锚杆支护下两向不等压深埋隧洞受力与变形弹性分析

为了给引水隧洞隧址选择和支护参数设计提供理论参考，采用均匀化方法，基于复变函数理论，推导了非均匀应力场下锚杆支护时深埋圆形隧洞的应力及位移弹性解析解，并给出了洞周切向应力及径向位移随围岩弹性模量、侧压力系数、锚杆长度、半径和环向间距等参数的变化规律。通过算例分析，得出以下结论:（1）随着围岩弹性模量的增大，隧洞洞周各点的切向应力和径向位移均减小，且对围岩弹性模量（单位:GPa）在5,10]区间最敏感；（2）侧压力系数在（0,1]区间时，洞周最大切向应力和径向位移随其增大而减小；在1,2]区间则相反，并对侧压力系数在1,2]区间更敏感；（3）随着锚杆长度的增大，洞周的切向应力和径向位移逐渐减小；随着锚杆半径增大，洞周的切向应力逐渐增大，径向位移逐渐减小；而随着锚杆环向间距的增大，洞周应力和位移的变化趋势与锚杆半径的规律相反。

Elastic Analysis of Stress and Deformation of Deep Buried Tunnel Supported by Bolts Under Two-Direction Unequal Pressure

In order to provide theoretical reference for the selection of diversion tunnel site and the support parameter design, based on complex function theory, the homogenization method was used to derive the analytical elastic solution of stress and displacement of deep buried circular tunnel with bolt under non-uniform stress field. And the variation laws of tangential stress and radial displacement around tunnel with the elastic modulus of surrounding rock, lateral pressure coefficient, bolt length, radius and radial spacing were given. Through example analysis, the following conclusions were drawn: (1) With the increase of elastic modulus of surrounding rock, the tangential stress and radial displacement around the tunnel decrease, and are most sensitive to the elastic modulus of surrounding rock (Unit: GPa) in the range of 5,10]; (2) When the lateral pressure coefficient is in the range of (0,1], the maximum tangential stress and radial displacement around tunnel decrease with the increase of coefficient; when the coefficient in the interval 1,2], the law is opposite. and the stress and displacement are more sensitive to the lateral pressure coefficient in the interval 1,2]; (3) With the increase of bolt length, the tangential stress and radial displacement around tunnel decrease; with the increase of bolt radius, the tangential stress around tunnel increases, and the radial displacement decreases; With the increase of circumferential spacing of bolts, the variation trend is opposite to the laws of bolt radius.