Analytical and numerical studies on the behavior of a freezing soil layer

Abstract

This paper focuses on investigating how a particular but classical configuration of a finite homogeneous soil layer, once studied by Terzaghi and currently subjected to freezing temperatures, behaves and how different boundary conditions can intervene and affect the thermo-hydro-mechanical (THM) responses. Spatial homogeneity is a strong assumption but has the decisive advantage of simplicity, allowing eventually the construction of an analytical solution, useful both to enhance understanding and as a benchmark. The essential relations on the constitutive behavior of saturated poroelastic soils are firstly recalled, in the general non-linear case where material parameters are state-dependent. Solutions to both linearized governing equations with constant material parameters and general non-linear equations with state-dependent parameters are then developed respectively by analytical derivation and by a commercial code COMSOL based on finite elements method accounting for two different sets of boundary conditions. The validity of this numerical modelling is partially verified using the analytical solution in the limiting case of state-independent parameters. Comparison between the results given by the linearized analytical solutions and the non-linear numerical model reveals the important impact of ice content variations on various material parameters that modify significantly the THM responses. Nonetheless, the analytical solutions based on linearized equations give a correct order-of-magnitude estimate, especially at moderate temperature variations, and remain a useful tool for preliminary design checks. Numerical results accounting for two different hydraulic boundary conditions at the ground surface reveal how such factors can modify significantly the THM evolution of the soil mass. In the last part of the paper, a limited parametric study on the effect of permeability relative to liquid water flow highlights how this parameter plays an important role in the development of excess water pressures hence ground movements.