管幕法是超浅埋隧道施工过程中常用的一种超前预支护方法,准确确定管幕变形是安全施工的重要保障,但已有计算方法大多忽略了荷载传递机理及开挖引起的应力释放与扰动效应。鉴于此,首先考虑了隧道拱顶土拱效应及管间环向微拱效应,提出了耦合管幕法隧道荷载传递机理的拱顶竖向荷载计算方程;引入Pasternak弹性地基梁理论,采用荷载释放系数,考虑掌子面后方应力释放效应;通过改变扰动段与支护未封闭段基床系数,表征开挖扰动效应与初期支护延滞特性,进而提出了一套耦合“多效应”的超浅埋隧道管幕变形计算方法。将所提计算方法应用至某管幕法隧道工程,对比了管幕变形现场监测数据与既有理论计算结果,验证了所提计算方法的合理性与准确性。最后,应用所提计算方法,分析了掌子面前方土体基床系数、开挖进尺、支护未封闭段长度等敏感性参数对管幕变形影响规律。结果表明:适当提高掌子面前方土体基床系数和降低开挖进尺,可有效控制管幕变形;改变支护未封闭段长度对管幕变形影响甚微。所提计算方法可为准确预测超浅埋隧道管幕变形提供理论指导。

[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.