# Nonlinear Solid-Fluid Coupled Seismic Response Analysis of Layered Liquefiable Deposit
## 3 Numerical Analysis and Results
### Nonlinear Stress Response  
Under earthquake excitations, the loose sand exhibits nonlinear behavior. The liquefaction in loose sand is closely related to the build-up of EPWP and the reduction of effective stresses. Figures 4 and 5 present a nonlinear shear stress-strain relation and effective stress path along the soil depth under the El-Centro motion. As shown in Figure 4, the shear stress and strain of the crust clay layer exhibit a linear relationship, indicating that the soil shear stiffness remains the same during the earthquake excitation. For the loose sand layers at the burial depths of 3 m, 10 m, and 15 m, the hysteresis loops of the shear stress and strain gradually flatten, and the shear stiffness gradually decreases under cyclic loading until the saturated loose sand layer reaches the liquefaction initiation state. The cyclic shear strain in the saturated sand layer increases rapidly after the initial liquefaction, wherein the maximum single amplitude shear strain \(\gamma_{SA}\) reaches 22.3% in the upper loose sand layer. The maximum single amplitude shear strain \(\gamma_{SA}\) in the loose sand layer reaches  
Figure 3: Acceleration time histories, Arias intensity build-up, and Fourier spectra of the input motions.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **El-Centro Motion** & **Kobe Motion** \\ \hline Magnitude, Mw & 7.1 & 6.9 \\ Epicentral distance (km) & 11.5 & 0.4 \\ PGA (g) & 0.35 & 0.83 \\ PGV (cm/s) & 38.11 & 91.11 \\ Time (s) & 40 & 40 \\ Arias Intensity (m/s) & 1.81 & 8.39 \\ Predominant period (s) & 0.68 & 1.71 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Parameters of the two ground-motion records used in this study.  
2.5% at the interface of the loose sand and dense sand layers, which indicates that the numerical model used in this paper can effectively simulate the cyclic shear deformation characteristics of the saturated sand layer after liquefaction initiation. For the dense sand layer, it is more difficult to liquefy and soil shear stiffness remains almost unchanged, which can be attributed to the surrounding higher effective confining pressure and the soil densification in the dense sand layer. Figures 6 and 7 illustrate the shear stress-strain relationships and effective stress path under the Kobe motion, which are, in general, similar to those of the El-Centro case in Figures 4 and 5. The responses of the soil layers at different burial depths under the Kobe motion are smaller than those subjected to the El-Centro case. The maximum single amplitude shear strain \(\gamma_{SA}\) reaches 16.5% at the interface of the crust clay and loose sand layers, and 3.7% at the interface of the loose sand and dense sand layers. The difference may be attributed to the fact that the El-Centro motion is a characteristic far-field ground motion. The main shaking of the El-Centro motion lasts longer with similar peak acceleration amplitudes, thereby resulting in a higher degree of nonlinear shear deformation at the site. However, the Kobe motion has the feature of a near-field ground