures can be simulated by including coupled consolidation/swelling, dynamic behaviour can be accounted for, and – perhaps most importantly no postulated failure mechanism or mode of behaviour of the problem is required, as these are predicted by the analysis itself.
*Potts, D. M. (2003). Geotechnique 53, No.6, 535-573