# Nonlinear Solid-Fluid Coupled Seismic Response Analysis of Layered Liquefiable Deposit
## 1 Introduction  
Earthquake-induced ground failure, resulting from liquefaction of loose sand, silt, and gravelly soil deposits, has caused tremendous damage to engineering structures and infrastructure. Ground failures due to the lateral spreading of soil liquefaction at sites on horizontally stratified or mildly sloping ground impose significant threats to both aboveground and underground engineering structures. Dramatic damage caused by liquefaction has been reported in past historical earthquakes [1], such as Niigata, Japan 1964, Japan 2011, Christchurch, New Zealand 2011, and Palu, Indonesia 2018. During the 2011 Great East Japan Earthquake, the settlement in the Tokyo Bay area was generally in the range of 30 to 50 cm and settlement at some severely liquefied sites was as large as 70 to 100 cm. This macroscopic phenomenon means that the soil strata generate substantial consolidation settlement due to the generation and dissipation of excess pore water pressure (EPWP), which may lead to significant damage to engineering structures. Therefore, it is critical to study the dynamic characteristics of the sites that are susceptible to seismic liquefaction [2]. Numerical simulation is an important tool to help estimate the site response and assess the seismic safety of engineering sites. Many numerical studies on the seismic response ofsaturated soil sites have been carried out in recent years. [PERSON] et al. [3] proposed a coupled effective stress method by combining the Hardin-D'mreich model with the pore pressure growth model proposed by [PERSON] et al. [4]. Then, the proposed method was validated against the seismic acceleration records of the Port Island downhole array during the 1995 Hanshin earthquake in Japan. [PERSON] et al. (2012) [5] numerically simulated the seismic liquefaction process of the two sites utilizing three different constitutive models after calibrating the parameters of the nonlinear constitutive models against field test data. The results indicated that dilatancy is an important factor in capturing appropriate ground motions in liquefiable sites. [PERSON] et al. (2018) [6] systematically compared the response characteristics of the liquefiable site using two different constitutive models of sand (i.e., Pressure Dependent Multi Yield02 model and SANISAND model), in terms of settlement, acceleration, and excess pore water pressure, under seismic loading using two numerical computational platforms, OpenSees and FLAC. By comparing the results of centrifuge-free field tests, it was discovered that the two constitutive models can predict most seismic responses for the liquefiable site, but there is still a need for improvement in simulating soil settlement. [PERSON] et al. (2019) [7] developed a simplified pore pressure model based on the stress-based approach in a 1D computer code to carry out effective stress analyses of the liquefiable site. The code provides reliable predictions by comparing the test results of ideal soil profiles, a centrifuge test, and seismic events recorded on a well-instrumented test site. Based on the physical modeling and numerical simulation, [PERSON] and [PERSON] (2020) [8] evaluated the seismic behavior of liquefiable sub-layers and their effect on the seismic ground response. The study showed that the thicker and shallower liquefiable sublayers can effectively reduce the energy of seismic waves and earthquake-induced forces and the thinner liquefiable sublayers at greater depths could increase seismic intensity and reduce settlement. [PERSON] et al. (2021) [9] proposed a loosely coupled nonlinear effective stress method for site seismic response analysis. In this method, the nonlinear hysteresis model of soil was combined with an EPWP generation model characterized by cyclic shear-volume strain coupling, which established the coupling relationship between the degradation of cyclic stiffness and the generation of EPWP associated with earthquake events.