In an earthquake, the strong interaction between the surrounding rock and the lining structure causes the lining structure susceptible to extrusion or shear damage, and predicting the internal force distribution trend of the lining structure by the analytical method was advantageous for the preliminary design of the tunnel structure. In this work, the quasi-static method was used to approximate the displacement and deformation caused by the P-wave seismic load as far-field compressive stress. The analytical solution of the internal force for the lining structure was obtained by the analytical method, and the reliability of the analytical method was further verified. The dynamic response law of the lining structure was analyzed using numerical solutions in conjunction with engineering examples. The results show that the analytical method can be used to predict the trend of internal force distribution in the lining structure under seismic action, which has important theoretical guiding significance for the preliminary design of the tunnel structure. With the decrease in the hardness of the loess surrounding, the relative deviation of the theoretical, numerical, and literature results gradually decreases. With the increase of ground motion intensity, the interaction between the loess surrounding and the lining structure becomes more intense, and the internal force of the lining structure gradually increases. The numerical results were greater than the analytical results due to the consideration of the influence of initial stress. Under the action of the P-wave earthquake, the extreme values of the internal force with the lining structure mainly occurred at the location of the vault, arch waist, and inverted, and the most unfavorable positions of circular loess tunnel lining structures under P-wave seismic load was proposed.

中文翻译：

---

纵波作用下深埋圆形黄土隧道动力响应


地震时，围岩与衬砌结构之间的强烈相互作用导致衬砌结构容易受到挤压或剪切破坏，通过解析方法预测衬砌结构的内力分布趋势有利于隧道的初步设计结构。本文采用准静态方法将纵波地震载荷引起的位移和变形近似为远场压应力。通过解析方法得到了衬砌结构内力的解析解，进一步验证了解析方法的可靠性。采用数值解法并结合工程实例分析了衬砌结构的动力响应规律。研究结果表明，该解析方法可以预测地震作用下衬砌结构内力分布的趋势，对隧道结构的初步设计具有重要的理论指导意义。随着周围黄土硬度的降低，理论、数值和文献结果的相对偏差逐渐减小。随着地震动强度的增加，周围黄土与衬砌结构的相互作用愈加强烈，衬砌结构的内力逐渐增大。由于考虑了初始应力的影响，数值结果大于解析结果。 在纵波地震作用下，衬砌结构内力极值主要出现在拱顶、拱腰、倒拱等位置，是纵波地震作用下圆形黄土隧道衬砌结构最不利的位置。提出了波浪地震荷载。