Computers and Concrete

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Fractal equations to represent optimized grain size distributions used for concrete mix design

  • Sebsadji, Soumia K. (LMST Lab., Department of Civil Engineering, University of Sciences and Technology of Oran Mohamed Boudiaf (USTO MB)) ;
  • Chouicha, Kaddour (LMST Lab., Department of Civil Engineering, University of Sciences and Technology of Oran Mohamed Boudiaf (USTO MB))
  • Received : 2020.08.19
  • Accepted : 2020.11.20
  • Published : 2020.12.25
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Abstract

Grading of aggregate influences significantly almost all of the concrete performances. The purpose of this paper is to propose practicable equations that express the optimized total aggregate gradation, by weight or by number of particles in a concrete mix. The principle is based on the fractal feature of the grading of combined aggregate in a solid skeleton of concrete. Therefore, equations are derived based on the so-called fractal dimension of the grain size distribution of aggregates. Obtained model was then applied in such a way a correlation between some properties of the dry concrete mix and the fractal dimension of the aggregate gradation has been built. This demonstrates that the parameter fractal dimension is an efficacious tool to establish a unified model to study the solid phase of concrete in order to design aggregate gradation to meet certain requirements or even to predict some characteristics of the dry concrete mixture.

Keywords

References

  1. Abdul Hassan, N., Airey, G.D. and Hainin, M.R. (2014), "Characterisation of micro-structural damage in asphalt mixtures using image analysis", Constr. Build. Mater., 54, 27-38. https://doi:10.1016/j.conbuildmat.2013.12.047.
  2. Ashraf, W. and Noor, M.A. (2011), "Performance-evaluation of concrete properties for different combined aggregate gradation approaches", Procedia Eng., 14, 2627-2634. https://doi:10.1016/j.proeng.2011.07.330.
  3. Brouwers, H.J.H. and Radix, H.J. (2005), "Self-compacting concrete: Theoretical and experimental study", Cement Concrete Res., 35(6), 2116-2136. https://doi:10.1016/j.cemconres.2005.06.002.
  4. Bu, J., Chen, X., Liu, S., Li, S. and Shen, N. (2018), "Experimental study on the dynamic behavior of pervious concrete for permeable pavement", Comput. Concrete, 22(3), 291-303. https://doi:10.12989/cac.2018.22.3.291.
  5. Chen, Y.Y., Tuan, B.L.A. and Hwang, C.L. (2013), "Effect of paste amount on the properties of self-consolidating concrete containing fly ash and slag", Constr. Build. Mater., 47, 340-346. https://doi:10.1016/j.conbuildmat.2013.05.050.
  6. Chouicha, K. (2006), "La dimension fractale et l'etendue granulaire comme paramètres d'identification des melanges granulaires", Mater. Struct., 39(7), 665-681. https://doi:10.1617/s11527-006-9113-0.
  7. Chung, S.Y., Elrahman, M.A. and Stephan, D. (2017), "Effect of different gradings of lightweight aggregates on the properties of concrete", Appl. Sci., 7(6), 1-15. https://doi.org/10.3390/app7060585.
  8. Cook, M.D., Ghaeezadah, A. and Ley, M.T. (2018), "Impacts of coarse-aggregate gradation on the workability of slip-formed concrete", J. Mater. Civil Eng., 30(2), 1-8. https://doi:10.1061/(ASCE)MT.1943-5533.0002126.
  9. Esmaeilkhanian, B., Khayat, K.H. and Wallevik, O.H. (2017), "Mix design approach for low-powder self-consolidating concrete: Eco-SCC-content optimization and performance", Mater. Struct. Constr., 50(2), 1-18. https://doi:10.1617/s11527-017-0993-y.
  10. Fennis, S.A.A.M. and Walraven, J.C. (2012), "Using particle packing technology for sustainable concrete mixture design", Heron, 57(2), 73-101. http://resolver.tudelft.nl/uuid:93af1749-0b97-416a-ba27-907ae4921a7f.
  11. Fujikawa, M., Sakai, T. and Aoki, S. (2003), "Application of fractal analysis to quantitative evaluation of three-dimensional shape irregularity of concrete aggregates", Mater. Sci. Res. Int., 9(1), 102-107. https://doi:10.2472/jsms.52.3appendix_102.
  12. He, H. (2010), "Computational modelling of particle packing in concrete", Ph.D. Dissertation, Delft University of Technology, Delft, The Netherlands.
  13. He, H., Stroeven, P., Stroeven, M. and Sluys, L.J. (2012), "Optimization of particle packing by analytical and computer simulation approaches", Comput. Concrete, 9(2), 119-131. http://data.doi.or.kr/qr/10.12989/cac.2012.9.2.119.
  14. Hettiarachchi, H.A.C.K. and Mampearachchi, W.K. (2019), "Validity of aggregate packing models in mixture design of interlocking concrete block pavers (ICBP)", Road Mater. Pavement Des., 20(2), 462-474. https://doi:10.1080/14680629.2017.1393001.
  15. Hunger, M. (2010), "An integral design concept for ecological self-sompacting concrete", Ph.D. Dissertation, Eindhoven University of Technology, The Netherlands.
  16. Hunger, M. and Brouwers, H.J.H. (2006), "Development of Self-Compacting Eco-Concrete", Proceedings 16th IBausil, International Conference on Building Materials, Weimar, Germany, September.
  17. Issa, M.A., Issa, M.A., Islam, M.S. and Chudnovsky, A. (2003), "Fractal dimension-a measure of fracture roughness and toughness of concrete", Eng. Fract. Mech., 70(1), 125-137. https://doi:10.1016/S0013-7944(02)00019-X.
  18. Jiao, D., Shi, C., Yuan, Q., An, X., Liu, Y. and Li, H. (2017), "Effect of constituents on rheological properties of fresh concrete-A review", Cement Concrete Compos., 83, 146-159. https://doi:10.1016/j.cemconcomp.2017.07.016.
  19. Jin, S., Zhang, J. and Han, S. (2017), "Fractal analysis of relation between strength and pore structure of hardened mortar", Constr. Build. Mater., 135, 1-7. https://doi:10.1016/j.conbuildmat.2016.12.152.
  20. Keke, S., Xiaoqin, P., Shuping, W. and Lu, Z. (2019), "Design method for the mix proportion of geopolymer concrete based on the paste thickness of coated aggregate", J. Clean. Prod., 232, 508-517. https://doi:10.1016/j.jclepro.2019.05.254.
  21. Khan, A., Do, J. and Kim, D. (2016), "Cost effective optimal mix proportioning of high strength self-compacting concrete using response surface methodology", Comput. Concrete, 17(5), 629-638. http://dx.doi.org/10.12989/cac.2016.17.5.629.
  22. Lecomte, A. and Thomas, A. (1992), "Caractère fractal des melanges granulaires pour betons de haute compacite", Mater. Struct., 25(5), 255-264. https://doi:10.1007/BF02472666.
  23. Li, L.G. and Kwan, A.K.H. (2013), "Concrete mix design based on water film thickness and paste film thickness", Cem. Concr. Compos., 39, 33-42. https://doi:10.1016/j.cemconcomp.2013.03.021.
  24. Li, S., Dong, Q., Ni, F., Jiang, J. and Han, Y. (2018), "Evaluation of susceptibility of high-temperature performance of asphalt mixture to morphological feature of aggregates by Fractal theory", J. Mater. Civil Eng., 30(11), 1-8. https://doi:10.1061/(ASCE)MT.1943-5533.0002498.
  25. Liu, X., Qu, S., Chen, R. and Chen, S. (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:10.1061/(ASCE)MT.1943-5533.0002365.
  26. Liu, Y. and Jeng, D.S. (2019), "Pore structure of grain-size fractal granular material", Mater., 12(13), 2053. https://doi:10.3390/ma12132053.
  27. Lu, Q., Qiu, Q., Zheng, J., Wang, J. and Zeng, Q. (2019), "Fractal dimension of concrete incorporating silica fume and its correlations to pore structure, strength and permeability", Constr. Build. Mater., 228, 116986. https://doi:10.1016/j.conbuildmat.2019.116986.
  28. Martineau, B. (2017), "Formulation of a general gradation curve and its transformation to equivalent sigmoid form to represent grain size distribution", Road Mater. Pavement Des., 18(1), 199-207. https://doi:10.1080/14680629.2015.1124048.
  29. Mehdipour, I. and Khayat, K.H. (2017), "Effect of particle-size distribution and specific surface area of different binder systems on packing density and flow characteristics of cement paste", Cement Concrete Compos., 78, 120-131. https://doi:10.1016/j.cemconcomp.2017.01.005.
  30. Moini, M., Sobolev, K., Flores-Vivian, I. and Amirjanov, A. (2019), "Modeling and experimental evaluation of aggregate packing for effective application in concrete", J. Mater. Civil Eng., 31(3), 1-10. https://doi:10.1061/(ASCE)MT.1943-5533.0002628.
  31. Mueller, F.V. (2012), "Design criteria for low binder self-compacting concrete, Eco-SCC", Ph.D. Dissertation, Reykjavik University, Iceland.
  32. Nincevic, K., Boumakis, I., Marcon, M. and Wan-Wendner, R. (2019), "Aggregate effect on concrete cone capacity", Eng. Struct., 191(8), 358-369. https://doi:10.1016/j.engstruct.2019.04.028.
  33. Oreste, P. and Castellano, M. (2012), "An applied study on the debris recycling in tunneling", Am. J. Environ. Sci., 8(2), 179-184. https://doi:10.3844/ajessp.2012.179.184.
  34. Pan, Z., Wang, D., Ma, R. and Chen, A. (2018), "A study on ITZ percolation threshold in mortar with ellipsoidal aggregate particles", Comput. Concrete, 22(6), 551-561. https://doi:10.12989/cac.2018.22.6.551.
  35. Prokopski, G. and Konkol, J. (2005), "The fractal analysis of the fracture surface of concretes made from different coarse aggregates", Comput. Concrete, 2(3), 239-248. https://doi.org/10.12989/cac.2005.2.3.239.
  36. Ren, W. and Xu, J. (2017), "Fractal characteristics of concrete fragmentation under impact loading", J. Mater. Civil Eng., 29(4), 1-9. https://doi:10.1061/(ASCE)MT.1943-5533.0001764.
  37. Richardson, D.N. (2005), "Aggregate gradation optimization, Literature search", Report N° RDT 05-001, RI 98-035, Missouri University of Science and Technology, Rolla, USA.
  38. Rudy, A. and Olek, J. (2012), "Optimization of mixture proportions for concrete pavements, influence of supplementary cementitious materials, paste content and aggregate gradation", Publication FHWA/IN/JTRP-2012/34. Joint Transportation Research Program, Indiana Dpt. of Transportation and Purdue University, West Lafayette, Indiana, USA. https://doi:10.5703/1288284315038.
  39. Sebsadji, S.K. and Chouicha, K. (2012), "Determining periodic representative volumes of concrete mixtures based on the fractal analysis", Int. J. Solid. Struct., 49(21), 2941-2950. https://doi:10.1016/j.ijsolstr.2012.05.017.
  40. Sohail, M.G., Wang, B., Jain, A., Kahraman, R., Ozerkan, N.G., Gencturk, B., Dawood, M. and Belarbi, A. (2018), "Advancements in concrete mix designs: High-performance and ultrahigh-performance concretes from 1970 to 2016", J. Mater. Civil Eng., 30(3), 04017310. https://doi:10.1061/(ASCE)MT.1943-5533.0002144.
  41. Sun, H.Q. and Ding, J. (2011), "The comparison of fractal dimensions of cracks on reinforced concrete beam", Adv. Mater. Res., 291-294, 1126-1130. https://doi:10.4028/www.scientific.net/AMR.291-294.1126.
  42. Tang, Z., Dong, X., Chai, B. and Yang, Y. (2014), "Evaluation of particle size distribution of coal gangue through fractal method in Dongkuang Mine, Heshan, China", J. Mater. Civil Eng., 26(8), 06014018. https://doi.org/10.1061/(ASCE)MT.1943-5533.0001045.
  43. Urumovic, K. (2016), "The referential grain size and effective porosity in the Kozeny-Carman model. Hydrol", Earth Syst. Sci., 20(5), 1669-1680. https://doi:10.5194/hess-20-1669-2016.
  44. Vogt, C. (2010), "Ultrafine particles in concrete: Influence of ultrafine particles on concrete properties and application to concrete mix design", Doctoral Thesis, Royal Institute of Technology, Stockholm, Sweden.
  45. Wang, X., Wang, K., Taylor, P. and Morcous, G. (2014), "Assessing particle packing based self-consolidating concrete mix design method", Constr. Build. Mater., 70(11), 439-452. https://doi:10.1016/j.conbuildmat.2014.08.002.
  46. Wang, Z., Cheng, Q., Cao, L., Xia, Q. and Chen, Z. (2007), "Fractal modelling of the microstructure property of quartz mylonite during deformation process", Math. Geol., 39(1), 53-68. https://doi:10.1007/s11004-006-9065-5.
  47. Yang, X., Wang, F., Yang, X. and Zhou, Q. (2017), "Fractal dimension in concrete and implementation for meso-simulation", Constr. Build. Mater., 143, 464-472. https://doi:10.1016/j.conbuildmat.2017.03.157.
  48. Yousuf, S., Sanchez, L.F.M. and Shammeh, S.A. (2019), "The use of particle packing models (PPMs) to design structural low cement concrete as an alternative for construction industry", J. Build. Eng., 25, 100815. https://doi.org/10.1016/j.jobe.2019.100815.
  49. Yu, Q.L. and Brouwers, H.J.H. (2012), "Development of a selfcompacting gypsum-based lightweight composite", Cement Concete. Compos., 34(9), 1033-1043. https://doi:10.1016/j.cemconcomp.2012.05.004.
  50. Yu, Q.L., Spiesz, P. and Brouwers, H.J.H. (2015), "Ultra-lightweight concrete: Conceptual design and performance evaluation", Cement Concrete Compos., 61, 18-28. https://doi.org/10.1016/j.cemconcomp.2015.04.012.
  51. Yu, R., Spiesz, P. and Brouwers, H.J.H. (2015), "Development of Ultra-High Performance Fibre Reinforced Concrete (UHPFRC): Towards an efficient utilization of binders and fibres", Constr. Build. Mater., 79, 273-282. https://doi:10.1016/j.conbuildmat.2015.01.050.