Amirabedi H., Asghari Sh., Mesri Gandoshmin T., Balandeh N. and Johari E. 2019. Estimating the soil saturated hydraulic conductivity in Ardabil Plain soils using artificial neural networks and regression models. Applied Soil Research. 7(4):124-136. (In Persian)
Banitalebi G., Beigi Harchegani H., and Ghobadinia M. 2017. The Effect of long- term irrigation with municipal treated wastewater on the saturated hydraulic conductivity of a silt loam soil and its estimation- a case study. Journal of Water and Soil Science, 21(1): 171-184. (In Persian)
Bird N. R. A., Perrier E., and Rieu M. 2000. The water retention function for a model of soil structure with pore and solid fractal distributions. European Journal of Soil Science, 51(1): 55–63.
Brooks R.H., and Corey A.T., 1964. Hydraulic Properties of Porous Media. Hydrology Papers 3, Colorado State University, Fort Collins, 27 p.
Chari M M., and Dahmardeh Ghaleno, M. R. 2019. Evaluating fractal dimension of the soil particle size distributions and soil water retention curve obtained from soil texture components. Archives of Agronomy and Soil Science, 1-11. doi:10.1080/03650340.2019.1686140
Cihan A., Perfect E., and Tyner J. S. 2007. Water retention models for scale-variant and scale invariant drainage of mass prefractal porous media. Vadose Zone Journal, 6(4): 786–792.
Deinert M.R., Dathe A., Parlange J.Y., and Cady K.B. 2008. Capillary pressure in a porous medium with distinct pore surface and pore volume fractal dimensions. Physical Review, E77 (2): 021203.
Gao Y., and Sun D. 2017. Soil-water retention behavior of compacted soil with different densities over a wide suction range and its prediction. Computers and Geotechnics
, 91: 17–26, https://doi.org/10.1016/j.compgeo.2017.06.016
Ghanbarian B., and Daigle H. 2015. Fractal dimension of soil fragment mass-size distribution: A critical analysis. Geoderma, 245–246: 98–103.
Ghanbarian, B., and Sahimi M. 2017. Electrical conductivity of partially saturated packings of particles. Transport in Porous Media, 118: 1–16.
Ghanbarian B., Hamamoto S., Kawamoto K., Sakaki T., Moldrup P., Nishimura T., and Komatsu T. 2018. Saturation-dependent gas transport in sand packs: Experiments and theoretical applications, Advances in Water Resources, 122: 139–147.
Ghanbarian B., Ioannidis M. A., and Hunt A. G. 2017a. Theoretical insight into the empirical tortuosity-connectivity factor in the Burdine-Brooks-Corey water relative permeability model. Water Resources Research, 53: 10395-10410.
Ghanbarian B., Hunt A. G., Skaggs T. H., and Jarvis N. 2017b. Upscaling soil saturated hydraulic conductivity from pore throat characteristics. Advances in Water Resources, 104:105-113. doi: 10.1016/j.advwatres.2017.03.016.
Ghanbarian, B., Hunt A. G., and Daigle H., 2016. Fluid flow in porous media with rough pore-solid interface, Water Resources Research, 52: 2045–2058.
Ghanbarian-Alavijeh B., and Hunt A. G. 2012 Unsaturated hydraulic conductivity in porous media: Percolation theory, Geoderma, 187–188: 77-84.
Ghanbarian-Alavijeh B., Milla´n H., and Huang G. 2011. A review of fractal, prefractal and pore-solid-fractal models for parameterizing the soil water retention curve, Canadian Journal of Soil Science, 91: 1-14., doi:10.4141/CJSS10008.
Gimenez D., Perfect E., Rawls W. J., and Pachepsky Y. 1997. Fractal models for predicting soil hydraulic properties: a review. Engineering Geology, 48: 161–183.
Huang G., and Zhang R. 2005. Evaluation of soil water retention curve with the pore–solid fractal model. Geoderma, 127(1–2): 52–61.
Hunt A. G., and Gee G. W. 2002. Application of critical path analysis to fractal porous media: comparison with examples from the Hanford site. Advances in Water Resources, 25: 129–146.
Hunt A. G., Ewing R. P., and Horton R. 2013. What’s Wrong with Soil Physics? Soil Science Society of America Journal, 77(6): 1877-1887.
Hunt A., Ewing R., and Ghanbarian B. 2014. Fractal Models of Porous Media. In: Percolation Theory for Flow in Porous Media. Lecture Notes in Physics, vol. 880. Springer, Cham.
Millan H., and Gonzalez-Posada M. 2005. Modelling soil water retention scaling. Comparison of a classical fractal model with a piecewise approach. Geoderma, 125: 25–38.
Millán H., Aguilar M., Domínguez J., Céspedes L., Velasco E., and González M., 2006. A note on the physics of soil water retention through fractal parameters. Fractals, 14: 143-148.
Mishra S., and Parker J. C. 1990. On the relation between saturated conductivity and capillary retention characteristics. Ground Water, 28(5): 775-777.
Nasta P., Vrugt J. A., and Romano N., 2013. Prediction of the saturated hydraulic conductivity from Brooks and Corey's water retention parameters. Water Resources Research, 49(5): 2918-2925.
Nimmo J. R., and Perkins K.S. 2002. Aggregate stability and size distribution. In Dane, J.H., and Topp, GC., eds., Methods of Soil Analysis, part 4. Physical methods: Soil Science Society of America Journal, Madison, pp. 317–328.
Perfect E. 1999. Estimating mass fractal dimensions from water retention curves. Geoderma, 88: 221–231.
Perfect E., and Kay B. D. 1995. Applications of fractals in soil and tillage research: a review. Soil and Tillage Research, 36(1–2): 1–20.
Perrier E., Bird N., and Rieu M. 1999. Generalizing a fractal model of soil structure: the pore-solid fractal approach. Geoderma, 88: 137–164.
Rawls W. J., Brakensiek D. L., and Logsdon S. D. 1993. Predicting saturated hydraulic conductivity utilizing fractal principles. Soil Science Society of America Journal, 57: 1193–1197.
Rezaei Abajelu E., and Zeinalzadeh K. 2017. Two and Three-Phases Fractal Models Application in Soil Saturated Hydraulic Conductivity Estimation. Journal of Water and Soil, 30(6):1905-1917. (In Persian)
Rieu M., and Sposito G. 1991. Fractal fragmentation, soil porosity, and soil water properties: I. Theory, II. Applications. Soil Science Society of America Journal, 55: 1231–1244.
Russell A. R., and Buzzi O. 2012. A fractal basis for soil-water characteristics curves with hydraulic hysteresis, Ge´otechnique, 62(3): 269-274.
Shaker Shahmarbeigloo P., Khodaverdiloo H. and Momtaz H.R. 2019. Testing of new inputs to predict near-saturated soil hydraulic conductivity. Applied Soil Research, 7(1): 54-69. (In Persian)
Tao G., Chen Y., Xiao H., Chen Q., and Wan J. 2019. Determining Soil-Water Characteristic Curves from Mercury Intrusion Porosimeter Test Data Using Fractal Theory. Energies, 12(752): 1-15.
The MathWorks Inc. R2017a. MATLAB: The language of technical computing. Version 9.2. Natick, MA.
Tyler S. W., and Wheatcraft S. W. 1989. Application of fractal mathematics to soil water retention estimation. Soil Science Society of America Journal, 53)4(: 987–996.
Tyler S.W., and Wheatcraft S.W. 1990. Fractal processes in soil water retention. Water Resources Research, 26: 1047–1054.
Van Genuchten M. T. 1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journal, 44(5): 892-898.
Wang K., Zhang R., and Wang F. 2005. Testing the pore-solid fractal model for the soil water retention function. Soil Science Society of America Journal, 69(3): 776–782.
Wentworth, C. K. 1922. A scale of grade and class terms for clastic sediments. The journal of geology 30(5), 377-392.
Yu B., Cai J., and Zou M. 2009. On the physical properties of apparent two-phase fractal porous media. Vadose Zone Journal, 8(1): 177–186.