Аннотация:The consolidation problems involve the study of soil compaction under load with the possibility of liquid outflow. Coupled consolidation boundary-value problem are derived from the general conservation laws of continuum mechanics (the equilibrium equation, the conservation of solid and liquid phases of the soil, and nonlinear Darcy's filtration law) using spatial averaging over a representative volume element (RVE). In the nonlinear framework soil porosity depends on skeleton displacements, the permeability coefficient tensor is a function of the effective stresses first invariant. Effective stresses are part of the averaged stresses in the solid phase caused by fluid-independent internal forces transmitted through the contacts between the grains of the soil skeleton.A completely physically and geometrically nonlinear formulation of the consolidation problem is given using the Lagrange approach with adaptation for the solid phase and the Euler approach for the fluid under the assumption of quasistatic deformation of the rock skeleton. The ALE (Arbitrary Lagrangian-Eulerian) method was used to link these approaches. Exactly, Lagrangian coordinates of the solid phase are chosen as the curvilinear coordinates of the ALE method. This method allows to exploit the convective velocity of the fluid relative to the solid phase. As a result, fluid filtration is formulated using Lagrangian mesh for the solid skeleton.To solve the nonlinear consolidation problem by numerical methods, the linearized variational equations in the current configuration are obtained. For spatial discretization, the finite element method (FEM) was used: trilinear finite elements for approximation of the filtration equation itself and quadratic finite elements for approximation of the equilibrium equations. An implicit time discretization was used for both filtration and equilibrium equations with Uzawa algorithm at each time step.To determine the effective moduli, a mathematically rigorous approach was used, called the asymptotic homogenization method, or the multi-scale method. The constitutive equations and relationships between material functions and state parameters were obtained using experimental data known in the literature. Numerical examples of water-saturated soil nonlinear deformation are given.