Constitutive law of flow in porous media for a pipe element

This law is only used for non linear analysis of seepage in porous media.
The case of free surface seepage is also treated.
This law is used for one‑dimensional flow.

Prepro: LECOUP.F
Lagamine: ECOU1.F

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The permeability $k$ is an intrinsic permeability $\left(\left[L^2\right]\right)$ \[k_{intrinsic}=K\frac{\mu_f}{\rho_fg} \\ [L^2]=[LT^{-1}]\frac{[ML^{-1}T^{-1}]}{[ML^{-3}][LT^{-2}]} \]

Where $K$ is the permeability coefficient $(\left[LT^{-1}\right])$

The evolution of the stored fluid volume ($\theta$) with the fluid pressure ($p$) is given by the following functions:

1. in case of seepage with free surface: \[\theta = n_0 \left( \frac{1}{\pi} \arctan\left(\frac{p-\beta}{\alpha}\right) +\frac{1}{2}\right) + C_p^* \left(p-\beta\right)\]
   with:
   • $C_P^* = C_p$ below the free surface
   • $C_P^* = 0$ above the free surface
2. in absence of free surface: \[n = n_0 + C_p\]

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