基于曲梁理论的褶皱构造中覆岩变形与应力分析

Analysis on deformation and stress of overlying rock in fold structure based on elastic theory of curved beam

为了分析褶皱构造中煤层开采后覆岩的变形与应力,引入了适用于极坐标下曲梁的位移函数,分析了用位移函数表示的曲梁偏微分控制方程和位移分量、应力分量;在此基础上,依据差分原理将微分方程转化为差分方程,并编制了差分方程求解程序。根据某矿区工作面的褶皱构造等地质资料,研究了工作面由向斜槽点推进到背斜脊点过程中覆岩的变形与应力。结果表明:1)覆岩水平位移主要表现为向采空区方向的变形,且最大水平位移主要表现在转折端附近;覆岩垂直位移主要表现为向采空区方向的下沉变形,且在工作面的推进过程中最大垂直位移稳定在距离开切眼70 m附近。2)覆岩中水平方向的应力在切眼前方为拉应力,而工作面后方为压应力;竖直方向的应力主要表现为拉应力,且主要位于工作面后方。

In order to analyze the deformation and stress of overlying rock after coal mining in fold structure,a displacement function suitable for curved beam in polar coordinates was introduced.The partial differential governing equation of curved beam was obtained by theoretical analysis.Then the displacement components and stress components were expressed by using above function.On above basis,these partial differential equations were translated into difference equations.Meanwhile,the program for solving difference equations was compiled according to finite difference method.Based on geological data in a working face(such as fold structure),the deformation and stress of overlying rock in the working face advancing process from syncline bottom to anticline top were studied.Results are as follows:1)The horizontal displacement of overlying rock is mainly in goaf direction,and its maximum value is close to the hinge zone of fold.In contrast,the vertical displacement of overlying rock is mainly subsidence deformation towards the goaf,and its maximum value is stable at the distance of 70 m away from open-off cut during working face advancing.2)The horizontal stress in overlying rock is tensile stress in front of the open-off cut,while it is the compressive stress in the rear of working face.The vertical stress in overlying rock is mainly tensile stress,which is mainly in the rear of working face.Meanwhile,the maximum shear stress is mainly in the rear of working face.