The article considers solutions to two problems, obtained in plane and spatial statements of stress redistribution in soil body, weakened with a semicircular or a hemispherical excavation pit. For plane deformation case a semicircular excavation, simulating a foundation pit extended in horizontal projection, is accepted. For spatial problem case a hemispherical excavation is accepted. The solutions were obtained in a closed form and can be used for comparing influence areas of extended and spatial pits of equal geometrical parameters. Stress-strain state behavior of “weakened” soil bodies is analyzed, taking into account the action of a uniformly distributed load, modeling weight of a building located in the excavation pit influence area. Visual results of calculations in forms of distinctive stress diagrams and isolines of additional and total stresses are presented. Practical utility of the solutions obtained consists in the possibility of varying parameters of the pits and the distance to the angular zone of distributed load. Quantitative characteristic of changes in additional stresses, which determine the size of the pit influence area and on which additional deformations of nearby buildings and structures depend on is of particular interest.

The article considers features of creating horizontal protective shields made of steel pipes for construction of tunnel-type structures in a closed manner. Types of horizontal protective shields and methods of their construction are analyzed. Variants of modern tunnel structures arranged in difficult geological conditions with the use of lining from large diameter pipes along the perimeter of the entire structure are given. Factors influencing the choice of a rational shield shape and an appropriate design model for solving the problem of the stress-strain state of the soil body weakened by a horizontal cavity of a closed type are taken into account, considering various options for propping and external influence on the soil body under studyThe obtained value of settlement of the upper layer of the support also depends on the dynamic loads from the railway tracks, but does not take into account the sequence of the technological process of construction of an underground tunnel, which is a guideline for subsequent projects.

The article solves the problem of stress and strain state of the subgrade waned by cylindrical neckline, modeling the karst pothole area. The solution was obtained taking into account nonlinear behavior of the soil subgrade based on using the A.I.Bonkin bilinear subjection. In the article are presented the visual results of calculations as the isofields of stresses and strains. The obtained solution allowed us to offer for consideration an updated analytical model of karst-resisting foundations of buildings and constructions. In the proposed analytical model was adopted a variable coefficient of subgrade reaction, varying according to the bilinear law.

The paper deals with the formulation and solution of the consolidation problem for weak water-saturated soil bases by using exponential functions to describe the initial pore water pressure with zero boundary conditions on the surface of the base and at infinity. The solution of this problem was obtained in closed form by the source function method. Expressions are given for the pore water pressure and degree of consolidation, as well as an example of such calculation.