A user-friendly modified pore-solid fractal model

Ding, Dianyuan; Zhao, Ying; Feng, Hao; Cheng, Bing; Hill, Robert L.

doi:10.1038/srep39029

Cited by 7 publications

(4 citation statements)

References 47 publications

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“…A soil's fractal dimension reflects its capacity to fill pore spaces with soil particles. Smaller pore size is usually observed in soil associated with a higher ratio of finer particles (i.e., clay content), and the soil structure with a higher ratio of finer particles would be more compacted, thus showing a larger fractal dimension [69]. Conversely, a looser soil structure leads to a smaller fractal dimension.…”

Section: Fractal Dimension Of Different Textural Soilmentioning

confidence: 99%

Evaluation of Soil-Water Characteristic Curves for Different Textural Soils Using Fractal Analysis

Yang

et al. 2023

Water

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The soil-water characteristic curve (SWCC) is an essential tool to determine hydraulic and mechanical properties of unsaturated soils. As an inherent influencing factor, soil texture controls the characteristics of SWCCs. Fractal theory can quantitatively describe the physical characteristics of soil. This study used particle size distribution data and water content data contained in the UNSODA2.0 database to explore the fractal characteristics of 12 soil types with different textures under different matrix suctions. The SWCC fractal model was adopted to characterize the hydraulic properties of soil with various soil textures. The findings revealed that the mass fractal dimensions of particles from these 12 different soil types significantly differed and were closely related to the clay content. Fractal dimension increased with increasing clay content. The fractal dimension established a good relationship between soil structure and hydraulic properties. Fractal analysis can be used to determine the connection between physical properties and soil hydraulic parameters. The estimated results of the SWCC fractal model indicated that it had a good performance regarding the description of SWCCs for the 12 soil textures. The soil structure could be described through fractal dimensions, which can effectively indicate soil hydraulic characteristics. The estimated fractal dimension of this model could be obtained by particle size distribution. Furthermore, using the SWCC fractal model, we found that the SWCC of coarse textured soil changed sharply in the low suction stage and its residual water content was small, and the SWCC of fine textured soil changed gently with a large residual water content. The water retention capacity followed the order clay > silty clay > sandy clay > clay loam > silty clay loam > sandy clay loam > loam > silt loam > sandy loam > silt > loamy sand > sand.

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Section: Fractal Dimension Of Different Textural Soilmentioning

confidence: 99%

Evaluation of Soil-Water Characteristic Curves for Different Textural Soils Using Fractal Analysis

Yang

et al. 2023

Water

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“…In most studies about soil structure, it is studied as a fractal object [16,17,[24][25][26][27][28]. In this context, we'll offer an interpretation of the relationship (1 − φ) s + φ 2s = 1.…”

Section: A General Model Of Hydraulic Conductivitymentioning

confidence: 99%

“…The form parameters can even be reduced to one. If we assume λ = mn in the Equation ( 27) we obtain van Genuchten equation, Equation (28), which makes the function Θ(ψ) explicit where the form parameters {m, n} are still independent. If we accept the relationships between λ and m used to obtain Equations ( 33)- (37), the Equation ( 27) will have only one form parameter (m).…”

Section: Generalized Power Functionmentioning

confidence: 99%

Relating Hydraulic Conductivity Curve to Soil-Water Retention Curve Using a Fractal Model

2020

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In the study of water transference in soil according to Darcy law, the knowledge of hydrodynamic characteristics, formed by the water retention curve θ(ψ), and the hydraulic conductivity curve K(ψ) are of great importance. The first one relates the water volumetric content (θ) with the water-soil pressure (ψ); the second one, the hydraulic conductivity (K) with the water-soil pressure. The objective of this work is to establish relationships between both curves using concepts of probability theory and fractal geometry in order to reduce the number of unknown functions. The introduction of four definitions used at the literature of the pore effective radius that is involve in the general model has permitted to establish four new specials models to predict the relative hydraulic conductivity. Some additional considerations related to the definitions of flow effective area and the tortuosity factor have allow us to deduce four classical models that are extensively used in different studies. In particular, we have given some interpretations of its empirical parameters in the fractal geometry context. The resulting functions for hydrodynamic characteristics can be utilized in many studies of water movement in the soil.

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“…Fractal dimension extends the concept of “dimension”, because it can be a fraction, rather than an integer as in conventional Euclidean space, indicating the degree of complexity of fractal behaviors. Fractal theory now serves as a powerful, perhaps fundamental, tool for characterizing scale-invariance in many fields 19 20 21 22 23 24 25 26 27 .…”

mentioning

confidence: 99%

Definition of fractal topography to essential understanding of scale-invariance

Jin

Lĭ

et al. 2017

Sci Rep

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Fractal behavior is scale-invariant and widely characterized by fractal dimension. However, the cor-respondence between them is that fractal behavior uniquely determines a fractal dimension while a fractal dimension can be related to many possible fractal behaviors. Therefore, fractal behavior is independent of the fractal generator and its geometries, spatial pattern, and statistical properties in addition to scale. To mathematically describe fractal behavior, we propose a novel concept of fractal topography defined by two scale-invariant parameters, scaling lacunarity (P) and scaling coverage (F). The scaling lacunarity is defined as the scale ratio between two successive fractal generators, whereas the scaling coverage is defined as the number ratio between them. Consequently, a strictly scale-invariant definition for self-similar fractals can be derived as D = log F /log P. To reflect the direction-dependence of fractal behaviors, we introduce another parameter Hxy, a general Hurst exponent, which is analytically expressed by Hxy = log Px/log Py where Px and Py are the scaling lacunarities in the x and y directions, respectively. Thus, a unified definition of fractal dimension is proposed for arbitrary self-similar and self-affine fractals by averaging the fractal dimensions of all directions in a d-dimensional space, which . Our definitions provide a theoretical, mechanistic basis for understanding the essentials of the scale-invariant property that reduces the complexity of modeling fractals.

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A user-friendly modified pore-solid fractal model

Cited by 7 publications

References 47 publications

Evaluation of Soil-Water Characteristic Curves for Different Textural Soils Using Fractal Analysis

Evaluation of Soil-Water Characteristic Curves for Different Textural Soils Using Fractal Analysis

Relating Hydraulic Conductivity Curve to Soil-Water Retention Curve Using a Fractal Model

Definition of fractal topography to essential understanding of scale-invariance

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