## 3 Experimental Results and Analyses
### Hysteretic Curve and Skeleton Curve
#### 3.2.1 Hysteretic Curve
After that, the abutment keeps moving in the negative direction (Curve DE). By the time the abutment reaches the displacement of \(-\)14 mm (Point E), the pull force climbs up to \(-\)6.61 kN. After the abutment reaches the maximum displacement in the negative direction (Point E), its movement begin to return back to the positive direction (Curve EF), and the actuator force declines moderately. As the force decreases to 0 kN (Point F), the residual deformation in the negative direction is \(-\)10.81 mm (Point E, as shown in Figure 14), which is about 77.2% of the displacement load (\(-\)14  
Figure 14: Illustration of \(\pm\)14 mm displacement load. mm). Moreover, the negative residual deformation is far larger than the positive one (+3.63 mm). After that, the abutment keeps moving to the positive direction (Curve FA\({}_{1}\)) and arrives at the initial position (Point A\({}_{1}\)). Then, the unbalanced force of the actuator grows to +23.44 kN, which is also the initial force of third cycle of \(\pm\)14 mm displacement load step, and slightly larger than that in the second cycle. Generally, the energy dissipation capacity of the structure is represented by the area of hysteretic curve in the coordinate axis. In Figure 13b, the area of hysteresis curve in the first quadrant is larger than that of the third quadrant, which means the energy dissipation capacity of soil-abutment-pile interaction when test specimen moves to the positive direction is much larger than that of the soil-pile interaction when specimen moves to the negative direction. The area of hysteresis curve in the second quadrant is larger than that of the third quadrant, which indicates that the energy dissipation capacity when bridge expands is greater than that when the bridge contracts. Many researchers also applied the equivalent viscous damping to evaluate the energy dissipation capacity of the system [35]. The equivalent viscous damping is calculated using the following equation [36], as shown in Figure 15.  
\[\zeta_{e}=\frac{A_{h}}{2\pi\,\triangle\,F} \tag{1}\]  
where: \(A_{h}\) = area of a full cycle of force-displacement response, N\(\cdot\)mm; \(F\) = Maximum force occurring within a cycle, N; \(\Delta\) = Maximum displacement occurring within a cycle, mm. Figure 16 shows the equivalent viscous damping of the soil-abutment-pile and soil-pile interactions under different displacement steps. Generally, the larger the equivalent viscous damping is, the stronger of energy dissipation capacity and the better of seismic behavior are. As shown in Figure 16, the equivalent viscous damping of the soil-abutment-pile system grows rapidly when the displacement load increases from 0 mm to 8 mm. Then, when the displacement increases from 8 mm to 16 mm, the ratio tends to be stable and reaches a maximum value of 0.25. The equivalent viscous damping of soil-pile structure is about 0.17, which varies little under different displacement steps. According to Reference [37], the soil-abutment-pile system in IAJBs has favorable energy dissipation capacity and seismic behavior. Figure 15: Hysteretic area for damping calculation.