Abstract
Packing density is a key factor in governing the properties of materials such as concrete, asphalt, ceramic etc. Therefore, determination of packing density of a particulate mixture accurately, is of great importance. However, involvement of many external and internal factors such as surface texture, shape, method of packing etc. has made it very complicated and tedious to determine the packing density. The study investigated the combined effect of particle surface texture, size ratio and large particle volume fraction on packing density and developed a descriptive model to predict the packing density. Further, design graphs were also developed for the convenience. The study revealed that the British pendulum number value of the surface texture linearly varies with the packing density. The rougher the surface, the lower the packing density. The interparticle friction hinders the particle rearrangement. Hence, the ability to achieve a higher packing state is reduced. Further, irregularities in the surface boundary create void spaces, increasing the total voids in the mix. Thus, the packing density reduces. The increase of the size ratio decreases the packing density linearly. The packing density variation with a large particle volume fraction follows a 3rd order polynomial curve. The trend analysis was conducted to develop the descriptive model and design graphs to predict the packing density of binary mixtures.
Similar content being viewed by others
References
Hettiarachchi, H.A.C.K., Mampearachchi, W.K.: Validity of aggregate packing models in mixture design of interlocking concrete block pavers (ICBP). Road Mater. Pavement Design 20(2), 462–474 (2019). https://doi.org/10.1080/14680629.2017.1393001
Hettiarachchi, H.A.C.K., Mampearachchi, W.K.: Effect of vibration frequency, size ratio and large particle volume fraction on packing density of binary spherical mixtures. Powder Technol. 336, 150–160 (2018)
Kwan, A., Fung, W.: Packing density measurement and modelling of fine aggregate and mortar. Cement Concr. Compos. 31(6), 349–357 (2009)
Kwan, A.K.H., Chan, K.W., Wong, V.: A 3-parameter particle packing model incorporating the wedging effect. Powder Technol. 237(Supplement C), 172–179 (2013)
Roquier, G.: The 4-parameter compressible packing model (CPM) for crushed aggregate particles. Powder Technol. 320, 133–142 (2017)
Roquier, G.: The 4-parameter compressible packing model (CPM) including a new theory about wall effect and loosening effect for spheres. Powder Technol. 302, 247–253 (2016)
Aim, R.B., Le Goff, P.: Effet de paroi dans les empilements désordonnés de sphères et application à la porosité de mélanges binaires. Powder Technol. 1(5), 281–290 (1968)
Andreasen, A., Andersen, J.: About the relationship between density and particle spacing in products made of loose particles. Kolloid 50, 217–218 (1930)
Andreasen, A.M., Andersen, J.: Relation between grain size and interstitial space in products of unconsolidated granules. Kolloid-Zeitschrift 50(3), 217–228 (1930)
de Larrard, F.: Granular Structures and Concrete Formulation. Études et recherches des laboratoires des ponts et chaussées (2000)
de Larrard, F., Sedran, T.: Optimization of ultra-high-performance concrete by the use of a packing model. Cement Concrete Res. 24(6), 997–1009 (1994)
Dewar, J.: Computer Modelling of Concrete Mixtures. CRC Press, Boca Raton (2002)
Fuller, W.B.: The law of proportioning concrete. Trans. Am. Soc. Civ. Eng. 59, 67–143 (1907)
Funk, J., Dinger, D., Funk Jr., J.: Coal Grinding and Particle Size Distribution Studies for Coal–Water Slurries at High Solids Loading. Alfred University Research Foundation, Alfred (1980)
Furnas, C.: Grading aggregates-I. Mathematical relations for beds of broken solids of maximum density. Ind. Eng. Chem. 23(9), 1052–1058 (1931)
Goltermann, P., Johansen, V., Palbol, L.: Packing of aggregates: an alternative tool to determine the optimal aggregate mix. ACI Mater. J. 94(5), 435–443 (1997)
Kwan, A.K.H., Wong, V., Fung, W.W.S.: A 3-parameter packing density model for angular rock aggregate particles. Powder Technol. 274(Supplement C), 54–162 (2015)
Powers, T.C.: The Properties of Fresh Concrete. Wiley, New York (1969)
Roquier, G.: The 4-parameter compressible packing model (CPM) for crushed aggregate particles. Powder Technol. 320(Supplement C), 133–142 (2017)
Sedran, T., De Larrard, F.: Optimization of self-compacting concrete thanks to packing model. In: Proceedings 1st SCC Symposium, CBI Sweden, RILEM PRO7 (1999)
Stovall, T., De Larrard, F., Buil, M.: Linear packing density model of grain mixtures. Powder Technol. 48(1), 1–12 (1986)
Toufar, W., Born, M., Klose, E.: Contribution of optimisation of components of different density in polydispersed particles systems. Freib. Bookl. A 558, 29–44 (1976)
Vesilind, P.A.: The Rosin–Rammler particle size distribution. Resour. Recov. Conserv. 5(3), 275–277 (1980)
Wong, V., Kwan, A.K.H.: A 3-parameter model for packing density prediction of ternary mixes of spherical particles. Powder Technol. 268((Supplement C)), 357–367 (2014)
Yu, A., Zou, R., Standish, N.: Modifying the linear packing model for predicting the porosity of nonspherical particle mixtures. Ind. Eng. Chem. Res. 35(10), 3730–3741 (1996)
Yerazunis, S., Bartlett, J., Nissan, A.: Packing of binary mixtures of spheres and irregular particles. Nature 195(4836), 33–35 (1962)
Yerazunis, S., Cornell, S., Wintner, B.: Dense random packing of binary mixtures of spheres. Nature 207(4999), 835 (1965)
Santiso, E., Müller, E.A.: Dense packing of binary and polydisperse hard spheres. Mol. Phys. 100(15), 2461–2469 (2002)
de Lange Kristiansen, K., Wouterse, A., Philipse, A.: Simulation of random packing of binary sphere mixtures by mechanical contraction. Phys. A Stat. Mech. Appl. 358(2–4), 249–262 (2005)
Scott, G., Kilgour, D.: The density of random close packing of spheres. J. Phys. D Appl. Phys. 2(6), 863 (1969)
Visscher, W.M., Bolsterli, M.: Random packing of equal and unequal spheres in two and three dimensions. Nature 239(5374), 504 (1972)
Epstein, N., Young, M.: Random loose packing of binary mixtures of spheres. Nature 196(4857), 885–886 (1962)
Clarke, A., Wiley, J.: Numerical simulation of the dense random packing of a binary mixture of hard spheres: amorphous metals. Phys. Rev. B 35(14), 7350 (1987)
O’Toole, P.I., Hudson, T.S.: New high-density packings of similarly sized binary spheres. J. Phys. Chem. C 115(39), 19037–19040 (2011)
Yu, A.B., Standish, N., McLean, A.: Porosity calculation of binary mixtures of nonspherical particles. J. Am. Ceram. Soc. 76(11), 2813–2816 (1993)
Aim, R.B., Goff, P.L.: Effet de paroi dans les empilements désordonnés de sphères et application à la porosité de mélanges binaires. Powder Technol. 1, 281 (1967)
Dodds, J.: The porosity and contact points in multicomponent random sphere packings calculated by a simple statistical geometric model. J. Colloid Interface Sci. 77(2), 317–327 (1980)
Kummerfeld, J.K., Hudson, T.S., Harrowell, P.: The densest packing of AB binary hard-sphere homogeneous compounds across all size ratios. J. Phys. Chem. B 112(35), 10773–10776 (2008)
Zheng, J., Carlson, W.B., Reed, J.S.: The packing density of binary powder mixtures. J. Eur. Ceram. Soc. 15(5), 479–483 (1995)
Chang, C.S., Deng, Y.: A nonlinear packing model for multi-sized particle mixtures. Powder Technol. 336, 449–464 (2018)
Chen, Z.C., et al.: Effect of particle packing on extrusion behavior of pastes. J. Mater. Sci. 35(21), 5301–5307 (2000)
Furnas, C.C.: Flow of Gases Through Beds of Broken Solids. Bureau of Mines, Washington, DC (1928)
Powers, M.C.: A new roundness scale for sedimentary particles. J. Sediment. Res. 23(2), 117–119 (1953)
Andreasen, A.: Über die Beziehung zwischen Kornabstufung und Zwischenraum in Produkten aus losen Körnern (mit einigen Experimenten). Kolloid-Zeitschrift 50(3), 217–228 (1930)
Funk, J.E., Dinger, D.R.: Predictive process control of crowded particulate suspensions: applied to ceramic manufacturing. Springer, Berlin (1994)
Rosin, P., Rammler, E.: Die kornzusammensetzung des mahlgutes im lichte der wahrscheinlichkeitslehre. Kolloid-Zeitschrift 67(1), 16–26 (1934)
Goltermann, P., Johansen, V., Palbøl, L.: Packing of aggregates: an alternative tool to determine the optimal aggregate mix. Mater. J. 94(5), 435–443 (1997)
Alexander, M.G.M.: Aggregates in concrete, vol. 1. Taylor and Francis, Oxon (2005)
Mangulkar, M., Jamkar, S.: Review of particle packing theories used for concrete mix proportioning. In: Contributory Papers, vol. 141, (2013)
Lamond, J.F., Pielert, J.H.: Significance of tests and properties of concrete and concrete-making materials. Vol. 169. ASTM International (2006)
Janoo, V.C.: Quantification of Shape, Angularity, and Surface Texture of Base Course Materials. State of Vermont agency of transportation, Vermont (1998)
Little, D., Button, J., Jayawickrama, P., Mansour, S., Solaimanian, B.H.: Quantify shape, angularity and surface texture of aggregates using image analysis and study their effect on performance, pp. 1–143. Texas Transportation Institute, Texas (2003)
Erdoğan, S.T., Fowler, D.: Determination of aggregate shape properties using x-ray tomographic methods and the effect of shape on concrete rheology. International Center for Aggregates Research, Alexandria (2005)
Kwan, A., Mora, C.: Effects of various, shape parameters on packing of aggregate particles. Mag. Concrete Res. 53, 91–100 (2002)
Mora, C., Kwan, A.: Sphericity, shape factor, and convexity measurement of coarse aggregate for concrete using digital image processing. Cement Concrete Res. 30(3), 351–358 (2000)
Wenzel, R.N.: Surface roughness and contact angle. J. Phys. Chem. 53(9), 1466–1467 (1949)
Blanks, R.F.: Modern concepts applied to concrete aggregate. In: Proceedings of the American Society of Civil Engineers. ASCE (1949)
Terzaghi, K.P., Peck, R.B., Mesri, G.: Soil Mechanics in Engineering Practice. Wiley, New York (1967)
Barskale, R.D., Itani, S.Y.: Influence of aggregate shape on base behavior. Transp. Res. Rec. 1227, 1241–1254 (1989)
Bikerman, J.: Adhesion of asphalt to stone. J. Mater. 1, 34–47 (1966)
Wright, P.: A method of measuring the surface texture of aggregate. Mag. Concrete Res. 7(21), 151–160 (1955)
Lee, Y.-H., et al. The fractal dimension as a measure of the roughness of rock discontinuity profiles. In: International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts. Elsevier (1990)
Wilson, J., Klotz, L.D., Nagaraj, C.: Automated measurement of aggregate indices of shape. Part. Sci. Technol. 15(1), 13–35 (1997)
Wang, Z.F., et al.: Effect of temperature and structure on the free volume and water vapor permeability in hydrophilic polyurethanes. J. Membr. Sci. 241(2), 355–361 (2004)
Corley-Lay, J.: Friction and surface texture characterization of 14 pavement test sections in Greenville, North Carolina. Transp. Res. Rec. J. Transp. Res. Board 1639, 155–161 (1998)
Goodman, S.N.: Quantification of Pavement Textural and Frictional Characteristics Using Digital Image Analysis, PhD diss., Carleton University (2009)
Ahammed, M.A., Tighe, S.L.: Asphalt pavements surface texture and skid resistance—exploring the reality. Can. J. Civ. Eng. 39(1), 1–9 (2011)
Leu, M., Henry, J.: Prediction of skid resistance as a function of speed from pavement texture measurements. Transp. Res. Rec. 666, 7–13 (1978)
Lee, Y.P.K., Fwa, T.F., Choo, Y.S.: Effect of pavement surface texture on British pendulum test. J. Eastern Asia Soc. Transp. Stud. 6, 1247–1257 (2005)
Wambold, J.C., Henry, J.J., Hegmon, R.R.: Evaluation of pavement surface texture significance and measurement techniques. Wear 83(2), 351–368 (1982)
International, A., ASTM E303 - 93(2013) Standard Test Method for Measuring Surface Frictional Properties Using the British Pendulum Tester. West Conshohocken (2013)
McGeary, R.: Mechanical packing of spherical particles. J. Am. Ceram. Soc. 44(10), 513–522 (1961)
Ayer, J., Soppet, F.: Vibratory compaction: I, compaction of spherical shapes. J. Am. Ceram. Soc. 48(4), 180–183 (1965)
Meng, L., Lu, P., Li, S.: Packing properties of binary mixtures in disordered sphere systems. Particuology 16, 155–166 (2014)
Farr, R.S., Groot, R.D.: Close packing density of polydisperse hard spheres. J. Chem. Phys. 131(24), 244104 (2009)
Kyrylyuk, A.V., Wouterse, A., Philipse, A.P.: Percolation and jamming in random heterogeneous materials with competing length scales. In: Bucak, S. (ed.) Trends in Colloid and Interface Science, vol. 23. Springer, Berlin, pp. 29–33 (2010)
De Larrard, F.: Concrete Mixture Proportioning: A Scientific Approach. CRC Press, Boca Raton (2014)
Acknowledgements
This work was supported by the senate research council grant funded by the University of Moratuwa under Grant No. SRC/LT/2015/13.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Hettiarachchi, C., Mampearachchi, W.K. Effect of surface texture, size ratio and large particle volume fraction on packing density of binary spherical mixtures. Granular Matter 22, 8 (2020). https://doi.org/10.1007/s10035-019-0978-3
Received:
Published:
DOI: https://doi.org/10.1007/s10035-019-0978-3