# A Simplified Analysis Method for Seismic Response of
## 4 Example Verification
### Comparison of Shear Stress Distribution along the Pile Body  
Figure 6 compares the distribution curves of shear stress along the pile length obtained by the dynamic time history analysis method and the EBSM-RAM. The distribution characteristics of shear stress in the pile body conform to the laws of existing research results [27]. In the figure, \"NJL\" represents the EBSM-RAM, and \"Time\" represents the time history analysis calculation result. The dynamic time history analysis results are extracted as the shear stress distribution of the central pile and the corner piles at the moment when the total shear force at the top of the pile is maximum, and \"avg\" represents the result of the average action of three seismic waves. In the quasi-static calculation results, \"avg\" represents the final result calculated by taking the average value of the equivalent shear modulus corresponding to three different seismic waves for the soil parameters and the average value of the three effective inertial accelerations for the shear load. In the time history analysis results, \"avg\" represents the average of the results calculated separately for three different seismic waves.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Soil** & **High** & **Type** & \(\rho\)**s/g/cm\({}^{3}\)** & \(V\)**s/m/s** \\ \hline
1 & 18.44–27 & Clay & 1.95 & 111 \\
2 & 15–18.44 & Sand & 2.01 & 190 \\
3 & 13–15 & Clay & 1.88 & 161 \\
4 & 2–13 & Clay & 1.98 & 246 \\
5 & \(-\)4–2 & Clay & 1.91 & 262 \\
6 & \(-\)17—4 & Clay & 1.98 & 313 \\
7 & \(-\)21—17 & Sand & 2.03 & 335 \\
8 & \(-\)26—21 & Bedrock & 2.45 & 1569 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Soil parameters for free field computation.  
Figure 5: Artificial seismic wave.  
Figure 6: \(Cont\).  
Comparing Figure 6a-c, it can be seen that the time history analysis results under different earthquakes are similar but not the same, and the results of the time history analysis of a single seismic wave are different from those of the EBSM-RAM in some cases. However, when the average value of no less than three seismic wave inputs is taken according to the specification, the results of the simplified method and the time history analysis method are in good agreement, as shown in Figure 6d. Whether it is a corner pile or a center pile, for the comparison of the average results of the three seismic waves, the distribution characteristics of the shear stress along the pile body are very close to the results of the time history analysis, which can reflect the sudden change of shear stress in the soft and hard soil layers.  
Comparing the calculation results corresponding to different reduction coefficients, it can be seen that the change of the reduction coefficient has a significant effect on the shear stress near the top of the pile, and the effect is less obvious the farther away from the top of the pile. This is because the reduction factor is mainly changed by the inertial load generated by the superstructure on the pile foundation, and the inertial load is gradually transmitted downward through the top of the pile. Hence, the impact of the top of the pile is naturally the most significant.