# Seismic Fragility Analysis of the Transmission Tower-Line System Considering Bol Slippage
## 4 Seismic Fragility Analysis of the TTLS with Fixed Foundation  
In this paper, the seismic peak acceleration (PGA) is used as the intensity measure (IM) of incremental dynamic analysis, and the maximum top displacement of the transmission tower is used as the structural seismic demand index (SD) to construct the seismic probabilistic demand model. The selected 15 seismic waves were adjusted by the equal spacing amplitude modulation method, and the peak accelerations of the seismic waves were adjusted from 0.2 g to 3 g, with a spacing of 0.2 g. It should be noted that both towers are subjected to the same ground motion. Figure 9 shows the PGA-displacement curves of the RM and the JM under 15 seismic waves. Under the influence of 15 seismic waves, the maximum tower top displacement range for the RM is 0.65-1.8 m, whereas for the JM, the range is significantly higher, ranging from 1.28 m to 2.85 m. Therefore, ignoring the bolt slippage effect underestimates the displacement response of the transmission tower. Subsequently, the simulation results are substituted into Equation (2), and the calculation models of the seismic demand index for TTLSs are determined using the regression fitting method, as shown in Figure 10. By calculating the R2 values of the two fitting models, the calculation formula of the determined seismic demand index is strongly correlated with the simulation results. The seismic fragility of the tower-line system under 15 seismic waves is calculated using the structural seismic fragility calculation in Equations (3) and (4). Figure 11 shows the seismic fragility curves of RM and JM. The exceeding probability of each limit state for the TTLS gradually increases with increasing PGA, and when considering the bolt slippage effect, the seismic fragility curve of the system shifts to the left. When the PGA is 2 g, the exceedance probabilities of the four limit states for RM are 61.43%, 20.76%, 9.87%, and 1.55%, respectively. Similarly, for JM, the exceedance probabilities of the corresponding four limit states are 69.93%, 26.08%, 14.90%, and 4.26%, respectively. Compared to those of RM, the failure probabilities of JM increase by 1.13 times, 1.25 times, 1.5 times, and 2.74 times, respectively, for the corresponding four limit states. This phenomenon indicates \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{3}{*}{**Limit State**} & \multicolumn{4}{c}{**RM**} & \multicolumn{4}{c}{**JM**} \\ \cline{2-10}  & \multirow{2}{*}{**Uniform Load**} & **Inverted Triangle** & **Height Equivalent** & **Average Value** & **Uniform Load** & **Inverted Triangle** & **Height Equivalent** & **Average Value** \\ \hline LS1 & 0.61 & 0.61 & 0.62 & 0.61 & 1.10 & 1.11 & 1.13 & 1.11 \\ LS2 & 0.80 & 0.81 & 0.83 & 0.81 & 1.64 & 1.66 & 1.68 & 1.66 \\ LS3 & 1.12 & 1.13 & 1.15 & 1.13 & 2.17 & 2.19 & 2.20 & 2.19 \\ LS4 & 1.21 & 1.22 & 1.25 & 1.23 & 2.32 & 2.34 & 2.35 & 2.34 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The tower top displacement at different limit states (unit: m). Figure 9: IDA curves for TTLSs: (**a**) RM; (**b**) JM. that the reciprocating slippage behavior of bolted joints can increase the seismic failure probability of a tower-line system. Under the same ground motion intensity, ignoring the bolt slippage effect would overestimate the seismic performance of the tower-line system and, more obviously, underestimate the failure probabilities for severe damage state LS3 and collapse state LS4.