考虑轴力与刚度突变的盾构隧道纵向地震响应解析 English Version
Theoretical analysis for the longitudinal seismic response of shield tunnel by considering axial force and variable stiffness
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摘要: 为合理估算盾构隧道纵向地震响应，将隧道简化为Pasternak弹性地基上的Timoshenko梁，考虑轴力与刚度突变的影响，推导出纵向与横向地层位移作用下的微分控制方程，并通过有限差分理论进行求解。进一步地，将理论计算结果与有限元模拟结果对比，验证了理论方法的有效性和可靠性，并探讨了盾构隧道加强段与常规段的纵向刚度比、地基反力系数、残余轴力等关键参数对隧道纵向地震响应的影响规律。结果表明：盾构隧道刚度的提升能够有效提高隧道的抗震性能，但在刚度突变处附近，隧道刚度相对较小的区段（常规段或劣化段）在地震作用下可能发生较大的环间局部非连续变形（张开、错台）；降低隧道纵向刚度比以及缩短加强段的长度，可以显著减少刚度突变对隧道纵向地震响应的不利影响。盾构隧道的环间局部变形与地基反力系数呈正相关，且局部变形随着地震波波长的增大先增后减；当地基反力系数较大时，且地震波波长在20m~120m范围内，隧道刚度突变处可能发生较大的张开和错台。隧道残余轴力能够在一定程度上提升盾构隧道抗震性能，且入射角和隧道刚度相对较小时，提升效果更为显著。以上研究成果可为盾构隧道纵向抗震设计提供指导。Abstract: In order to estimate the seismic response of the tunnel reasonably, the shield tunnel is regarded as a Timoshenko beam upon Pasternak elastic foundation. Considering the axial force and the variable stiffness, the theoretical calculation model under the joint action of longitudinal and transverse strata displacements is proposed and solved by the finite difference method. The theoretical solutions are compared with the numerical simulation results to verify its validity and reliability, then the influences of six key parameters on the longitudinal seismic response were further explored. The increase in shield tunnel stiffness can effectively improve the seismic performance of the tunnel. However, in the vicinity of the stiffness variation, the segments with relatively small tunnel stiffness (regular or degraded segments) may experience higher local deformation under seismic action. Reducing the longitudinal stiffness ratio and shortening the length of reinforcement section, can significantly mitigate the adverse seismic response of tunnel lining caused by variable stiffness. The local deformation at the tunnel is positively correlated with the foundation reaction coefficient, and the local deformation increases and then decreases with the increase of wavelength. Seismic waves with wavelengths between 20 m and 120 m are more likely to lead to larger the opening and dislocation of shield tunnel, on the scenario of higher foundation reaction coefficient. The residual axial force can improve the seismic performance of shield tunnel to a certain extent, especially when the angle of incidence and tunnel stiffness are relatively small. These researches can provide some guidance for the longitudinal seismic design of shield tunnels.
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