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

 在覆岩均布力和增量压力共同作用且光滑连接的荷载形式作用下，将煤壁前方煤层和直接顶视为弹性地基，在工作面中部选取单位宽度的岩层结构作为研究对象，建立采空区与工作面前方坚硬顶板的超静定挠度微分方程组。在满足所有自然边界条件和连续条件的基础上，求得此微分方程组的精确解，导得初次断裂前、后煤壁前方的顶板挠度、弯矩和弯曲应变能量密度分布关系式。对30 MPa的顶板层位荷载和0.6～1.0 GPa的地基刚度，根据所提出的关系式，用Matlab软件的计算绘图形式，给出初次断裂前、后顶板挠度、弯矩、顶板超前断裂位置、弯曲应变能积聚与释放随地基刚度减小而增大的规律。得到顶板超前断裂位置在煤壁前方6.14～7.75 m处，从工作面煤壁到其前方20.45～22.90 m区域是顶板能量积聚集中区，该区域有相当于断裂后顶板弯曲应变能的10～13倍的弯曲应变能在顶板断裂期间释放。从几何上阐明2条顶板弯曲应变能量密度分布曲线之间的面积即为顶板断裂时释放的能量。通过调整所得到关系式的参数，可计算不同采深、不同岩性和岩层结构的工作面煤壁前方的顶板挠度、弯矩和弯曲应变能量密度关系，对冲击矿压防治、顶板管理和放顶有重要参考意义。

ANALYTIC SOLUTIONS OF DEFLECTION, BENDING MOMENT AND ENERGY CHANGE OF TIGHT ROOF OF ADVANCED WORKING SURFACE DURING INITIAL FRACTURING

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.