The porosity of a linear poroelastic medium per unit volume of the undeformed medium.
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template<class Scalar>
class Dumux::PorosityLinearPoroElasticity< Scalar >
In linear poroelasticity [28], the porosity relative to a reference state with porosity \(\phi_0\) is
\[ \phi = \phi_0 + \alpha \Delta\varepsilon_v + \frac{\Delta p}{N},
\qquad
\frac{1}{N} = \frac{\alpha - \phi_0}{K_s} = \frac{(\alpha - \phi_0)(1 - \alpha)}{K},
\]
where \(\Delta\varepsilon_v\) and \(\Delta p\) are the changes of the volumetric strain \(\varepsilon_v = \nabla \cdot \mathbf{u}\) and of the pore pressure with respect to the reference state, \(\alpha = 1 - K/K_s\) is the Biot coefficient, \(K\) is the drained bulk modulus of the solid skeleton and \(K_s\) is the bulk modulus of the solid grains.
This porosity (Lagrangian porosity) is the pore volume per unit volume of the undeformed medium, which is the porosity entering the storage term of a fluid mass balance on the undeformed grid. With a pore fluid of bulk modulus \(K_f\), this storage term corresponds to the Biot modulus \(M\) with \(1/M = \phi_0/K_f + 1/N\). For incompressible grains ( \(\alpha = 1\)), the porosity is \(\phi = \phi_0 + \Delta\varepsilon_v\).
- Template Parameters
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| Scalar | The type used for scalar values |
1.16.1