Study on fracture mechanism and stability control of longwall working face with thick hard roof in coal mine

This study investigates the spatial fracture mechanics of thick and hard roofs during working face advancement through theoretical modelling and physical simulation. To address the limitations of the traditional Euler–Bernoulli beam theory for thick roof conditions, the Timoshenko beam theory is introduced to establish a roof mechanical model that accounts for shear deformation. Combined with the Winkler elastic foundation, theoretical expressions for the advanced fracture distance and fracture angle of the roof along both the advancing and length directions are derived for the initial weighting and periodic weighting stages. Theoretical analysis indicates that roof thickness, elastic modulus, and foundation coefficient significantly influence fracture behaviour. The advanced fracture distance decreases with increasing foundation coefficient and elastic modulus, but increases with increasing roof thickness. The fracture angle decreases with increasing weighting interval and foundation coefficient, but increases with increasing roof thickness and elastic modulus, while the influence of Poisson’s ratio is relatively weak. Physical simulation experiments using a digital image correlation system recorded the principal strain evolution during the fracture process of different rock layers. Under the experimental conditions, the failure strain thresholds of the immediate roof, main roof, and key stratum were approximately 2%, 6%, and 8%, respectively, with higher strain thresholds corresponding to higher rock layer strength, indicating that the key stratum accumulates the highest strain energy before failure and releases the greatest energy upon failure. The theoretical calculations are in good agreement with the physical simulation results in terms of fracture location and fracture angle during both the initial weighting and periodic weighting stages, thereby validating the reliability of the proposed model. The findings provide a theoretical basis for support design, weighting prediction, and roof control under thick and hard roof conditions.