An analytical solution for the geometric broken characteristics of the overlying strata and its physical modeling study in longwall coal mining

The broken positions of the overlying strata might lead to different geometric configurations of the caving overburden and also have an impact on the coal mine pressure behaviors and dynamic mine hazards in the open face area. This paper has developed a roof failure analytical model combining the beam on the elastic foundation theory and the cantilever beam theory. The model gives the analytical solutions for the roof broken positions, rock broken angle, and strata broken angle. The results show that (1) the roof broken position is moved forward ahead of the face with decreasing feature coefficient, (2) the strata broken angle is not only influenced by the feature coefficient but also in direct proportion to the ratio of the uniformly distributed load over the roof stiffness, and (3) the theoretical model is capable of simulating the three geometric configurations of the disturbed overlying strata, i.e., the regular trapezoid-shaped, rectangular-shaped, and inverted trapezoid-shaped configurations. An improved physical modeling study is performed in order based on the deviation analysis on the conventional physical modeling studies. The physical model physically realistically reproduces three of the abovementioned geometric caving configurations predicted by the analytical model.