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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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

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	Articles by authors
	LI Yongsuo1
	2
	QI Kai3
	HU Da1
	2*
	TAN Ze1
	2
	SHEN Zhaolong1
	2

Cite this article:

LI Yongsuo1,2,QI Kai3, et al. Analytical solution for stress-displacement in shallow triple-parallel tunnels considering construction sequencing[J]. , 2026, 45(11): 3254-3265.

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

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