A Fractal Model to Interpret Porosity-Dependent Hydraulic Properties for Unsaturated Soils

Abstract

is paper presents a simple fractal model to quantify the effects of initial porosity on the soil-water retention curve and hydraulic conductivity of unsaturated soils. In the proposed conceptual model, the change of maximum pore radius, which largely determines the change of the air-entry value, is directly related to the fractal dimension of pore volume (D) and porosity change. e hydraulic properties of unsaturated soils are then governed by the maximum pore radius, the fractal dimension of pore volume (D), and the fractal dimension of drainable pore volume (D d ≤ D). e new fractal model removes the empirical fitting parameters that have no physical meaning from existing models for porosity-dependent water retention and hydraulic behaviour and employs parameters of fractal dimensions that are intrinsic to the nature of the fractal porous materials. e proposed model is then validated against experimental data from the literature on soil-water retention behaviour and unsaturated conductivity.

A Fractal Approach for Predicting Unsaturated Hydraulic Conductivity of Deformable Clay

“…Furthermore, it is simple and convenient for practical engineering application. 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 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.…”

“…Cai et al [50] presented an indirect prediction approach for the relative hydraulic conductivity taking account of the effect of initial void ratios. Fortunately, based on the fractal theory, Zhou et al [51] proposed the unsaturated hydraulic conductivity model considering the effect of porosity. In this method, two fractal dimensions were used to describe the fractal characteristics of pore structure.…”

“…The change law of maximum pore size with porosity was predicted from the existing empirical model; then, the air-entry value can be predicted. Eventually, based on the Mualem model, Zhou et al [51] derived a fractal model of relative hydraulic conductivity considering the effect of porosity.…”

Effect of Porosity on Soil-Water Retention Curves: Theoretical and Experimental Aspects

“…The SWRC relation is a key hydraulic property to describe fluid flow phenomena in unsaturated soils, which can be affected by the porosity or the density of the soil [1,2]. A variation in soil porosity is common in fluid-solid interaction problems [3,4], and this change will result in an obvious change of SWRC [5]. Sometimes, it needs to predict the SWRCs for soil with different porosities.…”