# Estimation of Seismically-Induced Crest Settlement of Earth Core Rockfill Dams
## 5 Conclusions  
A series of nonlinear finite difference analyses was performed to calculate settlements at the crest of earth core rockfill dams (ECRDs) subjected to earthquake loading. Before performing the analyses,  
\begin{table}
\begin{tabular}{l l l l l l l l l l l} \hline \hline  & \multicolumn{3}{c}{**1-Parameter Model**} & \multicolumn{3}{c}{**2-Parameter Model**} & \multicolumn{3}{c}{**3-Parameter Model**} & \multicolumn{3}{c}{**4-Parameter Model**} \\ \hline \(\text{GM}_{1}\) & \(PGA\) & \(PGV\) & \(I_{a}\) & \(M\) & \(PGA\) & \(PGA\) & \(PGA\) & \(PGA\) & \(PGA\) & \(PGA\) \\ \(\text{GM}_{2}\) & & & & & \(PGV\) & \(I_{a}\) & \(M\) & \(PGV\) & \(M\) & \(PGV\) & \(PGV\) \\ \(\text{GM}_{3}\) & & & & & & & \(M\) & \(I_{a}\) & \(I_{a}\) & \(I_{a}\) \\ \(\text{GM}_{4}\) & & & & & & & & & \(M\) \\ \hline \(a_{1}\) & 1.803 & 2.16 & 0.127 & 0.774 & 1.735 & 1.606 & 0.845 & 2.197 & 0.748 & 1.616 & 2.15 \\ \(a_{2}\) & & & & & 0.089 & 0.264 & 0.079 & \(-\)0.847 & 0.203 & \(-\)1.25 & \(-\)2.422 \\ \(a_{3}\) & & & & & & & 0.339 & 0.075 & 0.094 & 0.1 \\ \(a_{4}\) & & & & & & & & & 0.396 \\ \hline R\({}^{2}\) & 0.773 & 0.71 & 0.334 & 0.82 & 0.774 & 0.803 & 0.873 & 0.811 & 0.89 & 0.891 & 0.941 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Coefficients for the crest settlement prediction model.  
Figure 7: Crest settlement plotted against ground motion parameters. (a) \(PGA\), (b) peak ground velocity (\(PGV\)), (c) moment magnitude (\(M\)), and (d) Arias Intensity (\(I_{a}\)).  
the numerical model was validated against centrifuge test recordings. The conclusions drawn from this study were as follows.  
1. The nonlinear model of the dam was demonstrated to provide reliable estimate of the seismic response of ECRDs when compared with the centrifuge test measurements. It was therefore revealed that the nonlinear model was capable of predicting the settlement and could be used for the evaluation of the seismic performance of ECRDs.
2. The calculated settlements using twenty ground motions were compared with field recordings. The results compared well with the recordings for peak ground acceleration (_PGA_) exceeding 0.2 g. It was therefore further validated that the numerical model could be used in the seismic design.
3. The settlements were also plotted against ground motion parameters, including the free-field surface _PGA_, peak ground velocity (_PGV_), Arias intensity (_Ia_), and moment magnitude (_M_). Predictive equations for the crest settlement were also presented. It was demonstrated that _PGA_ provided a good estimate of the settlement. However, _Ia_ provided the most favorable fit with the calculations. Therefore, using the primary parameter to predict the crest was recommended.  
[PERSON] and [PERSON]-C.P. conceived the idea, outlined the work, and reviewed the paper; [PERSON]-Q.N. performed numerical analyses and co-wrote the paper; [PERSON]-[PERSON] analyzed the calculated responses and performed multivariate regression analyses; [PERSON]-H.C. outlined the scope of the work and reviewed the manuscript.  
This research was supported by Fundamental Technology Development Program for Extreme Disaster Response funded by Korean Ministry Of Interior and Safety (MOIS), grant number 2017-MOIS31-002 and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (NRF-2019R1A2C1011323).  
The authors declare no conflict of interest.