# Study on the Seismic Response of Shield Tunnel Structures with the Preload Loss of Bolts
## 1 Introduction  
Shield tunnelling is an efficient, fast, and environmentally friendly method for underground transportation construction [1, 2]. The method has become an indispensable part of urban infrastructure development in the process of urbanization. Seismic resistance was not considered when building underground structures in the past. However, seismic safety for these structures has gained significant attention with increasing instances of seismic damage to underground structures. A shield tunnel is a typical underground structure. The seismic dynamic responses of shield tunnels have become a current research hotspot [3, 4]. Extensive studies on shield tunnels have been conducted using various methods, including theoretical analysis, numerical simulations, and shake table tests. [PERSON] et al. and [PERSON] et al. [3, 5, 6] proposed the modified seismic coefficient method for internal forces in deep-buried tunnel structures subjected to seismic effects. Regarding the dynamic response of shield tunnels, researchers have not only conducted extensive research on the tunnel's structure but also analysed various factors that could potentially influence the seismic performance of the tunnel. [PERSON] et al. [7] investigated the impact of damping layers on the dynamic response of tunnels, confirming that a damping layer can effectively reduce theseismic response of a tunnel's secondary lining. [PERSON] et al. [4] studied the influence of key segment positioning on the mechanical characteristics of tunnel structures and further proposed an optimization scheme for shield tunnel segment assembly. [PERSON] et al. [8] established a shield tunnel model that incorporates segment joints and analysed the impact of segment types on the seismic response of tunnel structures. [PERSON] et al. [9] employed numerical simulation to analyse the seismic response of tunnels at various burial depths, taking into account seismic peak intensity and concrete strength. [PERSON] et al. [10] utilized the finite element method to analyse the dynamic response of subway shield tunnels under the influence of the El-Centro earthquake. [PERSON] et al. [11] investigated the structure-soil interaction of shield tunnels in complex geological strata, as well as the damage characteristics of tunnel structures under seismic effects. In addition, researchers have also conducted relevant studies using shake table tests. [PERSON] et al. [12] designed shake table tests to study the characteristics of seismic wave propagation in different strata and discovered a turning point in the seismic wave amplification factor. Given the substantial size of actual shield tunnel segments and their complex joints, it is challenging to simulate experiments for long-distance shield tunnels. [PERSON] et al. [13] proposed a method to simplify long-distance shield tunnels into equivalent rings and homogeneous circular rings, providing a reference for the design of shake table tests for complex shield tunnels. [PERSON] et al. [14] conducted large-scale shake table tests based on subway structures, using the seismic response of cast-in-situ subway stations as a reference, to study the seismic performance and response of subway structures. Currently, researchers primarily focus on factors affecting the seismic performance of shield tunnels, including assembly methods, geological conditions (soft soil, hard rock), and seismic wave characteristics (seismic frequency, peak ground acceleration). There is limited research on the influence of joint performance in shield tunnels. As discontinuous structures, shield tunnels use bolts to connect adjacent segmental blocks. Therefore, the effectiveness of bolted connections directly affects the overall stiffness of shield tunnels. The relative stiffness between the structure and the foundation is one of the decisive factors affecting the performance of shield tunnels under seismic loading. Hence, the performance of connections directly influences the seismic performance of shield tunnels.