# Effect of Soil Damping on the Soil-Pile-Structure Interaction Analyses in Cohesionless Soils
## 3 Analysis Results
### Verification Analysis
#### 3.1.2 Liquefiable Soil (Case 2)  
The soil-pile-structure system response in the liquefiable soils under Event I and Event J (Case 2) were investigated by comparing the analysis results with the centrifuge test outputs. Figure 10a shows the acceleration response spectra for Event I, where the hyperbolic model slightly overestimates the response while the MC model better captures the general trend. However, the MC model significantly underestimates the accelerations in Event J (Figure 10b), in which the hyperbolic model yields closer results. The reason for the high superstructure response in the centrifuge test under Event J has been reported as the reduction in the pore pressures, which result in increased effective stresses ([PERSON], [11], and reduced damping. Since the pore water pressures were not considered in the models employed in this study, the analysis results were overdamped compared to the centrifuge  
Figure 8: ARS of the structure (D = 5%) for verification analyses (Case 1): (**a**) [PERSON] [30] and (**b**) [PERSON] [31] (Event K).  
Figure 9: Bending moment variation with depth for verification analyses (Case 1): (**a**) [PERSON] [30] and (**b**) [PERSON] [31] (Event K).  
results. The spectral accelerations obtained through the hyperbolic model were closer to the centrifuge test results since the hyperbolic model provides lower damping.  
The model responses in the liquefiable soil case were compared through the maximum bending moments along the pile. Figure 10(a) compares Event I, where the bending moments were closer in the MC model, to the centrifuge test results. In contrast, the hyperbolic model slightly overestimated the bending moments at the shallow depths and underestimated the depths greater than 3 m. Figure 10(b) shows the pile response under Event J. Both models underestimated the bending moments for shallow depths due to the low superstructure accelerations. However, the hyperbolic model led to a closer pile response in Event J than the MC model. Overall, the MC model caused higher damping than the hyperbolic model due to the perfectly plastic behavior, especially under high-intensity motions. Accordingly, the resulting pile and structure responses were lower in the MC than in the hyperbolic model.  
Figure 11: Bending moment variation with depth for verification analyses (Case 2): (**a**) Event I [31], and (**b**) Event J [31].  
Figure 10: ARS of the structure (D = 5%) for verification analyses (Case 2): (**a**) Event I [31] and (**b**) Event J [31].  
In general, differences in the spectral accelerations and bending moments were observed the verification analysis. Similar inconsistencies were observed in past studies that have used the same centrifuge tests for verification purposes [12; 33; 34; 37]. The primary reason might be the uncertainties in soil behavior. The complex nature of centrifuge tests, and sequential loading that might change the relative density of soil after each test, could be the secondary effect of the uncertainties that could not be taken into consideration in the numerical analyses. Therefore, the verification analysis results were assumed to be promising, considering the complex nature of the problem.