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Subsubsection 4.8.2.4: Referentially Isotropic Permeability Up Subsection 4.8.2: Permeability Materials Subsubsection 4.8.2.6: Referentially Transversely Isotropic Permeability

#### 4.8.2.5 Referentially Orthotropic Permeability

The material type for a poroelastic material with strain-dependent permeability which is orthotropic in the reference configuration is “perm-ref-ortho”. The following material parameters need to be defined:
 isotropic hydraulic permeability [L/Ft] hydraulic permeabilities along orthogonal directions () [L/Ft] hydraulic permeabilities along orthogonal directions () [L/Ft] isotropic exponential strain-dependence coefficient () [ ] orthotropic exponential strain-dependence coefficient (, ) [ ] isotropic power-law exponent () [ ] power-law exponent (, ) [ ]
This material uses a strain-dependent permeability tensor that accommodates strain-induced anisotropy: where, is the Jacobian of the deformation, i.e. where is the deformation gradient. are second order tensors representing the spatial structural tensors describing the orthogonal planes of symmetry, given by where are orthonormal vectors normal to the planes of symmetry (defined as described in Section 4.1.1.2↑). Note that the permeability in the reference state ( is given by .
Example:
<permeability name="Permeability" type="perm-ref-ortho">
<perm0>0.001</perm0>
<perm1>0.01, 0.02, 0.03</perm1>
<perm2>0.001, 0.002, 0.003</perm2>
<M0>0.5</M0>
<M>1.5, 2.0, 2.5</M>
<alpha0>1.5</alpha0>
<alpha>2, 2.5, 3</alpha>
</permeability>


Subsubsection 4.8.2.4: Referentially Isotropic Permeability Up Subsection 4.8.2: Permeability Materials Subsubsection 4.8.2.6: Referentially Transversely Isotropic Permeability