Deformation Analysis of Bending Stratum Based on Displacement Function Method

Bending strata is an inevitable consequence of coal mining, which will waste mineral resources and influence their production. In this paper, the displacement function suitable for curved beam in polar coordinates is introduced, and the partial differential governing equation of curved beam is obtained by theoretical analysis. Then, the expressions of displacement components and stress components are expressed by displacement function. On this basis, the program for solving the partial differential equation is compiled using the difference principle. Finally, these theoretical formulas of curved beam are applied to analyze the displacement distribution of bending rock and the influencing factors of deformation in coal mining. These main results show that the value of deformation is increasing with the increase of inner radius, tectonic stress and mining depth, while it is decreasing with the increase of thickness of overburden layer. Moreover, the advancing angle effects significantly not only the value of deformation, but also the position of max value. The value of deformation is more suitable for mining position at about 30°. Obviously, the inner radius and advancing angle have more effect on deformation than other factors. These conclusions provide scientific basis and reference for coal mine engineering.