Fractal-based hydraulic model of unsaturated flow in deformable soils considering the evolution of pore size distribution

Abstract

This paper presents a fractal-based hydraulic model for unsaturated flow, which includes the soil water retention curve (SWRC) and relative hydraulic conductivity curve (RHCC), and considers the evolution of pore size distribution (PSD) during soil deformation. In this model, soil PSD is assumed to follow the fractal scaling law, and soil deformation is characterized by a change in the fractal dimension and air entry value. By combining the intrinsic constraint between void ratio and fractal dimension, the fractal description of PSD evolution during volumetric deformation of soils is clearly defined, and the void ratio-dependent SWRC and RHCC are derived. All model parameters can be calibrated from the SWRC data of soils under two initial void ratios, and can then be used to predict the SWRC and RHCC of the soil under arbitrary deformation states. Eight experimental data sets, including SWRC and RHCC data under different initial void ratios, are used to evaluate the proposed model. Results show that: (1) the fractal-based hydraulic model can well describe the influence of volumetric deformation on the hydraulic properties of unsaturated soils, and (2) ignoring the evolution of PSD during soil compression will significantly overestimate the water retention ability and hydraulic conductivity of soils.