1. Reference problem#

1.1. Geometry#

We are using a one-dimensional problem in Cartesian coordinates, corresponding to a hypothesis of plane deformations in the direction \(y\).

The « structure » considered is finally a segment of length \(L\mathrm{=}20m\).

Liquid water	Density \(({\mathrm{kg.m}}^{-3})\) Specific heat at constant pressure \(({\mathrm{J.K}}^{-1})\) Dynamic viscosity of liquid water \((\mathrm{Pa.s})\) Coefficient of thermal expansion of liquid \(({K}^{-1})\) Compressibility \(({\mathit{Pa}}^{\mathrm{-}1})\)	\({10}^{3}\) \(4180\) \(0.001\) \(1.{10}^{-4}\) \({K}_{e}=5.{10}^{-10}\)
Solid	Drained Young’s Module \(E(\mathrm{Pa})\) Poisson’s ratio Coefficient of thermal expansion of solid \(({K}^{-1})\)	\(2.166{10}^{9}\) \(0.3\) \({10}^{-5}\)
Initial state	Porosity Temperature \((K)\) Liquid pressure \((\mathrm{Pa})\) Vapor pressure \((\mathrm{Pa})\)	\(0.14\) \(293\) \(0\) \(2320\)
Homogenized coefficients	Homogenized density \(({\mathrm{kg.m}}^{-3})\) Biot coefficient Intrinsic permeability \(({m}^{2})\) Thermal conductivity \(({\mathrm{W.K}}^{-1}{m}^{-1})\) Constant stress heat \(({\mathrm{J.K}}^{-1})\)	\(2410\) \(1\) \({K}_{\text{int}}={10}^{-19}\) \({\lambda }_{T}=1.8\) 565.

A vertical bar in vertical positioning is heated:

With \({\lambda }_{T}\frac{\mathrm{\partial }T}{\mathrm{\partial }x}\mathrm{=}{\Psi }_{T}\) independent of time \(t\)

Which corresponds to:

In \(x\mathrm{=}0\): zero displacement, zero hydraulic flow, imposed heat flow \({\Psi }_{T}=100{\mathrm{W.m}}^{-2}\) constant in time
In \(x\mathrm{=}L\): zero displacement, zero hydraulic flow, zero heat flow.

\(u(x)\mathrm{=}P(x)\mathrm{=}0\) \(T(x)={T}_{0}=20°C\) everywhere.