On apparent viscosity evolution of non-cohesive saturated soils during liquefaction: revealed from phase field theory

This paper presents the evolution model of apparent viscosity during whole scenario of liquefaction using the Ginzburg-Landau theory as a unified frame. The apparent viscosity is treated as a macroscopic indicator of the phase-transition process, through which the progressive loss of solid-like resistance and the emergence of fluid-like behavior can be characterized. Homogeneity method is first adopted to rescale the biphase porous state to subsequently construct the phenomenon-based energy functional. In comparison to conventional Landau functional, the order parameter denoting the degree of liquefaction, is introduced herein to bridge the macroscopic property to inner variables. The viscosity model is obtained by solving the Ginzburg-Landau formalism and further verified via experimental data and empirical non-Newtonian formula. Results elucidate the predictive capability and universality of the presented model to portray the fluidic feature of liquefiable soil. A simplified single-phase plane Couette granular flow is further analyzed to examine the phase-transition response under controlled shear. Results show a transition from distributed liquefaction to shallow shear-localized fluidization near the critical condition, indicating that viscosity degradation and and shear localization can be interpreted as coupled behavior of a Landau-type phase transition. Finally, the relation between order parameter and excess pore pressure is discussed. It is found that the elbow of viscosity-time history can correspond to excess pore pressure ratio equaling to 0.9 in different loading conditions. This relation implies that measurable state indicators can act as environmental variables controlling the order-parameter evolution, offering a route toward a unified phase-transition framework for liquefaction.