考虑施工时序效应的浅埋三孔平行隧道群应力–位移解析方法

doi:10.3724/1000-6915.jrme.2026.0068

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摘要随着城市地下空间开发的集约化，多孔隧道群工程日益增多，由于分步开挖引起的累积地层扰动对工程安全构成了严峻挑战。然而，传统的解析解难以有效表征多连通域内的时变应力重分布，导致对复杂的“群洞效应”预测精度不足。为此，提出一种考虑施工时序影响的浅埋三孔平行隧道群应力–位移解析方法。研究融合Schwarz交替迭代法与复变函数理论，通过在3个孔洞边界间反复传递由开挖引起的附加应力，将复杂的三连通域问题转化为一系列单连通域问题的迭代求解，从而实现对三孔相互作用机制的精确解析。验证结果表明，该模型预测的地表沉降相对误差小于10%，且其计算效率较三维有限元法提升约3倍，极具工程快速预评估价值。研究进一步揭示了施工时序与空间参数的关键影响规律：（1）工序优化：采用“中间后挖”（即先两侧后中间）的施工顺序可有效缓解叠加效应，使最大沉降量减少约15%；（2）间距阈值：隧道净距与地表沉降呈非线性负相关，当间距小于2.5倍洞径时，沉降叠加效应增幅超过40%；（3）埋深效应：增加中间隧道埋深虽可显著降低20%～30%的地表最大沉降，但会加剧围岩塑性区的扩展深度。该研究克服了传统经验公式在表征复杂空间效应方面的局限，为密集城市隧道群的间距优化与施工工法选择提供了强有力的理论支撑。

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	黎永索1
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	祁凯3
	胡达1
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	谭泽1
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	申朝龙1
	2

关键词 ：隧道工程, 三孔平行隧道, 施工时序, Schwarz交替法, 复变函数, 地表沉降

Abstract：With the accelerated development of urban underground space, the construction of multi-tunnel clusters has become increasingly common. The cumulative ground disturbance induced by sequential excavation poses a critical safety challenge. However, traditional analytical solutions often fail to adequately characterize the time-dependent stress redistribution in multiply connected domains, resulting in insufficiently accurate predictions of the complex group-hole effect. To address this issue, this study proposes a novel analytical method for evaluating the stress and displacement evolution of shallow-buried, triple-parallel tunnels while explicitly accounting for construction sequencing. By integrating the Schwarz alternating iterative method with complex-variable theory, the proposed approach iteratively transfers excavation-induced additional stresses between tunnel boundaries. This strategy transforms the complex triply connected domain into a sequence of solvable singly connected-domain problems, enabling an accurate description of tunnel–tunnel interaction mechanisms. Validation results indicate that the proposed model predicts surface settlement with a relative error of less than 10%. Moreover, its computational efficiency is approximately three times that of the three-dimensional finite element method (FEM), demonstrating its considerable potential for rapid engineering pre-evaluation. The results further reveal several critical relationships involving construction sequencing and spatial parameters: (1) Excavation sequence: Excavating the middle tunnel last effectively mitigates the superposition effect and reduces the maximum surface settlement by approximately 15%; (2) Spacing threshold: Clear tunnel spacing exhibits a nonlinear negative correlation with surface settlement. Specifically, the superposition effect increases by more than 40% when the spacing is less than 2.5 times the tunnel diameter (2.5D); (3) Depth effect: Although increasing the depth of the middle tunnel can significantly reduce the maximum surface settlement by 20%–30%, it also increases the depth of plastic-zone development in the surrounding rock. This study overcomes the limitations of traditional empirical formulas in characterizing complex spatial effects and provides robust theoretical support for optimizing tunnel spacing and selecting construction methods in densely developed urban tunnel clusters.

Key words： tunnel engineering triple-parallel tunnels construction sequencing Schwarz alternating method complex variable function surface settlement

引用本文:

黎永索1，2，祁凯3，胡达1，2*，谭泽1，2，申朝龙1，2. 考虑施工时序效应的浅埋三孔平行隧道群应力–位移解析方法[J]. 岩石力学与工程学报, 2026, 45(11): 3254-3265.
LI Yongsuo1, 2, QI Kai3, HU Da1, 2*, TAN Ze1, 2, SHEN Zhaolong1, 2. Analytical solution for stress-displacement in shallow triple-parallel tunnels considering construction sequencing. , 2026, 45(11): 3254-3265.

链接本文:

https://rockmech.whrsm.ac.cn/CN/10.3724/1000-6915.jrme.2026.0068 或 https://rockmech.whrsm.ac.cn/CN/Y2026/V45/I11/3254

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