# Seismic Performance Evaluation of Highway Bridges under Scour and Chloride Ion Corrosion
## 2 Earthquake and Scour Combination in the Failure Probability of Bridge
### Application for a Practical Project  
#### 2.2.1 The Introduction of Bridge Model and the Determination of Scour Depth Distribution  
A continuous rigid-frame highway bridge across a river with the over span arranged as 42 m + 76 m + 42 m was taken as an example bridge for simulation. A reinforced concrete box girder was set as the superstructure. A rectangular solid section was adopted for the main piers, whose top section size is 1.8 m \(\times\) 6.2 m and bottom section size is 1.8 m \(\times\) 4.5 m. Double-column piers were adopted for transition piers with 1.5 m diameter. The diameter of the pile foundation at the main pier is 2 m and at the transition pier is 1.8 m. Concrete grades of the girder, pile foundation at the main pier, and the main pier adopted C55, C35, and C40, respectively, and reinforcement adopted HRB400. According to the Bridge Code (MOT 2020) for Seismic Design of Buildings: GB50011-2010 [34], the design earthquake is grouped into the first set, seismic fortification category of the bridge site area is Class B, and basic intensity is VIII degree. Forty-eight seismic time-history waves consisting of 24 artificial acceleration time-history waves of Class III site and 24 seismic waves of Class II site from the peer database were chosen as the input of ground motion. The FE model was established according to the following principles. Spatial beam elements were utilized to simulate girder and pier and shell elements were adopted to simulate bearing platform. The second-phase pavement was equivalently expressed by line load and area load. Rayleigh damping was set in this bridge with a damping ratio of 0.05. The transition pier was equipped with a friction pendulum bearing which can be simplified to a mechanical model with bilinear restoring force. The FE model of the bridge under scour conditions is shown in Figure 2. The dynamic characteristics of the bridge obtained from the FE model are shown in Table 2.  
The static p-y curve between pile foundation and soil can be performed in the FE model by nonlinear connection elements which can be deleted to simulate the scour effect on pile foundation. The p-y curve is calculated according to the formula in API specification [35]. P-y curves at different depths within 18 m below the sour line are displayed in Figure 2.  
Figure 2: Finite element model of the example bridge. The function of peak ground acceleration (PGA) probability distribution which obeys type II distribution of the extreme value can be obtained by converting the seismic intensity into PGA [36; 37; 38; 39]. The random sample of earthquake intensity was carried out according to its probability distribution to calculate the corresponding cumulative probability density. The corresponding relationship between a set of PGA and its cumulative probability density can be obtained by converting seismic intensity into PGA, which can be fitted and derived to acquire the probability distribution function of PGA in any design reference period. The formula is as follows. \[F_{t}(a)=\exp\left[-\frac{t}{50}\left(\frac{a}{0.06735}\right)^{-1.945}\right] \tag{6}\]  
where \(F_{t}(a)\) is the probability distribution function of PGA; \(t\) is the design reference period of bridge; and \(a\) is the value of PGA. The PGA distribution for the input parameter of ground motion is displayed in Figure 2.  
The river spanned by the example bridge has water all year and is characterized by rapid rise and fall. River scouring mainly occurred at the pile foundation of the No. 1 main pier. With reference to the geological and hydrological report of the area where the bridge site is located and the Monte Carlo method [40; 41], parameters in the above formula for calculating the scour depth can be determined. A large number of random samples were taken according to the distribution shown in Table 1 and the value of probability density corresponding to each refinement interval could be acquired by extracting and refining those sample values.