考虑重力影响的含空洞地层浅埋隧道围岩应力及位移解析解

为了明确地层空洞对浅埋隧道施工引起的地层应力和位移的影响，建立了含空洞地层浅埋圆形隧道围岩应力和位移解析模型，该模型既能考虑隧道开挖边界上的重力释放过程，又能考虑隧道与空洞的相互作用。采用复变函数法和Schwarz交替法对模型进行了理论求解，并将该模型解析解与有限元数值解进行了对比分析，两者吻合较好。基于所建立的解析模型，分析了应力释放系数、空洞位置及尺寸对地层应力和变形的影响规律。结果表明：随着应力释放系数和空洞尺寸的增大以及空洞与隧道间距的减小，空洞影响效应逐渐增大；空洞位于隧道拱顶时影响最为显著，空洞位于隧道斜上方时影响次之；空洞导致圆心连线两侧0°~5°范围内的隧道洞周环向应力减小，两侧5°~45°范围内的环向应力增大；空洞导致靠其一侧的隧道收缩变形增大，其中圆心连线位置上的隧道收缩变形增长最为显著；而地表最大差异沉降位于空洞正上方处。研究成果对含空洞地层浅埋隧道施工引起的围岩变形和应力预测具有重要的理论意义和应用价值。

An Analytical Solution for Stress and Displacement of Surrounding Rock for a Shallow Tunnel with a Cavity in Strata Considering Gravity Condition

To study the stress and displacement of the surrounding rock for a shallow circular tunnel with a cavity in the strata, an analytical model in which the interaction between the tunnel and the cavity as well as the influence of gravity can be considered was proposed. The complex function method and Schwarz alternating method were applied to solve the model theoretically. Then, the analytical solution in this study was compared with the finite element numerical solution, and the results showed that they were in good agreement. Based on the analytical model, the effects of the stress release coefficient and position and size of the cavity on the stress and displacement were analyzed. The results showed that the influences of the cavity increase gradually with increase of stress release coefficient and cavity size but decrease with the distance between cavity and tunnel. The influence is the most significant when the cavity is located in the tunnel vault, followed by the inclined top. The hoop stress is decreased in the range of 0-5° but increased in the range of 5°-45° on both sides of the line between the centers of the cavity and the tunnel. The maximum differential subsidence is located directly above the cavity. The research has important theoretical significances and application values for the prediction of deformations and stresses caused by a shallow tunnel with a cavity in the stratum.