PM4Silt Material (Beta)

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

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>
matTag

integer tag identifying material

Primary:

S_u

Undrained shear strength

Su_Rat

Undrained shear strength ratio. If both S_u and Su_Rat values are specified, the value of S_u is used.

G_o

Shear modulus constant

h_po

Contraction rate parameter

Den

Mass density of the material

Su_factor

Optional, Undrained shear strength reduction factor

P_atm

Optional, Atmospheric pressure

Secondary:

nu

Optional, Poisson’s ratio. Default value is 0.3.

nG

Optional, Shear modulus exponent. Default value is 0.75.

h0

Optional, Variable that adjusts the ratio of plastic modulus to elastic modulus. Default value is 0.5.

eInit

Optional, Initial void ratios. Default value is 0.90.

lambda

Optional, The slope of critical state line in e-ln(p) space. Default value is 0.060.

phicv

Optional, Critical state effective friction angle. Default value is 32 degrees.

nb_wet

Optional, Bounding surface parameter for loose of critical state conditions, 1.0 ≥ $nb_wet ≥ 0.01. Default value is 0.8.

nb_dry

Optional, Bounding surface parameter for dense of critical state conditions, $nb_dry ≥ 0. Default value is 0.5.

nd

Optional, Dilatancy surface parameter $nd ≥ 0. Default value is 0.3.

Ado

Optional, Dilatancy parameter. Default value is 0.8.

ru_max

Optional, Maximum pore pressure ratio based on p’.

z_max

Optional, Fabric-dilatancy tensor parameter

cz

Optional, Fabric-dilatancy tensor parameter. Default value is 100.0.

ce

Optional, Variable that adjusts the rate of strain accumulation in cyclic loading

cgd

Optional, Variable that adjusts degradation of elastic modulus with accumulation of fabric. Default value is 3.0.

ckaf

Optional, Variable that controls the effect that sustained static shear stresses have on plastic modulus. Default value is 4.0.

m_m

Optional, Yield surface constant (radius of yield surface in stress ratio space). Default value is 0.01.

CG_consol

Optional, Reduction factor of elastic modulus for reconsolidation. $CG_consol ≥ 1. Default value is 2.0.

The material formulation for the PM4Silt object is “PlaneStrain”


Code Developed by: Long Chen, Pedro Arduino, U Washington


Notes

  • Valid Element Recorder queries are
    • stress, strain
    • alpha (or backstressratio) for <math></math>
    • fabric for \(\mathbf{z}\)
    • alpha_in (or alphain) for <math></math>

e.g. recorder Element -eleRange 1 $numElem -time -file stress.out stress

  • Elastic or Elastoplastic response could be enforced by
{|

|Elastic: ||updateMaterialStage -material $matTag -stage 0 |- |Elastoplastic: ||updateMaterialStage -material $matTag -stage 1 |}

  • If default values are used for secondary parameters, the model must be initialized after elastic gravity stage by

setParameter -value 0 -ele $elementTag FirstCall $matTag

  • Post-shake reconsolidation can be activated by

setParameter -value 1 -ele $elementTag Postshake $matTag

Example

<table border=1 width=600> <tr> <td width=90>Example 1 </td>

<td>2D undrained monotonic direct simple shear test using one element</td> </tr> <tr> <td>Example 2</td> <td>2D undrained cyclic direct simple shear test using one element</td> </tr>

</table>

References

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

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