The use of fractal geometry in determination of fracture toughness of metakaolinite modified concrete

Mandelbrot B.B. Les Objets Fractals: Forme, Hasard et Dimension, Flammarion, Paris, 1975.
  Google Scholar

Mandelbrot B.B. Fractals. Form, chance and dimension. W.H. Freeman, San Francisco, 1977.
  Google Scholar

Winslow D.N. The fractal nature of the surface of cement paste. Cem. Concr. Res. 15 (1985) 817-824.
DOI: https://doi.org/10.1016/0008-8846(85)90148-6   Google Scholar

Saouma V.E., Barton C.C. Fractals, fractures, and size effects in concrete. J. Eng. Mech. 120 (1994) 835-854.
  Google Scholar

Prokopski G., Langier B. Effect of water/cement ratio and silica fume addition on the fracture toughness and morphology of fractured surfaces of gravel concretes. Cem. Concr. Res. 30 (2000) 1427-1433.
  Google Scholar

Yan A., Wu K.-R., Zhang D., Yao W. Effect of fracture path on the fracture energy of high-strength concrete. Cem. Concr. Res. 31 (2001) 1601-1606.
  Google Scholar

Issa M.A., Issa M.A., Islam Md.S, Chudnovsky A. Fractal dimension – a measure of fracture roughness and toughness of concrete. Eng. Fract. Mech. 70 (2003) 125-137.
  Google Scholar

Prokopski G., Konkol J. The fractal analysis of the fracture surface of concretes made from different coarse aggregates. Computers and Concrete 2 (2005) 239-248.
  Google Scholar

Carpinteri A., Spagnoli A., Vantadori S., Viappiani D. Influence of the crack morphology on the fatigue crack growth rate: A continuously-kinked crack model based on fractals. Eng. Fract. Mech. 75 (2008) 579–589.
  Google Scholar

Ficker T. Fractal strength of cement gels and universal dimension of fracture surfaces. Theor. Appl. Fract. Mech. 50 (2008) 167–171.
  Google Scholar

Zhang H., Wei D.M. Fractal effect and anisotropic constitutive model for concrete. Theor. Appl. Fract. Mech. 51 (2009) 167-173.
  Google Scholar

Zhang H., Wei D.M. Fracture and damage behaviors of concrete in the fractal space. J. Mod. Phys. 1 (2010) 48-58.
  Google Scholar

Zhang H., Wei D.M. Estimation of fracture toughness, driving force, and fracture energy for fractal cracks using the method of imaginary smooth crack. Eng. Fract. Mech. 77 (2010) 621-630.
  Google Scholar

Konkol J., Prokopski G. Morfologia przełomu oraz odporność na pękanie betonów modyfikowanych dodatkiem popiołu fluidalnego lub metakaolinitu. Zeszyty Naukowe Politechniki Rzeszowskiej, Seria Budownictwo i Inżynieria Środowiska, z. 58, nr 3/11/III (2011) 321-330.
  Google Scholar

Konkol J. Wykorzystanie parametrów fraktalnych i stereologicznych do opisu odporności na pękanie betonów modyfikowanych wybranymi dodatkami typu II. Zeszyty Naukowe Politechniki Rzeszowskiej, seria Budownictwo i Inżynieria Środowiska, z 59, nr 3/12/III (2012) 222-232.
  Google Scholar

Brandt A.M., Prokopski G. On the fractal dimension of fracture surfaces of concrete elements. J. Mater. Sci. 28 (1993) 4762-4766.
  Google Scholar

Czarnecki L., Garbacz A., Kurach J. On the characterization on polymer concrete fracture surface. Cem. Concr. Compos. 23 (2001) 399-409.
  Google Scholar

Czarnecki L, Chmielewska B. Fracture and fractography of silane modified resin mortars. Int. J. Restor. Build. Monum. 9 (2003) 603–18
  Google Scholar

Erdem S., Blankson M.A. Fractal-fracture analysis and characterization of impact-fractured surface in different types of concrete using digital image analysis and 3D nanomap laser profilometery. Constr. Build Mater. 40 (2013) 70-76.
  Google Scholar

Wild S., Khabit J.M., Jones A., Relative strength pozzolanic activity and cement hydration in superplasticised metakaolin concrete. Cem. Concr. Res. 26 (1996) 1537–44.
  Google Scholar

B.B. Sabir, S. Wild, J. Bai, Metakaolin and cacined clays as Pozzolans for concrete: a review. Cem. Concr. Compos. 23 (2001) 441–54.
DOI: https://doi.org/10.1016/S0958-9465(00)00092-5   Google Scholar

Jones T.R. Metakaolin as a pozzolanic addition to concrete, w Structure and Performance of Cements (red. J. Bensted, P. Barnes). Spoon Press, London, New York 2002.
  Google Scholar

Poon C.S., Kou S.C., Lam L. Compressive strength, chloride diffusivity and pore structure of high performance metakaolin and silica fume concrete. Constr. Build Mater. 20 (2006) 858-865.
  Google Scholar

Siddique R., Klaus J. Influence of metakaolin on the properties of mortar and concrete: A review. Appl. Clay Sci. 43 (2009) 392–400.
DOI: https://doi.org/10.1016/j.clay.2008.11.007   Google Scholar

Pavlíková M., Brtník T, Keppert M., Černý R. Wpływ metakaolinitu, jako częściowego zamiennika cementu, na właściwości zapraw wysoko-wartościowych. Cement Wapno Beton 9 (2009) 113-122.
  Google Scholar

Ramezanianpour A.A., Jovein H.B. Influence of metakaolin as supplementary cementing material on strength and durability of concretes. Constr. Build Mater. 30 (2012) 470–479.
  Google Scholar

Madandoust R., Mousavi S.Y. Fresh and hardened properties of self-compacting concrete containing metakaolin. Constr. Build Mater. 35 (2012) 752–760.
  Google Scholar

Dvorkin L., Bezusyak A., Lushnikova N., Ribakov Y. Using mathematical modeling for design of self compacting high strength concrete with metakaolin admixture. Constr. Build Mater. 37 (2012) 851-64.
  Google Scholar

Rashad A.M. Metakaolin as cementitious material: History, scours, production and composition –A comprehensive overview. Constr. Build Mater. 41 (2013) 303–318.
DOI: https://doi.org/10.1016/j.conbuildmat.2012.12.001   Google Scholar

Prokopski G. Mechanika pękania betonów cementowych. Oficyna Wydawnicza Politechniki Rzeszowskiej, Rzeszów, 2009.
  Google Scholar

Determination of fracture parameters (KIcS and CTODc) of plain concrete using three-point bend test. RILEM Draft Recommendations, TC 89 - FMT Fracture Mechanics of Concrete Test Methods. Materials and Structures 23, 1990.
DOI: https://doi.org/10.1007/BF02472029   Google Scholar