[case] SaturationVanGenuchten

A strain dependent bimodal water retention model.

It is based on the van Genuchten model.

The equation is as follows

\[S_{e} = \left((e_{m}+a \Delta e) \left[\frac{1}{((\frac{p_{c}}{p_{b}})^{n}+1)}\right]^{m} + (e_{M} - a \Delta e) \left[\frac{1}{((\frac{p_{c}}{p_{{b,M}}})^{n} +1)}\right]^{n} \right) \frac{1}{e}\]

with effective saturation defined as \(S_{e}=\frac{S-S_r}{S_{max}-S_r}\), where \(S_r\) and \(S_{max}\) are the residual saturation and the maximum saturation, respectively. The exponent \(m \in (0,1)\) is the same as in the van Genuchten equation ( see SaturationVanGenuchten). In the original work another exponent \(n\) is used, but usually set to \(n = 1 / (1 - m)\), and also in this implementation. The pressure scaling parameter \(p_{b}\) is added by the user and is the scaling parameter of the micropores. The scaling parameter of the macropores can be calculated as follows \(p_{b,M} = p_{b} d_{diff}\) The total void ratio and the void ratio of the micropores are \(e_0\) and \(e_m\). Another scaling factor \(a\) scales the effect of the strain

The changing void ratio is calculated as \(\Delta e = -\frac{(1-e)\epsilon_{vol}}{e}\), with \(\epsilon_{vol}\) as the volumetric strain. The result is then clamped between the residual and maximum liquid saturations.

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Used in the following test data files

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