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Analytical solution for the longitudinal response of cross-fault shield tunnel considering plastic deformation of circumferential joints

考虑环缝接头塑性变形的跨断层盾构隧道纵向响应解析解

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Abstract

This paper proposes an analytical model for the longitudinal deformation response of cross-fault shield tunnels, in which the tunnel is assumed to be a Timoshenko beam placed on Winkler’s foundation. The plastic deformation behavior of circumferential joints and the influence of horizontal foundation friction are considered in the proposed model. A case study of normal faulting based on convincing numerical simulations is carried out to verify the rationality of the proposed model. Subsequently, the plastic deformation characteristics and distribution of circumferential joints are analyzed, and the factors affecting the longitudinal response of the tunnel are discussed through parametric analysis. The analysis results demonstrate that the proposed analytical model is reliable and applicable to calculating the longitudinal response of cross-fault shield tunnel, especially in evaluating the deformation of the circumferential joints under normal faulting. Severe plastic deformation is observed on the annular joints when the shield tunnel is subjected to 10 cm faulting. Under crossing active fault, the ground has a more significant restriction on the longitudinal deformation of the shield tunnel, resulting in a larger deformation of circumferential joints. A larger elastic modulus of the ground leads to a more notable longitudinal deformation of the tunnel lining. When the width of the fault fracture zone is not considered, the results of longitudinal internal force and deformation of shield tunnels are conservative. In the plastic deformation stage of the circumferential joints, the larger the plastic equivalent bending stiffness ratio of the shield tunnel, the slighter the plastic deformation of circumferential joints. The proposed analytical solution can be used to predict the joint deformation of cross-fault shield tunnels and provide guidance for the waterproof design of shield tunnels.

摘要

本文基于Winkler地基Timoshenko梁理论, 考虑水平地基摩阻力及盾构隧道环缝接头塑性变形 特征, 提出了一种跨断层盾构隧道纵向响应解析模型。首先, 以正断层错动工况为例, 采用数值模拟 方法验证解析解的合理性。然后, 分析了盾构隧道环缝接头的塑性变形特征, 并通过参数分析讨论了 影响隧道纵向变形响应的因素。研究结果表明: 断层错动下盾构隧道环缝接头张开及错台变形均较为 显著, 解析模型计算得到的盾构隧道纵向力学响应特征与数值模型计算结果规律一致; 在断层错动 10 cm时, 盾构隧道环缝接头已产生显著的塑性变形; 在穿越活动断层工况中, 地层对隧道纵向变形 的限制作用更加明显, 导致环缝接头变形量更大; 地基刚度越大, 盾构隧道纵向变形响应越显著。当 不考虑断层破碎带宽度时, 计算得到隧道纵向力学响应值是偏安全的; 在隧道环缝接头弹性变形阶 段, 弹性弯曲刚度有效率越大, 接头张开量越小; 在环缝接头塑性变形阶段, 盾构隧道二次塑性等效 弯曲刚度比越大, 盾构隧道环缝接头塑性变形越小。本文提出的解析模型可以预测跨断层盾构隧道环缝接头变形, 同时可以为盾构隧道接缝防水设计提供理论指导。

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Authors and Affiliations

  1. Key Laboratory of Urban Underground Engineering of Ministry of Education, Beijing Jiaotong University, Beijing, 100044, China

    Han-yuan Li  (李瀚源), Xing-gao Li  (李兴高) & Yi Yang  (杨益)

  2. School of Civil Engineering, Beijing Jiaotong University, Beijing, 100044, China

    Han-yuan Li  (李瀚源), Xing-gao Li  (李兴高) & Yi Yang  (杨益)

  3. Jinan Rail Transit Group Co., Ltd., Jinan, 250101, China

    Hao Liu  (刘浩)

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  1. Han-yuan Li  (李瀚源)
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  2. Xing-gao Li  (李兴高)
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  4. Hao Liu  (刘浩)
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Contributions

LI Xing-gao developed the overarching research goals and edited the draft of manuscript. The analytical solution was obtained by LI Hanyuan. LI Han-yuan validated the proposed method with 3D numerical simulation and wrote the first draft of manuscript. YANG Yi and LIU Hao edited the manuscript.

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Correspondence to Xing-gao Li  (李兴高).

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Conflict of interest

LI Han-yuan, LI Xing-gao, YANG Yi and LIU Hao declare that they have no conflict of interest.

Foundation item: Project(2015CB057800) supported by the National Basic Research Development Program of China; Project(2021-K-025) supported by the Science and Technology Foundation of Ministry of Housing and Urban-rural Development, China

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Li, Hy., Li, Xg., Yang, Y. et al. Analytical solution for the longitudinal response of cross-fault shield tunnel considering plastic deformation of circumferential joints. J. Cent. South Univ. 30, 1675–1694 (2023). https://doi.org/10.1007/s11771-023-5326-4

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