Investigation of Newtonian and non-Newtonian Bingham fluid models for lateral flow simulation of liquefied soil

Abstract

This study applies a Newtonian model and non-Newtonian Bingham model to simulate the lateral flow of liquefied soil and investigates the models’ parameters. First, the study derives analytical solutions for the lateral flow velocity under free-field conditions in both the transient and steady states for both models. The study determines that the solution derived for the Newtonian model can be applied to derive that for the Bingham model through a simple transformation considering the contribution of undrained residual shear strength of liquefied soil. Second, three-dimensional numerical analyses are executed using COMSOL to investigate the boundary conditions of experimental models, which significantly affect the fluid behavior of liquefied soil. The results reveal that the model length and sidewall effects can be ignored at a length-to-thickness ratio of >30 and width-to-thickness ratio of >6, respectively. The Bingham model can describe the behavior of liquefied soil under different boundary conditions using a single set of parameters. Through normalization, the Bingham and Newtonian models can share the same normalized velocity–time curve. Additionally, the Bingham model with boundary conditions can have a similar curve to that under the free-field condition through the replacement of the original viscosity coefficient with an apparent viscosity coefficient.