## 4 Results and Discussion  
### Soil Amplification  
The amplification factor was estimated by normalizing the peak acceleration of the motion measured in the soil and the free field (PGA\({}_{\text{FFM}}\)) to the input motion measured at the base (PGA\({}_{\text{BM}}\)). Figure 4 illustrates the soil amplification factor with the depth of the three soil models at three levels of PGA\({}_{\text{BM}}\). It was found that earthquake motion was amplified according to depth and amplified slightly more at lower earthquake intensities, especially in the soil near the ground surface. The smaller amplification at high earthquake intensities with a PGA\({}_{\text{BM}}\) of 0.3 \(g\) was observed due to the nonlinear behavior of soil, leading to a reduction in soil stiffness. The amplification in the mixed layer at the L2 profile was slightly higher than those at the L1 profile because a lower confining pressure was applied to this layer in L2 profile, and the soil becoming slightly looser after several earthquakes, as indicated in Figure 1. An exception was observed in the layered profiles (Figure 4b,c) at a PGA\({}_{\text{BM}}\) of 0.3 \(g\). The measured PGA\({}_{\text{FFM}}\) was smaller than the peak acceleration recorded at the A5 accelerometer. Note that A5 was placed in the thin, soft layer below the S1 structure, as indicated in Figure 1. The effects of structural vibration and reflected waves from the interface between layers in a high amplitude earthquake could cause this increase in the motion of the soil beneath the structure [17].  
Figure 5a compares the variation of PGA\({}_{\text{FFM}}\) in the layered profiles with that in the Uni profile. Although the input intensity at the base was kept roughly the same, the PGA\({}_{\text{FFM}}\) in the L1 and L2 profiles were smaller than those in the Uni profile by about 14% and 7%, respectively. There was an increase in the PGA\({}_{\text{FFM}}\) with an increase in the thickness of the soft upper layer at all tested input levels, which has also been observed in numerous other studies and field data [12; 27; 30; 31]. However, the soil's response beneath the structure indicated an inverse trend when the horizontal and vertical peak acceleration measured at the A5 (PGA\({}_{\text{A5}}\)) and A6 accelerometers (PGA\({}_{\text{A6}}\)) increased with decreasing T, as indicated in Figure 5b,c. At low input intensity, the values of PGA\({}_{\text{A5}}\) in L1 and L2 profiles were close to those in the Uni profile. However, for larger earthquakes, PGA\({}_{\text{A5}}\) in L1 and L2 profiles highly exceeded those from the Uni profile by about 27% and 13%. A more severe increment can be seen in the vertical motion (PGA\({}_{\text{A6}}\)), where it was 53% and 37% higher for the respective L1 and L2 profiles. Several studies [13; 17; 32] reported a reduction in the stiffness of soil beneath the structure (in the soft layer) at high input intensity. This was caused by the stress concentrations formed beneath the structure and could account for the increments in response to the soil in both horizontal and vertical directions. As the  
Figure 4: Amplification factor in the soil at (**a**) Uni, (**b**) L1, and (**c**) L2 profiles.  
thickness of the soft layer decreased, the response of soil increased due to the significantly concentrated stress in the soft soil layer caused by the structure. Moreover, compared to the increase in horizontal motion in the layered profiles, the vertical motion increments were more significant regardless of input intensity or thickness of the soft upper layer, which implies the influence comes from the dynamic vertical force in the structure.  
Figure 5: Comparison of (**a**) peak acceleration (PGA)\({}_{\text{FFM}}\), (**b**) PGA\({}_{\text{A5}}\) (horizontal motion), and (**c**) PGA\({}_{\text{A6}}\) (vertical motion) obtained on layered profiles (i.e., L1 and L2) with those on uniform profile (Uni). The values in the figure indicate the maximum difference between the two measured data.