考虑土拱效应的双线矩形隧道地表沉降预测多拱解析模型

    A Multi-Arch Analytical Model for Predicting Ground Settlement Induced by Twin Rectangular Tunnels Considering Soil Arching Effects

    • 摘要: 双线矩形隧道施工中,土拱效应对隧道间相互作用及地层扰动机制的影响复杂且机理不明,制约了地表沉降预测的精度。为此,本文提出一种考虑土拱效应的双线矩形隧道地表沉降解析预测新方法。该方法首先构建了包含弹性拱与隧道间摩擦拱的“多拱模型”,并推导了其应力演化方程;其次,运用复变函数理论推导矩形隧道应力应变解析解,并据此改进Loganathan公式,建立了适用于双线矩形隧道工况的地表沉降预测模型。最后,通过建立不同深距比(H/S)的有限元模型,对所提方法的预测结果与Peck公式(未考虑土拱效应)进行了对比验证。研究发现,地表沉降槽形态与隧道埋深与净间距之比(H/S,S为隧道净距)密切相关:当H/S ≤1/3或H/S >2时呈“V”形(后者条件下可近似按单隧道分析);当1/3 < H/S ≤1时呈“W”形;当1 < H/S ≤2时呈“U”形。验证结果表明,与Peck公式相比,所提方法能更准确地预测不同工况下的地表沉降,尤其能反映土拱效应的影响,可为城市双线矩形隧道设计与施工提供理论参考。

       

      Abstract: The intricate influence of soil arching effects on tunnel-soil-tunnel interactions and ground disturbance mechanisms during the construction of twin rectangular tunnels remains a challenge, critically limiting the precision of surface settlement predictions. To address this, an innovative analytical method is proposed for predicting surface settlement induced by twin rectangular tunnels, explicitly incorporating soil arching effects. This method first establishes a “multi-arch model,” comprising an elastic arch and an inter-tunnel friction arch, for which stress evolution equations are derived. Subsequently, analytical stress-strain solutions for rectangular tunnels are formulated using complex variable theory. This foundation is then utilized to refine the Loganathan formula, leading to a tailored settlement prediction model applicable to twin rectangular tunnel scenarios. The proposed method’s predictive capabilities are validated against finite element models (FEM) across various depth-to-spacing ratios (H/S, where S is the net tunnel spacing) and benchmarked against the conventional Peck’s formula, which neglects soil arching. The study reveals a strong correlation between the surface settlement trough morphology and the H/S ratio: a ‘V’-shaped trough is observed for H/S ≤ 1/3 or H/S &gt; 2 (the latter approximating single tunnel behavior); a ‘W’-shape for 1/3 &lt; H/S ≤ 1; and a ‘U’-shape for 1 &lt; H/S ≤ 2. Validation results demonstrate that the proposed method offers superior accuracy in predicting surface settlement under diverse conditions compared to Peck’s formula, particularly in capturing the influence of soil arching. This research provides valuable theoretical insights for the design and construction of urban twin rectangular tunnels.

       

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