1. The main lines#

1.1. Background of studies THM#

First of all, it is necessary to define the very precise framework for Thermo-Hydro-Mechanical calculations. Their exclusive application is the study of porous media. Knowing this, modeling THM covers the mechanical evolution of these environments and the flows within them. The latter concern one or two fluids and are governed by Darcy’s laws (Darcean fluids). The complete THM problem therefore deals with the flow of fluid (s), skeletal mechanics, as well as thermics: the resolution is very often entirely coupled.

Note:

In the expression of Darcy’s laws that is used here, the differential acceleration of water is overlooked. In the case of very permeable and very porous environments subject to seismic loading, this may constitute a limit.

1.2. Generalities#

The calculations are based on THM families of behavior laws for saturated and unsaturated porous media. The mechanics of porous media brings together a very exhaustive collection of physical phenomena affecting solids and fluids. It hypothesizes a coupling between the mechanical evolutions of solids and fluids, seen as continuous media, with hydraulic evolutions, which solve the problems of diffusion of fluids within walls or volumes, and thermal evolutions. The formulation of Thermo-hydro-mechanical modeling (THM) in porous media as it is done in Code_Aster is detailed in [R7.01.11] and [R7.01.10]. All the notations used here therefore refer to it. However, some essential notations are mentioned below:

With regard to fluids, we consider (the most complete case) two phases (liquid and gas) and two components called water and air for convenience. The following indices are then used:

\(w\) for liquid water

\(\text{ad}\) for dissolved air

\(\text{as}\) for dry air

\(\text{vp}\) for water vapor

The thermodynamic variables are:

  • the pressures of the constituents: \({p}_{w}(x,t)\), \({p}_{\text{ad}}(x,t)\),, \({p}_{\text{vp}}(x,t)\), \({p}_{\text{as}}(x,t)\),

  • the temperature of medium \(T(x,t)\).

These different variables are not completely independent. In fact, if we consider a single component, the thermodynamic balance between its phases imposes a relationship between the pressure of the vapor and the pressure of the liquid of this component. Finally, there is only one independent pressure per component, just as there is only one mass conservation equation. The number of independent pressures is therefore equal to the number of independent components. The choice of these pressures varies according to the laws of behavior.

For the so-called saturated case (a single air or water component), we chose the pressure of this single component.

For the so-called unsaturated case (presence of air and water), we chose as independent variables:

  • the total pressure of gas \({p}_{\text{gz}}(x,t)={p}_{\text{vp}}+{p}_{\text{as}}\),

  • capillary pressure \({p}_{c}(x,t)={p}_{\text{gz}}-{p}_{\text{lq}}={p}_{\text{gz}}-{p}_{w}-{p}_{\text{ad}}\).

We will see later the Aster terminology for these variables.

1.3. Calculation steps#

For the steps necessary to implement an Aster calculation, regardless of aspects purely THM, reference will be made to the documentation for each command used.

In any Aster calculation, several key steps must be performed:

  • Choice of modeling

  • Material data

  • Initialization

  • Calculation

  • Post-treatment

    These points are detailed in the next chapter.