Particle size distribution models, their characteristics and fitting capability

Journal of Hydrology

Volumn 529, Issue , 2015, Pages 872-889

  Bayat, Hossein ^a   Rastgo, Mostafa ^a   Mansouri Zadeh, Moharram ^a   Vereecken, Harry ^b  

^a BU ALI SINA UNIVERSITY   (Iran)

^b FORSCHUNGSZENTRUM JÜLICH   (Germany)

Author keywords

Fitting; Mathematical PSD models; Models parameters; Particle size distribution

Indexed keywords

CURVE FITTING; ESTIMATION; FRACTALS; LIGHT TRANSMISSION; PARTICLE SIZE ANALYSIS; SIZE DISTRIBUTION; SOIL MECHANICS; SOILS;

FITTING; FITTING ACCURACY; MATHEMATICAL BASIS; PSD MODELS; SOIL HYDRAULIC PROPERTIES; THREE-PARAMETER WEIBULL; TWO-PARAMETER WEIBULL MODEL; VAN GENUCHTEN MODEL;

PARTICLE SIZE;

DATABASE; FRACTAL ANALYSIS; HYDRAULIC PROPERTY; NUMERICAL MODEL; PARTICLE SIZE; SIZE DISTRIBUTION;

EID: 84941985623     PISSN: 00221694     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jhydrol.2015.08.067     Document Type: Review

References (102)

1. Allen T. Particle Size Measurement 1996, vol. 2. Kluwer Academic Print on Demand.
2. Arya L.M., Paris J.F. A physicoempirical model to predict the soil moisture characteristic from particle-size distribution and bulk density data. Soil Sci. Soc. Am. J. 1981, 45(6):1023-1030.
3. Ashagrie Y., Zech W., Guggenberger G. Transformation of a podocarpus falcatus dominated natural forest into a monoculture eucalyptus globulus plantation at munesa, ethiopia: soil organic C, N and S dynamics in primary particle and aggregate-size fractions. Agric. Ecosyst. Environ. 2005, 106(1):89-98.
4. Aşkin T., Özdemir N. Soil bulk density as related to soil particle size distribution and organic matter content. Agriculture 2003, 9:52-56.
5. Bagarello V., Ferro V., Giordano G. Estimating soil particle-size distribution for Sicilian soils. J. Agric. Eng. 2009, 40(3):33-39.
6. Bagarello V., Provenzano G., Sgroi A. Fitting particle size distribution models to data from Burundian soils for the BEST procedure and other purposes. Biosyst. Eng. 2009, 104(3):435-441.
7. Bailey K. Numerical taxonomy and cluster analysis. Typol. Taxon. 1994, 34:24.
8. Bartoli F., Philippy R., Doirisse M., Niquet S., Dubuit M. Structure and self-similarity in silty and sandy soils: the fractal approach. J. Soil Sci. 1991, 42(2):167-185.
9. Baveye P., Boast C.W. Comments and letters to the editor. Urbana 1998, 51:61801.
10. Bayat H., Neyshabouri M., Mohammadi K., Nariman-Zadeh N. Estimating water retention with pedotransfer functions using multi-objective group method of data handling and ANNs. Pedosphere 2011, 21(1):107-114.
11. Bayat H., Neyshabouri M.R., Mohammadi K., Nariman-Zadeh N., Irannejad M. Improving water content estimations using penetration resistance and principal component analysis. Soil Till Res. 2013, 129:83-92.
12. Bayat H., Neyshabouri M.R., Mohammadi K., Nariman-Zadeh N., Irannejad M., Gregory A.S. Combination of artificial neural networks and fractal theory to predict soil water retention curve. Comput. Electron. Agr. 2013, 92:92-103.
13. Beke G., Lindwall C., Entz T., Channappa T. Sediment and runoff water characteristics as influenced by cropping and tillage practices. Can. J. Soil Sci. 1989, 69(3):639-647.
14. Bird N., Perrier E., Rieu M. The water retention function for a model of soil structure with pore and solid fractal distributions. Eur. J. Soil Sci. 2000, 51(1):55-63.
15. Bittelli M., Campbell G.S., Flury M. Characterization of particle-size distribution in soils with a fragmentation model. Soil Sci. Soc. Am. J. 1999, 63(4):782-788.
16. Boadu F., Long L. Statistical distribution of natural fractures and the possible physical generating mechanism. Pure Appl. Geophys. 1994, 142(2):273-293.
17. Brady N.C., Weil R.R. Elements of the Nature and Properties of Soils 2010, Pearson Educational International, Upper Saddle River, NJ.
18. Broersma K., Lavkulich L. Organic matter distribution with particle-size in surface horizons of some sombric soils in Vancouver Island. Can. J. Soil Sci. 1980, 60(3):583-586.
19. Brown W.K., Wohletz K.H. Derivation of the Weibull distribution based on physical principles and its connection to the Rosin-Rammler and lognormal distributions. J. Appl. Phys. 1995, 78(4):2758-2763.
20. Buchan G.D., Grewal K., Robson A. Improved models of particle-size distribution: an illustration of model comparison techniques. Soil Sci. Soc. Am. J. 1993, 57(4):901-908.
21. Buchanan S., So H., Kopittke P., Menzies N. Influence of texture in bauxite residues on void ratio, water holding characteristics, and penetration resistance. Geoderma 2010, 158(3):421-426.
22. Burgos P., Madejón E., Cabrera F. Nitrogen mineralization and nitrate leaching of a sandy soil amended with different organic wastes. Waste Manage. Res. 2006, 24(2):175-182.
23. Burnham K.P., Anderson D.R. Model Selection and Multimodel Inference. A Practical Information-Theoretic Approach 2002, Springer Science & Business Media.
24. Campbell G., Shiozawa S. Prediction of hydraulic properties of soils using particle-size distribution and bulk density data. Indirect Methods for Estimating the Hydraulic Properties of Unsaturated Soils 1992, 317-328. University of California, Riverside.
25. Carpinteri A., Pugno N. A multifractal comminution approach for drilling scaling laws. Powder Technol. 2003, 131(1):93-98.
26. Chiu C.-Y., Chen T.-H., Imberger K., Tian G. Particle size fractionation of fungal and bacterial biomass in subalpine grassland and forest soils. Geoderma 2006, 130(3):265-271.
27. Cornelis W.M., Ronsyn J., Van Meirvenne M., Hartmann R. Evaluation of pedotransfer functions for predicting the soil moisture retention curve. Soil Sci. Soc. Am. J. 2001, 65(3):638-648.
28. Cosby B., Hornberger G., Clapp R., Ginn T. A statistical exploration of the relationships of soil moisture characteristics to the physical properties of soils. Water Resour. Res. 1984, 20(6):682-690.
29. Craig R.F. Craig's Soil Mechanics 2004, CRC Press.
30. Dane J., Puckett W. Field soil hydraulic properties based on physical and mineralogical information. Indirect Methods for Estimating the Hydraulic Properties of Unsaturated Soils 1992, 389-403. US Salinity Lab, Riverside, CA.
31. Ersahin S., Gunal H., Kutlu T., Yetgin B., Coban S. Estimating specific surface area and cation exchange capacity in soils using fractal dimension of particle-size distribution. Geoderma 2006, 136(3):588-597.
32. Ferrer Julia M., Estrela Monreal T., Sánchez del Corral Jiménez A., García Meléndez E. Constructing a saturated hydraulic conductivity map of Spain using pedotransfer functions and spatial prediction. Geoderma 2004, 123(3):257-277.
33. Filgueira R.R., Fournier L.L., Cerisola C.I., Gelati P., García M.G. Particle-size distribution in soils: a critical study of the fractal model validation. Geoderma 2006, 134(3):327-334.
34. Filgueira R.R., Pachepsky Y.A., Fournier L.L. Time-mass scaling in soil texture analysis. Soil Sci. Soc. Am. J. 2003, 67(6):1703-1706.
35. Fréchet M. Sur la loi de probabilité de l'écart maximum. Ann. de la Soc. polonaise de Math. 1927, 6:93-116.
36. Fredlund M.D., Fredlund D., Wilson G.W. An equation to represent grain-size distribution. Can. Geotech. J. 2000, 37(4):817-827.
37. Froehlich D.C., Benson C.A. Sizing dumped rock riprap. J. Hydraul. Eng. 1996, 122(7):389-396.
38. Ghafoor A., Koestel J., Larsbo M., Moeys J., Jarvis N. Soil properties and susceptibility to preferential solute transport in tilled topsoil at the catchment scale. J. Hydrol. 2013, 492:190-199.
39. Gómez-Muñoz B., Bol R., Hatch D., García-Ruiz R. Carbon mineralization and distribution of nutrients within different particle-size fractions of commercially produced olive mill pomace. Bioresour. Technol. 2011, 102(21):9997-10005.
40. Gupta S., Larson W. Estimating soil water retention characteristics from particle size distribution, organic matter percent, and bulk density. Water Resour. Res. 1979, 15(6):1633-1635.
41. Harris C. The application of size distribution equations to multi-event comminution processes. Trans. AIME 1968, 241:343-358.
42. Hartigan J.A. Clustering Algorithms 1975, John Wiley & Sons Inc.
43. Haverkamp R.t., Parlange J.-Y. Predicting the water-retention curve from particle-size distribution: 1. Sandy soils without organic matter1. Soil Sci. 1986, 142(6):325-339.
44. Hillel D. Fundamentals of Soil Physics 1980, Academic Press, Inc. (London) Ltd.
45. Hocking R.R. A Biometrics invited paper. The analysis and selection of variables in linear regression. Biometrics 1976, 1-49.
46. Huang L., et al. Soil particle heterogeneity affects the growth of a rhizomatous wetland plant. PLoS ONE 2013, 8(7):e69836.
47. Hwang S.I. Effect of texture on the performance of soil particle-size distribution models. Geoderma 2004, 123(3):363-371.
48. Hwang S.I., Lee K.P., Lee D.S., Powers S.E. Models for estimating soil particle-size distributions. Soil Sci. Soc. Am. J. 2002, 66(4):1143-1150.
49. Imhoff S., da Silva A.P., Dexter A. Factors contributing to the tensile strength and friability of Oxisols. Soil Sci. Soc. Am. J. 2002, 66(5):1656-1661.
50. Imhoff S., Da Silva A.P., Fallow D. Susceptibility to compaction, load support capacity, and soil compressibility of Hapludox. Soil Sci. Soc. Am. J. 2004, 68(1):17-24.
51. Jaky J. Soil Mechanics 1944, Egyetemi Nyomada, Budapest, Hungarian.
52. Kays B.L., Patterson J.C. Soil drainage and infiltration. Urban Forest Soils: A Reference Workbook 1982, SUNY-Coll. Environ. Sci. and Forestry, Syracuse, NY.
53. Kone B., et al. Modelling the relationship between soil color and particle size for soil survey in ferralsol environments. Soil Environ. (Pakistan) 2009.
54. Kozak E., Sokołowska Z., Stepniewski W., Pachepsky Y.A., Sokołowski S. A modified number-based method for estimating fragmentation fractal dimensions of soils. Soil Sci. Soc. Am. J. 1996, 60(5):1291-1297.
55. Kravchenko A., Zhang R. Estimating the soil water retention from particle-size distributions: a fractal approach. Soil Sci. 1998, 163(3):171-179.
56. Lamorski K., et al. Modelling soil water retention using support vector machines with genetic algorithm optimisation. Sci. World J. 2014, 2014:1-10.
57. Lassabatere L., et al. Beerkan estimation of soil transfer parameters through infiltration experiments-BEST. Soil Sci. Soc. Am. J. 2006, 70(2):521-532.
58. Leij, F., Alves, W., van Genuchten, M.T., Williams, J., 1996. The UNSODA unsaturated soil hydraulic database, version 1.0. EPA Report, EPA/600, 96, pp. 095.
59. Ma W., Li X.-X., Li C.-J. Modulation of soil particle size and nutrient availability in the maize rhizosheath. Pedosphere 2011, 21(4):483-490.
60. Macías-García A., Cuerda-Correa E.M., Díaz-Díez M. Application of the Rosin-Rammler and Gates-Gaudin-Schuhmann models to the particle size distribution analysis of agglomerated cork. Materi. Charact. 2004, 52(2):159-164.
61. Mandelbrot B.B. The Fractal Geometry of Nature 1983, vol. 173. Macmillan.
62. Mandelbrot B.B. The Fractal Geometry of Nature 1983, Times Books.
63. MATLAB, 2012. The MathWorks. Inc., Natick, Massachusetts, United States.
64. Millan H., Gonzalez-Posada M., Aguilar M., Dominguez J., Cespedes L. On the fractal scaling of soil data. Particle-size distributions. Geoderma 2003, 117(1):117-128.
65. Molina N., Caceres M., Pietroboni A. Factors affecting aggregate stability and water dispersible clay of recently cultivated semiarid soils of Argentina. Arid Land Res. Manage. 2001, 15(1):77-87.
66. Nemes A., Schaap M., Leij F., Wösten J. Description of the unsaturated soil hydraulic database UNSODA version 2.0. J. Hydrol. 2001, 251(3):151-162.
67. Nesbitt A., Breytenbach W. A particle size distribution model for manufactured particulate solids of narrow and intermediate size ranges. Powder Technol. 2006, 164(3):117-123.
68. Nieder R., Benbi D.K., Scherer H.W. Fixation and defixation of ammonium in soils: a review. Biol. Fertil. Soils 2011, 47(1):1-14.
69. Nimmo J. Porosity and pore size distribution. Encycl. Soils Environ. 2004, 3:295-303.
70. Pachepsky Y., Gimenez D., Logsdon S., Allmaras R., Kozak E. Comment on number-size distributions, soil structure, and fractals-On interpretation and misinterpretation of fractal models-Reply. Soil. Sci. Soc. 1997, 61(6):1800-1801. AMER 677 SOUTH SEGOE ROAD, MADISON, WI 53711.
71. Panayiotopoulos K., Kostopoulou S., Hatjiyiannakis E. Variation of physical and mechanical properties with depth in Alfisols. Int. Agrophys. 2004, 18(1):55-64.
72. Perrier E., Bird N. Modelling soil fragmentation: the pore solid fractal approach. Soil Till. Res. 2002, 64(1):91-99.
73. Perrier E., Bird N. The PSF model of soil structure: a multiscale approach. Scaling methods in soil physics 2003, 1-18.
74. Perrier E., Bird N., Rieu M. Generalizing the fractal model of soil structure: the pore-solid fractal approach. Geoderma 1999, 88(3):137-164.
75. Puckett W., Dane J., Hajek B. Physical and mineralogical data to determine soil hydraulic properties. Soil Sci. Soc. Am. J. 1985, 49(4):831-836.
76. Rawls W., Brakensiek D., Saxton K. Estimation of soil water properties. Trans. ASAE 1982, 25(5):1316-1320.
77. Rizea N., Radu L., Rodica L., Stroe V.M., Aldea M.M. Reaction buffering capacity of soils in the zlatna area. Sci. Pap. Ser. A LII 2009, 70.
78. Rosin P., Rammler E. The laws governing the fineness of powdered coal. J. Inst. Fuel 1933, 7(31):29-36.
79. Rousseva S. Data transformations between soil texture schemes. Eur. J. Soil Sci. 1997, 48(4):749-758.
80. Russel, M., 1957. Physical properties in soil. US Agricultural Year Book, pp. 31-38.
81. Sarle W.S. Algorithms for clustering data. Technometrics 1990, 32(2):227-229.
82. Schuhmann, R., 1940. Principles of Comminution, I-Size Distribution and Surface Calculations. American Institute of Mining, Metallurgical and Petroleum Engineers Technical Publication 1189. Mining Technology, vol. 4, pp. l-11.
83. Semmel H., Horn R., Hell U., Dexter A., Schulze E. The dynamics of soil aggregate formation and the effect on soil physical properties. Soil Technol. 1990, 3(2):113-129.
84. Senesi N., Xing B., Huang P.M. Biophysico-Chemical Processes Involving Natural Nonliving Organic Matter in Environmental Systems, vol. 2 2009, John Wiley & Sons.
85. Shi Z., et al. Soil erosion processes and sediment sorting associated with transport mechanisms on steep slopes. J. Hydrol. 2012, 454:123-130.
86. Solomentsev, E., 2001. Maximum-modulus principle. Hazewinkel, Michiel, Encyclopaedia of Mathematics.
87. Sumner M.E. Handbook of Soil Science 1999, CRC Press.
88. Tuhkuri J. Analysis of ice fragmentation process from measured particle size distributions of crushed ice. Cold Reg. Sci. Technol. 1994, 23(1):69-82.
89. Turcotte D. Fractals and fragmentation. J. Geophys. Res.: Solid Earth (1978-2012) 1986, 91(B2):1921-1926.
90. Turcotte D.L. Fractals and Chaos in Geology and Geophysics 1997, Cambridge Univ. Press, Cambridge, UK, 398 p.
91. Tyler S.W., Wheatcraft S.W. Application of fractal mathematics to soil water retention estimation. Soil Sci. Soc. Am. J. 1989, 53(4):987-996.
92. Tyler S.W., Wheatcraft S.W. Fractal scaling of soil particle-size distributions: analysis and limitations. Soil Sci. Soc. Am. J. 1992, 56(2):362-369.
93. Vereecken H., et al. Using pedotransfer functions to estimate the van Genuchten-Mualem soil hydraulic properties: a review. Vadose Zone J. 2010, 9(4):795-820.
94. Vipulanandan C., Ozgurel H.G. Simplified relationships for particle-size distribution and permeation groutability limits for soils. J. Geotech. Geoenviron. Eng. 2009, 135(9):1190-1197.
95. Weibull W. A statistical distribution function of wide applicability. J. Appl. Mech. 1951, 18(3):293-297.
96. Wohletz K., Sheridan M., Brown W. Particle size distributions and the sequential fragmentation/transport theory applied to volcanic ash. J. Geophys. Res.: Solid Earth (1978-2012) 1989, 94(B11):15703-15721.
97. Wu Q., Borkovec M., Sticher H. On particle-size distributions in soils. Soil Sci. Soc. Am. J. 1993, 57(4):883-890.
98. Xu G., Li Z., Li P. 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 2013, 101:17-23.
99. Yang P., Luo Y., Shi Y. Soil fractal character token by particle-mass distribution. Chinese Sci. Bull 1993, 38:1896-1899.
100. Young I., Crawford J., Anderson A., McBratney A. Comment on number-size distributions, soil structure, and fractals. Soil Sci. Soc. Am. J. 1997, 61(6):1799-1800.
101. Zhuang J., Jin Y., Miyazaki T. Estimating water retention characteristic from soil particle-size distribution using a non-similar media concept. Soil Sci. 2001, 166(5):308-321.
102. Zobeck T.M., Gill T.E., Popham T.W. A two-parameter Weibull function to describe airborne dust particle size distributions. Earth Surf. Proc. Land. 1999, 24(10):943-955.