1. Reference problem

In this test case, we study the hydraulic behavior of a saturated porous medium constituted by a single fluid: water in its liquid phase. In Code_Aster, it is an HM model. According to the models, the associated fluid behavior law is either of type LIQU_SATU (models A and C) or of type LIQU_GAZ_ATM (models B and D).

1.1. Geometry

Illustration 1: Geometry

Coordinates of points \((m)\):

\(A(\mathrm{-}0.5,\mathrm{-}0.5)\); \(C(0.5,0.5)\)

\(B(0.5,\mathrm{-}0.5)\); \(D(\mathrm{-}0.5,0.5)\)

1.2. Material properties

Liquid water	Density \(({\mathrm{kg.m}}^{-3})\) Dynamic viscosity of liquid water \((\mathrm{Pa.s})\) 1/Compressibility \(({\mathit{Pa}}^{\mathrm{-}1})\)	\({10}^{3}\) \(0.001\) \({K}_{e}=3.77{10}^{-9}\)
Solid	Drained Young’s Modulus \(E(\mathrm{Pa})\) Poisson’s Ratio	\(225{10}^{6}\) \(0\)
Initial state	Porosity Temperature \((K)\) Liquid Pressure \((\mathrm{Pa})\) Vapor Pressure \((\mathrm{Pa})\)	\(0.4\) \(273\) \(0\) \(1\)
Constants	Ideal gas constant	\(8.32\)
Homogenized coefficients	Homogenized density \(({\mathrm{kg.m}}^{-3})\) Sorption isothermal Biot coefficient Intrinsic permeability \(({m}^{2})\)	\(1600\) \(1\) \({K}_{\text{int}}={10}^{-18}\)

Table 1.2-1 : Material data

The gravity of water is overlooked.

1.3. Boundary conditions and loads

Full item:

blocked trips \({u}_{x}={u}_{y}={u}_{z}=0\)

(this is a purely hydraulic case, the mechanics being blocked).

Upper side:

water flow: \({Q}_{\mathrm{lq}}=0.005{\mathrm{kg.s}}^{-1}\mathrm{.}{m}^{-2}\)

Lower side:

water flow \({Q}_{\mathrm{lq}}=0\)

Side faces:

Elsewhere: zero flow

1.4. Initial conditions

The displacement fields and liquid pressure fields are initially zero and the reference temperature is set to \({T}_{0}\mathrm{=}273°K\).