The paper puts forward an approach to the numerical solution of applied problems on the failure of media and solids, which is based on the notions of evolution and self-organization of nonlinear systems under loading. The method allows treating catastrophic events as the development of events in blow-up regimes. A geomedium under gravity, including the one with various man-made hollows (boreholes, galleries and mine faces, different underground structures), is considered as a nonlinear dynamic block system that evolves in the gravity field by the synergetic rules. We study the mechanical behavior of such nonlinear dynamic systems from a continuous macroscopic standpoint. This permits efficient application of continuum mechanics methods, approaches and numerical methods of simulating the deformation and fracture processes. With a high-performance computing cluster we calculate the roof evolution and collapse above the worked-out area depending on the rate of face advance. It is shown that at high advance rates the evolution regimes of the loaded mass are highly nonequilibrium. As a result, extended hanging roof zones in this area are prone to catastrophic collapse.

The approach of physical mesomechanics is applied to the problem of coal fracture. The coal is regarded as a natural composite with a hierarchical inner structure. The applied problem of dust particle formation during cutting is considered. First, the features of the stress-strain state at cutting are determined at the macroscale in numerical calculations. The outcome is used for numerical modeling of fracture and dust particle formation at the mesolevel. A typical mesovolume containing 6 types of coal ingredients and pores of different sizes was taken for calculations. Computer simulations of mechanical behavior up to the failure of the mesovolume under different types of loading have been carried out. At the macroscale use of an elastic-plastic model with taking into account damage accumulation and dilatancy effects as well as explicit crack opening by a grid node splitting technique is made. At the mesoscale the elastic-plastic model with a combined fracture criterion is adopted. It has been shown that such an approach makes it possible to estimate quantitative parameters of dust particle formation of 2-100 μm size during the coal fracture.

Using the fractal analysis of optical images of coal fracture surfaces the characteristic fracture scales for different coal ranks were recognized in the range 1-1 000 μm. The fracture scales revealed fit quite well the universal geomaterial divisibility series that means the each next block in the hierarchy scales is approximately 3 times larger than the previous one. Deviations of the measurement results from the value of 3 could be explained by the influence of block shape.

Using fractal analysis of light microscopic images of fracture surface of nine coal ranks typical fracture mesoscales in different directions in the range 1-1000 μm have been determined. Anisotropy of the block structure was revealed. Two block shape factors characterizing the fracture surface of coal at two scale levels ΔL1 and ΔL2 were found. The value of shape factor averaged over all measurements is equal to 2.8.

The approach of physical mesomechanics is applied to the problem of coal fracture. The coal is regarded as a natural composite with a hierarchical inner structure. Results of experimental investigation of fracture surface of different coal ranks are presented. Analysis of specimen surface fractal dimension revealed three scale levels of block-type inner structure of coals. Scale levels of fracture surfaces of several coal ranks have been investigated. Indirect measurement procedure of the fractal dimension (Dc) definition based on optical microscope patterns treatment has been used for a quantitative characterization of fracture surfaces of coals. The technique has been proposed in (3) and has shown its high effectiveness for examination of scale levels of plastic defor- mation and fracture for metal polycrystals. Optical images of the fracture surfaces of coal were ob- tained on the basis of testing machine «IMASH-2078» with a measuring complex of high resolution TOMSC. The size of the recorded segment of the sample surface comprises 550 ×550 μm

The approach of physical mesomechanics is applied to the problem of coal fracture. The coal is regarded as a natural composite with a hierarchic al inner structure. The applied problem of dust particle formation during cutting is considered. Macro-, meso-, and microscales are included into the study. First, the features of the stress-strain state at cutting are determined at the macroscale in numerical calculation. The outcome is used for numerical modeling of fracture and dust particle formation at the mesolevel. The microlevel is presented by evolution of microdamadges . The mesoscale simulations receive primary emphasis. A typical mesovolume containing 6 types of coal ingredients and pores of different sizes was taken for calculations. Computer simulations of mechanical behavior up to the failure of the mesovolume under different types of loading have been carried out. At the macroscale use of the elastic plastic model with taking into account damage accumulation and dilatancy effects as well as explicit crack opening by grid node splitting technique is made. At the mesoscale elastic plastic model with a combined fracture criterion is adopted. It has been shown that such an approach makes it possible to estimate quantitative parameters of dust particle formation of 2-100 μm size during the coal fracture.