The Influence of Non-Isothermal Conditions on Pressure Head Jumps in the Nonlinear Consolidation Problem in the Presence of Geobarriers

A nonlinear boundary value problem is considered for a system of parabolic equations in an inhomogeneous region, that requires conjugation conditions. The boundary value problem serves as a mathematical model of the nonlinear non-isothermal filtrationconsolidation process in a heterogeneous soil mass. A distinctive feature at the physical level is the application of a nonlinear Darcy’s law incorporating the threshold gradient, where this gradient depends on the thermal state of the porous medium. These features are also reflected in the conjugation conditions. The finite element method is applied to obtain approximate discontinuous solutions of the corresponding system of quasilinear parabolic equations. The existence and uniqueness of an approximate generalized solution are proven. Estimates for the accuracy of the finite element solutions are also established in terms of total approximation. A model test example is used to analyze the differences in pressure head and temperature distributions between the case studied in this article and the classical formulation.