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Exponential model

A simple exponential model in which the effective degree of saturation \(S^e\) is related to the suction with only one parameter \(\zeta\) 1:

\[\begin{equation*} S^e = e^{-\zeta \cdot s} \end{equation*}\]

Note that in numgeo*, the version using the degree of saturation \(S^w\) is implemented:

\[\begin{equation*} S^w = S^{wr}+ (1-S^{wr}) e^{-\zeta \cdot s} \end{equation*}\]

In contrary to the commonly used formulation 1, the suction \(s\) is used instead of the pressure head in Equation. Therefore, the parameter \(\zeta\) is related to the original formulation (\(\zeta^o\)) via \(\zeta = \zeta^o/\gamma^w\). The input takes the form:

*Hydraulic = Exponential [,Swr]
zeta

  1. Ayman A. Abed and Wojciech T. Sołowski. A study on how to couple thermo-hydro-mechanical behaviour of unsaturated soils: physical equations, numerical implementation and examples. Computers and Geotechnics, 92:132–155, 2017. URL: https://www.sciencedirect.com/science/article/pii/S0266352X17302033, doi:10.1016/j.compgeo.2017.07.021. ↩↩