The article describes the landslide processes formation processes modeling in free and reinforced slopes. Unlike many well-known approaches, the proposed approach does not introduce simplifying hypotheses. As, for example, hypotheses about the slip lines form or about the slope conventionally “solid” areas form. The slope stability problem is considered in the general formulation of a three-dimensional or two-dimensional (plane strain) plasticity theory. The limiting equilibrium approach and the continuation methods by the loading parameter are used. The resolving equations are constructed in the form of a finite element method (FEM) in displacements. It is shown how, in addition to physical, to take into account geometrical and constructive nonlinearity.The small fragment limiting state hypotheses can be assigned arbitrary. In the general formulation, a complex loading process is assumed — an external load can grow arbitrarily. In this case, the growth load linear nature is used within one external loading branch. Inside the branch, a “cycle in a cycle” process is organized in small increments of load. The process continues either until the limit state of the considered computational domain is reached, or until the load and the transition growth next branch end to the next one.

The article discusses the dynamic processes simulation in landslide slopes during dynamic effects. Dynamic effects can be caused by pulsed, including shock loads. Also, the movement of vehicles along the slope is considered. The solution is based on the general massive load movement dynamic problem formulation = on a massive basis. Discretization over the spatial domain is obtained in the finite element method (FEM) form. The equations solution is performed by the continuation method with respect to the time parameter. Direct methods of the integrating dynamics problems are used. Considering the high dimensionality of the problem in the spatial formulation, to construct a numerical solution, we use the previously obtained explicit absolutely stable direct integration schemes. The methods used can be considered as explicit, absolutely stable schemes for the direct integration of a dynamic problem with a variable mass in time. Recommendations for evaluating the numerical solution accuracy are given.

For massive monolithic foundation slabs, the problem of early cracking due to the intense heat release of concrete during the hardening process is relevant. The purpose of this article is to develop a simplified method for determining thermal stresses during the construction of massive monolithic foundation slabs. The proposed technique is based on the hypothesis of parabolic temperature distribution over the thickness of the structure at each moment of time. In addition to the parabolic distribution, the half-wave cosine distribution is also used. A hypothesis is also introduced about the same conditions of heat exchange with the environment on the lower and upper surfaces of the foundation. As a result, formulas are obtained that establish a direct relationship between thermal stresses and the temperature difference between the center and the surface. The solution to the test problem for the foundation slab is presented and compared with an alternative technique that does not use the hypothesis about the character of the temperature distribution over the thickness. Also, the inverse problem of determining the allowable temperature drop between the center and the surface of the structure is solved, at which the stresses on the upper surface at each moment of time will not exceed the tensile strength of concrete.