[doc] Comparison of different Bishop's models.

web/content/docs/benchmarks/richards-mechanics/bishops-effective-stress.pandoc

@@ -0,0 +1,33 @@
++++
+project = "RichardsMechanics/bishops_effective_stress_power_law.prj"
+author = "Dmitri Naumov"
+date = "2020-02-27"
+title = "Bishop's effective stress models comparison"
+weight = 153
+
+[menu]
+  [menu.benchmarks]
+    parent = "richards-mechanics"
+
++++
+
+{{< data-link >}}
+
+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.
+{{< img src="../BishopsEffectiveStress.png" >}}