水压影响下煤层底板采动破坏深度弹性力学解

Elasticity solution for failure depth of mining floor under water pressure

准确预测采场底板破坏深度是承压水上采煤的一个关键问题,而目前常用的解析解公式没有考虑底板水压力的影响。为此,将底板视为各向同性均质弹性体,支撑压力和水压力作为均布条形荷载分别作用在底板上下面,依据弹性半空间理论的符拉芒和明德林解,推导出采场底板的应力表达式。在此基础上,分析了水压力对底板应力分布规律的影响。根据应力计算结果,利用带拉伸破坏的Mohr-Coulomb准则对底板破坏深度进行计算,并探讨了水压力和隔水底板厚度对计算结果的影响。算例显示,水压力对底板垂直应力和剪应力影响较小,而对水平应力影响较大,使其出现应力扩散现象。底板剪切和拉伸破坏深度和范围随水压力的加大而明显增大,随着隔水层厚度的增大只略微降低,表明加大隔水层厚度并不能有效降低底板破坏深度。实例应用表明,水压力影响下的底板破坏深度计算值与实测值基本吻合,较不考虑水压力的计算精度要高。

Accurate estimation of floor failure depth is a key problem in mining above the confined aquifers. However, the popular analytical solution formula at present has not considered the influence of the floor water pressure in engineering practice. Therefore, the analytical solution for stress components of mining floor was derived based on Flamant and Mindlin solutions of elastic half space theory with the floor rock mass considered as a homogeneous isotropic elastic body and the abutment pressure and floor water pressure as uniform strip load on the upper and the lower surface of the floor respectively.,. On this basis, influence of water pressure on the stress distribution was analyzed. According to the stress calculation results, the floor failure depth was calculated based on the Mohr-Coulomb yield criterion with tensile failure, and the influence of the water pressure and thickness of floor aquifuge on the calcu- lation results was discussed. The results of an example have shown that the water pressure has a littleinfluence on the vertical stress and shear stress of mining floor, but it has a great influence on the hori- zontal stress, which makes the horizontal stress diffuse. The floor failure depth and scope of shear and tensile increase evidently with the water pressure, but only slightly decrease with the thickness of aqui- fuge. The results have indicated that increasing the thickness of aquifuge cannot effectively reduce the floor failure depth. The application demonstrates that the calculation value of the floor failure depth is basically consistent with the measured value due to considering water pressure＇s action. And its compu- tational accuracy is higher than that without consideration of the effect of water pressure.