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In mining engineering, the thick and hard roof threatens the safe production. Based on Reissner plate theory and combined with weighted residual method, with four edges clamped as the boundary conditions, this paper deduces the theoretical formula of the first breaking span of thick and hard roof. Based on Vlasov plate theory, with four edges simply supported as the boundary conditions, this paper deduces the theoretical formula of the periodic breaking span of thick and hard roof. The two formulas are used to verify the breaking span of thick and hard roof of Tashan Coal Mine, proving that its accuracy is higher than that of traditional beam theory. This paper studies the distribution characteristics of strain energy density in front of the coal seam during the mining process by numerical simulation, which is compared with the results of field microseismic experiments. It is found that the strain energy density of the coal seam has a good correlation with the probability of microseismic events. This paper provides theoretical support for more precise calculation of breaking span of the thick and hard roof and technical support for the practical stability analysis of the surrounding rock under the thick and hard roof

mathematical problems in engineering

The Breaking Span of Thick and Hard Roof Based on the Thick Plate Theory and Strain Energy Distribution Characteristics of Coal Seam and Its Application