基于双参数地基的隧道预支护拱棚壳体力学模型

隧道预支护技术作为重要施工辅助方法，除有效加固围岩外，还具有良好的承载、抑制变形作用。为了更好地模拟隧道预支护拱棚真实受力，基于注浆管棚、水平旋喷拱棚所呈现出的壳体特性，首先，建立正交曲线坐标系，通过位移函数求解控制方程，然后，引入Pasternak地基模型，建立了Pasternak双参数地基的拱棚壳体力学模型，最后，推导出拱棚挠度、内力、地基反力的解析解表达式。将所提模型进行案例计算和数值验证，再对预支护拱棚的变形、横纵向受力以及地基接触反力进行分析，探讨了拱棚设计参数对旋喷拱棚变形的影响。与既有文献的分析方法对比，所提模型考虑了岩土体的连续性和注浆加固区整体性影响，相比传统方法理论上更贴近拱棚预支护真实受力状态；解析法和数值法得出的整体挠度曲线均呈“勺形”分布，结果吻合程度较好。力学分析表明：纵向上，拱棚能很好地调整压力分布，一定程度上使内部围岩处于免压状态；以开挖面为界，拱棚纵向弯矩、剪力的影响范围约5倍开挖进尺；横向上，拱脚处剪应力起主导作用，拱顶处主要由正应力主导且容易发生材料破坏；不同参数对拱棚结构变形影响程度不同，总体表现出：初始挠度>开挖进尺>桩径>埋深>开挖高度。

Mechanical Shell Model of Tunnel Arch Shed Pre-support Based on Two-parameter Foundation

As an important construction auxiliary method, tunnel pre-supporting technology not only effectively strengthens the surrounding rock, but also has good bearing and restraining deformation. In order to better simulate the real stress of the tunnel pre-supporting arch shed, firstly, the orthogonal curve coordinate system was established based on the shell characteristics of the grouting pipe shed and the horizontal jet grouting arch shed, and the control equation was solved by the displacement function. Then, the Pasternak foundation model was introduced, and the mechanical shell model of the arch shed on the Pasternak two-parameter foundation was established. Finally, the analytical solution expressions of the deflection, internal force and foundation reaction force of the arch shed were derived. The proposed model was subjected to case calculation and numerical verification, and then the deformation, transverse and longitudinal forces and foundation contact reaction force of the pre-supporting arch shed were analyzed, and the influence of arch shed design parameters on the deformation of the jet grouting arch shed was discussed. Compared with the analysis methods in the existing literature, the proposed model considers the continuity of rock-soil mass and the integrity of the grouting reinforcement area, which is closer to the real stress state of arch shed pre-support in theory compared with the traditional method. The overall deflection curves obtained by the analytical method and the numerical method are all '' spoon-shaped '' distribution, and the results are in good agreement. The mechanical analysis shows that in the longitudinal direction, the arch shed can adjust the pressure distribution well to a certain extent, the internal surrounding rock is in a pressure-free state. Taking the excavation face as the boundary, the influence range of the longitudinal bending moment and shear force of the arch shed is about 5 times the excavation footage. Transversely, the shear stress at the arch foot plays a leading role, and the vault is mainly dominated by normal stress and prone to material damage. Different parameters have different effects on the deformation of the arch shed structure. The overall performance is that initial deflection > excavation footage > pile diameter > buried depth > excavation height.