[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

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


  • 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 \(S_0\).

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