1. Introduction

Here we present a THM family of behavior laws for saturated and unsaturated environments. We describe the relationships that make it possible to calculate hydraulic and thermal quantities, taking into account strong couplings between these phenomena and also with mechanical deformations. The relationships presented here can be coupled with any law of mechanical behavior, provided that the hypothesis called effective Bishop’s constraints are made and that the law of mechanical behavior defines elastic constants (useful for coupled terms). For this reason, the purely mechanical part of the laws is not presented here.

The models selected are based on the presentation of porous media developed in particular by O. Coussy [1]. Behavioral relationships are obtained from thermodynamic considerations and with homogenization arguments that we do not present here, and which are fully described in the document by P. Charles [2]. Likewise, the general writing of equilibrium and conservation equations is not detailed, and the reader is referred to documents [R5.03.01] [3] and [R7.01.10] [4], which contain definitions useful for the understanding of this document.

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.

Each of the components of the porous medium therefore has mechanical, hydraulic and thermal behavior. The theory attempts to bring all these physical phenomena together. Chemical phenomena (transformations of constituents, reactions producing constituents etc…), as well as radiological phenomena are not taken into account at this stage of the development of Code_Aster. Mechanical, hydraulic and thermal phenomena are taken into account or not depending on the behavior invoked by the user in command STAT_NON_LINE, according to the following nomenclature:

Modeling	Phenomena taken into account
KIT_H	Hydraulics with unknown pressure
KIT_HM	Mechanics, hydraulics with unknown pressure
KIT_HHM	Mechanics, hydraulics with two unknown pressures
KIT_THH	Thermal, hydraulic with two unknown pressures
KIT_THM	Thermal, mechanical, hydraulic with unknown pressure
KIT_THHM	Thermal, mechanical, hydraulic with two unknown pressures

This document describes the laws for the most general case known as THHM. Simpler cases are obtained from the general case by simply cancelling out the quantities that are not present.