plastic-hardening

cohesion f

cohesion, $c$. The default and cut-off (allowable minimum) value is $10^{-5} \cdot p^{ref}$.

dilation f

ultimate dilation angle in degrees, $\psi$. The default is 0.0.

exponent f

exponent for elastic moduli, $m$. Allowable value is $0 \le m \le 0.999$.

friction f

ultimate friction angle in degrees, $\phi$. The default and cut-off (allowable minimum) value is 0.001 degrees.

stress-1-effective f

initial minimum principal effective stress, $\sigma^{ini}_1$. See the note*.

stress-2-effective f

initial median principal effective stress, $\sigma^{ini}_2$. See the note*.

stress-3-effective f

initial maximum principal effective stress, $\sigma^{ini}_3$. See the note*.

pressure-reference f

reference pressure, $p^{ref}$ . A non-zero value should be specified based on the unit of stress/pressure adopted in the model. Most commonly used and highly recommended reference pressure is the standard atmospheric pressure, e.g., 100.0 if in kPa, 1.0e5 if in Pa. or other value compatible to the adopted stress/pressure unit.

stiffness-50-reference f

secant stiffness, $E^{ref}_{50}$, at 50% of the ultimate deviatoric stress, $q_f$, when $\sigma_3 = - p^{ref}$ in a triaxial test. A non-zero value must be specified.

stiffness-0-reference f

[advanced] Initial stiffness, $E^{ref}_{0}$, at zero strain when $\sigma_3 = - p^{ref}$. It is required that $E^{ref}_{0} > E^{ref}_{ur}$. If not input or by default, $E^{ref}_{0} = 3 \cdot E^{ref}_{ur}$. Need to be assigned only when the flag for small-strain stiffness is on, otherwise its value is useless.

stiffness-oedometer-reference f

[advanced] tangent stiffness, $E^{ref}_{oed}$, when $\sigma_1 = - p^{ref}$ in an oedometer test. By default, $E^{ref}_{oed} = E^{ref}_{50}$ if $E^{ref}_{oed}$ is not specified while $E^{ref}_{50}$ has been specified.

stiffness-ur-reference f

[advanced] unloading-reloading stiffness, $E^{ref}_{ur}$, when $\sigma_3 = - p^{ref}$ in a triaxial test. This value must be greater than $2 \cdot E^{ref}_{50}$. By default, $E^{ref}_{ur} = 4 \cdot E^{ref}_{50}$.

coefficient-normally-consolidation f

[advanced] normal consolidation coefficient, $K_{nc}$. It is not allowed to be less than $\nu / (1-\nu)$, a range 0.5 to 0.7 is common. The default is $K_{nc} = 1 - \sin \phi$.

constant-alpha f

[advanced] dimensionless parameter in the cap yield function, $\alpha$. Initialized internally. See the note* for an alternative option.

factor-contraction f

[advanced] contraction factor, $F_c$, allowable range is 0.0 to 0.25. The default is 0.0.

factor-cut f

[advanced] cut-off factor, $f_{cut}$. The default is 0.1.

flag-initialization f

[advanced] flag for initialization. If set to 1, the internal variables will be recalculated. The default is 0.

flag-smallstrain f

[advanced] flag for small-strain stiffness . If set to on, the option of small-strain stiffness will be activated. The default is off.

over-consolidation-ratio f

[advanced] over consolidation ratio, $OCR$. For normally consolidated soil, the value should be input as 1.0. The default is 100.0, which denotes an “apparent” non-cap shear plastic hardening model.

poisson f

[advanced] Poisson’s ratio, $\nu$. The default is 0.2.

stiffness-cap-hardening f

[advanced] hardening modulus for cap hardening, $H_c$. Initialized internally. See the note* for an alternative option.

strain-70 f

[advanced] Shear strain at which $G_s / G_0$ = 72.2%, If not input or by default, $\gamma_{70} = 2 \times 10^{-4}$. Need to be assigned only when the flag for small-strain stiffness is on, otherwise its value is useless.

failure-ratio f

[advanced] failure ratio, $R_f$. The default is 0.9.

tension f

[advanced] tension limit, $\sigma^t$. The default is 0.0.

void-initial f

[advanced] initial void ratio, $e_{ini}$. If the current void ratio is not important, or you do not wish to activate the dilation smoothing technique, just use the default value. The default is 1.0.

void-maximum f

[advanced] allowable maximum void ratio, $e_{max}$ . The default is 999.0, which is not physical but it denotes that the dilation smoothing technical will nominally not activated.

bulk f

[read only] current loading-unloading bulk modulus, $K$

shear f

[read only] current unloading-reloading shear modulus, $G$

plastic-hardening-shear f

[read only] accumulated shear plastic hardening parameter, $\gamma^p$

plastic-hardening-volume f

[read only] accumulated volumetric plastic hardening parameter, $\varepsilon^p_v$

pressure-cap f

[read only] cap (preconsolidation) pressure, $p_c$. Determined by the current stress, $\alpha$, and $OCR$.

void f

[read only] current void ratio, $e$

Notes:

• The tension cut-off is ${\sigma}^t = min({\sigma}^t, c/\tan \phi)$.
• The parameters $\sigma^{ini}_1$, $\sigma^{ini}_2$, $\sigma^{ini}_3$ must be specified via commands or a FISH function the first time the PH model is assigned because it is a stress-dependent model. Negative values denote compressive stresses.
• Some parameter combinations may be rejected due to: 1) one or more parameters are out of predetermined limits; 2) internal parameters cannot be correctly determined; or 3) numerical instability.
• If both $\alpha$ and $H_c$ are specified non-zero values by the user, the PH model will use these user-defined parameters $\alpha$ and $H_c$, and the internal calculation for $\alpha$ and $H_c$ will not be performed.

Footnotes

Advanced properties have default values and do not require specification for simpler applications of the model.

Read only properties cannot be set by the user. However, they may be listed, plotted, or accessed through FISH.