中文摘要：

为了揭示盾构隧道在不同位移边界条件下的围岩位移分布情况,将该问题简化为含圆形孔洞的弹性半无限平面第二类基本问题,运用弹性复变函数理论,结合洞周5种不同位移收敛模式,推导了两个位移复势函数φ（z）和ψ（z）的表达式,给出了围岩任意一点位移分量（u,v）的解析通式,并讨论了不同埋深与不同位移边界条件下围岩位移分布规律。基于理论公式,预测了工程实例的地表沉降,并将预测结果与实测数据进行了对比分析。研究结果表明：（1）当隧道半径r_0=4.0 m、泊松比μ=0.3,隧道埋深h从2r_0增为6r_0时,地表相对沉降量最大值Δv_（max）变化范围为0.33~1.94,地表沉降影响范围约为28.7~124.1 m,地层相对水平位移最大值Δu_（max）随埋深变化不大,且最大值Δu_（max）处于隧道中心水平线附近;（2）在5种不同位移收敛模式中,有两种模式预测的地表沉降值与实测数据较为吻合,其理论解可为指导隧道设计和施工提供理论基础。

英文摘要：

To reveal the surrounding rock displacement distribution of shield tunnels under different displacementboundary conditions, it simplified it as the second basic problem of elastic semi-infinite plane with a circular hole,and the expression of two complex variable functions φ（z） and ψ（z） as well as an analytical general formula of thedisplacement component（u, v） at any point on a rock mass were deduced by combining the elastic complex functiontheory and five different displacement convergence modes around a tunnel. The displacement distribution rules ofsurrounding rock under different buried depths and displacement boundary conditions were discussed. Based on the theoretical formula, surface settlement of a certain project was predicted and a comparison between the predicted da-ta and measured data was made. The results show that： when the tunnel radius r_0 is 4.0 m, the Poisso ratio μ is 0.3,and the tunnel depth h is 2r_0 to 6r_0, then the maximum relative surface settlement Δu_（max） ranges from 0.33 to 1.94, andthe influence area induced by surface settlement ranges from 28.7 m to 124.1 m; the buried depth has little influ-ence on the maximum relative horizontal displacement Δu_（max）, which is located near the central horizontal line of atunnel; in five different modes of displacement convergences, the solution results of two displacement boundary con-ditions are consistent with the measured surface settlements, and therefore these two theoretical solutions can beused as a foundation of tunnel design and construction.