Abstract: To characterize the deformation and internal force distribution of the hard roof during coal seam mining and to assess the sensitivity of key parameters on its mechanical response, we model the coal seam and the immediate roof as an elastic foundation and select a unit width rock beam at the center of the working face as the research object. Based on the theory of elastic foundation beams and key strata, we establish an elastic foundation beam model for the main roof and obtain analytical solutions for roof deflection, bending moment, and shear force prior to initial fracture. We analyze the influence of five key parameters—the elastic modulus; the stiffness of the coal seam and the immediate roof; the thickness of the overlying soft-rock strata; the influence range of the advanced abutment pressure; and the main-roof thickness—on roof deflection, bending moment, and shear force Finally, using Design-Expert software, we design a five factor, three level response surface scheme and perform a sensitivity analysis of single factors and factor interactions on the hard roof’s mechanical characteristics. Results show that (1) the stiffness of the coal seam and the immediate roof significantly affect the overall roof deformation, while other factors primarily influence the goaf roof. Additionally, increasing the thickness of the overlying soft-rock strata increases roof deflection, whereas other factors have the opposite effect. (2) If the thickness of the overlying soft-rock strata increases linearly, the goaf roof bending moment and shear force also increase linearly. The influence range of the advanced abutment pressure and the main-roof thickness significantly affect the bending moment and shear force in the roof in front of the working face, whereas the elastic modulus and the stiffness of the coal seam and the immediate roof have little to no effect. (3) Factors governing geometric characteristics and load distribution—such as the thickness of the overlying soft-rock strata, the influence range of the advanced abutment pressure, and the main-roof thickness—generally have a greater effect on rock-beam deflection and internal forces than the mechanical properties of the rock mass (e.g., elastic modulus and the stiffness of the coal seam and the immediate roof). The model accounts for the dynamic variation of the upper load during coal-seam mining, providing a theoretical basis for studying the deformation and internal-force distribution of the main roof throughout mining.

Key words: main roof, elastic foundation beam, first periodic weighting, response surface method, sensitivity analysis