With the diversification of mining methods and complexity of mining environment, the phenomenon of coal seam mining in working face with variable length increases. According to the increasingly prominent safety mining situation of stope with variable length, taking the stope with variable length whose length change from small to large as the research object, the roof mechanics model under different support boundary conditions of stope with variable length has built by using elastic thin plate theory.The analytical expressions of the deflection, bending moment and stress before and after fracture during mining process are obtained by theoretical calculation. And the mechanical mechanism of roof fracture is analyzed theoretically. With the help of MATLAB numerical fitting software, the internal force distribution characteristics of several kinds of thin plate structures are studied by numerical examples.The instability mechanism of roof deformation, failure and collapse is revealed from the nature of rock movement.The study is intended to lay a solid theoretical foundation for roof management and surrounding rock control of working face with variable length.
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