# Seismic Fragility Analysis of the Transmission Tower-Line System Considering Bol Slippage
## 1 Introduction
The existing studies have Indicated that the mechanical behavior of bolted joints In angle steel transmission towers significantly affects the seismic performance of the towers [12]. Nevertheless, the above studies on the seismic fragility of the TTLS utilized the ideal rigid model (RM) and ignored the slippage behavior of bolted joints caused by external loads. [PERSON] and [PERSON] [13] obtained the bearing capacity curve of bolted joints from the elastic state to the plastic stage through monotonic tensile tests. [PERSON] et al. [14] studied the axial stiffness of bolted joints by model tests and numerical simulations, and the results showed that bolt slippage reduced the axial stiffness of bolted joints. [PERSON] et al. [15] considered the buckling behavior of members and the slippage effect of bolted joints, established the finite element model (FEM) of a single transmission tower, and analyzed the mechanical properties of the tower under wind loads using the pushover method. The results showed that the bolt slippage significantly increased the displacement of the tower. The research mentioned above mainly focused on the mechanical behavior of bolted joints connecting angle steel components caused by monotonic loads. However, for seismic loads, the vibration direction of seismic acceleration is reciprocating, resulting in the tower being subjected to cyclic loads. In addition, the mechanical behavior of bolted joints under monotonic loading and cyclic loading is not the same [16]. Thus, the reciprocating slippage behavior of bolted joints should be considered. [PERSON] and [PERSON] [17] proposed a novel algorithm for OpenSEES software to consider the mechanical behavior of a single bolted joint under cyclic loading. [PERSON] et al. [12] proposed a modeling method of the TTLS considering the bolt reciprocating slippage effect and analyzed the seismic response of the transmission line. The results showed that the seismic response of the tower was underestimated when the reciprocating slippage behavior of bolted joints was neglected. The above analyses on the seismic response of transmission lines Ideally assume that the tower Is located In a completely rigid foundation area, ignoring the deformation of the foundation soil. However, due to different geological characteristics and continuous external environmental loads, the foundation of the transmission tower experiences different degrees of deformation (settlement or horizontal displacement). Previous studies have shown that foundation deformation can affect the internal force and displacement of towers [18]. [PERSON] et al. [19; 20] studied the effects of foundation horizontal displacement on the bearing capacity of transmission towers by scaled tests and numerical simulations. The results showed that the foundation's horizontal displacement had a significant influence on the members of the tower near the displaced foundation. However, the rigid model (RM) was employed for the tower, which ignored the joint slippage effect. Based on the research presented in reference [12], [PERSON] et al. [21] investigated the influence of foundation deformation on the seismic response of TTLSs, considering the cyclic slippage behavior of bolted joints. The results indicated that the bolt slippage mitigated the additional stresses induced by foundation deformation. In summary, the literature contains very limited studies on the failure probability of transmission lines considering the reciprocating slippage behavior of bolted joints under an earthquake. Therefore, the seismic fragility of the TTLS considering the reciprocating slippage of bolted joints based on the research of [PERSON] et al. [12] is studied in this paper, and the influences of the bolted joint effect and foundation deformation are analyzed. In Section 2, the fragility analysis method is introduced, including the establishment of the model and the selection of seismic waves. In Section 3, the seismic limit performance index of the transmission line is determined.