Fractal models for predicting soil hydraulic properties: a review

Giménez, Daniel; Perfect, E.; Rawls, W. J.; Pachepsky, Y. A.

doi:10.1016/s0013-7952(97)00038-0

Cited by 213 publications

(118 citation statements)

References 94 publications

Supporting

Mentioning

109

Contrasting

Unclassified

Order By: Relevance

“…The main advantage of using fractal parameters and PSD curve model parameters as predictors was the improvement of the CEC prediction without additional measurements. This result is in agreement with some authors (Giménez et al, 1997) that used fractal dimension in characterizing the porous medium and improving the accuracy and reliability of the models. In the same way, Wu et al (2003) used some easily measurable data to predict soil CEC.…”

Section: T a B L E 2 Correlation Coefficients (R) Between Input And supporting

confidence: 92%

Prediction of CEC Using Fractal Parameters by Artificial Neural Networks

Bayat¹,

Davatgar²,

Jalali³

2014

International Agrophysics

View full text Add to dashboard Cite

A b s t r a c t. The prediction of cation exchange capacity from readily available soil properties remains a challenge. In this study, firstly, we extended the entire particle size distribution curve from limited soil texture data and, at the second step, calculated the fractal parameters from the particle size distribution curve. Three pedotransfer functions were developed based on soil properties, parameters of particle size distribution curve model and fractal parameters of particle size distribution curve fractal model using the artificial neural networks technique. 1 662 soil samples were collected and separated into eight groups. Particle size distribution curve model parameters were estimated from limited soil texture data by the Skaggs method and fractal parameters were calculated by Bird model. Using particle size distribution curve model parameters and fractal parameters in the pedotransfer functions resulted in improvements of cation exchange capacity predictions. The pedotransfer functions that used fractal parameters as predictors performed better than the those which used particle size distribution curve model parameters. This can be related to the non-linear relationship between cation exchange capacity and fractal parameters. Partitioning the soil samples significantly increased the accuracy and reliability of the pedotransfer functions. Substantial improvement was achieved by utilising fractal parameters in the clusters.K e y w o r d s: cation exchange capacity, fractal theory, particle size distribution, pedotransfer functions

show abstract

Section: T a B L E 2 Correlation Coefficients (R) Between Input And supporting

confidence: 92%

Prediction of CEC Using Fractal Parameters by Artificial Neural Networks

Bayat¹,

Davatgar²,

Jalali³

2014

International Agrophysics

View full text Add to dashboard Cite

show abstract

“…Here we test the CMF formula for simulated fronts governed by (1) with f (u) = a(1−u)(1−αu) for 0 α 1 on a number of finitely ramified generalizations of the Sierpiński carpet along with the classic Sierpiński carpet and its random version which are both infinitely ramified. Such fractals are of interest since some fractals in nature, such as porous rock with a scale-invariant distribution of holes 16 , are infinitely ramified.…”

Section: Introductionmentioning

confidence: 99%

The speed of reaction-diffusion fronts on fractals: testing the Campos-Méndez-Fort formula

Suwannasen¹,

Allen²,

Sprott³

2016

ScienceAsia

View full text Add to dashboard Cite

Campos, Méndez, and Fort (CMF) derived an approximate formula for the speed of reaction-diffusion fronts in fractal media. By way of a continuation of their earlier studies, we perform numerical simulations of reactiondiffusion equations with au(1 − u)(1 − αu) for 0 α 1 as the reaction term on various generalized Sierpiński carpets (including infinitely ramified and random ones). The CMF formula agrees well with the mean front speed as a function of a obtained from our simulations for the classic Sierpiński carpet, a randomized version of the carpet, and some finitely ramified carpets containing loops. In these cases the mean front speed also shows no significant dependence on α, as predicted by the CMF formula. However, the agreement is not so good in the case of the other carpets tested and this is probably a result of the mean distance of the front from the starting point against time behaving erratically in such cases. We also propose some nomenclature for generalized Sierpiński carpets and introduce a compact formulation of how to determine whether a point is on a generalized Sierpiński carpet lattice.

show abstract

“…A dynamic pore-scale network model was also reviewed and applied by Hassanizadeh et al (2002). Earlier work by Giménez et al (1997) reviewed the most important fractal models for predicting soil hydraulic properties, including the Cantor bar, Kock curve, Sierpiński carpet and Menger sponge. Vita (2011) evaluated specifically the Menger's Sponge model of porosity (essentially a three-dimensional depiction of Sierpiński carpet scheme) with the aim of improving accuracy by modelling towards infinitesimal pores.…”

Section: Geometrical Modelsmentioning

confidence: 99%

Porosity Reviewed: Quantitative Multi-Disciplinary Understanding, Recent Advances and Applications in Vadose Zone Hydrology

Dippenaar¹

2013

Geotech Geol Eng

View full text Add to dashboard Cite

Porosity -one of the most basic mechanical properties of a mediumhas implications in a vast range of disciplines and used for a similar vast range of applications. These include, for instance, the storage and flow of water; the compressible component of earth materials, which can be subjected to consolidation under loading; the variable parameter in the swelling and shrinkage of clays; and possibly a governing parameter in the formation of wetlands and perched water tables. This review notes the relevance of a fourfold quantification of porosity for vadose zone studies, viz. (1) type (matrix or structure), (2) scale (submicro to macro scale), (3) connectivity, and (4) water saturation. This is followed by a review of recent advances in the quantification and description of porosity in porous media (visual and remote sensing methods, porosimetry, geometrical approaches, empirical estimations, densest packing simulations, etc.), the applications to quantification of hydrological parameters, and a brief glimpse into the significance of porosity in a temporary hillslope wetland underlain by Archaean Lanseria gneiss in South Africa. Final comments are made regarding areas where quantification of porosity is problematic.Keywords: porosity; void ratio; vadose zone; effective porosity; fractal; microstructure; porosimetry; ferricrete; temporary hillslope wetland IntroductionAlbeit a straightforward concept (how hard can determining the ratio of voids to solids possibly be?), quantification of porosity is often significantly simplified. The importance of porosity in hydrology as a primary input parameter in almost all subsequent calculations is overlooked and the parameter is estimated without any validation, resulting in significant unquantifiable errors in hydraulic parameters. However, the simple percentage value of porosity is only one such aspect. The importance of type, scale and connectivity of porosity is commonly understood, but rarely evaluated in significant detail.A detailed discussion in Miller and Gray (2002) on the status of groundwater research accentuates a number of aspects requiring more research and where our understanding is often not sufficient. Reference is made particularly to preferential flow paths such as fractures and the resulting complicated accounting of interactions between these fractures and the flow through the primary pore space. They continue to elaborate on the difficulty of accounting for scale ranging from molecular to regional field problems. Fractured systems are singled out due to the difficulty in characterising and modelling fractures with available methods and because of their interaction with the porous matrix.As this is a review paper, basic concepts will be described concisely for the sake of cross-disciplinary agreement. It is impossible to cover the whole range of methods applicable to porosity. The purpose of this paper is primarily to summarise considerations in the quantification of porosity, to review recent advances in the quantification of porosity, to ap...

show abstract

Fractal models for predicting soil hydraulic properties: a review

Cited by 213 publications

References 94 publications

Prediction of CEC Using Fractal Parameters by Artificial Neural Networks

Prediction of CEC Using Fractal Parameters by Artificial Neural Networks

The speed of reaction-diffusion fronts on fractals: testing the Campos-Méndez-Fort formula

Porosity Reviewed: Quantitative Multi-Disciplinary Understanding, Recent Advances and Applications in Vadose Zone Hydrology

Contact Info

Product

Resources

About