1. Reference problem

1.1. Geometry

Geometry is a square [1mx1m]

1.2. Material properties

Elastic properties:

\(E\mathrm{=}150{10}^{6}\mathit{Pa}\)

\(\nu \mathrm{=}0.3\)

Parameters specific to the GonfElas model:

\({\beta }_{m}\mathrm{=}0.1142\)

Reference pressure \(A\mathrm{=}1.\mathit{Mpa}\)

Hydraulic properties:

Liquid water	Density (\({\mathit{kg.m}}^{\mathrm{-}3}\)) Heat at constant pressure (\({\mathit{J.K}}^{\mathrm{-}1}\)) coefficient of thermal expansion of liquid (\({K}^{\mathrm{-}1}\)) Compressibility (\(\mathit{Pa}\mathrm{-}1\)) Viscosity (\(\mathit{Pa.s}\))	1.103 4180 10-4 5.10-10 10-3
Gas	Molar mass (\(\mathit{kg.}{\mathit{Mol}}^{\mathrm{-}1}\)) Heat at constant pressure (\({\mathit{J.K}}^{\mathrm{-}1}\)) Viscosity (\(\mathit{Pa.s}\))	0.002 1000 9. 10-6
Skeleton	Heat capacity at constant stress (\({\mathit{J.K}}^{\mathrm{-}1}\))	1000
Constants	Ideal gas constant	8,315
Homogenized coefficients	Homogenized density (\({\mathit{kg.m}}^{\mathrm{-}3}\)) Biot coefficient Parameters of the Van-Genuchten model \(N\) \(\mathit{Pr}(\mathit{Mpa})\) \(\mathit{Sr}\)	2000 1 1.61 16.106 0
Reference state	Porosity Temperature (\(K\)) Capillary pressure (\(\mathit{Pa}\)) Gas pressure (\(\mathit{Pa}\))	0.366 303 0. 10

1.3. Initial conditions

At \(t=0\):

• \(\mathit{Pgaz}=1\mathit{atm}\)

• \(S=\mathrm{0,5}\) (i.e. \(\mathit{Pc}=\mathrm{44,7}\mathit{Mpa}\) and \({p}_{w}=-44.6\mathit{Mpa}\))

• Total compressive stress equal to -1 atm.

1.4. Boundary conditions and loads

All trips are blocked at the edge (\(\mathit{DX}\mathrm{=}\mathit{DY}\mathrm{=}0\)).

The flows are zero.

The initial saturation is \(\text{50 \%}\): we increase the saturation and we follow the evolution of the total stress. By definition, swelling pressure is the stress obtained upon complete restoration.

To do this, a loading of capillary pressure decreasing linearly in \(\mathrm{1s}\) between \(\mathrm{44,7}\mathit{Mpa}\) and \(\mathrm{-}10\mathit{Mpa}\) is imposed on the entire domain.