# Effect of Soil Damping on the Soil-Pile-Structure Interaction Analyses in Cohesionless Soils
## 3 Analysis Results
### Numerical Analyses  
Further numerical analyses were performed with the earthquake records given in Table 1 to reveal the effect of hysteretic soil damping more clearly. The superstructure accelerations, acceleration response spectra, and maximum bending moments along the pile were compared for the Hyperbolic and MC models. The numerical analysis results are presented for low-intensity and high-intensity response outputs. Figure 12 shows the acceleration time history of the superstructure, which consists of the first set of earthquake events: RSN143, RSN572, and RSN1614, where the peak structure acceleration (PA) values vary between 0.15 g and 0.31 g. The acceleration response spectra of the structure for the events are compared in Figure 13 with the ARS of the input motions (IM). According to the ARS results, the natural period of the single degree of freedom system is approximately 1 s, where the spectral accelerations reach the peak value. Peak spectral accelerations (PSA) vary from 0.94 g to 1.43 g in the hyperbolic model and between 0.62 g and 1.02 g for the MC model. Figure 14 shows the variation of the maximum bending moments with depth for the first set of earthquakes. The hyperbolic model results in 27%, 55%, and 63% higher bending moments than the MC model for RSN143, RSN572, and RSN1613, respectively. According to the analysis results, the structure and pile responses were greater in the hyperbolic model than in the MC for all the first set of earthquake records. Figure 15 shows the acceleration time histories of the superstructure for the second set of earthquakes, which consists of RSN285, RSN1091, and RSN1206, where the PA values vary between 0.24 g and 0.70 g. The acceleration response spectra of the structure for the second set of earthquakes were compared in Figure 16 with the ARS of the input motions (IM). According to the ARS results, the natural period of the single degree of freedom system is slightly higher than 1 s, where the spectral accelerations reach the peak value. Peak spectral accelerations varied from 1.73 g to 3.69 g in the hyperbolic model and between 0.94 g and 2.32 g for the MC model. Figure 17 shows the variation of the maximum bending moments with depth for the second set of earthquakes. The hyperbolic model results in 38%, 45%, and 49% higher bending moments than the MC model for RSN285, RSN1091, and RSN1206, respectively. Again, the structure responses were greater in the hyperbolic model than in the MC for all the second set of earthquake records. The results obtained from the soil-pile-structure interaction analyses have shown the effect of soil damping on the system response. Moreover, it was revealed that the selection of earthquake records plays a key role in the outputs. Although the peak ground accelerations of the input motions were close, the resulting superstructure accelerations were significantly different, depending on the frequency content. The peak structure acceleration (PA), the peak spectral acceleration (PSA), and maximum bending moments that occurred under the given earthquakes were summarized in Table 6 for both hyperbolic and MC models for comparison. Overall, the superstructure accelerations in the hyperbolic model were higher than in the MC model for all the selected earthquake records. Accordingly, the bending moments were greater again in the hyperbolic model. To summarize, the results of dynamic soil-pile-structure interaction analyses are highly influenced by the input motion and modeling approaches, such as the selection of the constitutive model. Figure 12: Acceleration time responses of the superstructure using Hyperbolic and MC models. (a) RSN143, (b) RSN572, (c) RSN1613. Figure 13: ARS of the superstructure (D = 5%) using Hyperbolic and MC models (a) RSN143, (b) RSN572, (c) RSN1613. Figure 14: Maximum bending moment vs. depth using Hyperbolic and MC models (**a**) RSN143, (**b**) RSN572, (**c**) RSN1613. Figure 15: Acceleration time histories of the superstructure using Hyperbolic and MC models. (**a**) RSN285, (**b**) RSN1091, (**c**) RSN1206.