A Simple Fractal-Based Model for Soil-Water Characteristic Curves Incorporating Effects of Initial Void Ratios

Abstract

Abstract:In this paper, a simple and efficient fractal-based approach is presented for capturing the effects of initial void ratio on the soil-water characteristic curve (SWCC) in a deformable unsaturated soil. In terms of testing results, the SWCCs (expressed by gravimetric water content) of the unsaturated soils at different initial void ratios were found to be mainly controlled by the air-entry value (ψ a ), while the fractal dimension (D) could be assumed to be constant. As a result, in contrast to the complexity of existing models, a simple and efficient model with only two parameters (i.e., D and ψ a ) was established for predicting the SWCC considering the effects of initial void ratio. The procedure for determining the model parameters with clear physical meaning were then elaborated. The applicability and accuracy of the proposed model were well demonstrated by comparing its predictions with four sets of independent experimental data from the tests conducted in current work, as well as the literature on a wide range of soils, including Wuhan Clay, Hefei and Guangxi expansive soil, Saskatchewan silt, and loess. Good agreements were obtained between the experimental data and the model predictions in all of the cases considered.

A Unified Fractal Model for Permeability Coefficient of Unsaturated Soil

“…Note that, for determining the fractal dimension D, only the test data in the range of ψ a can be adopted, as highlighted in the literature. 34…”

A Fractal Approach for Predicting Unsaturated Hydraulic Conductivity of Deformable Clay

“…By plotting the ln θ against −ln ψ, the fractal dimension can be calculated by D = 3 − k, in which k is the gradient of the graph. Note that the fractal dimension is seen as a constant for the same soil with different initial void ratios [53].…”

“…It is worth noting that the model presented in this paper is different from that proposed by Zhou et al [51]. In this paper, only one fractal dimension is used to describe the pore distribution characteristics, the air-entry value is directly predicted by the air-entry value model proposed by Tao et al [53], and a fractal model of relative hydraulic conductivity is derived by using the Tao-Kong model (Tao et al [54] indicated that the Tao-Kong model yields good predictions against measured data when the fractal dimension is large, while the predictions of the Mualem model agree well with the measured results of the relative hydraulic conductivity when the fractal dimension is relatively small). In contrast with the proposed model in this paper, the computational efforts of Zhou et al [51] are relatively complex.…”

“…Therefore, it can be seen that a new simple method is further expected to predict the relative hydraulic conductivity under deformation condition. According to the fractal theory, the predicted method of SWCC taking into account the influence of initial void ratio was proposed by Tao et al [53]. On this basis, a predicted method of relative hydraulic conductivity under deformation condition was presented in this paper combined with the fractal model of relative hydraulic conductivity.…”

Laboratory Testing to Research the Micro-Structure and Dynamic Characteristics of Frozen–Thawed Marine Soft Soil

“…There are a variety of factors that influence the characteristics of frozen-thawed soil. Firstly, the type of soil-which includes moisture content [6][7][8][9] and pore morphology [10,11]-is a critical factor of the soil characteristics. Zhai et al [12] found that, for consecutive freeze-thaw cycles, the proportion of micro-pores and mini-pores gradually decreased, while that of meso-pores and macropores increased.…”