## 6 Result and Discussion  
### Seismic Failure Assessment  
This section explains the seismic analysis by the validated and verified FEM, which is subjected to 30 selected GMs. As explained in the previous section, the FEM was only subjected to the horizontal two-directional GM components. One was applied to the x-axis, and another one was applied to the y-axis. From the modal analysis, the most vulnerable direction has been notified in the x-directional response, which leads to the result in evaluation and analysis in this manuscript to the x-direction only. The analysis was also performed considering four different years for showing the response of the aging effect during an earthquake. By adopting the calibrated FEM through system identification, at the initial stage (0 years), the young's modulus of elasticity is considered as non-damaged \(E_{0}\)[23]. The other cases are adopted by taking aging effects as 25, 50, and 75 years, respectively. The model was at first subjected to the gravity load in all cases and simultaneously the non-linear time history analysis had been performed at the foundation base and foundation side. As for CGD one of the most key limit states is the relative displacement against the fluid flow, the crest displacements acted here as the DM in IDA. Following the IM-DM points in the IDA from [PERSON] and [PERSON] [65], in each increment of GM, the mean and standard deviation (SD) were calculated to show the 50% fractile curve (mean), 16% fractile curve (mean-SD) and 84% fractile curve (mean+SD) were calculated. Figure 14 shows the IDA curves for the 30 earthquakes for each specified year along with the mean, curves of the dam crest serviceability. The dynamic analysis is allowed here in IDA from 0.1g to 1g for each earthquake scaling. To identify the two-limit states from the IDA, the mean, 16% and 84% fractile curves of the dam crest are visualized in Figure 15. The serviceability and safety points have been calculated from the slope of the curve as discussed in Section 2.2.1. The seismicity parameters for the failure probability have been tabulated for two performance levels in each year in Table 2. For the mean IDA, the crest displacement in the serviceability stage is observed from 0.259-0.159 (g) by increasing the age of the CGD. Besides the mean, the 16% and 84% limits these values from 0.269-0.175 (g) and  
Figure 14: Incremental dynamic analysis (IDA); (a) 0 years, (b) 25 years, (c) 50 years, (d) 75 years. Figure 15: Fractile IDA curves four different age consideration; (a) 0 years, (b) 25 years, (c) 50 years, (d) 75 years. 0.227-0.180 (g), respectively. Therefore, for serviceability level, these earthquakes will not obviously infect the dam. The controlling IM for the 0-year aged-CGD is from 0.227-0.269, corresponding which the displacement limit state for the fragility analysis. Similarly, for safety level, the controlling IM for 0 years aged-CGD is identified from 0.405-0.438. The case study of the considered dam is then seismically analyzed by these limit values by considering the key point as the crest displacement. The 3D of the existing multipurpose dam has been analyzed probabilistically through the time history, nonlinear analyses considering the effect of the hygro-chemo-mechanical effect on the structural vulnerability analysis. Crest displacement was carried out from the IDA curve to illustrate the fragility curves. By using Equation (5), fragility curves have been shown in Figure 16 to summarize the failure pattern for the mean, 16 and 84% fractile in serviceability and safety level. In case of a maximum credible earthquake, from any year consideration in Figure 16, the serviceability and safety show almost 1. If it is considered for the maximum credible earthquake, these serviceability points are observed as 0.90-0.95, wherein for safety point, it is almost also 1. From the analysis of the IDA, the corresponding fractile PGA for considering the crest displacement shows here the safe range in either the MDE or the MCE level.