# Safety Evaluation of a Water-Immersed Bridge Against Multiple Hazards via Machine Learning
## 8 Results and Discussion  
Indicated in Figure 16 is the fragility curve of the respective scouring depth under the same performance level. As shown, the failure probability was not proportional to the scour depth. In addition, the performance level of slightly damaged had the least failure probability. To show this trend in a clearer way, Figure 17 denotes the fragility curve of the respective performance level under the same scouring depth and water level. As shown, the fragility curves indicate that the deeper the scour depth, the higher the failure probability, and the lower the performance level, the higher the failure probability. Such conclusion is consistent with the concept held by general public reasoning that the strength of a bridge foundation will degrade after being scoured and eroded. However, varied water depth tends to affect the failure probability of the bridge. Indicated in Figure 18 are the fragility curves of each water depth under the same scouring depth (0 m) and the same performance level. Taking the slight damage level for example, the failure probability increased from 43% to 56% if the water depth increased from 0 m to 8 m at PGA of 0.2 g. As seen, the influence of water depth was on the nonconservation side, and the influence of water depth should be considered, especially, when longer piers are used. Indicated in Table 1 is the result of errors and relative coefficients obtained during LSSVM training for the case when the scour depth was 0 m. It is shown that the prediction performance was not perfect, but it was acceptable. To be more specific, [PERSON] [29] suggested that if the MAPE is less than 10%, the prediction performance is considered as highly accurate. If the MAPE is between 11% to 20%, the prediction performance is good. After completing the LSSVM training, the corresponding result can be obtained by inputting the input parameters, such as water depth and PGA, in the trained machine to compute the fragility curve. Indicated in Figure 19 is the fragility curve under different scouring depths when the water depth was 3.5 m. Note that the purpose of LSSVM is to provide results that are not calculated by an authentic model such as SAP2000. For example, scour depths shown in Figure 19 were 3.25, 5, 6.25, and 7.5 m. By comparing Figures 16 and 19, it is learned that the LSSVM will provide a similar kind of failure probability trend. When viewing from a moderate limit state, the failure probability between 4 and 8 m of scouring depth, as indicated in Figure 16, was 0.50-0.70 (at 0.3 g), and that in Figure 19 was 0.52-0.72 (at 0.3 g) between 3.25 and 7.5 m of scouring depth. This indicated that the failure probability slightly increased when the immersion depth increased from 0 to 3.5 m. Similar conclusions can be inferred under other performance levels indicated in Figures 16 and 19. Figure 16: Fragility curves of each scouring depth under 0 m bridge water level and the same performance level. Figure 17: Fragility curves of each performance level under 0 m bridge water level and the same scouring depth. Figure 19: Fragility curves of each scoring depth under the same water level and same performance level using LSSVM. Figure 18: Fragility curves of each water level under 0 m scouring depth and the same performance level. Through the aforesaid comparisons, we can learn that the fragility curves obtained from the fragility curve established by LSSVM and structural analysis are very close. The failure probability of multiple hazards can be calculated according to the scouring hazard curve (Figure 10), seismic hazard curve (Figure 12), and bridge conditional failure probability obtained from nonlinear pushover and time history analyses, given these specific hazards. A direct comparison of using two different approaches (authentic and LSSVM) are displayed as shown in Figure 20. It is seen that the trends of two approaches were similar. The greater the scour depth, the bigger the difference.