## 4 Displacement-Based Seismic Design of Pile  
Based on the typical failure process of the pile, new displacement-based seismic design criteria were proposed for the pile foundation of IAJBs, as shown in Figure 20. As this figure shows, in small earthquakes the pile foundation behaves linearly within the range of 0-2.0 \(\Delta\)y\({}_{1}\) (0-10.0 mm) lateral deformation of the pile head. The pile behaves elastically within the range of 0-1.0 \(\Delta\)y\({}_{1}\) (0-5.0 mm), and over 1.0 \(\Delta\)y\({}_{1}\) (5.0 mm) invisible cracks may appear in the pile due to the ambient temperature or seismic loadings. However, when the force is stopped, the cracks will close. In moderate earthquakes, the pile may suffer minor or moderate damage within the range of 2.0-8.0 \(\Delta\)y\({}_{1}\) (10.0-40.0 mm). Minor damages may occur in the pile at approximately 4 \(\Delta\)y\({}_{1}\) (20.0 mm) lateral deformation, which can be repaired. The pile may suffer moderate damage at approximately 8 \(\Delta\)y\({}_{1}\) (40.0 mm), which also can be repaired. In the rare earthquakes, the pile may suffer significant damage. The significant damage may occur in the range of 8.0-16.0 \(\Delta\)y\({}_{1}\) (40.0-80.0 mm) pile displacement and can be repaired. The displacement from 16 \(\Delta\)y\({}_{1}\) to 24.0 \(\Delta\)y\({}_{1}\) (80.0 mm to 120.0 mm) may cause significant damage to the pile with no collapse, and displacement over 24.0 \(\Delta\)y\({}_{1}\) may cause unacceptable damage in the pile foundation of IAJBs. The displacement-based seismic design criteria of three-stage seismic fortification and five damage level for the piers were proposed by AASHTO [35]. However, the seismic design criteria for the pile foundations are unavailable in AASHTO while it is mentioned that a significant inelastic deformation is permitted for the piles subjected to rare earthquakes. The last two stages of the pile had not taken in the design criteria as the pile cannot be repaired. Thus, new seismic design criteria of the pile, namely, three-stage seismic fortification and five damage levels, were proposed for IAJBs based on AASHTO.  
In Figure 20 and AASHTO [35], the yield displacements of the pile and piers, \(\Delta\)y\({}_{1}\) and \(\Delta\)y\({}_{2}\), are 5 mm and 25.0 mm (\(\approx\)1.0 in.), respectively, based on the test results. AASHTO [35] shows that in a small earthquake the pier has an elastic behavior within the range of 0-1.0 \(\Delta\)y\({}_{2}\) (0-25.0 mm) horizontal deformations at the pier top. In a moderate earthquake, the minor and moderate damages of the pier may appear in the range of 1-4 \(\Delta\)y\({}_{2}\) (25.0-100.0 mm) lateral deformation. The pier may suffer minor damage at approximately 2 \(\Delta\)y\({}_{2}\) (50.0 mm) of lateral deformation, which can be repaired. The moderate damage to the pier is more severe at approximately 4 \(\Delta\)y\({}_{2}\) (100.0 mm) displacement and can be repaired or the pier can be replaced. In a rare earthquake, significant damage may cause in the pier displacement lesser than 6 \(\Delta\)y\({}_{2}\) (150.0 mm), but without collapse. Unacceptable damage to the pier with the possibility of collapse may occur if pile displacement exceeds 6 \(\Delta\)y\({}_{2}\).  
By comparing Figure 20 and AASHTO [35] it can be seen that the design criteria of the pile have two stages more than the pier in a small earthquake. It can be also seen that the descent stages of the pier include significant damage and collapse, while there is no descent stage for the pile foundation.  
Figure 19: Typical force-displacement curve of a pile with its failure process.  
This because the pile supporting the abutment usually bears a lower vertical dead load as compared to the pier, where there is little chance of collapse for the pile and insignificant P-A effect.