4.15.1.14. PM4Silt

nDMaterial('PM4Silt', matTag, S_u, Su_Rat, G_o, h_po, Den <Su_factor, Patm, nu, nG, h0, eInit, lambda, phicv, nb_wet, nb_dry, nd, Ado, ru_max, zmax, cz, ce, Cgd, ckaf, m_m, CG_consol>)

Code Developed by: Long Chen and pedro at U.Washington.

[Boulanger-Ziotopoulou2018]

This command is used to construct a 2-dimensional PM4Silt material.

matTag (int) integer tag identifying material
S_u (float) Undrained shear strength
Su_Rat (float) Undrained shear strength ratio.
G_o (float) Shear modulus constant
h_po (float) Contraction rate parameter
Den (float) Mass density of the material
Su_factor (float) Optional: Undrained shear strength reduction factor
P_atm (float) Optional: Atmospheric pressure
nu (float) Optional: Poisson’s ratio. Default value is 0.3.
nG (float) Optional: Shear modulus exponent. Default value is 0.75.
h0 (float) Optional: Variable that adjusts the ratio of plastic modulus to elastic modulus. Default value is 0.5.
eInit (float) Optional: Initial void ratios. Default value is 0.90.
lambda (float) Optional: The slope of critical state line in e-ln(p) space. Default value is 0.060.
phicv (float) Optional: Critical state effective friction angle. Default value is 32 degrees.
nb_wet (float) Optional: Bounding surface parameter for loose of critical state conditions \(1.0 \geq nb_wet \geq 0.01\). Default value is 0.8. in cyclic loading
nb_dry (float) Optional: Bounding surface parameter for dense of critical state conditions \(nb_dry \geq 0\). Default value is 0.5.
nd (float) Optional: Dilatancy surface parameter \(nd \geq 0\). Default value is 0.3.
Ado (float) Optional: Dilatancy parameter. Default value is 0.8. with accumulation of fabric
ru_max (float) Optional: Maximum pore pressure ratio based on p’.
z_max (float) Optional: Fabric-dilatancy tensor parameter
cz (float) Optional: Fabric-dilatancy tensor parameter. Default value is 100.0.
ce (float) Optional: Variable that adjusts the rate of strain accumulation in cyclic loading
cgd (float) Optional: Variable that adjusts degradation of elastic modulus with accumulation of fabric. Default value is 3.0. in stress ratio space)
ckaf (float) Optional: Variable that controls the effect that sustained static shear stresses have on plastic modulus. Default value is 4.0.
m_m (float) Optional: Yield surface constant (radius of yield surface in stress ratio space). Default value is 0.01.
CG_consol (float) Optional: Reduction factor of elastic modulus for reconsolidation. \(CG_consol \geq 1\). Default value is 2.0.

Note

The material formulation for the PM4Silt object is PlaneStrain

If both S_u and Su_Rat values are specified the value of S_u is used.

Valid Element Recorder queries are stress, strain, alpha (or backstressratio) for \(\mathbf{\alpha}\), fabric for \(\mathbf{z}\), and alpha_in (or alphain) for \(\mathbf{\alpha_{in}}\)

Elastic or response could be enforced by

updateMaterialStage('-material', matTag, '-stage', 0)

Elastoplastic by

updateMaterialStage('-material', matTag, '-stage', 1)

The program will use the default value of a secondary parameter if a negative input is assigned to that parameter, e.g. Ado = -1. However, FirstCall is mandatory when switching from elastic to elastoplastic if negative inputs are assigned to stress-dependent secondary parameters, e.g. Ado and zmax. FirstCall can be set as,

setParameter('-value', 0, '-ele', elementTag, 'FirstCall', matTag)

Post-shake reconsolidation can be activated by

setParameter('-value', 1, '-ele', elementTag, 'Postshake', matTag)

The user should check that the results are not sensitive to time step size.

Refer to PM4Sand for examples.

[Boulanger-Ziotopoulou2018]R.W.Boulanger, K.Ziotopoulou. “PM4Silt(Version 1): A Silt Plasticity Model for Earthquake Engineering Applications”. Report No. UCD/CGM-18/01 2018