Support Roof Interaction Under Lower Hard Roof Conditions in Longwall Mining

Hard roofs in longwall mining may form large, suspended strata, which induce strong abutment stress redistribution. Therefore, a rational face support design is essential for ground control. This study develops an analytical numerical framework to evaluate support roof interaction under hard roof conditions. A segmented beam foundation model is established for the support roof system, and an equivalent variable foundation modulus is introduced to represent the reduced bearing capacity of yielded coal ahead of the working face. The analytical results are checked against a Particle Flow Code (PFC) and Fast Lagrangian Analysis of Continua (FLAC) coupled model, showing good agreement in the magnitude and location of the peak abutment stress. Parametric analyses are then conducted to examine the effects of support intensity and support distance on roof deflection, rotation, bending moment, shear force, strain energy density, and abutment stress. The results show that increasing support capacity reduces roof deformation and coal wall stress, while redistributing the same capacity over a longer support distance more effectively lowers roof strain energy concentration and inclined fracture development. However, the longer distance, lower density arrangement may transfer stress deeper into the coal seam and increase peak stress fluctuation during face advance. The proposed study provides a practical method for comparing face support schemes under low position hard roof conditions.