任意形状隧道围岩应力与位移的解析延拓求解

Analytical Continuation Method for Solving Stress and Displacement of Surrounding Rock Buried Tunnel Excavation with Arbitrary Shape Section

考虑隧道断面开挖轮廓线为任意不规则形状的情况,基于复变函数方法中的解析延拓法对弹性半无限空间内隧道的围岩应力与位移进行求解,建立了任意形状隧道围岩中任意一点处的应力值和位移值的隐式解析表达式.然后以圆形断面隧道、马蹄形断面隧道作为特例,同时考虑隧道衬砌等内支撑法向反力作用的影响,求解出弹性半空间内任意一点处的应力值和位移值解析解的具体显式表达式,其中假设隧道埋深与隧道直径之比较大,从而不用考虑重力梯度的影响,将重力简化为作用在边界上的均布外荷载.最后与已有的解析解与数值解进行比较,证明了该方法的准确性.该求解方法拓展了解析延拓法的应用,并能快捷地评估任意断面形状隧道开挖中的围岩应力状态及位移变形情况.

In order to get the stress solutions and displacement solutions in rock around a tunnel excavation by taking into account of the internal pressure, an analytical solution is presented for excavation stress and displacement of tunne with arbitrar shape and size by analytic continuation method in anelastic half-plane. As a special case, two closed solutions are given respectively for stress and displacement field around a lined circular and horseshoe-shaped tunnel at great depth considering the influences of lining forces of tunnels. Because the depth is larger than the size of thetunnel, the effect of gravity gradient can be ignored, and gravity loads can be simplified as uniform normal loads along far-field boundary. Comparison between the results of numerical analysis by two-dimensional finite element method and those from the closed solutions indicates that the closed solution is reliable and applicable for assessment of the stress and displacement field around the tunnel in the arbitrary shape and size at great depth.