## 3 Acceleration Response and Crest Settlement of Slope  
### Horizontal Response Acceleration  
The PGA amplification factor S\({}_{\text{p}}\) is defined as the peak acceleration at a given depth normalized to the peak acceleration of the input motion in the centrifuge tests as a function of normalized elevation (h/H). * Unreinforced slope  
Figure 3 shows that, before reinforcement using stabilizing piles, the PGA amplification factor of the slope increases substantially along the elevation direction and reaches the maximum at the crest of the slope. Under the continuous application of five levels of  
Figure 2: Time histories of input motions forinstrument BA-0. seismic load, the PGA amplification factor at the crest of the slope (A-3) has a mean average value of about 1.97, thus exacerbating the elevation amplification effect. Moreover, at the same elevation on the slope, the PGA amplification factor of the deposit surface is greater than that of the bedrock surface, as shown in Figure 3(a) (BA-0,A-144 and A-179), and in Figure 3(b) (BA-0,A-2,A-6 and A-4). For example, at the height of 15.8 m (A-4, A-142 and A-179), the horizontal acceleration amplification factor distribution from the inside of the slope to the surface of the slope is illustrated in Figure 4. The mean average acceleration amplification factors from within to the surface are 1.10, 1.06, and 1.27, respectively. The difference in the PGA amplification factors between deposit surface and bedrock surface suggests typical surface amplification. The strength difference of the bedrock and deposit also affects the seismic amplification effect. The shear strength of the deposit is lower than that of the bedrock, and the PGA amplification factors in that deposit are greater than those in bedrock. Acceleration sensors A-2, A-6, and A-4 are placed in the bedrock, as shown in Figure 3(b), and the measured amplification factors are close to 1.0. Figure 5 shows the transfer coefficient from A-0 to A-3; the components at frequencies of about 5 to 7 Hz are amplified when the seismic wave propagates from the bottom to the crest of the slope in the 1#model. Figure 4: The horizontal acceleration amplification factor distribution from the inside of the slope to its surface at a height of 15.8 m in the 1# model in centrifuge tests. Figure 3: Maximum acceleration distributions along the normalized slope elevation in the 1# model in centrifuge tests: (a) deposit surface; (b) bedrock surface. * Slope reinforced by a discretely spaced pile row  
Figure 6 shows the distribution of response accelerations along the slope elevation when reinforced by stabilizing piles. It also shows increased amplification and surface amplification, as compared in Figure 5(a),b. As shown in Figure 5(a), the average PGA amplification factor obtained from the crest measuring point (A-1) under the continuous application of five levels of load is about 1.42, which is less than that obtained from A-3 (1.97) in Figure 3(a) when the slope is not reinforced by stabilizing piles. It is worth noting that the difference in PGA amplification factors between A-3 and A-144 is significant in the 2#model, as shown in Figure 5(a). The accelerations measured at A-144 and A-139, located below the stabilizing piles, were significantly suppressed, while the acceleration measured at A-3 and A-7, located above the stabilizing piles, increased slightly. A possible reason for this is that the stabilizing piles lead to a greater superposition of wave reflections in the passive zone under such seismic excitation, which generally shows that the amplification effect of horizontal response accelerations increases in front of the stabilizing piles and decreases below them.