Analysis on Catastrophe Theory during First Weighting Sliding Instability and Support Crushing of Main Roof with Large Mining Height in Shallow Coal Seam

Abstract

Roof sliding and instability along the coal wall usually occur in the working face at large mining heights during the process of the first weighting, which causes roof cutting and support crushing. A mechanical model consists of the main roof, immediate roof, and support based on the nonlinear characteristics of the failure and instability of the immediate roof under the abutment pressure, which we constructed to study the step sinking of the main roof, as well as to assign the reasonable value of the support resistance during the first weighting. The instability mechanism of the system was studied by the catastrophe theory and the principle of energy conservation. A conclusion was drawn that the combined cantilever beam structure for the immediate roof will form with the increase of the mining height, and the instability of the immediate roof causes the catastrophic instability of the system. The system instability was found to be related to the stiffness ratio K, material parameters, the load Q, and the first weighting interval of the main roof by analyzing the necessary and sufficient conditions for system instability. The influence degree of each parameter on the stiffness ratio K was as follows: elastic modulus E > support stiffness k1 > cross-section area a > immediate roof thickness H. The calculation equations of support resistance and subsidence of roof step were obtained. The method of judging the roof instability using catastrophe theory was proved as reasonable on the basis of the monitoring example of no. 12401 working face in Shendong mining area, China. On this basis, a reasonable value of support resistance was further calculated, and the working face was maintained safely when the support resistance exceeded 19,232 kN.