深埋隧道支护结构内力计算方法研究

深埋隧道是交通建设中的关键，对其力学行为进行深入研究具有重要的理论和工程实际意义。针对既有研究的不足，考虑到深埋隧道支护结构力学响应的空间差异性和施工过程围岩-支护结构的动态作用关系，建立了围岩竖向荷载与径向位移关于隧道横截面角度变化的平衡微分方程，获得了围岩压力作用下复合支护结构的内力解析解。根据支护反力与围岩径向位移的关系，推导了初支与围岩、初支与二衬间的围岩压力与位移解析解。结合数值模拟和现场监测结果进行分析，证实了计算方法的可靠性和有效性。最后基于该解析方法，对支护结构厚度和弹性模量进行了参数分析。结果表明支护结构的厚度和弹性模量与其弯矩正相关，且弹性模量对弯矩影响更大，初支厚度和弹模的变化对围岩压力和径向位移的影响比二衬对其影响更显著。研究成果可为准确预测支护结构任意截面位置的内力提供一定理论支撑。

Research on the calculation method of internal force of deep-buried tunnel support structure

Deep-buried tunnels play a key role in transportation construction, and an in-depth study of their mechanical behavior has important theoretical and engineering practical significance. Considering the spatial variation of the mechanical response of the support structure in deep-buried tunnels and the dynamic relationship between the surrounding rock and the support structure during the construction process, the equilibrium differential equation of the vertical load and radial displacement of the surrounding rock with respect to the change of the tunnel cross-section angle is established. The analytical solutions of the internal forces of the composite support structures are obtained. According to the relationship between support reaction force and radial displacement of surrounding rock, the analytical solution of pressure and displacement of surrounding rock between initial support and surrounding rock, initial support and the secondary lining is deduced. The correctness and effectiveness of the proposed method are verified by numerical simulation and the measured data. Finally, parametric analysis is conducted to investigate the responses of the tunnel by considering such factors as the thickness and the elastic modulus of the support structure as well as the lining installation time based on the analytical method. The results show that the thickness and elastic modulus of the support structure are positively correlated with its bending moment. Compared with the support structure thickness, the elastic modulus has more significant influence on the bending moment. Compared with the secondary lining, the surrounding rock pressure and radial displacement are more sensitive to the changes of the thickness and elastic modulus of the primary lining. The research results can provide the theoretical support for predicting the internal force at any section position of the support structure accurately.