# Seismic Fragility Analysis of the Transmission Tower-Line System Considering Bol Slippage
## 1 Introduction  
Previous earthquake investigations have indicated that earthquakes can cause severe damage to transmission lines and even lead to the collapse of transmission towers, which significantly hampers the reconstruction and rescue efforts in affected areas [1, 2]. To ensure the safe operation of transmission lines under earthquakes, the mechanical response of transmission tower-line systems (TTLSs) subjected to seismic loads has been studied, aiming to provide guidance for the design of transmission lines in earthquake-prone regions. [PERSON] et al. [3] manufactured a scaled model of a tower-line system and conducted shaking table tests to investigate its seismic performance under both far-field and near-fault ground motions. Subsequently, they extended their study by considering wave effects, local site conditions, and seismic wave coherence effects and conducted the shaking table tests on a long-span TTLS [4]. The results revealed that spatially correlated ground motions can significantly enhance the dynamic response of towers. [PERSON] et al. [5] established an Ultra High Voltage (UHV) tower-line system model by ABAQUS and employed the incremental dynamic analysis (IDA) method to investigate the impact of fault crossing angles and locations on the seismic response of transmission lines. The results showed that the optimal layout angle for UHV transmission lines to minimize the seismic response is 45\({}^{\circ}\) relative to the fault strike. [PERSON] et al. [6] derived the structural dynamic equation under multi-component ground motions by the shaking table tests and calculated the seismic response of the TTLS by numerical simulation. The results showed that multi-component ground motions must be considered when designing transmission towers in high-intensity earthquake areas. The aim of the above studies was to obtain the dynamic responses of structures Induced by earthquakes with specific seismic spectra and intensities, thereby providing areference for the seismic design of TTLSs. However, the randomness of ground motions is not considered, which leads to a failure in effectively evaluating the failure probability of the tower-line system under earthquakes. Thus, the fragility analysis method is used to evaluate the seismic failure probability of structures. [PERSON] et al. [7] studied the influence of different seismic incidence angles on the collapse probability of the TTLS using the IDA method. The results showed that the incidence direction influence of the rare ground motion with peak ground acceleration (PGA) of 0.32-0.46 g should be considered. Subsequently, they made a scaled model of the tower-line system and studied the influence of ground motion duration on the seismic response of the tower. After that, the seismic fragility was calculated using the IDA method [8]. The results indicated that long-duration ground motion increases the failure probability. [PERSON] et al. [9] studied the influence of individual (far-field and near-field) earthquakes and repeated earthquakes on the seismic performance of lattice towers through fragility analysis. The results showed that the damage of aftershocks and near-field earthquakes is more obvious. Based on the linear elastic theory, [PERSON] et al. [10] analyzed the dynamic time history of a representative high-voltage transmission tower in South Korea under an earthquake and drew the fragility curve by the maximum likelihood estimation method. The results showed that the 765 kV transmission tower members designed according to the South Korean codes may buckle. [PERSON] et al. [11] established uncertain numerical models of transmission towers and studied the influence of structural parameter uncertainty on the seismic fragility of towers. The results showed that the influence of material parameter uncertainty on fragility is more significant than that of the geometric size.