浅埋隧道围岩应力及位移的显式解析解

浅埋隧道施工引起的地层位移将传递至地表进而形成地表沉降,施工前准确预测地层位移是有效控制地表沉降的前提。基于复变函数法,利用逆映射函数求解z平面复势函数的级数形式,并结合柯西-黎曼方程（C-R条件）对Verruijt提出的浅埋隧道围岩应力及位移隐式解析解中的解析函数求导,得出了浅埋隧道应力及位移函数的级数显式表达式;与Verruijt隐式解析解相比,该显式解析解直观,便于被工程人员使用,其编程计算量也较小;为确定显式解析解中的未知系数,基于浅埋隧道洞室变形产生的原因,提出了3种隧道洞室边界的变形模式和2种变形比率,合理调整变形比率可以实现多种边界条件组合。工程实测地层位移与显示解析解的计算结果吻合度高,验证了所提显式解析解的正确性和实用性。

Explicit analytical solutions for stress and displacement of surrounding rock in shallow tunnels

The ground movements caused by urban shallow tunnelling can be passed to the ground surface and then form surface settlements. It is necessary to accurately predict the ground movements before tunnelling for effectively controlling the ground settlements. Based on the complex variable function method, the series forms of complex potential functions in z-plane are first obtained using the inverse mapping function. By taking the derivative of analytical functions proposed by Verruijt with Cauchy-Riemann equations, explicit analytical solutions for the stress and displacement induced by shallow tunnelling are obtained. The explicit solutions are intuitional and easily used by engineers, which have smaller amount of calculation than the solutions proposed by Verruijt. Moreover, by improving the previous researches on deformation modes of shallow tunnels, three deformation modes and two deformation ratios are put forward. Finaly, the explicit solutions are compared with the field test data of two tunnel projects, and the accuracy and practicability of the proposed explicit solutions are proved.