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Permeability

*Permeability [= model]
<subsequent line>

This keyword is used to prescribe the intrinsic permeability \(\bar{K}^s_{ij}\) (equal for all pore-fluids of the material and not to be confused with the hydraulic conductivity). The corresponding hydraulic conductivity \(K^\beta_{ij}\) of the saturated (or dry) material can be calculated as follows:

\(K^\beta_{ij} = \bar{K}^s_{ij} \cdot \frac{\gamma^\beta}{\mu^\beta}\)

therein \(\gamma^\beta\) is the specific weight and \(\mu^\beta\) the dynamic viscosity of the fluid phase \(\beta\) occupying the pore space. Notice that the influence of the gravity (or generally spoken the influence of body-forces) on the permeability is handled inside the finite element. The following models are available in numgeo:

  • *Permeability: the default permeability model assumes a constant anisotropic permeability of the material. 3 parameters (\(\bar{K}^s_{xx}, \bar{K}^s_{yy}, \bar{K}^s_{zz}\)) are required in the <subsequent line> following the keyword:

    *Permeability
    \(\bar{K}^s_{xx}, \bar{K}^s_{yy}, \bar{K}^s_{zz}\)

  • *Permeability = isotropic: assumes an isotropic permeability tensor (\(\bar{K}^s_{ii}=K\)) is assumed and only one parameter is required in the <subsequent line>:

    *Permeability = isotropic
    \(K\)

  • *Permeability = Kozeny-Carman: use a Kozeny/Carman type constitutive model 12 to prescribe the permeability as a function of the void ratio, i.e. \(\bar{K}^s_{ij}(e)\).

    \(k(n) = \frac{1}{c} \frac{\gamma^w}{\eta^w} \frac{n^3}{(1-n)^2} d_{e}^2.\)

    Therein, \(\gamma^w = 10\) kN/m\(^3\) is the specific weight and \(\eta^w\) the dynamic viscosity of the pore-water. This constitutive model requires two parameters: the effective grain size \(d_e\) and the fitting parameter \(c\). For more information on the constitutive model, the reader is referred to the Theory Manual of numgeo.

    *Permeability = Kozeny-Carman
    \(c\),\(d_e\)

  1. Kozeny Josef. Über kapillare Leitung des Wassers im Boden. Volume 136. Hölder-Pichler-Tempsky, A.-G.[Abt.]: Akad. d. Wiss., 1927. URL: www.biologiezentrum.at. ↩

  2. P. C. Carman. Permeability of saturated sands, soils and clays. The Journal of Agricultural Science, 29(2):262–273, 1939. doi:10.1017/S0021859600051789. ↩