基于Vlasov地基和Timoshenko梁耦合模型的盾构掘进诱发既有隧道非线性变形解析解

Analytical Solution of Nonlinear Deformation Induced by Shield Tunneling Based on Vlasov Foundation and Timoshenko Beam Coupling Model in Existing Tunnels

摘要: 在工程实践中，盾构隧道施工诱发既有隧道变形脱空后，将会产生危及其结构安全的严重问题。基于Vlasov地基和Timoshenko梁耦合模型，构建了考虑既有隧道–土体界面脱空影响的盾构穿越既有隧道响应解析解。首先，采用Loganathan和Polous公式计算盾构开挖诱发的土体自由位移场，并将既有隧道看作置于Vlasov双参数地基上的具有恒定截面的Timoshenko梁模型。然后，根据隧道连续条件建立隧道位移控制方程，通过有限差分法求解隧道纵向变形，建立脱空判断条件，带入线弹性解求解考虑脱空发生的解析解。最后，将本文解析解与三组工程实测数据进行对比验证，取得了较好的一致性。此外，考虑地层损失率、地基压缩参数、地基剪切参数等因素进行敏感性分析。结果表明，考虑脱空作用的理论解更为符合实际，不考虑脱空所得隧道位移结果偏小；地基压缩参数和地基剪切参数对既有隧道–土体界面脱空行为具有显著影响；当地基剪切参数越大，既有隧道–土体界面更易脱空，产生更大的脱空范围；地基压缩参数越小，既有隧道沉降越大，既有隧道–土体界面越容易脱空。

Abstract: In engineering practice, shield tunnel construction can induce deformation and cavitation in existing tunnels, which can pose serious problems that threaten their structural safety. Firstly, the Loganathan and Polous formulae are employed to calculate the free soil displacement field induced by shield excavation. The existing tunnel is considered as a Timoshenko beam model with constant cross-section placed on Vlasov two-parameter foundation. Subsequently, the tunnel displacement control equations are established in accordance with the tunnel continuity condition. The longitudinal deformation of the tunnel is then solved by the finite difference method in order to establish the judgement condition of dehollowing. This is subsequently brought into the linear elastic solution in order to solve the analytical solution, taking into account the occurrence of dehollowing. Finally, the analytical solution presented in this paper is compared and verified with three groups of engineering measured data, and a satisfactory level of agreement is achieved. Furthermore, sensitivity analyses is conducted, taking into account the rate of formation loss, foundation compression parameters, foundation shear parameters. The results show that the theoretical solution considering the caving effect is more in line with the reality, while the tunnel displacement result obtained without considering caving is smaller. The compression parameters of the foundation and the shear parameters of the foundation have a significant influence on the voids behavior of the existing tunnel-soil interface. When the shear parameters of the foundation are larger, the existing tunnel-soil interface is more likely to voids, resulting in a larger voids range. The smaller the compression parameters of the foundation are, the greater the settlement of the existing tunnel will be, and the more likely the interface between the existing tunnel and the soil will be to voids.