Comparative evaluation of soil aggregate stability using classical and fractal methods

Document Type : Original Research Paper


Assistant Professor, Islamic Azad University, Science and Research Branch, Tehran, Iran


Improving water and soil productivity and its management by considering soil structure, soil textures and soil physics parameters are an important criterion for the suitable management of soil and water resources. One of the relatively new methods proposed to explain soil structure in a quantitative manner is the so-called fractal geometry concept. In this concept, by determining the fractal dimension of bulk soil, the stability of aggregates can be quantitatively analyzed at different scales. The objective of this study has been to quantify the soil structure stability using some classic indicators and also fractal approach in a large scale. Consequently, 41 intact soil samples were taken from an agricultural area and their particle size distribution, soil bulk density and aggregate bulk density, were measured. The weighted mean diameter and geometric mean diameter of both dry and wet aggregates were measured using the dry and wet sieving method. The fractal dimensions of all dry and wet aggregates were obtained using the fractal models of Mandelbrot, Tyler-Wheatcraft and Rieu-Sposito. The results indicated that fractal dimensions of the number-size model of Mandelbrot for dry sieve series and the number-size model of Rieu-Sposito in the wet sieve series perform quite well (R2=0.82). These two models could have the suitable determination coefficient with classical geometric mean and weighted mean diameters of aggregates (R2=0.69).


Main Subjects

Dathe, A., Eins, S., Niemeyer, J. and Gerold, G. (2001). The surface fractal dimension of the soil-pore interface as measured by image analysis. Geoderma, 103: 203-229.
Ding, Q. and Ding, W. (2007). Comparing stress wavelets with fragment fractals for soil structure quantification. Soil Till. Res, 93: 316–323.
Duhour, A., Costa, C., Momoa, F., Falco, L. and Malacalza, L. (2009). Response of earthworm communities to soil disturbance: Fractal dimension of soil and species’ rank-abundance curves. Appl, Soil Ecol, 43: 83–88.
Eghbal, B., Mielke, L.N., Calvo, G.A. and Wilhelm, W.W. (1993). Fractal description of soil fragmentation for various tillage methods. Soil Sci. Soc. Am. J., 57: 1337-1341.
Filgueira, R.R., Fournier, L.L., Cerisola, C.I., Gelati, P. and Garcia, M.G. (2006). Particle–size distribution in soils: a critical study of the fractal model validation. Geoderma, 134: 327–334.
Gülser, C. (2006). Effect of forage cropping treatments on soil structure and relationships with fractal dimensions. Geoderma, 131: 33-44.
Halley, J.M., Hartley, S., Kallimanis, A.S., Kunin, W.E., Lennon, J.J. and Sgardelis, S.P. (2004). Uses and abuses of fractal methodology in ecology. Ecology Letters, 7: 254–271.
Harris, R.F., Chesers, G. and Allen, O.N. (1965). Dynamics of soil aggregation. Advance in Agr, 18: 107-160.
Lal, R. and Pierce, R.J. (Eds.). (1991). Soil Management for Sustainability. Soil and Water Conservation Society, Ankeny, Iowa, USA.
Leao, T.P. and Perfect, E. (2010). Modeling water movement in horizontal columns using fractal theory. Scientific Electronic Library Online, 34: 1463-1468.
Mandelbrot, B.B. (1977). Fractals-form, chance and dimension. Freeman Company, San Francisco, California, USA.
Mandelbrot, B.B. (1982). The fractal geometry of nature. W.H. Freeman, San francisco, CA, USA.
Miao, C.Y., Wang, Y.F. and Wei, X. (2007). Fractal characteristics of soil particles in surface layer of black soil. Chin. Appl. Ecol. J., 1(9): 1987–1993. In Chinese.
Mohammadian Khorasani, Sh., Homaee, M. and Pazira, E. (2020). Investigating the ability of fractal models to estimate retention curve to improve water and soil resources management. Water Productivity Journal, 1(1): 39-50.
Montero, E.R. (2005). Dimensions analysis of soil particle–size distributions. Ecol. Model, 182: 305–315.
Perfect, E. and Blevins, R.L. (1997). Fractal characterization of soil aggregation and fragmentation as influenced by tillage treatment. Soil Sci. Soc. Am. J., 61: 896-900.
Perfect, E. and Kay, B.D. (1991). Fractal theory applied to soil aggregation. Soil Sci. Soc. Am. J., 55: 1552-1558.
Perfect, E., Kenst, A.B., Diaz-Zorita, M. and Grove, J.H. (2004). Fractal analysis of soil water desorption data collected on disturbed samples with water activity meters. Soil Sci. Soc. Am. J., 68: 1177–1184.
Pirmoradian, N., Sepaskhah, A.R. and Hajabbasi, M.A. (2005). Application of fractal theory to quantify soil aggregate stability as influenced by tillage treatments. Biosystems Engin, 90(2): 227-234.
Rieu, M. and Sposito, G. (1991a). Fractal fragmentation, soil porosity and soil water properties: I. Theory. Soil Sci. Soc. Am. J., 55: 1231-1238.
Rieu, M. and Sposito, G. (1991b). Fractal fragmentation, soil porosity and soil water properties: II. Applications. Soil Sci. Soc. Am. J., 55: 1239-1244.
Su, Y.Z., Zhao, H.L., Zhao, W.Z. and Zhang, T.H. (2004). Fractal features of soil particle size distribution and the implication for indicating desertification. Geoderma, 122: 43-49.
Tyler, S.W. and Wheatcraft, S.W. (1992). Fractal scaling of soil particle-size distribution: Analysis and limitations. Soil Sci. Soc. Am. J., 56: 362-369.
Zhao, S.W., Su, J., Yang, Y.h., Liu, N., Wu, J. and Shangguan, Z. (2006). A fractal method of estimating soil structure changes under different vegetations on Ziwuling mountains of the Loess plateau, China. Chin. Agric. Sci. J., 5(7): 530-538.
Zhou, X., Persaud, N. and Wang, H. (2004). Periodicities and scaling parameters of daily rainfall over semi-arid Botswana. Ecological Modeling, 182: 371–378.