层状底板采动应力场的解析计算模型研究

Research on analytic calculation model for mining induced stress in multi-layered floor rock

针对底板岩层分层分布的特征,建立了层状底板采动应力场的解析计算模型。通过Fourier变换,得到了任意深度的底板岩层应力和位移分量与采场支承压力之间的传递矩阵关系;基于传递矩阵推导出总体刚度矩阵,从而求得底板应力在积分变换域内的解答;然后基于离散快速傅里叶逆变换计算方法,采用Matlab编程求解出底板深度处的应力解析解,并与传统的均质底板模型计算结果进行了对比分析。分析结果表明:底板岩层的分层特征对其应力场分布存在明显的影响,本文所采用的刚度矩阵方法考虑了不同层岩体形变参数对采场支承压力传递规律的影响,得到的结果更符合实际。该研究对于准确计算采场底板应力分布和破坏深度具有一定的理论意义。

Considering the layered structure of floor rock masses,the calculation model for mining induced stress of multi-layered floor rock is established. First,the transfer matrix relating the abutment pressure and stress and displacement components of floor rock is obtained by using the Fourier transform. The stress for multi-layered floor in the integral transform domain was obtained from the global stiffness matrix,which is established based on the transfer matrix. Based on discrete fast Fourier transform( DFFT) method,the analytical solution of stress at the deep of floor is carried out by means of Matlab programming. Eventually the calculated results of the proposed model are compared with traditional method. The results show that layered characteristic of floor strata has a significant effect on the stress distribution of mining floor. The proposed theoretical model considers the influence of deformation parameters form different rock strata,result in the computation results are more close to the actual condition. Therefore,it is of certain theoretical significance to accurately calculate the distribution of floor stress and the failure depth of mining floor at failure.