Geomechanics and Engineering

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An optimized method based on fractal theory to calculate particle size distribution

  • Zhang, Zhihong (Key Laboratory of Urban Security & Disaster Engineering, Ministry of Education, Beijing University of Technology) ;
  • Yang, Fan (Key Laboratory of Urban Security & Disaster Engineering, Ministry of Education, Beijing University of Technology) ;
  • Li, Yanyan (Key Laboratory of Urban Security & Disaster Engineering, Ministry of Education, Beijing University of Technology)
  • Received : 2020.03.10
  • Accepted : 2021.11.04
  • Published : 2021.11.25
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Abstract

Particle size distribution has a great influence on the physical properties of granular soils. As an important packing material for engineering, the particle size distribution of granular soils needs to be optimized to yield optimal physical and mechanical performance. There are unknown parameters in existing calculation methods for particle size distribution of granular soils. In order to calculate the optimal particle size distribution curve to reach the densest state under existing conditions without unknown parameters, an optimized method has been proposed based on fractal theory in which all parameters can be obtained by particle screening. With this method, particle size distributions of granular soils can be easily quantified. Compared with experimental data obtained by other researchers, the physical characteristics of soils with a better PSD are better, suggesting the superiority of the proposed method. The fractal dimension of good PSDs calculated in this study ranges from 2.21 to 2.63. Further, laboratory consolidation tests show that the deformation of the prepared specimens calculated by the new method is smaller than that of other specimens with different particle size distributions, which further validates the proposed method.

Keywords

Acknowledgement

This work was funded by National Key R&D Program of China (2018YFC1505001).

References

  1. Abdel-Jawad, Y.A. and Abdullah, W.S. (2002), "Design of maximum density aggregate grading", Construct. Build. Mater., 16(8), 495-508. https://doi.org/10.1016/s0950-0618(02)00032-6.
  2. Altuhafi, F., Baudet, B. and Sammonds, P. (2010), "The mechanics of subglacial sediment: An example of new transitional behaviour", Canadian Geotech. J., 47(7), 775-790. https://doi.org/10.1139/T09-136.
  3. Altuhafi, F., Baudet, B.A. and Sammonds, P. (2011a), "On the particle size distribution of a basaltic till", Soils Foundations, 51(1), 113-121. https://doi.org/10.3208/sandf.51.113.
  4. Altuhafi, F. and Baudet, B.A. (2011b), "A hypothesis on the relative roles of crushing and abrasion in the mechanical genesis of a glacial sediment", Eng. Geology, 120(1), 1-9. https://doi.org/10.1016/j.enggeo.2011.03.002.
  5. Altuhafi, F.N. and Coop, M.R. (2011), "Changes to particle characteristics associated with the compression of sands", Geotechnique, 61(6), 459-471. https://doi.org/10.1680/geot.9.P.114.
  6. Bayat, H., Rastgo, M., Zadeh, M.M. and Vereecken, H. (2015), "Particle size distribution models, their characteristics and fitting capability", J. Hydrology, 529, 872-889. https://doi.org/10.1016/j.jhydrol.2015.08.067.
  7. Dai, B. B., Yang, J., Gu, X. Q. and Zhang, W. (2019), "A numerical analysis of the equivalent skeleton void ratio for silty sand", Geomech. Eng., 17(1):19-30. https://doi.org/10.12989/gae.2019.17.1.019.
  8. Bird, N.R.A., Perrier, E. and Rieu, M. (2010), "The water retention function for a model of soil structure with pore and solid fractal distributions", Eur. J. Soil Sci., 51(1), 55-63. https://doi.org/10.1046/j.1365-2389.2000.00278.x.
  9. Ghasemy, A., Rahimi, E. and Malekzadeh, A. (2019), "Introduction of a new method for determining the particle-size distribution of fine-grained soils", Measurement, 132, 79-86. https://doi.org/10.1016/j.measurement.2018.09.041.
  10. Jian, G. and Jun, L. (2017), "Analysis of the thresholds of granular mixtures using the discrete element method", Geomech. Eng., 12(4), 639-655. https://doi.org/10.12989/gae.2017.12.4.639.
  11. Hyodo, M., Wu, Y. and Kajiyama, S. (2017), "Effect of fines on the compression behaviour of poorly graded silica sand", Geomech. Eng., 12(1), 126-138. https://doi.org/10.12989/gae.2017.12.1.127.
  12. Lamorski, K., Slawinski, C., Moreno, F., Barna, G., Skierucha, W., and Arrue, J. L. (2014), "Modelling soil water retentionusing support vector machines with genetic algorithm optimisation", J. Sci. Indian Res. India, 32(1), 1-10. https://doi.org/10.1155/2014/740521.
  13. Lassabatere, L., Angulo-Jaramillo, R., Soria Ugalde, J.M., Cuenca, R., Braud, I. and Haverkamp, R. (2006), "Beerkan estimation of soil transfer parameters through Infiltration experiments-BEST", Soil Sci. Soc. American J., 70(2), 521-532. https://doi.org/10.2136/sssaj2005.0026.
  14. Li, Y. (2013), "Effects of particle shape and size distribution on the shear strength behavior of composite soils", Bulletin. Eng. Geology Environ., 72(3-4):371-381. https://doi.org/10.1007/s10064-013-0482-7.
  15. Mandelbrot, B.B. (1983), "The fractal geometry of nature", American J. Phys., 51(3), 286-287. https://doi.org/10.1119/1.13295.
  16. Matheson, M.G. (1986), "Relationship between compacted rockfill density and gradation", J. Geotech. Geoenviron., 112(112), 1119-1124. https://doi.org/10.1061/(ASCE)0733-410(1986)112:12(1119).
  17. Millan, H., Gonzalezposada, M., Aguilar, M., DomiNguez, J. and Cespedes, L. (2003), "On the fractal scaling of soil data. Particle-size distributions", Geoderma, 117(1), 117-128. https://doi.org/10.1016/S0016-7061(03)00138-1.
  18. Minh, N.H. and Cheng, Y.P. (2013), "A DEM investigation of the effect of particle-size distribution on one-dimensional compression", Geotechnique, 63(1), 44-53. https://doi.org/10.1680/geot.10.P.058.
  19. Ovalle, C., Frossard, E. and Dano, C. (2014), "The effect of size on the strength of coarse rock aggregates and large rockfill samples through experimental data", Acta Mech., 225(8), 2199-2216. https://doi.org/10.1007/s00707-014-1127-z.
  20. Perrier, E., Bird, N. and Rieu, M. (1999), "Generalizing the fractal model of soil structure: the pore-solid fractal approach", Geoderma, 88(3-4), 137-164. https://doi.org/10.1016/s0016-7061(98)00102-5.
  21. Shen, Y., Zhu, Y., Liu, H., Li, A. and Ge, H. (2018), "Macro-meso effects of gradation and particle morphology on the compressibility characteristics of calcareous sand", Bulletin Eng. Geology Environ, 77(3), 1047-1055. https://doi.org/10.1007/s10064-017-1157-6.
  22. Park, T. W., Kim, H. J., Tanvir, M. T., Lee, J. B. and Moon, S.G., (2018), "Influence of coarse particles on the physical properties and quick undrained shear strength of fine-grained soils", Geomech. Eng., 14(1), 99-105. https://doi.org/10.12989/gae.2018.14.1.099.
  23. Turcotte, L.D. (1986), "Fractals and fragmentation", J. Geophys. Res. Solid Earth, 91(B2), 1921-1926. https://doi.org/10.1029/jb091ib02p01921.
  24. Tyler, S.W. and Wheatcraft, S.W. (1992), "Fractal scaling of soil particle-size distributions: analysis and limitations", Soil Sci. Soc. American J., 56(2), 362. https://doi.org/10.2136/sssaj1992.03615995005600020005x.
  25. Vipulanandan, C. and Ozgurel, H.G. (2009), "Simplified relationships for particle-size distribution and permeation groutability limits for soils", J. Geotech. Geoenviron., 135(135), 1190-1197. https://doi.org/10.1061/(asce)gt.1943-5606.0000064.
  26. Wang, X. and Li, J. (2015), "Influence of particle gradation curve on granular packing characteristics", Procedia Eng., 102(9), 1827-1834. https://doi.org/10.1016/j.proeng.2015.01.320.
  27. Wu, W. and Li, W. (2017), "Porosity of bimodal sediment mixture with particle filling", Int. J. Sediment Res., 32(3), 253-259. https://doi.org/10.1016/j.ijsrc.2017.03.005.
  28. Xiaoming, L., Shizhang, Q., Renpeng, C. and Sha, C. (2018), "Development of a two-dimensional fractal model for analyzing the particle size distribution of geomaterials", J. Mater. Civil Eng., 30(8), 1-8. https://doi.org/10.1061/(ASCE)MT.1943-5533.0002365.
  29. Yasrebi, A. B., Wetherelt, A., Foster, P., Coggan, J., Afzal, P., Agterberg, F. and Ahangaran, D.K. (2014), "Application of a density-volume fractal model for rock characterisation of the Kahang porphyry deposit", Int. J. Rock. Mech. Min., 66(1), 188-193. https://doi.org/10.1016/j.ijrmms.2013.12.022.
  30. Sun, Y., Wang, Z. and Gao, Y. (2019), "Mechanistic representation of the grading-dependent aggregates resiliency using stress transmission column", Geomech. Eng., 17(4), 405-411. https://doi.org/10.12989/gae.2019.17.4.405.
  31. Zhang, X., Baudet, B.A., Hu, W. and Xu, Q. (2017), "Characterisation of the ultimate particle size distribution of uniform and gap-graded soils", Soils Foundations, 57(4), 603-618. https://doi.org/10.1016/j.sandf.2017.04.002.
  32. Zhu, S., Feng, Y.M., Feng, S.R. and Chen, W.Y. (2011), "Particles gradation optimization of blasting rockfill based on fractal theory", Adv. Eng. Mater., 366(366), 469-473. https://doi.org/10.4028/www.scientific.net/AMR.366.469.
  33. Zhuang, J., Jin, Y. and Miyazaki, T. (2001), "Estimating water retention characteristic from soil particle-size distribution using a non-similar media concept", Soil Sci., 166(5), 308-321. https://doi.org/10.1097/00010694-200105000-00002.
  34. Zobeck, T.M., Gill, T.E. and Popham, T.W. (2015), "A two-parameter Weibull function to describe airborne dust particle size distributions", Earth Surface Processes Landforms: J. British Geomorphol. Res. Group, 24(10), 943-955. https://doi.org/10.1002/(sici)1096-9837(199909)24:10<943::aidesp30>3.0.co;2-9.