## 5 Seismic Risk Analysis of the Entire Bridge  
### Hazard Analysis at the Bridge Site  
The most common site hazard analysis methods at present are empirical statistical methods, deterministic methods, and probabilistic methods. Because of the significant uncertainty in earthquake occurrence in terms of time, space, and intensity, the probabilistic method considers all potential seismic source areas for engineering sites as well as the possibility of ground motions at all levels in each potential seismic source area, and finally calculates the probability of ground motions exceeding a certain threshold at a given site, which is expressed in the form of a site hazard curve. As a result, it has become increasingly popular in recent years.  
According to relevant research findings [42; 43], spatial correlation exists between earthquake intensity measures. Considering the complexity of the effect mechanism, this paper adopts a point source model based on the concepts of exceedance probability and average return period in extreme value distribution theory [44]. Because the basic peak ground acceleration (A\({}_{0}\)) can be found in the Seismic Ground Motion Parameter Zonation Map of China (GB18306-2015) [45], with an exceedance probability of 10% during 50-year design reference period, A\({}_{0}\) was employed to directly derive the calculation formula of the site hazard curve in this investigation. At present, scholars around the world generally acknowledge that the probability distribution of various seismic motion parameters follows approximately an extreme distribution [44; 46; 47]. Based on recent research findings [48], PGA is assumed to simulate the extreme value type II distribution with the following expression:  
\[F_{II}(a)=\exp\left[-\left(\frac{a}{a_{g}}\right)^{-k}\right] \tag{26}\]  
where \(a_{g}\) is the PGA with the exceedance probability of 63.2%, \(k\) is the shape factor, and the value in current seismic design codes is 6.87 when the seismic intensity at the bridge site is Degree 7 [49].  
According to the relationship between the probability distribution function \(F(x)\) and the exceedance probability \(P(X\geq x)\), Formula (26) can be further transformed as follows:  
\[F_{II}(a)=1-P(A\geq a)=\exp\left[-\left(\frac{a}{a_{g}}\right)^{-k}\right] \tag{27}\]  
Taking the natural logarithms on both sides of Formula (27) and substituting the basic peak acceleration A0, the solution is solved simultaneously:  
\[P(A\geq a)=1-\exp\left[-0.1054\,\left(\frac{a}{A_{0}}\right)^{-k}\right] \tag{28}\]  
Because the current Seismic Ground Motion Zoning Map corresponds to the exceedance probability during a 50-year design reference period, the site hazard curve during a 100-year design reference period can be converted further. The calculation formula for the site hazard curve with PGA as the ground motion parameter can be obtained by substituting the conditions at the bridge site as follows: A0 = 0.20 g, \(k\) = 6.87.  
\[P(A\geq a\mid 100\,)=1-\exp\left[-0.2108\,\left(\frac{a}{0.20}\right)^{-k}\right] \tag{29}\]  
According to Formula (29), the exceedance probability \(P\) under ground motions with different PGA is calculated, then the site hazard curve of the entire bridge is drawn using this as the ordinate and PGA as the abscissa, as shown in Figure 12.  
In Figure 12, the exceedance probability of the ground motion decreases gradually as the PGA increases, indicating that the possibility of severe ground motion is decreasing. The site hazard curve drops sharply when PGA is between 0.10 g and 0.20 g, indicating that the probability of ground motion with PGA of 0.10 g to 0.20 g for the entire bridge is the highest. The site hazard curve can accurately reflect the design site's hazard information, providing ground motion parameters for use in engineering seismic design.