任意形状隧道围岩应力与位移的解析延拓求解

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。最后与已有的非均匀受压圆断面水平巷道围岩的应力和位移解公式进行对比，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。

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

In order to get the stress solutions and displacement solutions in rock around a tunnel excavation, taking into account of the internal pressure, an analytical solution was presented for the stresses and displacements around a lined tunnel with arbitrarily shape using Analytic Continuation Method in an elastic half-plane. According to the depth of a tunnel is larger more than the size of the tunnel, gravity loads were simplified uniform normal loads along far-field boundary. As a special case, a close solution for stress and displacement field around a lined circular tunnel at great depth was given. Under simplified conditions is consistent with existing solutions. The results show that the new method of accuracy. The method of solving extend the application of Analytic Continuation Method in tunnel engineering, taking into account of tunnel with arbitrary shape and the support force. It can be used to assess fast and effectively the stress state and deformation of Tunnel surrounding rock with arbitrarily shaped section.