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The results of numerical modeling of rheological processes both in the potash rock mass in the vicinity of an underground loading complex and in the lining of an underground structure are presented. An algorithm is proposed for solving the problems of calculating the durability of large-scale underground structures with an insufficient amount of initial data on the rheological properties of lining materials for underground structures and the enclosing rock mass. It is shown that even in such conditions, it is possible to qualitatively assess their geomechanical state in the long term. Comparison of various approaches to modeling rheological processes is made.

The problem on elastoplastic deformation and failure of rocks around cylindrical and spherical cavities under the action of internal and external pressure is considered. The pressure during hydraulic fracturing is customary determined by the theory of maximum normal stress. However, the known laboratory experimental studies are not confirmed by this theory. For this reason, it is proposed to determine the limiting pressure using different experimentally justified failure criteria.

The results of calculating the stability of a slope on which the dump is planned to be placed are presented. Safe direction of dumping on the slope is determined, which ensures the slope stability during mining mountaintop deposits of Kyrgyzstan.

The influence of block structure of the rock mass on the stability of sides of mountaintop quarries is estimated. The results of laboratory studies of deformation and destruction along the contacts of blocks, depending on the composition of filler between the blocks, are presented. It is found that shear resistance along the contacts of blocks depends on the composition and internal friction angle of the filler.

The formulation of the problem and results of studying the stress state of the support and rock mass around the excavation in rocks with low values of the fracture strength are presented. The features of performing geomechanical calculations in inhomogeneous continuous medium with significantly different mechanical properties and geometric dimensions are discussed. The nature of support deformation when filling the voids formed during the rock destruction in the roof and sides of the excavation with foaming phenolic resins is determined .

Based on the results of long-term researches in construction and subsequent operation of a railway tunnel using the automated monitoring system, the formation pattern of the stress-strain state of permanent lining made from cast reinforced concrete was obtained. It is found that vibrodynamic loads from transport to the tunnel foundation affect the exclusion of temporary unclosed support from the work with surrounding rock mass .

Studying of rock mass deformation with weak zones is based on the principal property of applied nature that limits incorrectness: the influence of an underground excavation on the stresses and displacements in rock mass attenuates to zero as the distance increases - this is a postulate. The author suggests reducing the problem to solving an additional problem on tensile stresses at the underground excavation boundary to ensure uniqueness and correctness of the elastic solution.

The mechanism of blasting destruction of coal is considered using a combined model of gas-saturated coal, which describes the relationship between explosive damage of a coal seam and subsequent gas release. On the basis of this model, the numerical method of smoothed particles is used to study the development of destruction zones and stress-strain state of a coal seam in the vicinity of a borehole charge after blasting. The obtained patterns help to predict the reaction of coal to explosive dynamic impact. This may be of considerable interest for the development of technology for preliminary degassing of coal seams, as well as for theoretical description of the processes occurring during coal and gas emissions. In this regard, the preparation mechanism of gas-dynamic fracture of a stack of outburst-hazardous (broken) coal under explosive action on a coal seam is considered. The research includes studying the conditions for crack formation in the zone farthest from the blast hole, modeling the filling of induced cracks with methane, which is initially in the coal in a dissolved state, and estimating the onset time of induced crack propagation due to free methane pressure in the crack. It was found that, depending on the mechanical and diffusion parameters of coal, the crack initiation time can vary from tens of seconds to many hours. The research results can be useful in the development of a theory of explosive action on a coal seam, which is used in a set of measures to reduce the hazard of sudden coal and gas emissions.

The physical and mechanical properties of soil from the place of landsliding are studied in laboratory conditions. The problem is solved under the assumption that the landslide mass before and after landsliding remains unchanged. The value of the landslide mass is determined. By constructing various possible sliding surfaces and determining stability factor for each of them, the most dangerous sliding surface was found. To ensure the safety of residential settlements and other objects located at the base of landslide slopes, it is necessary to know the distance that the landslide will travel when fully unloaded. The distance of displacement of landslide masses in the horizontal section is determined.

The density ratio is normalized with respect to the theoretical maximum density ratio of a sphere packing, which is 0.7405. The experimental data show that the density ratio of a packing of sized glass balls changes during cyclical shearing .