Soil liquefaction is one of the most dangerous threats to civil engineering structures constructed in sandy grounds when earthquakes occur, as evidenced by the 1964 Niigata earthquake in Japan [1], the 1976 Tangshan earthquake in China [2], the 1995 Hyogoken-Nambu earthquake in Japan [3], and the 2008 Wenchuan earthquake in China [4]. Liquefaction-induced ground failure can cause many kinds of geodisasters and structural damage, such as the settlement of buildings, the uplift of underground facilities, the lateral flow of ground, and even landslides. Therefore, scholars and engineers have devoted great effort to investigating the behaviors and mechanisms of soil liquefaction. Generally, soil liquefaction behaviors can be divided into two types: cyclic mobility and flow liquefaction [5–۷]. Cyclic mobility often occurs in medium-dense sand as a result of the stepwise increase in the pore water pressure and is in connection with repeated contractive and dilative responses when the effective stress approaches a zero state (Fig. 1(a)). Flow liquefaction often occurs in loose sand due to a rapid drop in shear strength and is mainly associated with a contractive response of the soil (Fig. 1(b)). Both types of liquefaction behaviors have been theoretically modeled over the past several decades. For cyclic mobility, liquefaction-induced deformation is generally finite and thus can be described by elastoplastic constitutive models established based on the principles of solid mechanics [8–۱۳]. For flow liquefaction, however, the behavior is more complex because it involves a process in which the soil will transit from a solid phase into a fluid phase and finally result in a very large flow deformation [14]. Because liquefied soil behaves similar to a fluid after liquefaction, the post-liquefaction behavior is no longer suitable to be described by traditional elastoplastic constitutive models. In recent years, some researchers began to adopt fluid dynamics methods to study the flow process of liquefied soil. In their studies, the liquefied soil is regarded as a fluid and thus its behavior can be modeled by a fluid constitutive model. Uzuoka et al. [15] made the first attempt to use a fluid constitutive model (Bingham model) to describe the large deformation caused by flow liquefaction. Chen et al. [16] found that the post-liquefaction behavior of sand can be well simulated by non-Newtonian fluid models. Moriguchi [17] used a CIP-based fluid dynamics method to describe the large deformation of geomaterials in liquefied state. Huang et al. [18] introduced the Bingham fluid model with the Mohr-Coulomb yield criterion into the smoothed particle hydrodynamics (SPH) framework to analyze the flow process of liquefied soil. Zhou et al. [19] proposed a fluid constitutive model for liquefied sand, in which the friction resistance and viscous resistance were expressed as a thixotropic shear-thinning fluid and a non-time-variant shear-thinning fluid, respectively. Although researchers have obtained many results by using the fluid constitutive model to simulate the post-liquefaction behaviors of soil, there is a limitation in these studies that only the fluid-like behavior after liquefaction can be simulated, and the solid-like behavior before liquefaction and the transition process from the solid phase to a fluid phase are omitted. Certainly, it is practicable to use an elastoplastic model to simulate the solid-like behavior before liquefaction, and then use a fluid constitutive model to simulate the fluid-like behavior after liquefaction.