====== ECOU-P ======
===== Description =====
Constitutive law of flow in porous media for a pipe element
==== The model ====
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.
==== Files ====
Prepro: LECOUP.F \\
Lagamine: ECOU1.F
===== Availability =====
|Plane stress state| YES |
|Plane strain state| YES |
|Axisymmetric state| YES |
|3D state| YES |
|Generalized plane state| YES |
===== Input file =====
==== Parameters defining the type of constitutive law ====
^ Line 1 (2I5, 60A1)^^
|IL|Law number|
|ITYPE| 116 |
|COMMENT| Any comment (up to 60 characters) that will be reproduced on the output listing|
==== Integer parameters ====
None
==== Real parameters ====
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 $(\left[LT^{-1}\right])$ 
^ Line 1 (7G10.0) ^^
|PERMEA|soil intrinsic permeability (=$k$)|
|RHO|specific mass of the fluid (=$\rho_f$)|
|POROS|soil porosity (=$n_0$)|
|EMMAG|storage coefficient (=$C_p$)|
|ALPHA|$\alpha$ & $\beta$: parameter used to define the curve $\theta = \theta(p)$|
|BETA|:::|
|AREA|cross section of the pipe|
^Line 2 (1G10.0)^^
|VISCO|fluid dynamic viscosity ($\mu_f=10^{-3}$=default value for water at 20°C)|

The evolution of the stored fluid volume ($\theta$) with the fluid pressure ($p$) is given by the following functions:
  - 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
  - in absence of free surface: \[n = n_0 + C_p\]

===== Stresses =====
==== Number of stresses ====
3
==== Meaning ====
|SIG(1)|fluid flow in the pipe|
|SIG(2)|fluid flow stored as a consequence of the evolution of soil porosity|
|SIG(3)|0 (meaningless)|

===== State variables =====
==== Number of state variables ====
1
==== List of state variables ====
|Q(1)| cross section of the pipe |