## 3 Experimental Results and Analyses
### Hysteretic Curve and Skeleton Curve  
#### 3.2.1 Hysteretic Curve  
Figure 13 shows the hysteretic curves of interaction of soil-abutment-pile system. Figure 13a shows the whole process of hysteretic curves, and Figure 13b only shows one cycle of hysteretic curve of \(\pm\)14 mm displacement load as a typical demonstration case (ABCDEFA\({}_{1}\) path shown in Figure 14). The hysteretic curves of soil-abutment-pile interaction in the first quadrant represent the abutment movements in the positive direction (From A to B in Figure 14), and the curves in the third quadrant represent the abutment movements in the negative direction (From D to E in Figure 14). Besides, the curves in the second quadrant represent the changing process from soil-pile interaction to soil-abutment-pile interaction (From B to D in Figure 14), and the curves in the fourth quadrant represent the changing process from soil-abutment-pile interaction to soil-pile interaction (From E to A\({}_{1}\) in Figure 14). Figure 12: Distribution of earth pressure along the longitudinal direction. Figure 13: Hysteresis curves. (**a**) Hysteretic curves for the entire process. (**b**) Hysteretic curve for one cycle. In Figure 13a, the hysteretic curves are dramatically asymmetrical that the first quadrant is plump and spindle-shaped, but other three quadrants are not spindle-shaped, which are greatly different from the traditional hysteretic curves of column or pile. As there are three cycles for each step of displacement load, it is found that the horizontal force shows an upward trend with the increase of cycle. Specifically, under the \(\pm\)10 mm displacement load step, the horizontal push force is +32.54 kN in the first cycle, but +36.78 kN in the third cycle, showing an increase of about 13.0%. The reason is that the interaction of soil-abutment-pile system gets stronger by the reciprocating displacement, which makes the soil behind the abutment or around the pile become compacted. This result is consistent with the soil ratcheting phenomenon in which the earth pressure behind abutment increases year by year under seasonal temperature variations [34]. As mentioned when the abutment moves towards the embankment (the positive direction in Figure 7), the MTS actuator produces a horizontal push force, and when the abutment moves away from the embankment (the negative direction in Figure 7), the actuator provides horizontal pull force. However, after several displacement cycles, when the force of actuator reduces to 0 kN, the actuator would not go back to the initial position and the deviation of horizontal displacement is induced. As shown in Figure 13b, when the actuator goes back to the initial position and the displacement of abutment is 0 mm (Point A), the force in the actuator is 22.79 kN (an unbalanced force). As the abutment moves to the positive direction (Curve AB), the soil resistance behind abutment increases continuously. The force exerted by the actuator increases to 52.49 kN when the abutment reaches the displacement of +14 mm (Point B). Then, when the abutment changes its direction and moves to the negative direction (Curve BC), the force exerted by the actuator drops dramatically. When the force reduces to 0 kN (Point C), the remaining displacement of the abutment is +3.63 mm (Point C, as shown in Figure 14). Herein the remaining displacement is defined as residual deformation. The reason is that the soil is a plastic material, the skeleton curve of force-displacement (Curve BC) is nonlinear during unloading, which leads to the residual deformation. By the way, when the actuator displacement reduces to 0 mm, the actuator force and the deformation of pile that deviates from the vertical central axis would not be equal to zero. The force is called as the unbalanced force, and the deformation of steel H-pile is called as the accumulative deformation. When continuous to load, the pull force exerted by the actuator begins to increase and is up to \(-\)1.81 kN (Curve CD) when the actuator moves back to the initial position (Point D).