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r0=4.0 m、泊松比μ=0.3,隧道埋深h从2r0增为6r0时,地表相对沉降量最大值Δvmax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Δumax随埋深变化不大,且最大值Δumax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.%To reveal the surrounding rock displacement distribution of shield tunnels under different displacement boundary 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 the displacement component (u, v) at any point on a rock mass were deduced by combining the elastic complex function theory and five different displacement convergence modes around a tunnel. The displacement distribution rules of surrounding 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 r0 is 4.0 m, the Poisso ratioμis 0.3, and the tunnel depth h is 2r0 to 6r0, then the maximum relative surface settlementΔvmax ranges from 0.33 to 1.94, and the 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 Δumax, which is located near the central horizontal line of a tunnel;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 be used as a foundation of tunnel design and construction.
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