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With the typical composite roof roadway and roof fall accidents in the Guizhou Province of China as the research background, the expression of damage parameters of composite roof was deduced according to Weibull statistical distribution, generalized Hooke’s law and Mises yield criterion, and the influence of shape and scale parameters of Weibull on damage characteristic was discussed. Based on the infinite slab theory, the expressions of deflection and layer separation of each layer of the composite roof were obtained, the critical load expression of each delamination was determined, and the influence of roadway width, overlying strata load, elastic modulus, shape parameters and scale parameters on the stability of composite roof was explored. The research shows that the bolt support can effectively reduce the layer separation between the composite roofs and enhance the stability of the composite roof. On this basis, it is proposed that for the surrounding rock control problem of roadways with composite roof, the active support technology with bolts as the core should be adopted.