## 5 Conclusions  
Nonlinear dynamic response and seismic performance of skewed integral abutment bridges under near-fault pulse and far-field non-pulse type ground motions were investigated, and parametric studies were conducted on the bridge skew angle and the backfill compactness. The conclusions are as follows:  
1. The longitudinal and transverse displacement of the abutment generally increases with the skew angle, mainly due to the decreased constraints of the backfill on abutment longitudinal displacements and the increased coupling between the longitudinal and transverse displacements of the bridge deck. The longitudinal and transverse displacement of the abutment generally decreases with the abutment backfill compactness. Under pulse type ground motions, the longitudinal and the transverse abutment displacement are obviously higher than the abutment displacements under non-pulse type ground motions, and the differences increase with the skew angle. 2. The bridge deck rotation generally increases with the skew angle due to the coupling between the longitudinal and transverse displacements, especially with densely compacted backfill. The deck rotation generally decreases with the abutment backfill compactness. Under pulse type ground motions, the bridge deck rotations are close and sometimes lower than the deck rotations under non-pulse type ground motions, except when the skew angle is 45\({}^{\circ}\) and with medium densely and loosely compacted backfill. 3. For SAB, the resultant force from soil pressure does not pass through the mass center of the bridge, so the superstructure twists and leads to a non-uniform distribution of soil pressure behind the abutments. The pressure at the obtuse corner is always higher than the acute corner, and the ratio increases with the skew angle as well as the backfill compactness. The ratio is even higher under the pulse type ground motions. 4. The longitudinal deflection of the pile top first decreases and then increases with the skew angle, while the transverse deflection of the pile top always increases with  
Figure 20: Maximum yield surface function value of the pile top. the skew angle. The longitudinal deflection decreases with the abutment backfill compactness, and so does the transverse deflection, but to a lesser extent. When the skew angle is larger than \(15^{\circ}\), both the longitudinal and the transverse deflection of the pile is higher under pulse type ground motions. 5. The moment around the weak-axis first decreases and then increases with the skew angle, while moment around the strong-axis always increases with the skew angle. The moment around the weak-axis and the strong-axis decrease with the abutment backfill compactness. When the skew angle is larger than \(15^{\circ}\), the moment at the pile top is higher under pulse type ground motions, especially with densely compacted backfill. 6. Under non-pulse type ground motions, the yield surface function \(\phi\) value as well as the maximum normal stress on the steel pile cross-section decrease with the backfill compactness, and increase with the skew angle for densely compacted backfill. Under pulse type ground motions, the \(\phi\) value still decreases with the backfill compactness, but it consistently and sharply increases with the skew angle for all types of backfill. The near-fault effects significantly increase the yield surface function \(\phi\) value as well as maximum normal stress in steel piles, and amplify the influence of the skew angle. [PERSON] provided the idea and gave professional seismic guidance on skewed integral abutment bridges and wrote the manuscript; [PERSON] analyzed the engineering data and prepare the paper draft; [PERSON] conducted the finite element analyses and prepare the paper draft. All authors have read and agreed to the published version of the manuscript. The authors gratefully acknowledge the financial supports for this research by the National Natural Science Foundation of China (NSFC) under grant number 51878447, 51678406.