Abstract
The concrete mixture design has been commonly conducted based on the compressive strength in concrete technology. Nevertheless, once a crack occurs in a structure, it can only be modeled realistically with the criteria of fracture mechanics. This investigation aims to accomplish some relationships between the fresh concrete properties such as the water/cement (w/c) ratio and the hardened concrete properties such as unstable fracture toughness and initiation fracture toughness. Therefore, twenty-two series of splitting square prismatic and wedge splitting (WS) specimens, with different w/c ratios and with two different maximum aggregate sizes (8 mm and 16 mm) were cast in this study. The two-parameter model (TPM) and the double-K model were used to simulate the results of the fracture toughness test. Subsequently, five mixtures with 20 mm crushed aggregate in the literature, which were previously analyzed according to the TPM for different w/c ratios, were modeled according to the double-K model in the current study. Consequently, two monograms combining the relationships between quantities of fresh concrete components and the aforementioned fracture toughness parameters were presented for concrete mixture design. Furthermore, a reliable approach based on the TPM was proposed for the WS test to determine unstable fracture toughness.
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References
Hillerborg A, Modéer M, Petersson P-E (1976) Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cem Concr Res 6:773–781. https://doi.org/10.1016/0008-8846(76)90007-7
Bažant ZP, Oh BH (1983) Crack band theory for fracture of concrete. Matériaux Constr 16:155–177. https://doi.org/10.1007/BF02486267
Jenq Y, Shah SP (1985) Two parameter fracture model for concrete. J Eng Mech 111:1227–1241. https://doi.org/10.1061/(ASCE)0733-9399(1985)111:10(1227)
Nallathambi P, Karihaloo BL (1986) Determination of specimen-size independent fracture toughness of plain concrete. Mag Concr Res 38:67–76. https://doi.org/10.1680/macr.1986.38.135.67
Carpinteri A (1989) Cusp catastrophe interpretation of fracture instability. J Mech Phys Solids 37:567–582. https://doi.org/10.1016/0022-5096(89)90029-X
Bažant ZP, Kazemi MT (1990) Determination of fracture energy, process zone longth and brittleness number from size effect, with application to rock and conerete. Int J Fract 44:111–131. https://doi.org/10.1007/BF00047063
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 98:111–149. https://doi.org/10.1023/A:1018668929989
Hu X, Duan K (2008) Size effect and quasi-brittle fracture: the role of FPZ. Int J Fract 154:3–14. https://doi.org/10.1007/s10704-008-9290-7
Brühwiler E, Wittmann FH (1990) The wedge splitting test, a new method of performing stable fracture mechanics tests. Eng Fract Mech 35:117–125. https://doi.org/10.1016/0013-7944(90)90189-N
Sabir BB, Asili M (1996) Stress analysis of a fracture test specimen for cementitious materials. Cem Concr Compos 18:141–151. https://doi.org/10.1016/0958-9465(96)00011-X
Ince R (2021) Usage of compact compression specimens to determine non-linear fracture parameters of concrete. Fatigue Fract Eng Mater Struct 44:410–426. https://doi.org/10.1111/ffe.13368
Ince R (2021) Utilization of splitting strips in fracture mechanics tests of quasi-brittle materials. Arch Appl Mech 91:2661–2679. https://doi.org/10.1007/s00419-021-01913-5
Xu S, Li Q, Wu Y et al (2021) RILEM standard: testing methods for determination of the double-K criterion for crack propagation in concrete using wedge-splitting tests and three-point bending beam tests, recommendation of RILEM TC265-TDK. Mater Struct 54:220. https://doi.org/10.1617/s11527-021-01786-8
Xu S, Li Q, Wu Y et al (2021) Influential factors for double-K fracture parameters analyzed by the round robin tests of RILEM TC265-TDK. Mater Struct 54:227. https://doi.org/10.1617/s11527-021-01791-x
Rong H, Dong W, Zhang X, Zhang B (2019) Size effect on fracture properties of concrete after sustained loading. Mater Struct 52:16. https://doi.org/10.1617/s11527-019-1326-0
Tang T, Ouyang C, Shah SP (1996) Simple method for determining material fracture parameters from peak loads. ACI Mater J 93:147–157. https://doi.org/10.14359/1413
Yang S, Tang T, Zollinger DG, Gurjar A (1997) Splitting tension tests to determine concrete fracture parameters by peak-load method. Adv Cem Based Mater 5:18–28. https://doi.org/10.1016/S1065-7355(97)90011-0
Yang S, Tang T (1998) A systematic method to determine optimal specimen geometry for measuring concrete fracture properties by the peak-load method. Cem Concr Aggregates 20:278. https://doi.org/10.1520/CCA10422J
Rocco C, Guinea GV, Planas J, Elices M (1999) Size effect and boundary conditions in the brazilian test: theoretical analysis. Mater Struct 32:437–444. https://doi.org/10.1007/BF02482715
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. https://doi.org/10.1016/j.engfracmech.2010.05.007
Ince R (2012) Determination of concrete fracture parameters based on peak-load method with diagonal split-tension cubes. Eng Fract Mech 82:100–114. https://doi.org/10.1016/j.engfracmech.2011.11.026
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. https://doi.org/10.1016/j.engfracmech.2012.08.024
Abrams DA (1918) Design of concrete mixtures. Lewis Inst Bull 1:1–20
Li Z (2011) Advanced concrete technology. Wiley
Ghimire A, Noor-E-Khuda S, Ullah SN, Suntharavadivel T (2022) Determination of Mohr-Coulomb failure envelope, mechanical properties and UPV of commercial cement-lime mortar. Mater Struct 55:111. https://doi.org/10.1617/s11527-022-01959-z
Monteiro PJM, Helene PRL, Kang SH (1993) Designing concrete mixtures for strength, elastic modulus and fracture energy. Mater Struct 26:443–452. https://doi.org/10.1007/BF02472804
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. https://doi.org/10.1016/j.matdes.2013.02.018
Ince R, Bildik AT (2021) A preliminary concrete mixture design based on fracture toughness. Mater Struct 54:11. https://doi.org/10.1617/s11527-020-01604-7
Emadi AA, Modarres A (2022) The impact of water to cement ratio on the fracture behavior of rubberized concrete. Constr Build Mater 315:125754. https://doi.org/10.1016/j.conbuildmat.2021.125754
Karihaloo BL, Nallathambi P (1991) Notched beam test: mode I fracture toughness. In: Shah SP, Carpinteri A (eds) Fracture mechanics test methods for concrete. CRC Press, pp 1–86
Shah SP (1990) Determination of fracture parameters (K Ic s and CTODc) of plain concrete using three-point bend tests. Mater Struct 23:457–460. https://doi.org/10.1007/BF02472029
Bažant ZP (1994) Discussion of “ fracture mechanics and size effect of concrete in tension ” by Tianxi Tang, Surendra P. Shah, and Chengsheng Ouyang (November, 1992, Vol. 118, No. 11). J Struct Eng 120:2555–2558. https://doi.org/10.1061/(ASCE)0733-9445(1994)120:8(2555)
Ince R, Fenerli C (2022) Determination of tensile strength of cementitious composites using fracture parameters of two-parameter model for concrete fracture. Constr Build Mater 344:128222. https://doi.org/10.1016/j.conbuildmat.2022.128222
Xu S, Reinhardt HW (1999) Determination of double-K criterion for crack propagation in quasi-brittle fracture, Part II: analytical evaluating and practical measuring methods for three-point bending notched beams. Int J Fract 98:151–177. https://doi.org/10.1023/A:1018740728458
Xu S, Reinhardt WH, Wu Z, Zhao Y (2003) Comparison between the double-K fracture model and the two parameter fracture model. Otto-Graf-Journal 14:131–157
Barr BIG, Evans WT, Dowers RC (1981) Fracture toughness of polypropylene fibre concrete. Int J Cem Compos Light Concr 3:115–122. https://doi.org/10.1016/0262-5075(81)90005-1
Tang T (1994) Effects of load-distributed width on split tension of unnotched and notched cylindrical specimens. J Test Eval 22:401. https://doi.org/10.1520/JTE12656J
Guinea GV, Elices M, Planas J (1996) Stress intensity factors for wedge-splitting geometry. Int J Fract 81:113–124. https://doi.org/10.1007/BF00033177
Saxena A, Hudak SJ (1978) Review and extension of compliance information for common crack growth specimens. Int J Fract 14:453–468. https://doi.org/10.1007/BF01390468
Bažant ZP, Becq-Giraudon E (2002) Statistical prediction of fracture parameters of concrete and implications for choice of testing standard. Cem Concr Res 32:529–556. https://doi.org/10.1016/S0008-8846(01)00723-2
Ince R (2004) Prediction of fracture parameters of concrete by artificial neural networks. Eng Fract Mech 71:2143–2159. https://doi.org/10.1016/j.engfracmech.2003.12.004
Ince R (2010) Artificial neural network-based analysis of effective crack model in concrete fracture. Fatigue Fract Eng Mater Struct 33:595–606. https://doi.org/10.1111/j.1460-2695.2010.01469.x
Ince R, Çetin SY (2019) Effect of grading type of aggregate on fracture parameters of concrete. Mag Concr Res 71:860–868. https://doi.org/10.1680/jmacr.18.00095
Ince R, Fenerli C (2021) Residual strength prediction based on size effect of cracked concrete members. Mag Concr Res 1–10. https://doi.org/10.1680/jmacr.21.00018
L’Hermite R (1955) Idées actuelles sur la technologie du béton. Documentation technique du bâtiment et des travaux publics
Kumar S, Barai SV (2010) Determining the double-K fracture parameters for three-point bending notched concrete beams using weight function. Fatigue Fract Eng Mater Struct 33:645–660. https://doi.org/10.1111/j.1460-2695.2010.01477.x
AC, (2014) ACI-318: Building code requirements for structural concrete and commentary for structural concrete. Farmington Hills, American concrete institute, Michigan
Walpole RE, Myers RH, Myers SL, Ye K (2012) Probability & statistics for engineers & scientists, 9th edn. Prentice Hall, Boston
Alyamaç KE, Ince R (2009) A preliminary concrete mix design for SCC with marble powders. Constr Build Mater 23:1201–1210. https://doi.org/10.1016/j.conbuildmat.2008.08.012
Lyse I (1932) Tests on consistency and strength of concrete having constant water content. Proc ASTM 32:1–13
Zhu L, Zhao C, Dai J (2021) Prediction of compressive strength of recycled aggregate concrete based on gray correlation analysis. Constr Build Mater 273:121750. https://doi.org/10.1016/j.conbuildmat.2020.121750
van Mier JGM (1997) Fracture processes of concrete: assessment of material parameters for fracture models. CRC Press, Boca Raton, FL
Shah SP, Swartz SE, Ouyang C (1995) Fracture mechanics of concrete: applications of fracture mechanics to concrete, rock and other quasi-brittle materials. John Wiley & Sons, Canada
Masoud MA, Rashad AM, Sakr K et al (2020) Possibility of using different types of Egyptian serpentine as fine and coarse aggregates for concrete production. Mater Struct 53:87. https://doi.org/10.1617/s11527-020-01525-5
Stephen SJ, Gettu R (2020) Fatigue fracture of fibre reinforced concrete in flexure. Mater Struct 53:56. https://doi.org/10.1617/s11527-020-01488-7
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Ince, R., Bildik, A.T. Batch design of cementitious composites for the double-K fracture model. Mater Struct 56, 145 (2023). https://doi.org/10.1617/s11527-023-02238-1
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DOI: https://doi.org/10.1617/s11527-023-02238-1