压剪复合受载下矿柱应力状态的Mohr圆分析与数值模拟研究

Mohr’s circle analysis and numerical simulation of stress state of pillarunder combined compression-shear loading

倾斜矿体开采中矿柱的应力状态分析是确保矿体安全开采的重要工作之一。以岩体力学理论为基础,建立了压剪荷载作用下倾斜矿柱的力学模型,推导出表征压剪受载矿柱应力状态的广义Mohr圆方程,分析了矿体倾角、荷载对广义Mohr圆圆心位置及半径的影响,揭示了倾斜矿柱应力演化的3种路径,并证明了3种应力路径分别满足直线方程、圆方程和平面方程。针对矿柱的3种应力路径,提出相应的应力路径演化主控模式。基于Mohr强度理论,分析3种主控模式下的应力路径对矿柱稳定性的影响,阐释倾斜矿柱比垂直矿柱更容易失稳的原因。最后,采用数值模拟方法研究得到矿柱的应力状态与采用广义Mohr圆分析得到的结果一致,且压剪受载矿柱的破坏模式为非对称的沙漏状。研究结果可为倾斜矿柱的稳定性分析提供一种思路。

The stress state analysis of the pillar in inclined bedded ore-body mining is a key issue to ensure the safe mining.Based on the theory of rock mechanics,a mechanical model of inclined pillars under compression and shear loads is established,and the generalized Mohr circle equations describing the stress state of the pillars under compression-shear loading is derived.The position and radius of the generalized Mohr’s circle center are affected by the dip of the ore body and the loading on pillar,which reveal three types of stress evolution paths of the inclined pillar.These three stress paths are found to satisfy the line,circle and plane equation,respectively.Moreover,three types of control modes on the stress path evolution are presented.Based on the Mohr strength theory,the influences of stress path on pillar stability under three main control modes are analyzed.The inclined pillar is more easily unstable than vertical pillar and details are explained in this paper.Finally,the stress state of pillar obtained by numerical simulation is consistent with that of the general Mohr’s method,demonstrating that the failure mode of pillar is asymmetric hourglass shape.The results provide a new idea for the stability analysis of inclined pillars.