Journal of Soils and Sediments

, Volume 15, Issue 4, pp 937–948 | Cite as

A modified method for estimating fine and coarse fractal dimensions of soil particle size distributions based on laser diffraction analysis

  • Hongtao Peng
  • Robert Horton
  • Tingwu Lei
  • Zhenchao Dai
  • Xiangping Wang
Soils, Sec2 • Global Change, Environ Risk Assess, Sustainable Land Use • Research Article



Particle size distribution (PSD) is one of the most commonly measured physical properties of soil. The fine fractal dimension, Df, and the coarse fractal dimension, Dc, are, respectively, based on the fine and coarse size fractions of soil particles. Laser diffraction effectively determines the volume PSD of soil. Original and modified methods for determining the Df and Dc of the volume PSD of soil are derived and presented in this work.

Materials and methods

The modified method is based on the assumption that the relationship between the number of particles and particle size is not linear. Df and Dc are determined using the original and modified methods to analyze volume PSD of 11 soil samples through laser diffraction based on the United States Department of Agriculture (USDA) and International Soil Science Society (ISSS) systems. Some soils have coarse fragments ranging from 2 to 1 mm (USDA system) or from 2 to 0.2 mm (ISSS system) in size, comprising 0 % of the total volume. As log 0 does not exist, the original and modified methods based on USDA or ISSS systems are unsuitable for estimating Dc. The arithmetic mean of the R2 values of the relevant log–log plots of all soil samples determined using the modified method to estimate Df is larger than that of the original method based on the USDA and ISSS systems. Using the modified method to estimate Df is therefore recommended.

Results and discussion

The overall trend of the values obtained indicates that the Df of coarse-textured soil approaches 2. If at least four decimal places are retained in estimations of Df, the probability of achieving identical Df values for any two soil samples with different size fractions is low. In this case, Df helps characterize soil texture. The arithmetic mean of the Df of all soil samples based on the USDA system is greater than that based on the ISSS system. Df is evidently dependent on selected fractions of separates present in a soil related to texture. The performance of the original and modified methods to estimate Df values based on the ISSS system is not good as indicated by F test at the significance level of 0.05.


The results of this study indicate that the original and modified methods based on the ISSS system are both not useful in estimating Df. We recommend that future studies of fine fractal dimensions be made with USDA particle size fractions.


Coarse fractal dimension Fine fractal dimension Particle size fraction Soil particle size distribution Soil texture 



International Soil Science Society


Particle size distribution


United States Department of Agriculture


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Hongtao Peng
    • 2
    • 3
  • Robert Horton
    • 4
  • Tingwu Lei
    • 1
    • 3
  • Zhenchao Dai
    • 5
  • Xiangping Wang
    • 6
  1. 1.College of Water Resources and Civil EngineeringChina Agricultural UniversityBeijingPeople’s Republic of China
  2. 2.University of Chinese Academy of SciencesBeijingPeople’s Republic of China
  3. 3.State Key Laboratory of Soil Erosion and Dryland Farming on the Loess Plateau, Institute of Soil and Water ConservationChinese Academy of Sciences & Ministry of Water ResourcesYanglingPeople’s Republic of China
  4. 4.Department of AgronomyIowa State UniversityAmesUSA
  5. 5.No. 2 Hydropower Force of Armed PoliceChongqingPeople’s Republic of China
  6. 6.Institute of Soil ScienceChinese Academy of SciencesNanjingPeople’s Republic of China

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