Abstract:
To solve the problem that traditional beam theory ignores shear deformation and fails to accurately calculate roof deflection in characterizing roof stability of steeply inclined extra-thick coal seams, this study adopts the Timoshenko beam theory incorporating shear deformation. Aiming at the characteristics of such coal seams—steep inclination, large thickness and significant shear deformation impact—a roof mechanical model was established. Based on the Timoshenko beam theory, the stress and boundary conditions of the stope roof were clarified, and the governing equation of roof deflection was established and solved to form a calculation method for this type of coal seam mining. The deflection evolution of different roof sections was analyzed and compared with Euler-Bernoulli beam theory results. Key parameters including rock mass elastic modulus and filling body strength were analyzed to reveal dominant factors affecting roof deformation, and a technical path for roof subsidence control was proposed. Results show that the Timoshenko beam theory fully considers shear deformation’s influence on roof deflection: its deviation from numerical simulation is only 3.2%, much lower than the Euler-Bernoulli beam theory’s 9.4%, and it accurately reflects actual roof deformation and evolution. This study improves the roof deflection calculation theoretical system for such scenarios, providing important theoretical basis for support design and filling parameter regulation in coal seam roof control projects under similar geological conditions.