Prediction of Specific Surface area and Cation Exchange Capacity Using Fractal Dimension of Soil Particle Size Distribution

Document Type : Research Paper


1 Ph.D student of soil science, Tehran University

2 Ph.D student of soil science, Tabriz University

3 Associate professor, Faculty of Agriculture, Guilan university

4 Assistance Professor, Faculty of Agriculture, Guilan university


Cation exchange capacity and specific surface area are among some of the important soil characteristics the direct measurement of which is laborious, costly and time consuming. Therefore, fractal dimension of particle size distribution has been widely studied in relation with many such dynamic and static processes as transmission of water and solutes, water holding capacity, heat storage and conductivity, etc., and as a useful parameter, it has been proposed for property estimation as related to soil texture. Throughout the present research, the relationship between fractal dimensions of particle size distributions (Dm) vs. specific surface and cation exchange capacity for 40 soil samples (32 samples for finding the empirical functions and 8 for testing of the derived functions), from Gilevan region, with textures ranging from sandy to clay and different parent materials were evaluated. The obtained results showed that the value of Dm of the soil samples ranged from 2.45 to 2.99; the finer the soil texture, the larger the fractal dimension Dm. The Dm-specific surface area and Dm-cation exchange capacity relationships were described by power functions (R2=0.87 and 0.80, (significant at probability level of 0.01)), respectively. Testing of Dm-clay content, Dm-specific surface area and Dm-cation exchange capacity relationships showed significant correlation (probability level of 0.01) for the measured vs. predicted data. The results indicated that Dm can be used as an integrating index for estimating the specific surface area as well as cation exchange capacity of soils from particle-size distribution, useful in modelings and simulations.


Ahmadi, A., Neyshabouri, M. R., and Asadi, H. (2011). Relationship between Fractal Dimension of Particle Size Distribution and Some Physical Properties of Soils. Water and Soil Science Journal of Tabriz University, 20.1(4), 72-81. (In Farsi)
Amini M., Abbaspour, K. C., Khademi, H., Fathianpour, N., Afyuni, M., and Schulin, R. (2005). Neural Network Models to Predict Cation Exchange Capacity in Arid Regions of Iran. European Journal of Soil Science, 56:551-559.
Arnepalli, D. N., Shanthakumar, S., Hanumantha, R. B., and Singh, D. N. (2008). Comparison of methods for determining specific-surface area of fine-grained soils. Geotechnical and Geological Engineering, 26, 121-132.
Bayat, H. (2009). Development of pedotransfer functions to predict soil moisture curve using artificial neural networks and group method of data handling by using fractal parameters and principle component as predictors. Ph. D.
اسماعیل نژاد و همکاران: پیش بینی سطح ویژه و ظرفیت تبادل کاتیونی ... 473
dissertation, University of Tabriz, pp. 274. (In Farsi)
Bayat, H., Davatgar, N., and Moallemi, S. (2012). Using of Specific Surface to Improve the Prediction of Soil CEC by Artificial Neural Networks. Water and Soil Science Journal of Tabriz University, 21(4), 105-119. (In Farsi)
Bittelli, M., Campbell, G. S., and Flury, M. (1999). Characterization of particle-size distribution in soils with a fragmentation model. Soil Science Society of American Journal, 63, 782–788.
Bleam, W. F. (1990). The nature of cation-substitution sites in phyllosilicates. Clays and Clay Minerals, 38(5), 527–536.
Burt, R. (2004). Soil survey laboratory methods manual. Soil survey investigations report No. 42, Version 4. United States Department of Agriculture, Natural Resources Conservation Service, National Soil Survey Center.
Cerato, A. B. and Lutenegger, A. J. (2002). Determination of surface area of fine grained soils by the ethylene glycol monoethyl ether (EGME) method. Geotechnical Testing Journal, 25, 1–7.
Ersahin, S., Gunal, H., Kutlu, T., Yetgin, B., and Coban, S. (2006). Estimating specific surface area and cation exchange capacity in soils using fractal dimension of particle-size distribution. Geoderma 136, 588–597.
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.
Gunal, H., Ersahin, S., Buket Y. U., Budak, M., and Acir, N. (2011). Soil particle size distribution and solid fractal dimension as influenced by pretreatments. Journal of Agricultural Sciences, 17, 217-229.
Hepper, E. N., Buschiazzo, D. E., Hevia, G. G., Urioste, A., and Anton, L. (2006). Clay mineralogy, cation exchange capacity and specific surface area of loess soils with different volcanic ash contents. Geoderma, 135, 216-223.
Huang, G. and Zhang, R. (2005). Evaluation of soil water retention curve with the pore–solid fractal model. Geoderma, 127, 52–61.
Hwang, S. I., Lee, K. P., Lee, D. S., and Powers, S. E. (2002). Models for estimating soil particle-size distributions. Soil Science Society of America Journal, 66, 1143–1150.
Khawmee, K., Suddhiprakarn, A., Kheoruenromne, I., and Singh, B. (2013). Surface charge properties of kaolinite from Thai soils. Geoderma, 192, 120-131.
Koorevaar, P., Menelik, G., and Dirksen, C. (1983). Elements of Soil Physics. Elsevier Science Publishers, Netherlands.
Kutlu, T., Ersahin, S., and Yetgin, B. (2008). Relations between solid fractal dimension and some physical properties of soils formed over alluvial and colluvial deposits. Food Agriculture Environment, 6, 445-449.
Lal, R. and Shukla, M. K. (2004). Principles of Soil Physics. Marcel Dekker, Inc. New York.
Liu, X., Zhang, G., Heathman, G. C., Wang, Y., and Huang, C. (2009) Fractal features of soil particle-size distribution as affected by plant communities in the forested region of Mountain Yimeng, China. Geoderma, 154, 123-130.
Mandelbort, B. B. (1999). The Fractal Geometry of Nature. W.H. Freeman and Company, New York.
Moallemi, S. and Davatgar, N. (2011). Comparison of regression and artificial neural network pedotransfer for CEC estimation , Guilan soils. Soil and Water Siences Journal of Esfahan University, 55, 169-181. (In Farsi)
Moallemi, S., Davatger, N., and Darighgoftar, F. (2009). Relationship between CEC and some physical and chemical properties in Guilan soils. Soil Researches, 23(2), 173-179. (In Farsi)
Neyshabouri, M. R., Ahmadi, A., Rouhipuor, H., Asadi, H., and Irannajad, M. (2011). Soil texture fractions and fractal dimension of particle size distribution as predictors of interrill erodibility. Turkish Journal of Agriculture and Forestry, 35, 95-102.
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 Science Society of America Journal, 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 Engineering, 90(2), 227-234.
Sepaskhah, A. R. and Tafteh, A. (2013). Pedotransfer function for estimation of soil-specific surface area using soil fractal dimension of improved particle-size distribution. Archives of Agronomy and Soil Science, 59(1), 93–103.
Sepaskhah, A. R., Tabarzad, A., and Fooladman, H. R. (2010). Physical and empirical models for estimation of specific surface area of soils. Archives of Agronomy and Soil Science, 56(3), 325-335.
Seybold, C. A., Grossman, R. B., and Reinsch, T. G. (2005). Predicting cation exchange capacity for soil survey using linear models. Soil Science Society of America Journal, 69, 856-863.
Sokolowska, Z., Hajnos, M., Hoffmann, C., Renger, M., and Sokolowski, S. (2001). Comparison of fractal dimensions of soils estimated from adsorption isotherms, mercury intrusion, and particle-size distribution. Journal of Plant Nutrition and Soil Science, 164(5), 591–599.
Sposito, G. (2008). The Chemistry of Soils. 2nd edition, Oxford University Press, New York.
Su, Y. Z., Zhao, H. L., Zhao, W. Z., and Zhang, T. H. (2004). Fractal features of soil particle size
474 تحقیقات آب و خاک ایران، دورة 45 ، شمارة 4، زمستان 1393
distribution and the implication for indicating desertification. Geoderma, 122, 43–49.
Tang, L., Zeng, G. M., Nourbakhsh, F., and Shen, G. L. (2009). Artificial neural network approach for predicting cation exchange capacity in soil based on physico-chemical properties. Environmental Engineering Science, 26, 137-146.
Timlin, D. J., Ahuja, L. R., Pachepsky, Y. A., Williams, R. D., Giménez, D., and Rawls, D. (1999). Use of Brooks–Corey parameters to improve estimates of saturated conductivity from effective porosity. Soil Science Society of America Journal, 63, 1086–1092.
Tyler, S. W. and Wheatcraft, S. W. (1992). Fractal scaling of soil-particle size distributions: analysis and limitations. Soil Science Society of America Journal, 56, 362–369.
Wang, D., Fu, B., Zhao, W., Hu, H., and Wang, Y. (2008). Multifractal characteristics of soil particle size distribution under different land-use types on the Loess Plateau, China. Catena, 72, 29–36.
Wang, X., Li, M. H., Liu, S., and Liu, G. (2006). Fractal characteristics of soils under different land-use patterns in the arid and semiarid regions of the Tibetan Plateau, China. Geoderma, 134, 56–61.
Xu, G., Li, Z., and Li, P. (2013) Fractal features of soil particle-size distribution and total soil nitrogen distribution in a typical watershed in the source area of the middle Dan River, China. Catena, 101, 17-23.
Xu, Y. (2004). Calculation of unsaturated hydraulic conductivity using a fractal model for the pore-size distribution. Computers and Geotechnics, 31(7), 549–557.
Zhao, S., Su, J., Yang, Y., 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. Agricultural Sciences in China, 5(7), 530-538.