Seismic events have underscored the significant impact of Rayleigh waves on the seismic resilience of shallow-buried tunnels. Existing analytical models often overlook key factors influencing seismic responses, including shear deformations, the rotational inertia of the tunnel cross-section, soil spring shear interaction, and the coupling of axial and transverse dynamic responses. These issues are particularly relevant to metro shield tunnels, which exhibit distinct deformation patterns and burial depths. To address these limitations, an improved model is proposed to analyze the longitudinal seismic response of shield tunnels subjected to Rayleigh waves, integrating the Timoshenko beam theory with the viscoelastic Pasternak foundation model. The analytical solution is derived using Fourier and Laplace transforms, with their convolution theorem applied to capture the complex interactions. The accuracy of the proposed solution is validated through comparison with finite element method (FEM) results. The main contributions of this work are: (1) The improved analytical solution enhances the accuracy of internal force amplitude predictions near critical frequencies, thus reducing the risk of unsafe design estimates; (2) The identification of characteristic frequencies and relative stiffness ratios associated with peak axial force, bending moment, and shear force, highlighting the need for a balanced consideration of tensile, compressive, bending, and shear behaviors for optimal seismic performance; (3) The findings reveal that maximum bending moments and shear forces occur at a burial depth of 0.1 times the Rayleigh wavelength, with a significant reduction of approximately 80% observed at a depth of one Rayleigh wavelength.

中文翻译：

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改进的闭式解决方案，用于受瑞利波作用的浅埋盾构隧道的地震响应


地震事件凸显了瑞利波对浅埋隧道抗震能力的重大影响。现有的分析模型经常忽略影响地震响应的关键因素，包括剪切变形、隧道横截面的旋转惯量、土弹簧剪切相互作用以及轴向和横向动力响应的耦合。这些问题与地铁盾构隧道尤其相关，因为地铁盾构隧道表现出明显的变形模式和埋藏深度。为了解决这些限制，提出了一种改进的模型来分析受瑞利波影响的盾构隧道的纵向地震响应，将 Timoshenko 梁理论与粘弹性 Pasternak 基础模型相结合。解析解是使用傅里叶变换和拉普拉斯变换推导的，并应用它们的卷积定理来捕获复杂的交互。通过与有限元法 （FEM） 结果的比较验证了所提解的准确性。这项工作的主要贡献是：（1） 改进的解析解提高了临界频率附近内力幅值预测的准确性，从而降低了不安全设计估计的风险;（2） 确定与峰值轴力、弯矩和剪切力相关的特征频率和相对刚度比，强调需要平衡考虑拉伸、压缩、弯曲和剪切行为以实现最佳地震性能;（3） 研究结果表明，最大弯矩和剪切力发生在 0.1 倍瑞利波长的埋深处，在一个瑞利波长的深度观察到显着减少约 80%。