坚硬顶板周期来压覆岩破断力学机理研究

Study on mechanics mechanism of overburden breaking under periodic weighting of hard roof

坚硬顶板破断运移规律一直是采矿领域研究的热点,针对覆岩内部破断裂隙分布不明晰的问题,以砌体梁理论中的关键块体为研究对象,建立了线性增压荷载下悬臂梁模型,根据弹性力学应力逆解法,在艾里应力函数满足双调和方程的基础上,采用叠加原理推导并验证了满足模型应力边界条件的内应力分量解析解。在此基础上,以Mohr-Coulomb屈服准则作为破断判据,推导了破断迹线隐函数方程式。采用Matlab软件计算和绘图得到了破断迹线,通过算例校验分析了岩石黏聚力、内摩擦角对破断迹线的影响规律,验证了破裂迹线求解的正确性。这对于进一步认识覆岩破断力学机理具有一定的意义。

The migration law of hard roof breaking has always been a hot topic in the field of mining research.In response to the problem of unclear distribution of breaking cracks inside the overburden,the key blocks in the theory of masonry beams were taken as the research object,the model of a cantilever beam under the linear supercharged load was established.According to the inverse solution of stress in elastic mechanics,on the basis of Airy stress function satisfying the biharmonic equation,the analytic solution of internal stress component satisfying the model stress boundary conditions was derived and verified by superposition principle.The Mohr-Coulomb yield criterion was used as breaking criterion,and the breaking trace implicit function equation was deduced.The breaking trace was obtained by MATLAB software calculation and drawing.By examples the rule for the influence of the rock cohesion,the internal friction angle and what on the breaking trace was verified and analyzed,and the correctness of the solution for the fracture trace was verified.It has certain significance for further understanding of the mechanical mechanism of oveburden fracture.