Analytical solutions for the initial and periodic fracture of hard roof in longwall mining considering progressive deterioration of coal seam stiffness

Abstract

The mechanical response of the roof and coal seam is important to the stability control in coal mining engineering. Given the nonlinear evolution of overburden pressure and the variation in coal seam stiffness caused by mining, the roof-coal seam was discretized into a series of smaller segments, characterized by linear roof pressure and constant foundation stiffness. The analytical solutions for the mechanical response of each segment were derived using the governing equations for the initial and periodically fractured roof. Using an iterative numerical algorithm, integral coefficients and exact foundation stiffness values were determined based on the evolution of progressive degradation in coal seam stiffness. The theoretical results show good agreement with existing numerical and analytical solutions. The degradation of coal seam stiffness leads to a non-monotonic evolution of bearing pressure, initially increasing, followed by a decrease, which aligns closely with field-monitored data. The sensitivity analysis further revealed that overburden pressure, roof thickness, and coal seam thickness exert a significant influence on deflection and internal forces of the roof. The proposed solution offers theoretical guidance for safety evaluation and hydraulic support design in longwall mining.