## 3 Nonlinear Time-History Analyses on Skewed Integral Abutment Bridges  
### Selection of Near-Fault Ground Motions  
A design response spectrum was generated for the prototype bridge, based on a site category of class II, a seismic fortification intensity of degree VIII, a design seismic group of class C, a design seismic acceleration of 0.2 g, as well as the bed rock conditions of the region. The response spectrum of the near-fault seismic ground motion records from the strong ground motion database in PEER [40] were then matched with the design response spectrum above, and three records with the best fitting accuracy were chosen, which were the ground motion records from the Yarimaca Test Site station in the Kocaeli earthquake (EQ1), the Newhall-W_Pico_Canyon_Rd Test Site station in the Northridge earthquake (EQ2), and the Takatori Test Site station in the Kobe earthquake(EQ3). Magnitudes of the chosen earthquake records varied from M6.7 to M7.9, the distances from the Test Site  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multirow{2}{*}{**Abutment Backfill**} & \multirow{2}{*}{**Skew Angle (\({}^{\circ}\))**} & \multirow{2}{*}{**Period (s)**} & \multirow{2}{*}{**Mode Shape**} & \multicolumn{2}{c}{**X Dir**} & \multicolumn{1}{c}{**Y Dir**} \\ \cline{5-6}  & & & & & **Mass (\%)** \\ \hline
1 & Loosely compacted sand & 0 & 0.351 & LT & 92.0 & 0.0 \\
2 & Loosely compacted sand & 15 & 0.338 & LT & 87.0 & 6.7 \\
3 & Loosely compacted sand & 30 & 0.326 & LT + TT & 69.0 & 24.0 \\
4 & Loosely compacted sand & 45 & 0.308 & LT + TT & 47.0 & 46.0 \\
5 & Medium-densely compacted sand & 0 & 0.311 & LT & 88.0 & 0.0 \\
6 & Medium-densely compacted sand & 15 & 0.298 & LT & 85.0 & 6.1 \\
7 & Medium-densely compacted sand & 30 & 0.287 & LT + TT & 69.0 & 23.0 \\
8 & Medium-densely compacted sand & 45 & 0.271 & LT + TT & 45.0 & 40.0 \\
9 & Densely compacted sand & 0 & 0.272 & LT & 77.0 & 0.0 \\
10 (Prototype) & Densely compacted sand & 15 & 0.256 & LT & 80.0 & 5.4 \\
11 & Densely compacted sand & 30 & 0.248 & LT + TT & 67.0 & 21.0 \\
12 & Densely compacted sand & 45 & 0.234 & LT + TT & 43.0 & 40.0 \\
13 & Soil-free & 0 & 0.606 & LT & 97.0 & 0.0 \\
14 & Soil-free & 15 & 0.593 & LT & 97.0 & 0.0 \\
15 & Soil-free & 30 & 0.587 & LT & 95.0 & 2.0 \\
16 & Soil-free & 45 & 0.589 & LT & 89.0 & 8.4 \\ \hline \hline \end{tabular} Notes: LT—longitudinal translation; TT—transverse translation.  
\end{table}
Table 2: Dynamic properties of SIAB models.  
stations to the rupture sources were all less than 10 km, the peak ground velocities (PGV) were significantly higher than 20 cm/s, and the PGV to peak ground acceleration (PGA) ratios were larger than 0.2 s. Parameters of the three selected near-fault ground motions are listed in Table 3.  
Three corresponding non-pulse artificial seismic records (GM2, GM4, GM6) were produced using the SIMQKE_GR software, which were consistent with the response spectra of the near-fault seismic records (GM1, GM3, GM5). The acceleration, velocity, and displacement time-histories of both the pulse and non-pulse type ground motions are shown in Figure 5, where it is clear that there are distinctive two-side or one-side pulses in the velocity time-histories of pulse type ground motions with rupture forward-directivity effect or reverse-directivity effect. The acceleration response spectra of all ground motions are shown in Figure 6, where it is clear that the acceleration response spectra of the pulse type ground motions fit well with the non-pulse ones. The PGV/PGA ratios of non-pulse type ground motions are generally small, and less than 0.11 in this paper. Table 3 presents