OGS
[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.