Soil aggregates as mass fractals

Soil Research ◽  
1995 ◽  
Vol 33 (5) ◽  
pp. 757 ◽  
Author(s):  
AN Anderson ◽  
AB Mcbratney
Keyword(s):  
Fractal Dimension ◽  
Bulk Density ◽  
Soil Aggregates ◽  
Fractal Theory ◽  
Equivalent Form ◽  
Aggregate Size ◽  
Saturated Water ◽  
Mass Fractal Dimension ◽  
Moisture Characteristic ◽  
Saturated Water Content

Soil aggregates have a fractal mass. That is, they are porous and, as they are studied in greater detail, more pores may be observed. Mass fractals have scale-dependent bulk density. Larger objects, or soil aggregates, have a smaller bulk density. Bulk density in soil studies is sometimes assumed to be constant. If this was the case, soil aggregates would not be mass fractals, and their porosity would not change with scale. The fact that soil aggregates are mass fractals places restrictions on the estimation of the fragmentation fractal dimension (Df) of soil. The mass fractal dimension of soil (Dm) may be calculated from bulk density-aggregate size data. Linear and nonlinear methods of estimating Dm were compared and were shown to give similar results. The Dm is shown to influence porosity and the saturated water content. Fractal theory, in particular Dm, has implications for the calculation of the pore-size distribution and the moisture characteristic. By equating Campbell's (1985) Version of the Brooks-Corey water retention function, � Proportional �(-1 / b)and an equivalent form to the Brooks-Corey relation given by Crawford (1994), � Proportional �(Dm - d) it is suggested that D-m = d - 1/b, where d is the embedding dimension.

Evaluation of selected factors influencing aggregate fragmentation using fractal theory

1992 ◽  
Vol 72 (2) ◽  
pp. 97-106 ◽  
Author(s):  
V. Rasiah ◽  
B. D. Kay ◽  
E. Perfect
Keyword(s):  
Fractal Dimension ◽  
Probability Model ◽  
Soil Aggregates ◽  
Fractal Theory ◽  
Aggregate Stability ◽  
Aggregate Size ◽  
Red Clover ◽  
Probability Of Failure ◽  
Continuous Corn ◽  
Wet Sieving

Two fractal parameters, probability of failure (P) and fractal dimension (D), were used to evaluate the influence of cropping and wetting treatments, and aggregate size on fragmentation of soil aggregates during wet sieving. Five different sizes of aggregates (4–10, 2–4, 1–2, 0.5–1 and 0.25–0.5 mm) from five cropping treatments [conventionally cultivated continuous corn (CCC), CCC underseeded to red clover (CCR), minimally tilled continuous corn underseeded to red clover (CCRM), alfalfa (AL), and bromegrass (BR)] were subjected to two wetting treatments (rapid and slow) before being wet sieved. P increased nonlinearly with increasing aggregate size. The P of the slowly wetted agggregates was always less than that of the rapidly wetted aggregates. The P of larger aggregates, 2–4 and 4–10 mm, increased in the following order of cropping: BR = AL < CCRM < CCR = CCC. The D for the size distribution of 4- to 10-mm aggregates increased in the same order of cropping as that given previously. The D for the rapidly wetted aggregates was higher than that of the slowly wetted aggregates for all cropping treatments except CCC. The values of P predicted from a fractal probability model correlated well with the observed values. The results show that P and D of soil aggregates are strongly influenced by cropping and wetting treatments and aggregate size. Key words: Probability of failure, fractal dimension, wet sieving, wet aggregate stability, prewetting

Research on the AC-13 Skeleton Dense-Graded Asphalt Mixtures by Fractal Theory

2014 ◽  
Vol 971-973 ◽  
pp. 148-156
Author(s):  
Gui Hua Hu ◽  
Xiao Wei Chen ◽  
Xuan Cang Wang
Keyword(s):  
Fractal Dimension ◽  
Strong Correlation ◽  
Fractal Theory ◽  
Asphalt Mixture ◽  
Aggregate Size ◽  
Asphalt Mixtures ◽  
Degree Of Saturation ◽  
Paper Study ◽  
Mineral Aggregate ◽  
Fractal Character

This paper study on AC-13 skeleton dense-graded asphalt mixtures by fractal theory, obtaining that both aggregate size and gradation have fractal character. Compared three kinds of asphalt mixture, we found that there was a strong correlation between fractal dimension of aggregate and aggregate size distribution. AC-13 skeleton dense-graded asphalt mixtures were tested. The results show that the aggregate fractal dimension has a good correlation with mixture’s bulk density, mineral aggregate gap rate, percentage of voids and asphalt degree of saturation too. The study is useful for reference to the readers who engage in further study of the fractal theory’s application to asphalt mixtures.

Fractal Research on Cracks of Reinforced Concrete Beams with Different Aggregates Sizes

2011 ◽  
Vol 250-253 ◽  
pp. 1818-1822 ◽  
Author(s):  
Hong Quan Sun ◽  
Jun Ding ◽  
Jian Guo ◽  
Dong Liang Fu
Keyword(s):  
Fractal Dimension ◽  
Reinforced Concrete ◽  
Theoretical Basis ◽  
Concrete Beams ◽  
Fractal Theory ◽  
Aggregate Size ◽  
Fractal Dimensions ◽  
Reinforced Concrete Beams ◽  
Crack Evolution ◽  
Fractal Characteristics

Under the concentrated loads, the crack evolutions of reinforced concrete experimental beams (RCEB) with three different aggregate sizes are studied. Using fractal theory, the generation, development and distribution of the cracks on the RCEB are analyzed. The results show that the cracks on the RCEB have fractal characteristics obviously. By studying the fractal dimension of the cracks, the aggregate sizes have significant effect to the cracks on the RCEB. The relationships of the fractal dimensions of the crack evolution in loading processing and loads meet the power function laws. The researching results of this paper provide a new theoretical basis for selecting the appropriate aggregate size to improve the strength of reinforced concrete beams.

scholarly journals Dynamic characteristics and fractal representations of crack propagation of rock with different fissures under multiple impact loadings

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Bing Sun ◽  
Shun Liu ◽  
Sheng Zeng ◽  
Shanyong Wang ◽  
Shaoping Wang
Keyword(s):  
Fractal Dimension ◽  
Crack Propagation ◽  
Crack Growth ◽  
Impact Test ◽  
Fractal Theory ◽  
Dynamic Change ◽  
Fractal Dimensions ◽  
Peak Stress ◽  
Dynamic Mechanical Properties ◽  
Gravitational Potential Energy

AbstractTo investigate the influence of the fissure morphology on the dynamic mechanical properties of the rock and the crack propagation, a drop hammer impact test device was used to conduct impact failure tests on sandstones with different fissure numbers and fissure dips, simultaneously recorded the crack growth after each impact. The box fractal dimension is used to quantitatively analyze the dynamic change in the sandstone cracks and a fractal model of crack growth over time is established based on fractal theory. The results demonstrate that under impact test conditions of the same mass and different heights, the energy absorbed by sandstone accounts for about 26.7% of the gravitational potential energy. But at the same height and different mass, the energy absorbed by the sandstone accounts for about 68.6% of the total energy. As the fissure dip increases and the number of fissures increases, the dynamic peak stress and dynamic elastic modulus of the fractured sandstone gradually decrease. The fractal dimensions of crack evolution tend to increase with time as a whole and assume as a parabolic. Except for one fissure, 60° and 90° specimens, with the extension of time, the increase rate of fractal dimension is decreasing correspondingly.

scholarly journals Effect of Hydrophobic Silica Nanochannel Structure on the Running Speed of a Colloidal Damper

2021 ◽  
Vol 11 (15) ◽  
pp. 6808
Author(s):  
Gengbiao Chen ◽  
Zhiwen Liu
Keyword(s):  
Fractal Dimension ◽  
Silica Gel ◽  
Fractal Theory ◽  
Percolation Model ◽  
Silica Gels ◽  
Practical Significance ◽  
Running Speed ◽  
Fractal Percolation ◽  
Micropore Structure ◽  
Hydrophobic Silica

A colloidal damper (CD) can dissipate a significant amount of vibrations and impact energy owing to the interface power that is generated when it is used. It is of great practical significance to study the influence of the nanochannel structure of hydrophobic silica gel in the CD damping medium on the running speed of the CD. The fractal theory was applied to observe the characteristics of the micropore structure of the hydrophobic silica gel by scanning electron microscopy (SEM), the primary particles were selected to carry out fractal analysis, and the two-dimensional fractal dimension of the pore area and the tortuous fractal dimension of the hydrophobic silica gel pore structure were calculated. The fractal percolation model of water in hydrophobic silica nanochannels based on the slip theory could thus be obtained. This model revealed the relationship between the micropore structure parameters of the silica gel and the running speed of the CD. The CD running speed increases with the addition of grafted molecules and the reduction in pore size of the silica gel particles. Continuous loading velocity testing of the CD loaded with hydrophobic silica gels with different pore structures was conducted. By comparing the experimental results with the calculation results of the fractal percolation model, it was determined that the fractal percolation model can better characterize the change trend of the CD running velocity for the first loading, but the fractal dimension was changed from the second loading, caused by the small amount of water retained in the nanochannel, leading to the failure of fractal characterization.

scholarly journals Scale Characteristics and Optimization of Park Green Space in Megacities Based on the Fractal Measurement Model: A Case Study of Beijing, Shanghai, Guangzhou, and Shenzhen

2021 ◽  
Vol 13 (15) ◽  
pp. 8554
Author(s):  
Zhen Li ◽  
Wanmin Zhao ◽  
Miaoyao Nie
Keyword(s):  
Fractal Dimension ◽  
Evaluation System ◽  
Goodness Of Fit ◽  
Green Space ◽  
Fractal Theory ◽  
Measurement Model ◽  
Scale Structure ◽  
Qualitative Description ◽  
Urban Spatial Structure ◽  
Factors Affecting

This paper applies fractal theory to research of green space in megacity parks due to the lack of a sufficient qualitative description of the scale structure of park green space, a quantifiable evaluation system, and operable planning methods in traditional studies. Taking Beijing, Shanghai, Guangzhou, and Shenzhen as examples, GIS spatial analysis technology and the Zipf model are used to calculate the fractal dimension (q), the goodness of fit (R2), and the degree of difference (C) to deeply interpret the connotation of indicators and conduct a comparative analysis between cities to reveal fractal characteristics and laws. The research results show that (1) the fractal dimension is related to the complexity of the park green space system; (2) the fractal dimension characterizes the hierarchical iteration of the park green space to a certain extent and reflects the internal order of the scale distribution; (3) the scale distribution of green space in megacity parks deviates from the ideal pyramid configuration; and (4) there are various factors affecting the scale structure of park green space, such as natural base conditions, urban spatial structure, and the continuation of historical genes working together. On this basis, a series of targeted optimization strategies are proposed.

SORPTION OF CARBON AND PHOSPHORUS FROM LIQUID POULTRY MANURE BY SOIL AGGREGATES OF DIFFERING SIZE

1985 ◽  
Vol 65 (3) ◽  
pp. 467-473 ◽  
Author(s):  
V. K. BHATNAGAR ◽  
M. H. MILLER
Keyword(s):  
Soil Aggregates ◽  
Poultry Manure ◽  
Aggregate Size ◽  
Liquid Manure ◽  
Inorganic P ◽  
Supernatant Liquid ◽  
Extractable P ◽  
P Content ◽  
Manure Slurry ◽  
Total P

A series of laboratory experiments was conducted to determine the mechanism(s) responsible for a previously reported observation that addition of liquid manure to soil increased the NaHCO3-extractable P (Ext-P) of large aggregates (> 2 mm) more than that of smaller aggregates whereas addition of an inorganic P solution did not. Application of liquid poultry manure increased the total P, Ext-P and total C concentrations in large aggregates (> 2 mm) much more (> 2.5 ×) than that in small aggregates (< 1 mm). Addition of inorganic P solution or of supernatant liquid from a centrifuged manure slurry increased the P content of the large aggregates only slightly (1.2 ×). A greater increase in Ext-P in large aggregates was observed even when the smaller aggregates were purposely layered on top of the larger ones prior to addition of the liquid manure. A similar but less pronounced effect of aggregate size on increase in P or C concentration was observed when different sized aggregates were left in contact with an effectively infinite source of liquid manure for 24 h. It is concluded that the larger aggregates absorbed more of the bulk manure slurry than smaller aggregates. A partial sealing of small aggregates by particulates is suggested as a possible mechanism. Key words: Carbon, phosphorus, liquid manure, soil aggregates

Runoff Fractal Dimension of Songhua River Basin in Harbin Station Based on Db4 Wavelet

2012 ◽  
Vol 550-553 ◽  
pp. 2537-2540
Author(s):  
Hai Yan Gu ◽  
Yong Wang ◽  
Lei Yu
Keyword(s):  
Time Series ◽  
Fractal Dimension ◽  
River Basin ◽  
Fractal Theory ◽  
Measurement Methods ◽  
Self Similarity ◽  
Songhua River ◽  
Songhua River Basin ◽  
The Songhua River Basin ◽  
The Songhua River

The wavelet analysis and fractal theory into the analysis of hydrological time series, fluctuations in hydrological runoff sequence given the complexity of the measurement methods--- fractal dimension. The real monthly runoffs of 28 years from Songhua River basin in Harbin station are selected as research target. Wavelet transform combined with spectrum method is used to calculate the fractal dimension of runoff. Moreover, the result demonstrates that the runoff in Songhua River basin has the characteristic of self-similarity, and the complexity of runoff in the Songhua River basin in Harbin station is described quantificationally.

scholarly journals Effective Thermal Conductivity of Open Cell Polyurethane Foam Based on the Fractal Theory

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Kan Ankang ◽  
Han Houde
Keyword(s):  
Thermal Conductivity ◽  
Fractal Dimension ◽  
Effective Thermal Conductivity ◽  
Polyurethane Foam ◽  
Solid Phase ◽  
Fractal Theory ◽  
Heat Radiation ◽  
Total Thermal Conductivity ◽  
Equivalent Thermal Conductivity ◽  
Open Cell

Based on the fractal theory, the geometric structure inside an open cell polyurethane foam, which is widely used as adiabatic material, is illustrated. A simplified cell fractal model is created. In the model, the method of calculating the equivalent thermal conductivity of the porous foam is described and the fractal dimension is calculated. The mathematical formulas for the fractal equivalent thermal conductivity combined with gas and solid phase, for heat radiation equivalent thermal conductivity and for the total thermal conductivity, are deduced. However, the total effective heat flux is the summation of the heat conduction by the solid phase and the gas in pores, the radiation, and the convection between gas and solid phase. Fractal mathematical equation of effective thermal conductivity is derived with fractal dimension and vacancy porosity in the cell body. The calculated results have good agreement with the experimental data, and the difference is less than 5%. The main influencing factors are summarized. The research work is useful for the enhancement of adiabatic performance of foam materials and development of new materials.

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