Abstract：With the combined action of uniform stress and increment pressure of the mantle rock，and under the action of loading formation with smooth connection，taking unit width rock stratum structure at middle part of the working surface as study object，simultaneous differential equations of statically indeterminate deflection of the tight roof ahead of working surface and the worked out section are established. Here，the coal seam ahead of coal face and immediate roof are considered as elastic foundation. On the basis of all natural boundary conditions and continuity conditions being satisfied，accurate solutions of these equations are obtained；and several relational expressions about roof deflection，bending moment，bending strain energy density distribution ahead of coal face before and after initial fracturing are derived. As far as the roof horizon load with 30 MPa and 0.6–1.0 GPa foundation rigidity are concerned；based on the proposed relational expressions，computing and drawing form of Matlab software being used，many results such as roof deflection before and after initial fracturing，bending moment，advanced fracturing position of roof，and law of accumulation and release of bending strain energy increasing with foundation rigidity decreasing as well，are all taken on. It is obtained that the advanced fracturing position of roof is at – m ahead of coal face，and the area from coal face of the working surface to its front 20.45–22.90 m is concentrated area of roof energy. In this area，there is bending strain energy which is 10–13 times as large as energy stored in the roof after fracturing to be released with the roof fracturing. It is clarified geometrically that the area enclosed by two distribution curves of bending strain energy density of roof is the energy released by the roof with its fracturing. By adjusting the parameters of relational expressions mentioned above，these expressions can be used to calculate roof deflection ahead of the coal face of the working surface，bending moment and bending strain energy density which correspond respectively to different mining deepnesses and different rock properties and rock structures. The relational expressions have important reference meaning to prevention and curing for impact ground pressure，roof control and cover caving.
潘 岳，王志强，李爱武. 初次断裂期间超前工作面坚硬顶板挠度、弯矩和能量变化的解析解[J]. 岩石力学与工程学报, 2012, 31(1): 32-41.
PAN Yue，WANG Zhiqiang，LI Aiwu. ANALYTIC SOLUTIONS OF DEFLECTION，BENDING MOMENT AND ENERGY CHANGE OF TIGHT ROOF OF ADVANCED WORKING SURFACE DURING INITIAL FRACTURING. , 2012, 31(1): 32-41.
2012, Vol. 31 
