A mathematical model of tortuosity in soil considering particle arrangement

Abstract

Tortuosity is an important parameter for studying the permeability of soil. Existing studies of soil tortuosity are usually of empirical nature and attempt to relate tortuosity to soil porosity alone. By assuming a laminar flow through the pores of two‐dimensional square solid particles, we present a mathematical model for calculating soil tortuosity under different particle arrangements. The effect of the randomness of the particle arrangement on the tortuosity is evaluated, which generates the variation range of the tortuosity. The proposed model provides the upper and lower bounds of the tortuosity, while existing empirical models tend to fall within these bounds. The consistency between the proposed model and the numerical calculation provides a validity for the proposed model.