# Effect of Soil Damping on the Soil-Pile-Structure Interaction Analyses in Cohesionless Soils
## 4 Conclusions  
The aim of this study is to investigate the influence of hysteretic soil damping on the pile and structure response in the dynamic soil-pile-structure analyses. For this purpose, two well-known centrifuge tests were simulated and analyzed in FLAC\({}^{\text{3D}}\) for verification using two constitutive soil models. Further analyses were performed with the additional earthquake records in a single pile-soil-structure system. The conclusions from the fully nonlinear analyses are outlined below:  
* The nonlinear soil behavior can be modeled using the modulus degradation curves in numerical analyses of soil-pile-structure problems. According to the verification analyses, if the soil damping is integrated into the model accurately, the use of modulus degradation can represent the response even for liquefiable soils. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **RSN** & **143** & **572** & **1613** & **285** & **1091** & **1206** \\ \hline \multirow{3}{*}{PA (g)} & Hyperbolic & 0.24 & 0.31 & 0.24 & 0.53 & 0.37 & 0.70 \\  & MC & 0.18 & 0.19 & 0.15 & 0.33 & 0.24 & 0.41 \\ \multirow{3}{*}{PSA (g)} & Hyperbolic & 1.27 & 1.43 & 0.94 & 2.87 & 1.73 & 3.69 \\  & MC & 0.95 & 1.02 & 0.62 & 1.79 & 0.94 & 2.32 \\ \multirow{3}{*}{\(\text{M}_{\text{max}}\) (kN\(\cdot\)m)} & Hyperbolic & 533 & 701 & 543 & 1180 & 862 & 1580 \\ \cline{1-1}  & MC & 419 & 451 & 333 & 853 & 593 & 1060 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Summary of the numerical analysis results under various earthquakes. Figure 16: ARS of the superstructure (D = 5%) using Hyperbolic and MC models (**a**) RSN285, (**b**) RSN1091, (**c**) RSN1206. Figure 17: Maximum bending moment vs. depth using Hyperbolic and MC models (**a**) RSN285, (**b**) RSN1091, (**c**) RSN1206. * The constitutive models without a cut-off for \(G\)/\(G_{max}\) might cause significantly higher damping ratios. To overcome the higher damping ratio problem, the minimum \(G\)/\(G_{max}\) value was set to 0.05, and closer results were obtained in the verification analyses. Thus, the cut-off must be applied to eliminate higher damping ratios at large strains. Generally, the agreement between the 3D analysis results and centrifuge test outputs was reasonably good. * Dynamic single pile-soil-structure analyses performed with the additional earthquake records selected from the PEER database have confirmed the effect of soil damping on the pile and structure response. Peak structure accelerations, peak spectral accelerations, and bending moments along the pile were compared for hyperbolic and MC models. The peak structure accelerations and the peak bending moments for all earthquake records were greater in the hyperbolic model. The difference between the hyperbolic and MC models varies between 27 and 63%, depending on the applied earthquake record. The results have indicated that the soil damping ratio in the MC model could be considerably high, especially in the shallow depths, since the lower confining stresses cause the shear strength to be significantly low. * Apart from the damping effect, the analyses have shown that the selection of earthquake records significantly affects the structure and pile response. In particular, although the selected earthquakes have the same peak ground acceleration, as much as three times the difference might occur in the resulting structure accelerations (RSN 1613 and RSN 1206). The results have indicated that the damping ratio affects the soil-pile-structure response significantly; hence the selection of the constitutive soil model, which represents the damping characteristics of the soil-pile-structure system, is critical. In this study, the soil-pile-interaction problem was investigated through the single pile; however, group pile behavior should be examined in future studies to better understand the actual problem. Conceptualization, O.A. and E.E.E.-B. ; Data curation, O.A. ; Investigation, O.A. ; Methodology, O.A. and E.E.E.-B. ; Supervision, E.E.E.-B. ; Writing--original draft, O.A. ; Writing--review & editing, E.E.E.-B.