Analytical Solution for Fracture of Stope Roof Based on Pasternak Foundation Model

Abstract

To analyze the stress and deformation law of a stope roof, the coal seam and direct roof in front of the coal wall are regarded as an elastic foundation. The deflection-differential equation of the roof rock beam is established based on the Pasternak elastic foundation model. According to the boundary conditions and continuous conditions, the expressions of deflection and bending moment during the first and the periodic fracture of the roof rock beam were established. The first and periodic fracture step were also obtained. The analysis shows that the first break distance of the Pasternak model is 15.9% less than that of the Winkler model, and the deflection is 40.2% larger than that of the Winkler model. The maximum negative bending moment is 39.5% smaller than that of the Winkler model because the Pasternak model considers the continuity of the foundation deformation by the shear modulus. The maximum bending moment during the first fracture increases with the elastic characteristic coefficient n. During periodic fracture, the fracture position is located in the coal wall, and the maximum negative moment of the rock beam increases with an increase in elastic-characteristic coefficient. The results can provide some reference value for roof pressure and stability control of the stope.