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The Hardening Soil with small strain stiffness model is implemented by using the Modified Mohr-Coulomb model and Small strain overlay model, and needed two additional parameters as below:
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G0ref
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: Initial or very small-strain shear modulus
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Threshold strain (γ0.7)
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: Shear strain at which the shear modulus is about 70% of the initial small-strain shear modulus
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The strain range in which soils can be considered truly elastic is very small. With increasing strain range, soil stiffness decrease nonlinearly as the following graph.
To reflect the above characteristics, the Hardening Soil with small strain stiffness model uses the modified Hardin & Drnevich relationship as the following equation.
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Gs
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: Shear modulus
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G0
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: Initial shear modulus
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γ
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: Shear strain
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γ0.7
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: Shear strain at which the shear modulus is about 70% of the initial small-strain shear modulus
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[Nonlinear Parameters]
Following is the summary of parameters for the Hardening Soil (small strain stiffness) model.
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Parameter
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Description
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Reference value (kN, m)
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Soil stiffness and failure
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E50ref
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Secant stiffness in standard drained triaxial test
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Ei x (2 – Rf) /2
(Ei = Initial stiffness)
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Eoedref
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Tangent stiffness for primary oedometer loading
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E50ref
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Eurref
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Unload / reloading stiffness
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3 x E50ref
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m
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Power for stress-level dependency of stiffness
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0.5 ≤ m ≤ 1 (0.5 for hard soil,
1 for soft soil)
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C
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Effective cohesion
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Failure parameter as in MC model
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φ
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Effective friction angle
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Failure parameter as in MC model
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ψ
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Ultimate dilatancy angle
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0 ≤ ψ ≤ φ
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Advanced parameters (Recommend to use Reference value)
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Rf
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Failure Ratio (qf / qa)
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0.9 (< 1)
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Pref
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Reference pressure
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100
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K0NC
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K0 for normal consolidation
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1-sinφ (< 1)
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Tensile strength
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Cut off value for tensile hydrostatic pressure
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-
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Small strain stiffness
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Threshold
Shear strain
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Shear strain at which shear modulus has decayed
to 70% of initial shear stiffness (G0ref)
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β
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Shear modulus at small strain
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