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Top1. Introduction
Catastrophic earthquakes in the past decades such as 1920 Kansu, 1964 Niigata, 1964 Alaska, 1971 San Fernando, 1979 Imperial Valley, 1985 Chile, 1989 Loma Preita, 1995 Kobe 1999 Kocaeli, 2001 Bhuj, 2010 Chile and 2010 Canterbury had caused serious post-liquefaction damages to structures and buildings supported on shallow foundation. Various failure mechanisms such as sand boiling, cyclic densification, lateral spreading, loss of bearing capacity, cyclic softening lead to differential settlement of the foundation thereby causing damages to the superstructure (Seed et al., 2003). These failures have resulted in a great economic loss related to damages on infrastructures, buildings and ground. 1989 Loma Preita earthquake resulted in a building loss due to liquefaction of nearly $35 million (US Geological Survey) which were associated with many types of permanent ground deformation. Thus, liquefaction can induce a substantial amount of damage to foundation as well as super structure in the absence countermeasures.
Various researchers performed experimental research to study the liquefaction and post-liquefaction behaviour of shallow and deep foundations supported on liquefiable soil (Yoshimi and Tokimatsu, 1977; Liu and Dobry, 1997; Taboada and Dobry, 1998; Dashti et al., 2010; Allmond and Kutter, 2012; Marques et al., 2014; Ishikawa et al., 2015; Adamidis and Madabhushi, 2017; Mehrzad et al., 2018; Ghorbani et al., 2019).
In the last few years, the usage of 3D direct nonlinear finite element analyses to study the effect of liquefaction on foundations has increased. Rahmani and Pak (2012) used 3D numerical method in Opensees (finite element program) and investigated the response of pile foundations in liquefiable soil subjected to dynamic load. It was found that the lateral deflection and bending moment of piles were maximum at the pile head, which had a great influence on the seismic response of free-field soil. It was also shown that increase in frequency of the input ground motion, decreased the pile response to a great extent. Karimi and Dashti (2016) performed 3D dynamic analysis using Opensees, to capture the excess pore pressure generation, acceleration and settlement of liquefiable soil and the interaction effects on a shallow founded structure. Their results showed that excess pore pressure was maximum in free-field and minimum under the foundation. In contrast, acceleration was observed to be maximum under the foundation compared to free-field acceleration. Ramirez et al. (2019) studied the seismic response of shallow foundation and structure supported on liquefiable sandy soil which was improved by vertical drains. A 3D fully coupled dynamic method was used for the analysis through which it was inferred that even though the excess pore water pressure was dissipated at a faster rate, reduction in peak pressure was limited. Lu et al. (2020) analysed the seismic-liquefaction response of shallow foundation to evaluate liquefaction induced settlement. From the numerical analysis, they suggested a viscosity chart to estimate the liquefaction-induced settlement value depending upon the foundation size, soil unit weight and time period of ground motion.