1. Reference problem#

1.1. Geometry#

A cube with a side of \(1m\).

1.2. Material properties#

Elastic properties:

\(E+150.{10}^{6}\mathrm{Pa}\)

\(\nu =0.3\)

*Model specific settings**Infelas: *

  • \({\beta }_{m}=0.1142\)

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

Hydraulic properties:

Liquid water

Density (\({\mathrm{kg.m}}^{-3}\)) Heat at constant pressure (\({\mathrm{J.K}}^{-1}\)) coefficient of thermal expansion of liquid (\({K}^{-1}\)) Compressibility (\({\mathrm{Pa}}^{-1}\)) Viscosity (\(\mathrm{Pa.s}\))

1.103 4180 10-4 5.10-10 10-3

Gas

Molar mass (\(\mathrm{kg.}{\mathrm{Mol}}^{-1}\)) Heat at constant pressure (\({\mathrm{J.K}}^{-1}\)) Viscosity (\(\mathrm{Pa.s}\))

0.002 1000 9. 10-6

Skeleton

Heat capacity at constant stress (\({\mathrm{J.K}}^{-1}\))

1000

Constants

Ideal gas constant

8,315

Homogenized coefficients

Homogenized density (\({\mathrm{kg.m}}^{-3}\)) Biot coefficient Parameters of the Van-Genuchten model \(N\) \(\mathrm{Pr}(\mathrm{Mpa})\) \(\mathrm{Sr}\)

2000 1 1.61 16.106 0

Reference state

Porosity Temperature (\(°K\)) Capillary pressure (\(\mathrm{Pa}\)) Gas pressure (\(\mathrm{Pa}\))

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 (\(\mathit{DX}=\mathit{DY}=\mathit{DZ}=0\)).

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 \(\mathrm{44,7}\mathrm{Mpa}\) and \(-10\mathrm{Mpa}\) is imposed on the entire domain.

1.5. Bibliographical references#

  1. Gérard, P., Charlier R., Barnichon, J.D., Su, J.D., Su, K. Shao, Su, K. Shao, J-F, Duveau, G., Giot, R., Chavant, C. Collin, F. « Numerical modeling of coupled mechanics and gas transfer » Journal of Coupled Mechanics and Gas Transfer » Journal of Theoretical and Applied Mechanics, Journal of Theoretical and Applied Mechanics, Journal of Theoretical and Applied Mechanics, Sofia, 2008, vol. 38, No. 1, pp. 101-120.