确定椭圆形隧洞端头锚固锚杆轴力的解析方法

An analytical method for determining the axial force of point anchored rockbolts in an elliptical tunnel

岩石锚杆作为一种简单有效的支护手段,已被广泛应用于隧道和采矿等工程中。目前利用解析方法只对圆形隧洞端头锚固锚杆进行了力学分析,基于深埋椭圆形隧洞围岩内任意点作用有集中力的解析函数,推导出应力和位移的精确解析解,并给出显式表达式。通过叠加原理获得多个集中力作用下的应力和位移显式表达式,并考虑隧洞开挖引起的位移,根据变形协调条件建立了求解端头锚固式锚杆轴力的线性方程组,获得锚杆无预紧力和有预紧力2种情形下每根锚杆所承受的轴力分布规律。并使用ANSYS有限元软件对所获得的解析解进行对比验证。分析了锚杆刚度、锚杆长度以及预紧力对锚杆轴力的影响。

Rock bolts have been extensively used as an effective reinforcement means of tunnels and mining engineering projects. The existing analytical method is only available for the mechanical analysis of the point anchored rockbolt in a circular tunnel. Based on the analytical function of a concentrated force at an arbitrary point in the surrounding rock of a deep buried elliptical tunnel,explicit solutions of stress and displacement were deduced and explicit expressions of stress and displacement subjected to multiple concentrated forces were also obtained based on the superposition principle. Considering the displacement caused by tunnel excavation,the linear equations for solving the axial force of the point anchored rockbolt were established according to deformation coordination conditions,and the axial force distribution of each bolt with or without a pre-tightening force was obtained. The analytical solution obtained was verified by ANSYS software. Finally,the influences of the stiffness,anchor length and pre-tightening force on the axial forces were discussed.