3.1.6.8. PM4Silt Material

Code Developed by: Long Chen and Pedro Arduino at U.Washington.

This command is used to construct a 2-dimensional PM4Silt material ([Boulanger-Ziotopoulou2017]).

Function

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>

Argument	Type	Description
$matTag	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 ≥ $nb_wet ≥ 0.01. Default value is 0.8.
$nb_dry	float	Optional: Bounding surface parameter for dense of critical state conditions $nb_dry ≥ 0. Default value is 0.5.
$nd	float	Optional: Dilatancy surface parameter $nd ≥ 0. Default value is 0.3.
$Ado	float	Optional: Dilatancy parameter. Default value is 0.8.
$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.
$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 ≥ 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 Material 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