## 5 Results and Discussion
### Horizontal Relative Displacements of the Dam Crest  
Because the dam monolith is unsymmetric and the foundation is elastic, it is necessary to evaluate the relative displacements separately in opposite directions. The horizontal relative displacements of the dam crest (point A) to the bottom left corner (point B) and the bottom right corner (point C) of the foundation are analyzed, respectively, and Figures 9 and 10 show the time-histories of them. Here, limited to space, only the displacements of the dam crest under an incident angle of 75\({}^{\circ}\) are shown. The red curves show the pulse seismic records, and blue curves show the non-pulse records. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Materials** & **Elasticity Modulus (GPa)** & **Poisson’s Ratio** & **Density (kg/m3)** \\ \hline II-Conventional concrete & 42.6 & 0.167 & 2489 \\ I-2-Conventional concrete & 44.3 & 0.167 & 2487 \\ Roller compacted concrete & 47.4 & 0.167 & 2476 \\ Foundation rock & 30.4 & 0.170 & 2800 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Dynamics material parameters for the dam-foundation system. Figure 8: The CDP model parameters of the II-conventional concrete. Figure 9: The horizontal displacement of point A with respect to point B (under the input angle of 75\({}^{\circ}\)). The horizontal relative displacements of the dam crest vary with the input seismic waves displacement time histories. Although the selected near-fault pulse seismic records and non-pulse records have the same PGA, the pulse records are more destructive to the dam than the non-pulse records. When the input angle is 75\({}^{\circ}\), the maximum relative displacements of point A with respect to point B under three pulse ground motions are 0.184 m, 0.183 m, 0.146 m, respectively. The maximum relative displacements of point A with respect to point B under three non-pulse ground motions are 0.113 m, 0.110 m, 0.093 m, respectively. The average maximum relative displacement of point A and point B under pulse seismic motions is 1.62 times as compared with that under non-pulse seismic motions, and the average maximum relative displacement of point A and point C under pulse seismic motions is 1.71 times as compared with that under non-pulse seismic motions. It is worth noting that the horizontal relative displacements between the dam crest and the different parts on the foundation are different. It can be seen that the previous analysis method which assumes the foundation to be rigid cannot truly reflect the vibration performance of the dam body. The maximum absolute values of the displacement time-history curve under various input angles are extracted and compared with each other, as shown in Figures 11 and 12. The dynamic response of the dam under pulse seismic motions is remarkably higher than that under non-pulse seismic motions in all cases, especially when the incidence angle is large. Figure 11 shows that with an increase of the P wave incident angle, the relative displacements first increase and then decrease. The maximum relative displacement between point A and point B under the three near-fault pulse seismic records reaches the maximum value with the input angle of 75\({}^{\circ}\), and they are 7.48, 6.84, 3.54 times that with the angle of 0\({}^{\circ}\), respectively. The maximum relative displacement between point A and point B under the three non-pulse earthquake records also reaches the maximum value with the input angle of 75\({}^{\circ}\), and they are 4.31, 4.14, 3.02 times higher than that at the angle of 0\({}^{\circ}\), respectively. The maximum relative displacement between point A and point C under the three near-fault pulse earthquake records reaches the maximum value with the input angle of 60\({}^{\circ}\), and they are 2.44, 2.27, 2.81 times higher than that at the angle of 0\({}^{\circ}\), respectively.