The use of numerical methods in the calculation of machines and structures, taking into account their interaction with the elastic-plastic medium is largely determined by the complexity or even impossibility of analytical calculation due to the complexity of structural schemes, heterogeneity of material features, uneven soil layers, implementation of step-by-step work execution technologies and so on. Compatible calculations of structures and nonlinear basis, which are described by modern mechanical and soil models in one problem is a significant technical problem. And neither the existing “problem-oriented” software packages, nor the “universal” ones - do not fully contain such models. The tasks solution is possible only within the framework of numerical methods, the most common of which is the finite element method (FEM). The construction of the calculated finite element model raises many complex questions that require additional detailed study. In addition, the compliance with the state building norms and regulations is an important factor for further practical use. The combination of the latest achievements in the field of structural mechanics and soil mechanics is a promising direction for the development of effective approaches for building discrete models of spatial systems “structure-nonlinear base” for solving applied problems. On the basis of modern numerical implementations of the finite element method the article presents the theoretical foundations of the analysis of deformation processes of machines and structures in their contact interaction with the elastic-plastic nonlinear soil medium within the three-dimensional spatial problem taking into account the previous stress state and load history. The methodology of construction of computational models of joint deformation and mutual influence of rigid structures and essentially plastic external medium is developed, new special heterogeneous finite elements of SAFEM of general form with variable geometrical and physical-mechanical parameters and arbitrary boundary conditions for approximation of arrays of hardly connected reinforced soils are developed.

The article evaluates the possibility of using Hardening Soil Model and Coulomb-Mohr soil models with corrected input parameters by investigating the stress-strain state (SSS) of underground structures.

The article reflects the results of a systematic analysis of scientific and technical literature for the purpose of studying the existing classifications of landslides and landslide processes, the reasons for the activation of landslides, as well as normative and traditional methods of calculating the stability of slopes. The constant need to attract new sites for construction leads to the active use of areas with difficult engineering and geological conditions, including landslide and landslide-prone areas. The use of such areas entails certain risks and is a complex engineering task. Solving this problem is impossible without a detailed analysis of the existing state of the slope and a forecast of its behavior under the influence of potential natural and man-made influences. Various classifications of landslides, landslide processes and landslide systems are considered in the article . It is noted that there is still no generally accepted classification of landslides, which is due to the difference in terminological and conceptual bases in different countries. The complexity and heterogeneity of the morphology and genesis of slopes, as well as a large number of natural and man-made factors that can affect it, actually make it impossible to develop a unified classification convenient for use in various cases. An analysis of scientific and technical literature was carried out in order to identify natural and technogenicfactors that have an impact on the development of shear deformations. The work considers normative and traditional methods of calculating slopes. According to normative documents, general requirements and recommendations for the calculation of landslide and landslide-prone slopes are given. The division of analytical methods into certain groups, performed by different authors, and a brief overview of the most common methods are considered. These methods have certain advantages and disadvantages, which determine the rationality of their application in various conditions.

The article deals with the issue of modelling shear processes in plastic soils. The peculiarity and main difficulty of modelling landslide processes is the need to take into account a large number of various natural and technogenic influences on the slope, each of which can significantly affect its overall stability. It is also important to take into account not only the current state of the slope but also the forecasting of factors that may affect it over time. In this case, it may be justified to create complex models that include several interconnected sub-models to describe various physical phenomena. Considering the complexity of calculations to determine the stability of the slope or shear pressure on engineering protection structures, it is not surprising that all calculation methods rely on some assumptions when building calculation models to describe physical phenomena and reduce the complexity of calculations. However, it should be noted that the modelling of the non-linear behaviour of soils and the use of models that more accurately describe physical phenomena and processes occurring on slopes can significantly affect the results of calculations. The article presents the main relationships of the mathematical model of elastic-plastic deformation of soils. The given ratios allow taking into account such phenomena as dilatancy and contraction, which makes it possible to more accurately model the stress-strain state of the soil medium, the distribution of pressure in the soil, taking into account the change in physical and mechanical properties during the deformation process. In the article, the finite element method is chosen as the most effective method of numerical modelling of shear processes. Certain aspects of the implementation of calculations based on a complex model and the justification for determining the coefficient of slope stability within the framework of this method are presented.

Construction planning in complex engineering and geological conditions, which include landslide-prone areas, requires a detailed analysis of the existing state of the slope and the forecast of its behavior depending on changes in natural and technogenic factors. This possibility can be provided only by modeling deformation processes using numerical calculation methods. On the example of construction of a three-storey cottage on a landslide-prone slope, the analysis of the operating conditions of existing anti-landslide structures was carried out and their role in ensuring the slope stability was determined. The preliminary calculation of the slope stability was performed by the method of round cylindrical sliding surfaces for soils of natural humidity and in water-saturated state. The method of round cylindrical surfaces is a simplified method of calculating the slopes stability, which in the conditions of heterogeneous layered slope leads to the overestimation of its stability. Therefore, to determine the actual NSDT of the slope, the calculation profile was developed, on which several formulations of the above problem were performed. The calculation was performed on the basis of the developed methodology presented in the works of the article authors. The stress-strain state (SSS) of the slope is considered using the finite element method (FEM) and its torque circuit. The base is presented in the form of a modified model of fortified soils with the criterion of the limit state of Mises-Schleicher-Botkin. In numerical implementation, the slope on the basis of engineering surveys was presented as a finite-element discrete model with an elemental grid, a fragment of which is a separate engineering-geological element. The considered in the article example of the method of calculation of the system «supporting structure-nonlinear base-house» gives the opportunity to give a reliable assessment of the territory state and offer a number of rational measures for its engineering protection, which ensures reliable operation of buildings and structures.