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Hydraulic constitutive model

*Material, ...
...
*Hydraulic = <hydraulic model> [,Swr=residual water saturation]
*<parameter 1>, ... , <parameter n>
[*Jacobian = <method>]
...

Use this keyword to specify the hydraulic model to be used for the calculation of the degree of saturation. The subsequent lines <parameter 1>, ... , <parameter n>} depend on the constitutive model chosen. A list of available soil-water retention models implemented in numgeo is given in Section Soil-water retention models. In addition, optional settings (given in squared brackets [...] in above keyword snipped) can be prescribed by the user as outlined in Section Optional settings.

The *Hydraulic keyword is only allowed for materials with more than one phase.

Soil-water retention models

Model Dependence Hysteresis
Van Genuchten capillary pressure \(p^c\) no
Brooks & Corey capillary pressure \(p^c\) no
Fredlund & Xing capillary pressure \(p^c\) no
Exponential model capillary pressure \(p^c\) no
Karlsruhe Model capillary pressure \(p^c\), void ratio \(e\) yes

Optional settings

In addition to the selection of the constitutive model for the soil-water retention behaviour, users can specify the following optional settings:

  • Residual water saturation \(S^{wr}\)

    \(S^{wr}\) can be prescribed by adding [,Swr=<residual water saturation>] after the model specification. \(S^{wr}\) is given as fraction of 1, e.g. \(S^{wr}=0.32\) for a residual degree of saturation of 32 %. If this parameter is omitted, \(S^{wr}=0\) is assumed.

  • Jacobian \(d(S^w)/d(s)\)

    For the evaluation of the partial derivative \(d(S^w)/d(s)\) with respect to the suction three methods are available. The default setting is the usage of a "smoothed derivative". To specify the method a second input line is added after the material parameters. The additional input line reads *Jacobian = <method>, where <method> denotes the method used to evaluate \(d(S^w)/d(s)\).

    The methods available in numgeo are:

    • Analytical: The analytical derivative of the respective constitutive model for the current suction \(s\) is used.

    • Smoothed: The analytical derivation is smoothed by evaluating the Jacobian over 10 substeps. This is the default option.

    • Chord-Slope: A chord-slope approximation of the Jacobian for the current values of \(d (S^w)\) and \(d(s)\) is used.

    • Time-Step-Centered: The analytical derivation is averaged for the current suction \(s\) and previous suction \(s_0\).