## 4 Results and Discussion
### Displacement of Abutments
The maximum longitudinal displacement of the abutment from time-history analyses on all SIAB models with varying skew angles and backfill compactness are shown in Figure 10 below. It is shown in Figure 10 that the abutment longitudinal displacement generally increases with the skew angle. For example, when the abutment backfill is densely compacted, the ratio between the abutment longitudinal displacement with a 45\({}^{\circ}\) skew angle and the abutment displacement with no skew is 2.5 under non-pulse type ground motions, and 7.1 under pulse type ground motions, respectively. This is mainly because when the skew angle increases, the angle between the earth pressure behind the abutment and the longitudinal direction of the bridge increases, and the constraint effects of the abutment backfill on abutment longitudinal displacement decreases. However, the influence of skew angle diminishes for loosely compacted backfill under non-pulse type ground motions. It is also shown that the abutment longitudinal displacement decreases as the abutment backfill compactness increases, since the constraint effects of the abutment backfill increases. Figure 10: _Cont._  
Figure 9: Displacement time-history of the abutment under pulse and non-pulse type ground motions (Model 16). The maximum transverse displacement of the abutment from time-history analyses on all SIAB models with varying skew angles and backfill compactness are shown in Figure 10 below. As shown in Figure 10, the abutment transverse displacement increases with the skew angle, mainly due to the coupling between the longitudinal and transverse displacements of the bridge deck. For example, when the abutment backfill is densely compacted, the ratio between the abutment transverse displacement with a 45\({}^{\circ}\) skew angle and the abutment displacement with a 15\({}^{\circ}\) skew angle is about 1.7 under non-pulse or pulse type ground motions. The abutment transverse displacement generally decreases with the abutment backfill compactness, but to a much less extent compared to the longitudinal displacement. It is also shown in Figure 10 that the longitudinal and transverse abutment displacements under pulse type ground motions are generally higher than the non-pulse type ground motions, and the difference increases with the skew angle. When the skew angle reaches 45\({}^{\circ}\), the longitudinal and the transverse abutment displacement under pulse type ground motions is about 100% and 30-60% higher than the displacement under non-pulse type ground motions, respectively. The maximum rotation angle of the bridge deck from time-history analysis on all SIAB models with varying skew angles and backfill compactness are shown in Figure 11. As shown in Figure 11, similar to the abutment transverse displacement, the bridge deck rotation increases with the skew angle, mainly due to the coupling between the longitudinal and transverse displacements. When the abutment backfill is densely compacted, the ratio between the bridge deck rotation with a 45\({}^{\circ}\) skew angle and the bridge deck rotation with a 15\({}^{\circ}\) skew angle is about 1.96 under non-pulse type ground motions, and 1.74 under pulse type ground motions, respectively. The deck rotation decreases with the abutment backfill compactness, except for the case with a skew angle of 45\({}^{\circ}\) and non-pulse type ground motions, in which the bridge with densely compacted backfill has the highest rotation. Figure 10: Maximum displacement of the abutment.