Coal wall bending calculation and spalling risk classification using Chebyshev polynomials - Zhining Zhao; Weidong Pan; Baiyu Hu; Guocheng Zhang; Cang Deng; Xiyuan Qin; Yupei Deng (Geomechanics and Geophysics for Geo-Energy and Geo-Resources)
Abstract In view of the severe constraints of coal wall spalling and roof caving problems on the productivity release and intelligentization process of large mining height working faces, this paper comprehensively analyzes the key factors affecting coal wall stability in high-strength mining by using theoretical analysis and numerical simulation. Theoretically, a bimodular short-beam model for the coal’s plastic yield zone is built. The Chebyshev polynomial is used to solve the coal wall’s deflection curve equation under complex loads, and the step function quantifies factor impacts on coal wall deflection. The sensitivity ranking of key factors is: mining height > horizontal force from deep coal > coal elastic modulus > distance from coal wall to abutment pressure peak > roof-coal friction > support rib-protecting force > rib-protecting force height. Taking the Caojiantan 10 m working face as an example, an orthogonal numerical experiment is conducted on the five most sensitive factors. The plastic-zone proportion D in front of the coal wall evaluates stability. Normalization and grey correlation analysis verify and refine the factor sensitivity ranking. A multiple nonlinear regression equation between factors and D is fitted with MATLAB, with a goodness-of-fit of 81.3%, serving as a reference for intelligent control of coal wall spalling. Coal wall spalling risks are classified, and corresponding measures are proposed. These results offer theoretical and on-site guidance for intelligent coal wall stability decisions in similar scenarios.