Bishop's effective stress models comparison

Two models for the Bishop’s effective stress computation are presented; the power-law model, and saturation cut-off model. The models are: \[ \chi(S_\mathrm{L}) = S_\mathrm{L}^{m_\chi} \qquad \mbox{and}\qquad \chi(S_\mathrm{L}) = \chi = \begin{cases} 1 & \mbox{for $S_\text{L} \geq S_\text{cutoff}$} \\ 0 & \mbox{for $S_\text{L} < S_\text{cutoff}$.} \end{cases} \] Simulation result shows different influence of the effective stress on the displacement. In the test the medium is desaturated and then saturated again, which causes shrinkage and expansion of the domain. Power law with exponents 1, 1/5, and 5 and saturation cut-off at maximum liquid saturation of 0.95 are compared.