OGS
[case] LinearSaturationSwellingStress

This class defines a linear saturation rate dependent swelling stress model for the materials that swell strongly when water content increases.

Clay materials like bentonite have a high swelling capacity in dry state, and their swelling property can be described by this model.

The original model was proposed in [34] (equations (39) and (40) on pages 758–759). With a simplification of the parameters of the original formula and introducing a constraint to avoid shrinkage stress when saturation is below the initial saturation, the model takes the form

${\mathbf{\sigma}}^{\text{sw}} = {\alpha}_{\text{sw}} (S-S_0) \mathbf{I}, \, \forall S \in [S_0, S_\text{max}]$

where $${\alpha}_{\text{sw}}$$ is a coefficient, and $$S_0$$ is the initial saturation, and $$S_{\text{max}}$$ is the maximum saturation. The coefficient gives the swelling stress at full saturation, which can be computed as

${\alpha}_{\text{sw}} = \frac{{{\sigma}}^{\text{sw}}_{\text{max}}}{(S_{\text{max}}-S_0)}$

where $${{\sigma}}^{\text{sw}}_{\text{max}}$$ represents the swelling stress at full saturation.

In the numerical analysis, the stress always takes the incremental form. Therefore the model becomes as

$\Delta {\mathbf{\sigma}}^{\text{sw}} = {\alpha}_{\text{sw}} \Delta S \mathbf{I}, \, \forall S \in [S_0, S_\text{max}]$

Note:

• In the property, saturation means water saturation.
• The upper limit of saturation is not guaranteed, but it is required to be less or equal to $$S_\text{max}$$ when calling this property. Therefore it is not checked again in this class.Thus, this model only needs two input parameters: $${\alpha}_{\text{sw}}$$ and $$S_0$$.