The water retention function for a model of soil structure with pore and solid fractal distributions

Bird, N. R. A.; Perrier, Edith; Rieu, Michel

doi:10.1046/j.1365-2389.2000.00278.x

Cited by 177 publications

(182 citation statements)

References 22 publications

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“…At the second step, the fractal model of Bird et al (2000) was fitted on PSD curve data (that was extended at the first step) and fractal parameters were calculated. At the third step, basic soil properties (including the contents of sand, silt, and clay, OC and soil pH), PSD curve model parameters and fractal parameters were used to predict CEC using three PTFs for all data set.…”

Section: Methodsmentioning

confidence: 99%

“…However, the assumption may not be correct, but 999 µm is too close to the upper limit on radii of sand fraction (1 000 µm), then this assumption will not introduce much error to the model. Second step: In this study cumulative solid mass distribution of the Pore-Solid Fractal model was applied to PSD data (Bird et al, 2000):…”

Section: Methodsmentioning

confidence: 99%

“…Fractal theory has been employed successfully to explain the soil particle size distribution (PSD) by many authors such as Bird et al (2000). Ersahin et al (2006) related the CEC of the soils to the fractal dimension of PSD using regression method.…”

Section: Introductionmentioning

confidence: 99%

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Prediction of CEC Using Fractal Parameters by Artificial Neural Networks

Bayat¹,

Davatgar²,

Jalali³

2014

International Agrophysics

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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

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

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Prediction of CEC Using Fractal Parameters by Artificial Neural Networks

Bayat¹,

Davatgar²,

Jalali³

2014

International Agrophysics

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“…For a fractal distribution of particle sizes, the slope of the cumulative mass distribution versus size in a double logarithmic plot is (3 -D) (e.g. Bird et al, 2000). The fractal dimensions determined using this method are around 2.5 for pure sands (e.g.…”

Section: Introductionmentioning

confidence: 99%

Characterisation of the ultimate particle size distribution of uniform and gap-graded soils

Zhang

Baudet

et al. 2017

Soils and Foundations

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The ultimate particle size distribution of uniform and gap-graded soils is examined on specimens of carbonate sand that were subjected to large strains in a ring shear apparatus. The gap-graded soils were seen to retain a memory of their initial grading even at large strains. The particle size distributions were plotted in double logarithmic graphs either by mass or by number computed assuming different shapes. It was not possible to find linear subsets of the data, and since the samples were found experimentally to have converged to an ultimate grading, this suggests that the initial bimodal distribution prevented reaching an ultimate fractal distribution. Plots of the probability density functions of the particle sizes before and after shearing show the evolution of the gap-graded soils from a bimodal to a multi-modal distribution. This is accompanied by an evolution of the shape of the particles, visible in microphotographs and projections of the grains before and after test.

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“…In recent decades fractal models of porous media have become popular [27][28][29]98] because of the validation [99][100][101] of their predictions regarding the water content of porous media as functions of the pressure, relevant to processes of wetting and drying. A prior article in this journal [102] has addressed the relevance of such models to calculations of such properties as the hydraulic and electrical conductivities of real porous media, and it has found that there exists considerable support for their use.…”

Section: Porous Media Applicationsmentioning

confidence: 99%

Relevance of percolation theory to power‐law behavior of dynamic processes including transport in disordered media

Hunt

2009

Complexity

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P ower-law behavior seems ubiquitous in nature as well as in human endeavors. Flood statistics [1][2][3][4][5], water storage [6], drainage basin organization [7], relationships between channel dimensions and flow [8], extreme precipitation events [9], wind and weather fluctuations [10,11], stock and commodity markets fluctuations [12,13] , have all been noted to obey various power laws. Many physicists have searched for unifying concepts to explain such ubiquity. Perhaps, however, powerlaw behavior is not quite as universal as thought. Multifractal distributions originating from cascade processes as a related, but somewhat more complex, organizing principle have often been proposed to be the appropriate universal description [33, 34]. Some [35][36][37] have questioned whether a ''class'' of stretched exponential functions might better represent a larger or smaller fraction of the data. In the ac conductivity of disordered insulators, for example, several other frequencydependences [38-40], universal or not, have been suggested. This small sample of alternate ideas need not imply that alternative scenarios are always correct either. But simply because it is often asserted that nature follows power laws does not require such; in most cases the range and quality of data are probably not sufficient to distinguish the subtle differences between the various proposed distributions. But the recognition of the simplicity of the explanation that self-similar geometrical structures [41] could be the basis of so many geophysical manifestations of apparent power laws has certainly provided impetus to the interpretation that a large number of natural phenomena do follow power-law behavior.In the case that one believes that the observed behavior conforms to true power laws, what kind of underlying mechanism should one seek? At least six such unifying concepts, nonlinear dynamics (chaos) [42], self-organized criticality [43], hierarchical dynamics [44], highly optimized tolerance [45], minimum effort

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The water retention function for a model of soil structure with pore and solid fractal distributions

Cited by 177 publications

References 22 publications

Prediction of CEC Using Fractal Parameters by Artificial Neural Networks

Prediction of CEC Using Fractal Parameters by Artificial Neural Networks

Characterisation of the ultimate particle size distribution of uniform and gap-graded soils

Relevance of percolation theory to power‐law behavior of dynamic processes including transport in disordered media

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