# Nonlinear Solid-Fluid Coupled Seismic Response Analysis of Layered Liquefiable Deposit
## 5 Conclusions  
In this study, the fully-coupled nonlinear dynamic analyses of a layered liquefiable site were performed by adopting the OpenSees finite element program. The dynamic behavior of the liquefiable soils was modeled by an extensively validated soil constitutive model based on the critical state soil mechanics and bounding surface theory for sandy soil. The dynamic behavior of the non-liquefiable soils was modeled by a von [PERSON] multi-surface model, which can characterize the nonlinear hysteretic behavior of the crust clay soil under cyclic loading. The excess pore water pressure, acceleration, shear stress-strain, and effective stress path in a liquefiable site were investigated in detail during and after the earthquakes. The following conclusions can be drawn from this study.  
1. Under strong earthquake shaking, the loose sand can be liquefied quickly, accompanying the EPWP build-up. Numerical results show that liquefied sand loses the shear strength and behaves like a fluid, and shear waves can't be transmitted in liquefied soil. This phenomenon proves that the PM4 Sand constitutive model is capable of describing the post-liquefaction characteristics of soil.
2. The acceleration amplitude of the soil significantly decreases after soil liquefaction, which indicates that the liquefied soil hinders the propagation of seismic waves from  
Figure 16: Acceleration response spectra with 5% damping ratio: (**a**) 0 m; (**b**) \(-\)3 m; (**c**) \(-\)15 m under the El-Centro motion and (**d**) 0 m; (**e**) \(-\)3 m; (**f**) \(-\)15 m under the Kobe motion.  
the base of the numerical model to the ground surface. The peak accelerations of the ground surface under the El-Centro motion and the Kobe motion attenuate to 64% and 42% of the input ground motion, respectively.
3. The low permeability of crust clay prevents the upward dissipation of excess pore water pressure in the liquefiable sand, thus gradually accumulating excess pore water pressure at the interface of the crust clay and loose sand layers. The large post-liquefaction flow deformation occurs at the upper layer of the loose sand layer.
4. The total settlement increases by approximately 40% when considering the post-earthquake pore pressure dissipation and reconsolidation.
5. Compared with the loosely coupled effective stress analysis method, the fully coupled effective stress analysis method can better simulate the propagation of high-frequency ground shaking in layered saturated soils and the nonlinear seismic response characteristics of liquefiable soil layers.  
Y.S.: Conceptualization, Methodology, Software, Writing, Data curation, Writing-Original Draft, Formal analysis; Z.Z.: Conceptualization, Supervision, Formal analysis, Review & Editing; L.L.: Conceptualization, Formal analysis, Review & Editing, Funding acquisition; X.D.: Conceptualization, Supervision, Project administration, Funding acquisition. All authors have read and agreed to the published version of the manuscript.  
This work presented in this paper was supported by the Scientific Research Fund of Institute of Engineering Mechanics, China Earthquake Administration (Grant No. 2018D09), the National Key Research and Development Program of China (2018 YFC1504305), and the National Natural Science Foundation of China (51978020).  
Not applicable.  
All data generated or analyzed during this study are included in this published article.  
The authors declare no conflict of interest.