# Nonlinear Solid-Fluid Coupled Seismic Response Analysis of Layered Liquefiable Deposit
## 4 Further Comparison and Discussion  
To further evaluate the efficacy of the fully coupled nonlinear effective stress analysis approach utilized in this study, the numerical results were compared with those obtained using the one-dimensional site response analysis program DEEPSOIL V7.0 [29], which adopts a loosely coupled nonlinear dynamic effective stress analysis approach for layered saturated soil. For comparison purposes, the MKZ (Matasovic-Konder-Zelasko) nonlinear constitutive model loosely coupled with the pore water pressure model proposed by [PERSON] and [PERSON] [30] in DEEPSOIL was selected for the effective stress analysis of the nonlinear seismic response of liquefiable sites in this manuscript. The material parameters of different soil layers are listed in Table 4. Moreover, the pore pressure ratio time histories of the liquefiable site under the El-Centro motion and Kobe motion were obtained from OpenSees and DEEPSOIL, as shown in Figure 14. It can be seen that liquefaction occurs in the soil at \(-3\) m and \(-15\) m, and the moment to reach liquefaction is very close for both analysis methods. However, the DEEPSOIL only approximately simulates the overall EPWP accumulation process without remarkable oscillation phenomenon in the pore pressure ratio time histories. The oscillation phenomenon of EPWP has been frequently observed in liquefiable sites during the previous numerical simulations and dynamic experiments [31; 32; 33]. Therefore, the fully coupled nonlinear effective stress analysis approach in OpenSees can more realistically capture the development of EPWP in the liquefiable soil during earthquakes. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Soil Type**} & \multirow{2}{*}{\
\begin{tabular}{c} **Thickness** \\ **(m)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Matasovic Backbone Curve** \\ \end{tabular} } & \multicolumn{3}{c}{**MRDF Formulation**} & \multicolumn{3}{c}{**Dobry Pore Water Pressure Model**} \\ \cline{3-13}  & & & \(\beta\) & \(s\) & \(\gamma_{\mathbf{r}}\)(\(\times\)10\({}^{-4}\)) & \(P_{1}\) & \(P_{2}\) & \(P_{3}\) & \(r_{\mathbf{u}}\) & \(f\) & \(p\) & \(F\) & \(s\) & \(\gamma_{\mathbf{h}}\) (\%) & \(\
u\) \\ \hline Crust clay & 3.0 & 1.230 & 0.660 & 2.82 & 0.686 & 0.30 & 3.25 & - & - & - & - & - & - \\ Loose sand & 12.0 & 1.605 & 0.915 & 4.24 & 0.672 & 0.28 & 3.25 & 0.99 & 1 & 1 & 10.9 & 1 & 0.017 & 1 \\ Dense sand & 6.0 & 1.500 & 0.915 & 5.22 & 0.666 & 0.268 & 3.25 & 0.99 & 2 & 1.04 & 2.6 & 1.7 & 0.020 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Parameters of the Matasovic backbone curve, MRDF formulation, and the Dobry pore water pressure generation model. Figure 14: Development of excess pore pressure ratios: (**a**) \(-3\) m; (**b**) \(-15\) m under the El-Centro motion and (**c**) \(-3\) m; (**d**) \(-15\) m under the Kobe Motion. The acceleration time histories and spectral accelerations at different burial depths are depicted in Figures 15 and 16. It can be seen that although the peak accelerations at the same burial depth of the liquefiable site are close to each other using two numerical approaches, the results from OpenSees using the fully coupled nonlinear effective stress analysis approach consists of more high frequency contents in the acceleration time histories. The loosely coupled nonlinear effective stress analysis approach in DEEPSOIL fails to properly capture the high-frequency component of ground motions during the seismic propagation in the liquefiable site. Moreover, significant differences between the spectral accelerations and the predominant periods of the soil responses at three different burial depths using two numerical approaches. The spectral acceleration values calculated by OpenSees in short periods are significantly larger than those calculated by DEEPSOIL.