Thermodynamic foundations of coupled thermo-hydro-mechano-chemical processes in geological and geoengineering materials with complex rheology

The ongoing energy transition and technological advancements present increasingly complex challenges for numerical modeling, necessitating the development of multi-physics, multi-scale approaches. Recent progress in high-performance computing has catalyzed the rapid evolution of a new generation of numerical codes designed to tackle these complex problems. However, this progress demands revisiting and refining constitutive models to ensure they are rigorous, thermodynamically consistent, and suitable for computational implementation. In this work, we present a thermodynamic framework for coupled thermo-hydro-mechano-chemical processes in porous media undergoing elastic, viscous, and plastic deformation. The formulation is developed in an Eulerian description and assumes local thermodynamic equilibrium for each phase. By enforcing the second law of thermodynamics through non-negative entropy production, we derive a complete and thermodynamically admissible set of governing equations and closure relations for visco-elasto-plastic porous materials with thermal and chemical coupling. A key result is the identification of the conjugate thermodynamic force associated with porosity, which provides a consistent basis for formulating viscous, plastic, and reaction-induced porosity evolution. The equilibrium (elastic) closure relations are derived from the symmetry properties of the thermodynamic potentials, yielding a compliance matrix that unifies poroelastic, thermoelastic, and thermo-porous couplings. Classical limits are recovered naturally, including Biot and Gassmann relations for homogeneous matrices, Brown–Korringa relations for heterogeneous solids, and Darcy’s law as the low-frequency limit of the dynamic momentum balance. The framework also clarifies the role of inertial (added-mass) effects and relates them to pore-scale tortuosity. The derived equations are implemented in a numerical code, and a numerical example illustrating the propagation of a porosity wave in a viscoelastic medium is presented.