The present paper states and provides an analytical solution for the problem of evaluating the settlement and load-bearing capacity of weighty soil layers of limited thickness resting upon incompressible soil bases and an excavation pit wall upon exposure of the foundation to a distributed load in the vicinity of a wall. The authors develop a method for determining the stressed state component in the reduced engineering problem based on the Ribere–Faylon trigonometric series and for accounting for the nonlinear deformation properties of soils, building on the analytical dependencies of S.S. Grigoryan and S.P. Timoshenko. In order to determine the relationship between stress and strain, the Hencky’s physical equation systems were used. They factor in the impact of average stresses σm on the shear modulus of elasticity G (σm) and volumetric modulus of elasticity K (σm). The obtained solutions make it possible to assess the deformation of soil bases and the load-bearing capacity with respect to nonlinear properties in a way that accurately corresponds to the actual performance of subsoils exposed to loading. The theoretical results are followed by numerical experiments to prove their validity.

The present paper describes and provides an analytical solution for the problem of evaluating the settlement and load-bearing capacity of weighty soil layers of limited thickness resting upon incompressible soil bases and an excavation pit wall, upon exposure of the foundation to a distributed load in the vicinity of a wall. The authors developed a method for determining the stressed state component in the reduced engineering problem based on the Ribere–Faylon trigonometric series, accounting for the nonlinear deformation properties of soils. To determine the settlement over time of the foundation near the pit, we used the A.Z. Ter-Martirosyan’s model to describe shear deformations and the Kelvin–Voigt model to describe volume deformations, assuming that ε·z(t) = ε·v(t) + ε·γ(t), according to the Hencky’s system of physical equations. The obtained solutions make it possible to assess the long-term deformation of soil bases and the long-term load-bearing capacity with respect to nonlinear rheological properties in a way that accurately corresponds to the actual performance of subsoils exposed to loading. The theoretical results were followed by numerical experiments to prove their validity.

The present paper describes and provides an analytical solution to the problem of the stress state of a limited-thickness soil basis resting on an incompressible soil base, under the action of two distributed loads of different intensities near the retaining wall of an excavation pit. It is proposed that the method for identifying components of the stress statement within the framework of the engineering problem in question is improved, and the solution is based on the trigonometric Ribiere–Fileon series. The results obtained by the authors allow for an evaluation of the supplementary effect on a retaining wall produced by loads from heavy machinery and materials stored near this retaining wall. These findings are useful for the design of underground constructions of buildings and structures. Theoretical results are provided together with those of numerical experiments to validate the research reliability.