3.1.6.11. Pressure Dependent Multi Yield 02¶
PressureDependMultiYield02 material is modified from PressureDependMultiYield material, with:
Additional parameters ($contrac3 and $dilat3) to account for Kσ effect,
a parameter to account for the influence of previous dilation history on subsequent contraction phase ($contrac2), and
modified logic related to permanent shear strain accumulation ($liquefac1 and $liquefac2).
The command to generate such a material
TCL command:
nDMaterial PressureDependMultiYield02 $tag $nd $rho $refShearModul $refBulkModul $frictionAng $peakShearStra $refPress $pressDependCoe $PTAng $contrac1 $contrac3 $dilat1 $dilat3 <$noYieldSurf=20 <$r1 $Gs1 …> $contrac2=5. $dilat2=3. $liquefac1=1. $liquefac2=0. $e=0.6 $cs1=0.9 $cs2=0.02 $cs3=0.7 $pa=101 <$c=0.1>>
Argument |
Type |
Description |
|---|---|---|
tag |
integer |
A positive integer uniquely identifying the material among all nDMaterials. |
nd |
integer |
Number of dimensions, 2 for plane-strain, and 3 for 3D analysis. |
rho |
float |
Saturated soil mass density. |
refShearModul (Gr) |
float |
Reference low-strain shear modulus, specified at a reference mean effective confining pressure refPress of p’r. |
refBulkModul (Br) |
float |
Reference bulk modulus, specified at a reference mean effective confining pressure refPress of p’r. |
frictionAng (Φ) |
float |
Friction angle at peak shear strength, in degrees. |
peakShearStra (γmax) |
float |
An octahedral shear strain at which the maximum shear strength is reached, specified at a reference mean effective confining pressure refPress of p’r. |
refPress (p’r) |
float |
Reference mean effective confining pressure at which Gr, Br, and γmax are defined. |
pressDependCoe (d) |
float |
A positive constant defining variations of G and B as a function of instantaneous effective confinement p’ |
PTAng (ΦPT) |
float |
Phase transformation angle, in degrees. |
contrac1 $contrac2 |
float |
A non-negative constant defining the rate of shear-induced volume decrease (contraction) or pore pressure buildup. A larger value corresponds to faster contraction rate. |
contrac3 |
float |
A non-negative constant reflecting Kσ effect. |
dilat1 $dilat2 |
float |
Non-negative constants defining the rate of shear-induced volume increase (dilation). Larger values correspond to stronger dilation rate. |
dilat3 |
float |
A non-negative constant reflecting Kσ effect. |
noYieldSurf |
float |
Number of yield surfaces, optional (must be less than 40, default is 20). The surfaces are generated based on the hyperbolic relation. |
r Gs |
float |
Instead of automatic surfaces generation (Note 2), you can define yield surfaces directly based on desired shear modulus reduction curve. To do so, add a minus sign in front of noYieldSurf, then provide noYieldSurf pairs of shear strain (γ) and modulus ratio (Gs) values. For example, to define 10 surfaces: … -10γ1Gs1 … γ10Gs10 … |
liquefac1 |
float |
Damage parameter to define accumulated permanent shear strain as a function of dilation history. (Redefined and different from PressureDependMultiYield material). |
liquefac2 |
float |
Damage parameter to define biased accumulation of permanent shear strain as a function of load reversal history. (Redefined and different from PressureDependMultiYield material). |
e |
float |
Initial void ratio, optional (default is 0.6). |
cs1 cs2 cs3 $pa |
float |
Parameters defining a straight critical-state line ec in e-p’ space. (default values: cs1=0.9, cs2=0.02, cs3=0.7, pa =101 kPa). |
c |
float |
Numerical constant (default value = 0.3 kPa) |
Recorder queries and Outputs
The following information may be extracted for this material at a given integration point, using the OpenSees Element Recorder facility stress, strain, backbone, or tangent.
For 2D problems, the stress output follows this order: \(\sigma_{xx}\), \(\sigma_{yy}\), \(\sigma_{zz}\), \(\sigma_{xy}\), \(\eta_r\), where \(\eta_r\) is the ratio between the shear (deviatoric) stress and peak shear strength at the current confinement \((0<=\eta_r<=1.0)\). The strain output follows this order: \(\epsilon_{xx}\), \(\epsilon_{yy}\), \(\epsilon_{xy}\)
For 3D problems, the stress output follows this order: \(\sigma_{xx}\), \(\sigma_{yy}\), \(\sigma_{zz}\), \(\sigma_{xy}\),:math:sigma_{yz}, \(\sigma_{zx}\), \(\eta_r\) and the strain output follows this order: \(\epsilon_{xx}\), \(\epsilon_{yy}\), \(\epsilon_{zz}\), \(\gamma_{xy}\), \(\gamma_{yz}\), \(\gamma_{zx}\)
The
backbone"option records (secant) shear modulus reduction curves at one or more given confinements. The specific recorder command is as follows:
where p1, p2, … are the confinements at which modulus reduction curves are recorded. In the output file, corresponding to each given confinement there are two columns: shear strain γ and secant modulus Gs. The number of rows equals the number of yield surfaces.
Elastic or Elastoplastic response could be enforced by:
Elastic: updateMaterialStage -material $tag -stage 0
Elastoplastic: updateMaterialStage -material $tag -stage 1
SUGGESTED PARAMETER VALUES
Parameters |
Dr=30% |
Dr=40% |
Dr=50% |
Dr=60% |
Dr=75% |
|---|---|---|---|---|---|
rho |
1.7 ton/m3 |
1.8 ton/m3 |
1.9 ton/m3 |
2.0 ton/m3 |
2.1 ton/m3 |
refShearModul (at p’r=80 kPa) |
6.0x104 kPa |
9.0x104 kPa |
10.0x104 kPa |
11.0x104 kPa |
13.0x104 kPa |
refBulkModu (at p’r=80 kPa) |
16.0x104 kPa (Ko=0.5) |
22.0x104 kPa (Ko=0.47) |
23.3x104 kPa (Ko=0.45) |
24.0x104 kPa (Ko=0.43) |
26.0x104 kPa (Ko=0.4) |
frictionAng |
31 |
32 |
33.5 |
35 |
36.5 |
PTAng |
31 |
26 |
25.5 |
26 |
26 |
peakShearStra (at p’r=101 kPa or 14.65 psi) |
0.1 |
0.1 |
0.1 |
0.1 |
0.1 |
refPress (p’r) |
101 kPa |
101 kPa |
101 kPa |
101 kPa |
101 kPa |
pressDependCoe |
0.5 |
0.5 |
0.5 |
0.5 |
0.5 |
contrac1 |
0.087 |
0.067 |
0.045 |
0.028 |
0.013 |
contrac3 |
0.18 |
0.23 |
0.15 |
0.05 |
0.0 |
dilat1 |
0.0 |
0.06 |
0.06 |
0.1 |
0.3 |
dilat3 |
0.0 |
0.27 |
0.15 |
0.05 |
0.0 |
e |
0.85 |
0.77 |
0.7 |
0.65 |
0.55 |
Pressure Dependent Multi Yield 02 Examples
Description |
Tcl |
|---|---|
Single 2D 9-4 noded element, subjected to sinusoidal base shaking (PressureDepend02 material) |
|
Single 3D brick element, subjected to sinusoidal base shaking (PressureDepend02 material) |
|
Single 3D 20-8 noded element, subjected to sinusoidal base shaking (PressureDepend02 material) |
Code Developed by: UC San Diego (Dr. Zhaohui Yang), Github Documentation collected by: A. Najafi