Purpose. There are many problems in the design of anti-landslide constructions, therefore discrete constructions are an alternative to solid anti-landslides. Despite the advantages of such constructions, difficulties also arise when using them. In this work, it is envisaged to develop methods for determining the zone of influence of discrete restraining constructions on the interaction of a sliding soil mass with them and a method for assessing the conditions of a stable state of the soil, which interacts with discrete restraining constructions, by constructing analytical dependencies necessary to determine the zone size and the soil stability coefficient. Methodology. Theoretical studies of geomechanical processes using analytical and numerical mathematical methods, as well as analysis and generalization of theoretical research results were used to achieve the purpose. Findings. The research results presented in the work allow, during the design of landslide discrete constructions, to determine the area of interaction of the shear with discrete retaining constructions, as well as to take into account the stability coefficient of the soil laid between the elements of the discrete retaining structure. Dependences were obtained for determining the zone size in which the sliding soil mass interacts, with discrete retaining constructions, and the soil stability coefficient in the zone of its interaction with these constructions. Originality. Analytical dependencies allow to calculate the boom of lifting the soil dumping arch between the elements of the discrete anti-landslide restraining construction and the coefficient of soil stability. Practical value. The research results allow, when designing discrete restraining constructions, to determine the area of interaction of the shear with these constructions and the stability coefficient of the soil laid between the elements of the discrete restraining construction.

Purpose. The main purpose of the work is to construct accurate analytical dependences of the sedimentation of the roadbed base on its coordinates and the trapezoidal external load applied to the upper limit of the base. This will allow the foundation settlement profile to be calculated within and outside the embankment using the layer-by-layer stacking method. Methodology. Theoretical studies of geomechanical processes using analytical and numerical mathematical methods were applied to achieve the purpose, as well as analysis and generalization of the results of theoretical research. Findings. Analytical dependences of vertical and horizontal normal deformations on the half-plane coordinates to the upper limit of which the trapezoidal load is applied were obtained within the framework of the base model in the form of a linear elastic isotropic medium and the calculated scheme of planar deformation. On this basis, an algorithm for constructing a profile of a roadbed sedimentation made of soil materials has been developed. Originality. Analytical dependences of vertical normal deformations in the roadbed base with a trapezoidal profile on its coordinates are obtained. Practical value. The research materials presented in this work make it possible to construct the design profile of the roadbed of soil materials, taking into account the strong compressibility of the soil. In addition, the results obtained can be used to determine the lower limit of the compressible strata of the bases, to the upper limit of which a distributed load of either a triangular or a trapezoidal form is applied.