Mathematical Modeling Of Strong Roof Beds In Longwall Mining

Most coal bump occurrences in the U.S. are directly related to mining operations under strong roofs. An understanding of the behavior of bridging or cantilevering strong roofs over working longwall faces is a key to a safe and productive longwall operation. In this paper, an attempt has been made to study the behavior of strong roof beds using the elastic beam theories. Four structural models are formulated to simulate the locations of strong roofs and their distinct weighting stages. For each model, analytical solutions for the deflection, bending moment, stress, and the strain energy stored in both the coal scam and the strong roof are obtained. Solutions for the critical spans, which are controlled by the caveability of the strong roof beds, are developed. The effects of rocks' differing elastic moduli, under tension and compression, on the actual flexural rigidity, and stress redistribution are analyzed.