Semi-analytical Solutions of Elastic Stress in Circular Rock Stratum Based on the Theory of Curved Beam

Abstract-Circular rock stratum is inevitably encountered in underground mining engineering, resulting in waste of resources and dynamic instability. Based on the elastic theory of curved beam and finite difference computation, a displacement function is proposed in polar coordinates to solve two partial differential equations with the boundary conditions in elastic, isotropic and homogeneous rock. A semi-analytical solution of elastic stress in circular rock stratum is obtained according to the governing equation and stress components in the form of displacement function. In addition, the variations of stress distribution with different influencing factors are analyzed, which is helpful to a better understanding of the stability of circular stratum after coal extractions. Moreover, this semi-analytical elastic stress solution is applied to the fold structure in No.2502 mining area. Last but not the least, the dangerous positions in the process of coal extractions are pointed out for the safety and better construction in coal mine engineering.