Timoshenko-Pasternak Foundation Beam Model for Analyzing Primary Key Stratum Deformation in Backfill Mining

In the paper, the theoretical solution of the Timoshenko-Pasternak Foundation Beam is used to derive the simulation results of the traditional Euler-Winkler model, as well as the comparative graphs of the Timoshenko-Pasternak results. Additionally, the deflection, bending moment, rotation angle, and shear force diagrams of the foundation beam under different coal seam mining thicknesses (M) and different burial depths (D) for the Timoshenko-Pasternak model are presented.