This paper presents a general method for defining the macroscopic free-energy density function and its complementary forms for a porous medium saturated by two non-miscible fluids, in the case of compressible fluid and solid constituents, non-isothermal conditions and negligible interfacial surface energy. The major advantage of the proposed approach is that no limitation or simplification is posed on the choice of the free energies of the fluid constituents. As a result, a fully non-linear equation of state for the pore fluids can be incorporated within the proposed framework. The method is presented under the assumption that interfacial surface energy terms are negligible, thus recovering a Bishop parameter chi coinciding with the degree of saturation, which is expected to be applicable mostly to non-plastic soils. Moreover, small strains of the solid skeleton are assumed, but the method can be easily extended to a large strain formulation as discussed below. The paper analyzes also some particular cases concerning the incompressibility of all constituents, the geometric linearization and the incompressibility only of the solid constituent. The knowledge of the free energy density function is the starting point for the evaluation of the dissipation function, of energy and entropy balance and, in general, for the formulation of thermodynamically consistent constitutive models.

This paper presents a new and rigorous method for simulating thermo-elasto-plastic responses of soil during the cylindrical cavity expansion process under undrained conditions. The soil is modeled by a modified nonisothermal unified hardening model, which can properly consider thermal effects on mechanical responses, thermally induced excess pore water pressure as well as the overconsolidation characteristics. The temperaturedependent governing equations are derived by combining equilibrium equations and constitutive relations. New solution algorithms are developed to solve governing equations and update temperature -related parameters during the expansion process. Two typical scenarios, one is cavity expansion under different temperatures and another is temperature variation after expansion, are simulated. The proposed computational approach is validated through comparisons with results obtained from Abaqus numerical simulations, non -isothermal analyses, and experimental data. As demonstrated by extensive parametric studies, the proposed computational approach can reasonably capture the influence of temperature on cavity expansion, which can be further applied, modified, and developed for various industrial and geophysical problems involving thermoplastic soils.