1. Reference problem

1.1. Presentation

In this test case, we study the thermo-hydro-mechanical behavior of a saturated porous medium constituted by a single fluid: water in its liquid phase. In Code_Aster, this is a THM model. The associated law of fluid behavior is of type LIQU_SATU.

1.2. Geometry

We consider a cube with a side of 1 m centered on the center of the \((-\mathrm{0,5}\le x\le \mathrm{0,5};-\mathrm{0,5}\le y\le \mathrm{0,5};-\mathrm{0,5}\le z\le \mathrm{0,5};)\) axis.

1.3. Material properties

solid	Density \(({\mathrm{kg.m}}^{-3})\) Drained Young’s module \(E(\mathrm{Pa})\) Poisson’s ratio Coefficient of thermal expansion of solid \(({K}^{-1})\)	\(2.\times {10}^{3}\) \(225.\times {10}^{6}\) \(0.\) \(8.\times {10}^{-6}\)
Fluid	Density \(({\mathrm{kg.m}}^{-3})\) Heat at constant pressure \(({\mathrm{J.K}}^{-1})\) Coefficient of thermal expansion of liquid \(({K}^{-1})\) Derivative of the conductivity of the fluid with respect to temperature	\({10}^{3}\) \(2.85\times {10}^{6}\) \({10}^{-4}\) \(0.\)
Thermal	Homogenized conductivity \(({\mathrm{W.K}}^{-1}{m}^{-1})\) Derivative of conductivity homogenized with respect to temperature	\(1.7\) \(0.\)
Homogenization coefficients	Coefficient of \(\mathrm{Biot}\) Porosity	\({10}^{-12}\) \(0.4\)
Homogenized coefficients	Density \(({\mathrm{kg.m}}^{-3})\) Constant stress heat \(({\mathrm{J.K}}^{-1})\)	\(1.6\times {10}^{3}\) \(2.85\times {10}^{6}\)

1.4. Boundary conditions and loads

• Full item:

fluid pressure \(\mathrm{PRE1}=500.0\mathrm{Pa}\) (no flow or variation in the mass of water)

• Underside:

trips \({u}_{x}=0.0m,{u}_{y}=0.0m,{u}_{z}=0.0\mathrm{m.}\)

• Upper side:

Displacement \({u}_{z}={10}^{-3}m\)

1.5. Initial conditions

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