Abstract
The calculations of the mixture design of concrete have been widely performed according to the compressive strength or tensile strength. However, a cracked concrete/reinforced concrete structure can only be simulated by using the principles of fracture mechanics. The purpose of this study is to obtain certain expressions based on the properties of the fresh concrete and the fracture toughness of concrete, which is the fundamental parameter in analysis of the cracked structures. In accordance with this aim, the concrete mixture design method with the monogram proposed by Monteiro et al. for cement-based materials was utilized. Accordingly, 28 sets of batches with different slump values, cement contents, and water/cement ratios were cast to obtain this monogram. Fracture toughness tests on the notched beams and wedge-splitting (WS) specimens, and compression and splitting tests on cubes were conducted for hardened concrete. The fracture toughness test results were analyzed according to the effective crack model (ECM) in concrete fracture. Consequently, a mix design approach with a monogram was proposed to design according to the fracture mechanics of concrete. Furthermore, an approach based on the WS test was initially suggested to determine the fracture toughness of concrete for the ECM, which was essentially based on beams.
Similar content being viewed by others
References
Abrams DA (1918) Design of concrete mixtures. Lewis Institute Bulletin 1
Lydon FD (1982) Concrete mix design, 2nd edn. Applied Science Publishers, Essex
Ince R, Alyamaç KE (2008) Determination of fracture parameters of concrete based on water–cement ratio. Indian J Eng Mater Sci 15:14–22
Beygi MHA, Kazemi MT, Nikbin IM, Amiri JV (2013) The effect of water to cement ratio on fracture parameters and brittleness of self-compacting concrete. Mater Des 50:267–276
Kaplan MF (1961) Crack propagation and the fracture of concrete. ACI J 58(11):591–610
Shah SP, McGarry FJ (1971) Griffith fracture criterion and concrete. J Eng Mech Div (ASCE) 97:1663–1675
Hillerborg A, Modeer M, Petersson PE (1976) Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cem Conc Res 6:773–782
Bazant ZP, Oh BH (1983) Crack band theory for fracture of concrete. Mater Struct (RILEM) 16(3):155–177
Jenq YS, Shah SP (1985) Two-parameter fracture model for concrete. ASCE J Eng Mech 111(10):1227–1241
Nallathambi P, Karihaloo BL (1986) Determination of the specimen size independent fracture toughness of plain concrete. Mag Conc Res 38(135):67–76
Carpinteri A (1989) Cusp catastrophe interpretation of fracture instability. J Mech Phys Solids 37(5):567–582
Bazant ZP, Kazemi MT (1990) Determination of fracture energy, process zone length, and brittleness number from size effect with application to rock and concrete. Int J Fract 44(2):111–131
Carpinteri A (1994) Scaling laws and renormalization groups for strength and toughness of disordered materials. Int J Solids Struct 31(3):291–302
Carpinteri A, Chiaia B (1997) Multifractal scaling laws in the breaking behaviour of disordered materials. Chaos, Solitons Fractals 8(2):135–150
Xu S, Reinhardt HW (1999) Determination of double-K criterion for crack propagation in quasi-brittle fracture, part I: experimental investigation of crack propagation. Int J Fract 98(2):111–149
Carpinteri A, Chiaia B, Cornetti P (2002) A scale-invariant cohesive crack model for quasi-brittle materials. Eng Fract Mech 69:207–217
Hu X, Duan K (2008) Size effect and quasi-brittle fracture: the role of FPZ. Int J Fract 154:3–14
Carpinteri A, Corrado M (2009) An extended (fractal) overlapping crack model to describe crushing size-scale effects in compression. Eng Fail Anal 16:2530–2540
Carpinteri A, Accornero F (2019) Rotation versus curvature fractal scaling in bending failure. Phys Mesomech 22(1):46–51
Brühwiler E, Wittmann FH (1990) The wedge splitting test, a method of performing stable fracture tests. Eng Fract Mech 35:117–126
Gambhir ML (1993) Concrete technology, 4th edn. Tata Mc-Graw-Hill Publishing Company Limited, New Delhi
Tang T, Ouyang C, Shah SP (1996) A simple method for determining material fracture parameters from peak loads. ACI Mater J 93(2):147–157
Rocco C, Guinea GV, Planas J, Elices M (1999) Size effect and boundary condition in the Brazilian tests: theoretical analysis. Mater Struct 32:437–444
Ince R (2010) Determination of concrete fracture parameters based on two-parameter and size effect models using split-tension cubes. Eng Fract Mech 77:2233–2250
Ince R (2012) Determination of concrete fracture parameters based on peak-load method with diagonal split-tension cubes. Eng Fract Mech 82:100–114
Ince R (2012) Determination of the fracture parameters of the Double-K model using weight functions of split-tension specimens. Eng Fract Mech 96:416–432
Ince R (2017) The fracture mechanics formulas for split-tension strips. J Theor Appl Mech 55:607–619
Ince R, Çetin S (2019) Effect of grading type of aggregate on fracture parameters of concrete. Mag Conc Res 71(16):860–868
Monteiro PJM, Helene PRL, Kang SH (1993) Designing concrete mixtures for strength, elastic modulus and fracture energy. Mater Struct 26:443–452
Helene PRL (1987) Contribuiçao ao estudo do controle e dosagem dos concretos de cimento Portland. PhD Thesis. Sao Paulo University
Lyse I (1932) Test on consistence and strength of concrete having constant water content. ASTM Proc 32(1):629–636
Alyamac KE, Ince R (2009) A preliminary concrete mix design for SCC with marble powders. Constr Build Mater 23:1201–1210
Dewar JD (1999) Computer modeling of concrete mixtures, 1st edn. E & FN Spon Press, London
Shah SP, Swartz SE, Ouyang C (1995) Fracture mechanics of concrete: applications of fracture mechanics to concrete, rock and other quasi-brittle materials. Wiley, Canada
Karihaloo BL, Nallathambi P (1989) An improved effective crack model for the determination of fracture toughness of concrete. Cem Conc Res 19:603–610
Karihaloo BL, Nallathambi P (1991) Notched beam test: mode I fracture toughness. In: Fracture Mechanics Test Methods for Concrete, (Edited by S.P. Shah and A. Carpinteri), RILEM, Chapman & Hall, London, pp 1–86
Karihaloo BL (1995) Fracture mechanics and structural concrete, 1st edn. Longman Scientific and Technical, Essex
ACI-318 (2002) Building code requirements for structural concrete and commentary. Farmington Hills, Michigan
Karihaloo BL, Nallathambi P (1990) Size-effect prediction from effective crack model for plain concrete. Mater Struct 23:178–185
Hillemeier B, Hilsdorf HK (1977) Fracture mechanics studies on concrete compounds. Cem Conc Res 7:523–536
Rossi P, Brühwiler E, Chhuy S, Jenq YS, Shah SP (1991) Fracture properties of concrete as determined by means of wedge splitting tests and tapered double cantilever beam tests. In: Shah SP, Carpinteri A (eds) Fracture mechanics test methods for concrete. RILEM Chapman & Hall, London, pp 88–128
Srawley JE (1976) Wide range stress intensity factor expression for ASTM E399 standard fracture toughness specimens Int. J Fract 12:475–476
Bazant ZP, Becq-Giraudon E (2002) Statistical prediction of fracture parameters of concrete and implications for choice of testing standard. Cem Conc Res 32:529–556
Ince R (2004) Prediction of fracture parameters of concrete by artificial neural networks. Eng Fract Mech 71:2143–2159
Ince R (2010) Artificial neural network-based analysis of effective crack model in concrete fracture. Fatigue Fract Eng Mater Struct 33(9):595–606
L’Hermite R (1955) Idées actuelles sur la technologie du béton. Documentation Technique Du Bâtiment Et Des Travaux Publics, Paris
Ince R, Gör M, Eren ME, Alyamaç KE (2015) The effect of size on the splitting strength of cubic concrete members. Strain 51(2):135–146
Ince R, Gör M, Alyamaç KE, Eren ME (2016) Multi-fractal scaling law for split strength of concrete cubes. Magn Conc Res 68:141–150
Karihaloo BL, Nallathambi P (1990) Effective crack model for the determination of fracture toughness (KeIC) of concrete. Engng Fract Mech 35:637–645
Montgomery DC, Runger GC (2013) Applied statistics and probability for engineers, 6th edn. Wiley, New York
Van Mier JGM (1997) Fracture processes of concrete, 1st edn. CRC Press, New York
Rong H, Dong W, Zhang X, Zhang B (2019) Size effect on fracture properties of concrete after sustained loading. Mater Struct 52:16
Stephen SJ, Gettu R (2020) Fatigue fracture of fibre reinforced concrete in flexure. Mater Struct 53:56
Masoud MA, Rashad AM, Sakr K, Shahien MG, Zayed AM (2020) Possibility of using different types of Egyptian serpentine as fine and coarse aggregates for concrete production. Mater Struct 53:87
Author information
Authors and Affiliations
Corresponding author
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
Ince, R., Bildik, A.T. A preliminary concrete mixture design based on fracture toughness. Mater Struct 54, 11 (2021). https://doi.org/10.1617/s11527-020-01604-7
Received:
Accepted:
Published:
DOI: https://doi.org/10.1617/s11527-020-01604-7