Introduction. This article provides a solution to the problem of the settlement and bearing capacity of foundations with finite width based on rigid soil body adjacent to vertical excavation when applying a uniformly distributed load on its surface. It is assumed, that the vertical wall is fixed with sprung structures, although vertical displacement of soil is acceptable. Materials and methods. The solution of the problem was obtained by the method of trigonometric Ribere – Fileon series. Formulas for determining vertical and horizontal deformations on any coordinate x and on any horizontal (z > 0) are also given. To determine the relationship between stresses and deformations, systems of Genky’s physical equations are used, which take into account the influence of σm on the shear modulus G(σm) and on the volume deformation modulus K(σm) and transform to the system of Hook’s equations at G = const and K = const. Results. The problem of the stress-strain state of a weighty layer of soil of limited capacity on a rigid soil body adjacent to vertical excavation when applying a uniformly distributed load on its surface was analytically solved. The deformations of the soil base εz were determined as the sum of shear and volumetric deformations (εz = εzγ + εzν). Based on the deformations obtained, the unevenness of the foundation settlement adjacent to vertical excavation was estimated. Conclusions. From the analysis of the results of the task, it follows that the solution of the problem of the settlement and bearing capacity of foundations with finite width based on rigid soil body adjacent to vertical excavation when applying a uniformly distributed load on its surface allows to evaluate the deformation of the foundation soils taking into account nonlinear properties. Also it provides to assess the unevenness of the sediment foundations of buildings. The further development of new methods for quantifying the stress-strain statement of soils based on known theoretical solutions is one of the main tasks of modern design of foundations and foundations of buildings and structures.

Introduction. When the underground part of a high-rise building interacts with the surrounding soil massif behind the excavation pit, a complex heterogeneous stress-strain state occurs, transforming in space and time — during construction and during the exploitation of the building. Special issues arise when the soil massif is heterogeneous and has rheological properties, and an additional load acts near the pit excavation at the same time. Materials and methods. For the problem of the stress strain statement of soil with a weight behind the enclosure of a pit with a depth h, taking into account the influence of a distributed load q = const with a width b = 2a at a distance c from the edge of the enclosing structure of the pit, the stress components were obtained using a solution based on the Ribier – Filon trigonometric series. To determine the settlement over time of the foundation near the pit, the A.Z. Ter-Martirosyan’s model was used. To describe shear deformations and the Kelvin – Foigt’s model was used to describe volume deformations, assuming that ε.z(t) = ε.v(t) + ε.γ(t), according to the Henky’s system of physical equations. Results. An analytical method has been developed for quantifying the settlement of soil bases and foundations of nearby buildings behind the pit over the time. The graphs of the settlement-time with double curvature, as well as the graph of the long-term stability of the base are obtained. Conclusions. The solutions obtained can be used to determine the long-term settlements and bearing capacity of the foundations of buildings and structures with rheological properties near the pits. The selected geomechanical model of the foundation (its geometric parameters, initial and boundary conditions), as well as the computational model of the soil (linear, nonlinear and rheological) and the type of physical equations (Hooke system or Henky system), significantly affect the type of the settlement-time curve (S–t), as well as the bearing capacity of the soils. Collaborative using of A.Z. Ter-Martirosyan’s rheological model and Kelvin – Foigt’s rheological model makes it possible to obtain settlement-time graphs with double curvature, as well as a graph of the long-term stability of the soil base.

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Introduction. The construction of high-rise buildings, having elaborated substructures located inside deep excavations, entails a quantitative evaluation of the stress-strain state (SSS) of soils beyond the excavation wall with regard for the interaction with the surrounding built-up area and conditions of the contact with the enclosure structure. The paper analyzes the effect of distributed load p = const over a horizontal area having width b = 2a at the distance of с < a from the edge of a rectangular profile wall, which causes a non-uniform stress-strain state in the soil body having the shape of a quarter plane. It is assumed that the vertical wall is fixed with sprung structures, although vertical displacement of soil is acceptable. Materials and methods. The analytical solution to the problem of the effect of the distributed load on the horizontal soil body having the shape of a quarter plane is based on a well-known solution to the plane elastic problem designated for the half-space subjected to load p = const distributed over a strip. MathCAD software (SW) was employed to obtain the analytical solution; PLAXIS 2D software was used to obtain the numerical solution. Results. Analytical and numerical methods were applied to solve the problem of exposure of a horizontal soil body, having the shape of a quarter plane, to a distributed load. A comparative assessment and analysis of the stress strain state values were performed. Conclusions. Analytical and numerical solutions demonstrate good convergence pursuant to the analysis of the results. Therefore, further development of new methods for the quantitative evaluation of the stress strain state of the soil body based on the existing theoretical solutions is one of the main challenges to be tackled in advanced design of beddings and foundations.