基于积分变换采场底板应力与变形解析计算

Analytic solution for stress and deformation of stope floor based on integral transform

煤层开挖后,采空区卸载的同时侧帮产生支撑压力作用于侧帮底板上,导致底板应力重分布;根据最终应力场由初始应力场与开挖应力场叠加的特点,建立底板岩层的力学分析模型;采用Fourier积分变换方法求解双调和方程,并利用形式函数待定法求解对偶积分方程,得到底板应力场与位移场的解析表达式;然后根据Mohr-Coulomb准则判断底板岩层的塑性破坏深度。通过算例分析结果表明:在采空区底板中主应力随着深度的增加而增大至原岩应力;而在侧帮底板中最大主应力随深度的增加而逐渐减小至原岩应力;在侧帮底板深度小于10 m时,主应力发生旋转,3?变为中间主应力并且随深度逐渐减小,当随深度继续增加时又逐渐增大至原岩应力;在采空区的中心发生最大底臌位移为0.236 m,侧帮底板受支撑压力作用产生向下的位移;塑性破坏范围呈中间大两边小,最大破坏深度为31.2 m,为半开挖宽度的1.04倍。最后通过FLAC3D模拟煤层开采,发现两者计算结果虽存在一定的偏差,但总体趋势基本一致,说明该解析方法能较准确地分析底板的应力与位移,可为工程实践提供指导与计算方法。

After mining, the goaf unloads and the floor below lateral wall is subject to abutment pressure, which results in the stress redistribution. Therefore, it is necessary to establish a new mechanical model for the mining floor strata regarding to the feature of the final stress field of surrounding rock, which is a superposition of in situ stress field and excavating stress field after the exploitation of coal seam. Then the analytical expressions of stress and displacement of mining floor are deduced, in which the Fourier integral transform is used to solve the biharmonic equation and the form function method is employed to solve dual integral equation. Furthermore, the Mohr-Coulomb criterion is applied to determine the plastic failure depth of floor strata as well. The results of the example show that principal stresses in goaf floor increase up to in-situ stress with increasing the depth, but the maximum principal stress in the floor below lateral wall decreases up to in-situ stress with decreasing the depth. When the depth is lower than 10 m, the minimum principal stress,3？, changes to be the intermediate principal stress due to the rotation of the principal stresses and further decreases with the increase of depth, while 3？ turns to increase with the continually increased depth, until up to in-situ stress. It is also found that the maximum upheaval of the floor in the central region of goaf can reach 0.236 m, while lateral wall floor moves downward due to the effect of abutment pressure on the lateral wall floor. The plastic failure region is shown to be greater in the middle than two edges and the greatest failure depth reaches 31.2 m, which is 1.04 times the half width of excavation. At last, the FLAC3 D software is employed to simulate the excavation of coal seam. The tendency of simulation results compared with theoretical results is consistent except a certain departure. The proposed methods is proved to solve stress and displacement of floor accurately, which can provide significant guidance in practical engineering.