Calculation of Pipe Roof Deformation Considering Multi-effect Coupling in Ultra-shallow Buried Tunnel Construction

DUAN Yue-qiang

Journal of Changjiang River Scientific Research Institute ›› 2026, Vol. 43 ›› Issue (4) : 175-185.

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Journal of Changjiang River Scientific Research Institute ›› 2026, Vol. 43 ›› Issue (4) : 175-185. DOI: 10.11988/ckyyb.20250653
ROCK-SOIL ENGINEERING

Calculation of Pipe Roof Deformation Considering Multi-effect Coupling in Ultra-shallow Buried Tunnel Construction

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Abstract

[Objective] The accurate prediction of pipe roof deformation is critical for ensuring construction safety in ultra-shallow buried tunnels. Existing analytical methods frequently oversimplify the complex interaction mechanisms between the pipe roof and surrounding soil, particularly neglecting the load transfer mechanism, stress release effects during excavation, disturbance-induced soil weakening, and the time-dependent behavior of initial support systems. This study aims to develop a comprehensive theoretical framework that integrates these multiple effects into a unified model. The primary objectives include: establishing a vertical load equation that incorporates both the soil arching effect at the tunnel crown and the circumferential micro-arching effect between pipes; utilizing the Pasternak elastic foundation beam theory to simulate soil-structure interaction more accurately; introducing variable subgrade coefficients and a load release coefficient to represent stress redistribution and excavation disturbances; and ultimately formulating a reliable method for predicting pipe roof deformation under realistic construction conditions. The proposed model seeks to provide a practical and theoretically sound tool for design optimization and risk mitigation in pipe-roofed tunnel projects. [Methods] The research methodology combined theoretical derivation, numerical discretization, and empirical validation. First, the vertical load acting on the pipe roof was calculated by considering dual arching effects: the soil arching above the tunnel crown, modeled based on Terzaghi’s trap-door theory with inclined slip surfaces, and the micro-arching between adjacent pipes, with the load distribution derived assuming a parabolic arch axis between pipe contact points. The pipe roof was then modeled as an Euler-Bernoulli beam resting on a Pasternak elastic foundation, accounting for shear interaction between adjacent soil springs, offering a significant improvement over traditional Winkler-based models. To capture the construction-phase effects, the longitudinal span of the pipe roof was divided into five distinct zones: a fully enclosed support zone, an unenclosed support zone, an unsupported zone, a plastically disturbed zone, and an elastically disturbed zone, each with specific definitions of subgrade modulus and stress release rate. The governing differential equation was discretized using the finite difference method, with virtual nodes introduced to handle boundary conditions, and solved programmatically using MATLAB. The model was calibrated and validated against field monitoring data from a real-world ultra-shallow tunnel project, with additional comparative analysis against existing analytical models to demonstrate its superior performance. A detailed parametric study was conducted to evaluate the influence of the subgrade coefficient in front of the face, the excavation advance length, and the length of the unenclosed support segment. [Results] Validation against field data showed excellent agreement, with the predicted maximum deflection of 22.1 mm differing by only 5% from the measured value of 23.2 mm, confirming the model’s accuracy. The deformation curve generated by the proposed method was wider and smoother than those from existing theories, more accurately reflecting the continuous beam behavior of the pipe roof and aligning closely with monitoring results. Parametric analysis revealed that increasing the subgrade coefficient (k0) of the soil in front of the excavation face from 10 MPa/m to 90 MPa/m significantly reduced the maximum deformation from 33 mm to 17 mm, although the marginal benefit diminished beyond 90 MPa/m. In contrast, the excavation advance length (s) had an exponential impact on deformation. Increasing s from 1.0 m to 3.0 m caused the maximum deflection to approach 160 mm, far exceeding the typical control limit of 20 mm and severely threatening face stability. The length of the unenclosed support segment (b) was found to have a negligible effect on deformation. Furthermore, the load transfer capacity of the pipe roof was observed to be highly sensitive to all three parameters under high overburden ratios (H/B). Excessive increases in k0, s, or b under these conditions led to a significant transfer of load onto the soil in front of the face, increasing the risk of face instability. [Conclusion] This study successfully develops a multi-effect coupled analytical method for predicting pipe roof deformation in ultra-shallow buried tunnels. The integration of the soil arching effect, micro-arching effect, stress release, excavation disturbance, and support delay into a single model provides a more realistic and accurate representation of mechanical behavior than previously available methods. It emphasizes the effectiveness of improving the soil modulus in front of the tunnel face and strictly controlling the excavation advance length to manage deformation, while indicating that minimizing the unenclosed support length has limited benefits. However, the current study does not consider shear forces between differential elements, soil stiffness hardening, or small-strain behavior. Future research should incorporate these aspects to further enhance the model’s comprehensiveness and accuracy for a wider range of geotechnical conditions.

Key words

pipe roof method / ultra-shallow buried tunnel / load transfer mechanism / stress release effect / excavation disturbance effect

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DUAN Yue-qiang. Calculation of Pipe Roof Deformation Considering Multi-effect Coupling in Ultra-shallow Buried Tunnel Construction[J]. Journal of Changjiang River Scientific Research Institute. 2026, 43(4): 175-185 https://doi.org/10.11988/ckyyb.20250653

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Abstract
为使管棚受力分析模型能更好地模拟管棚的实际受力状态,基于注浆加固区域的受力特性分析,提出了考虑注浆加固区整体性的管棚受力分析模型。考虑注浆加固区的整体性,对管棚超前支护体系进行受力特性分析,提出可表征注浆加固区整体性的特征参数。综合考虑管棚注浆加固区整体性的特征参数、开挖面前方松动岩土体的支撑作用以及初期支护变形滞后效应等因素的影响,将管棚划分为二次衬砌段、初期支护段、开挖无支护段、开挖面前方扰动段和未扰动段;基于Winkler弹性地基模型,建立可考虑管棚注浆加固区整体性影响的管棚受力分析模型,并推导了管棚挠度和内力的计算公式。通过工程实例的对比分析,考虑注浆加固区整体性的管棚受力分析模型的计算结果更接近实测数据,从而验证了构建管棚模型的合理性。基于建立的管棚受力分析模型,分析注浆加固区的整体性对管棚变形和内力的影响规律,结果表明加固区弹性模量可显著减小管棚的变形和内力。管棚的参数分析表明,在实际工程中,增加钢管直径不能有效降低管棚挠度和内力,减小管棚挠度和内力最有效的方法为合理布置管棚的安装间距和采取合理的注浆量。
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To make the analysis model of the pipe-roof better predict the actual stress state of the pipe shed, basing on the analysis the stress characteristics of the grouting reinforcement area, it was proposed that the stress analysis model of the pipe shed can consider the integrity of the grouting reinforcement area. The characteristic parameter that represents the integrity of the shell reinforcement area was proposed by analyzing the mechanical characteristics of the advanced support system. The pipe-roof was divided into four lining sections based on the integrity of the grouting reinforcement area, the supporting function of the loose rock and soil in front of the excavating surface, and the lag of the initial support deformation. These are the initial branch section, the no-supporting section, the disturbance section and the undisturbed section in front of the excavating surface. Based on Winkler elastic foundation model, the analytical model of the pipe-roof that takes into account the integrity of the grouting area of the pipe-roof was established, and the expressions for the deflection and internal force of the pipe-roof were derived. By comparison with engineering examples, the calculation results of the analytical model are found to be close to the measured data, which verifies the accuracy of the model. Based on the pipe-roof model, the effect of the grouting reinforcement zone integrity on the deformation and internal force of the pipe-roof was analyzed. The results demonstrate that the elastic modulus of the reinforcement zone can significantly decrease the deformation and internal force of the pipe-roof. The parameter analysis of the pipe-roof shows that increasing the diameter of the steel pipe has negligible effect in the reduction of the deformation and internal force. Further, a reasonable spacing and grouting amount are shown to reduce the deformation and internal force of the pipe-roof effectively.
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Abstract
为了更好地研究隧道管棚的实际受力状态,根据隧道施工工序和施工影响,将隧道管棚划分为二衬段、初支段、开挖段以及掌子面前方的扰动段和未扰动段等五段,考虑管棚注浆后形成整体管棚拱的拱效应,建立了五段式隧道管棚的Winkler弹性地基梁新模型,推导了五段式隧道管棚模型的挠度和内力计算公式,并与既有工程案例进行对比分析,同时对不同的开挖进尺、管棚直径和加固区弹性模量进行了分析。结果表明:新模型得到的管棚挠度最大值和挠度最大值对应的位置与现场监测结果更为接近,能够解决已有管棚模型因边界条件设置不合理而造成的管棚变形在扰动段的末端出现的上拱现象,更符合管棚实际的变形情况;改变开挖进尺对管棚的挠度影响更大,管棚钢管直径为108 mm和114 mm时,其管棚支护效果相差不大;当E<sub>c</sub>(加固区弹性模量)>40.0 E<sub>g</sub>(围岩弹性模量)时,开挖进尺和钢管直径对管棚的挠度和弯矩的影响不大,因此,提高加固区的弹性模量是减小管棚挠度和内力最有效的方法。
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