1. Presentation of the model and notations

This model is a law of behavior in rock mechanics that makes it possible to describe the behavior of materials such as « swelling clay » (bentonite). It is a non-linear elastic model relating net stress to inflation pressure, which itself depends on suction (or capillary pressure). It can only be used for THHM and HHM behaviors.

This model is based on the following relationship:

(1.1)\[ d\ stackrel {~} {\ mathrm {\ sigma}} = {K} _ {sigma}}} = {K} _ {sigma}} = {K} _ {V} +b\ left (1+\ frac {\ mathit {Pc}} {s}} (\ mathit {Pc}} {s} (\ mathit {Pc}) (\ mathit {Pc}) d {\ mathrm {\ epsilon}} _ {beta}} +b\ left (1+\ frac {\ mathit {Pc}}} {A}\ right) {e} ^ {- {\ mathrm {\ beta}} +b\ left (1+\ frac {\ mathit {Pc}}} {m} {\ left (\ frac {s} {A}\ right)} ^ {2}}\ mathit {dPC}\]

with \(\tilde{\sigma }\): net constraint or effective constraint. Here we choose the net constraint (cf. section 2.1).

In the version of the model available here, the non-linearity of \({K}_{s}(\mathit{Pc})\) and its dependence on suction are not taken into account. In the end, we simply have \({K}_{s}(\mathit{Pc})={K}_{0}\).

With the following notations:

\({K}_{0}\) is the incompressibility module of the material

\(b\) is the Biot coefficient

\(A\) is a parameter that is homogeneous at one pressure

\({\mathrm{\beta }}_{m}\) is a dimensionless parameter

\(\mathit{Pc}\) is capillary pressure

The concept of inflation pressure \({P}_{\mathit{gf}}\) is also defined here, which will be used later.