Multigene Genetic Programming Based Prediction of Concrete Fracture Parameters of Unnotched Specimens
Vol. 9 No. 2 (2023): February
Research Articles
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Doi: 10.28991/CEJ-2023-09-02-011
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Sudhir, M. R., & Beulah, M. (2023). Multigene Genetic Programming Based Prediction of Concrete Fracture Parameters of Unnotched Specimens. Civil Engineering Journal, 9(2), 393–410. https://doi.org/10.28991/CEJ-2023-09-02-011
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[1] Karihaloo, B. L., Abdalla, H. M., & Xiao, Q. Z. (2003). Size effect in concrete beams. Engineering Fracture Mechanics, 70(7–8), 979–993. doi:10.1016/S0013-7944(02)00161-3.
[2] Abdalla, H. M., & Karihaloo, B. L. (2004). A method for constructing the bilinear tension softening diagram of concrete corresponding to its true fracture energy. Magazine of Concrete Research, 56(10), 597–604. doi:10.1680/macr.2004.56.10.597.
[3] Cedolin, L., & Cusatis, G. (2008). Identification of concrete fracture parameters through size effect experiments. Cement and Concrete Composites, 30(9), 788–797. doi:10.1016/j.cemconcomp.2008.05.007.
[4] Raghu Prasad, B. K. (2009). Experimental evaluation of fracture properties of concrete. Interim progress report under collaborative research project between BARC and Indian Institute of Science, Bangalore, India.
[5] Muralidhara, S., Prasad, B. K. R., Eskandari, H., & Karihaloo, B. L. (2010). Fracture process zone size and true fracture energy of concrete using acoustic emission. Construction and Building Materials, 24(4), 479–486. doi:10.1016/j.conbuildmat.2009.10.014.
[6] Skaryński, L., & Tejchman, J. (2010). Calculations of fracture process zones on meso-scale in notched concrete beams subjected to three-point bending. European Journal of Mechanics, A/Solids, 29(4), 746–760. doi:10.1016/j.euromechsol.2010.02.008.
[7] Ince, R., & Cetin, S. Y. (2019). Effect of grading type of aggregate on fracture parameters of concrete. Magazine of Concrete Research, 71(16), 860–868. doi:10.1680/jmacr.18.00095.
[8] Shah, S.P. & Ouyang, C. (1992). Measurement and Modeling of Fracture Processes in Concrete. Materials Science of Concrete. Materials Science of Concrete III, III(I), 243–270, Jan Skalny, United States.
[9] Mehta, P. K. (1986). Concrete. Structure, properties and materials. Prentice Hall, Hoboken, United States.
[10] Hillerborg, A., & Petersson, P. E. (1981). Fracture mechanical calculations, test methods and results for concrete and similar materials. Advances in Fracture Research, 4, 1515-1522.
[11] Mindess, S. (1984). The effect of specimen size on the fracture energy of concrete. Cement and Concrete Research, 14(3), 431–436. doi:10.1016/0008-8846(84)90062-0.
[12] Wittmann, F. H., Roelfstra, P. E., Mihashi, H., Huang, Y. Y., Zhang, X. H., & Nomura, N. (1987). Influence of age of loading, water-cement ratio and rate of loading on fracture energy of concrete. Materials and Structures, 20(2), 103–110. doi:10.1007/BF02472745.
[13] Bazant, Z. P. (2003). Fracture Mechanics of Concrete Structures: Proceedings of the First International Conference on Fracture Mechanics of Concrete Structures (FraMCoS1, 1-5 June 1992, ), Colorado, United States, CRC Press, London, United Kingdom. doi:10.1201/9781482286847.
[14] Hilsdorf, H. K., & Brameshuber, W. (1991). Code-type formulation of fracture mechanics concepts for concrete. International Journal of Fracture, 51(1), 61–72. doi:10.1007/BF00020853.
[15] Bazzant, Z. P., & Planas, J. (1998). Fracture and size effect in concrete and other quasibrittle materials. CRC Press, Boca Raton, United States.
[16] Planas, J., Elices, M., Guinea, G. V., Gómez, F. J., Cendón, D. A., & Arbilla, I. (2003). Generalizations and specializations of cohesive crack models. Engineering Fracture Mechanics, 70(14), 1759–1776. doi:10.1016/s0013-7944(03)00123-1.
[17] í˜stergaard, L., Lange, D., & Stang, H. (2004). Early-age stress-crack opening relationships for high performance concrete. Cement and Concrete Composites, 26(5), 563–572. doi:10.1016/S0958-9465(03)00074-X.
[18] Peterson, P. E. (1980). Fracture energy of concrete: Method of determination. Cement and Concrete Research, 10(1), 79–89. doi:10.1016/0008-8846(80)90054-X.
[19] Hoover, C. G., P. BaŠ¾ant, Z., Vorel, J., Wendner, R., & Hubler, M. H. (2013). Comprehensive concrete fracture tests: Description and results. Engineering Fracture Mechanics, 114, 92–103. doi:10.1016/j.engfracmech.2013.08.007.
[20] Hoover, C. G., & BaŠ¾ant, Z. Z. (2013). Comprehensive concrete fracture tests: Size effects of Types 1 & 2, crack length effect and postpeak. Engineering Fracture Mechanics, 110(281), 281–289. doi:10.1016/j.engfracmech.2013.08.008.
[21] Marí, A., Bairán, J., Cladera, A., Oller, E., & Ribas, C. (2015). Shear-flexural strength mechanical model for the design and assessment of reinforced concrete beams. Structure and Infrastructure Engineering, 11(11), 1399–1419. doi:10.1080/15732479.2014.964735.
[22] Herbrand, M., Stark, A., & Hegger, J. (2019). Size effect in unnotched concrete specimens in bending: An analytical approach. Structural Concrete, 20(2), 660–669. doi:10.1002/suco.201800136.
[23] Chen, Y., Han, X., Hu, X., Wang, B., & Zhu, W. (2019). A strength criterion for size effect on quasi-brittle fracture with and without notch. Proceedings of the 10th International Conference on Fracture Mechanics of Concrete and Concrete Structures. doi:10.21012/fc10.229373.
[24] Khalilpour, S., BaniAsad, E., & Dehestani, M. (2019). A review on concrete fracture energy and effective parameters. Cement and Concrete Research, 120, 294–321. doi:10.1016/j.cemconres.2019.03.013.
[25] Wang, X., Saifullah, H. A., Nishikawa, H., & Nakarai, K. (2020). Effect of water–cement ratio, aggregate type, and curing temperature on the fracture energy of concrete. Construction and Building Materials, 259, 119646. doi:10.1016/j.conbuildmat.2020.119646.
[26] Mobasher, B. (2022). M&S Highlight: Hillerborg (1985), the theoretical basis of a method to determine the fracture energy GF of concrete. Materials and Structures, 55(2), 1–3. doi:10.1617/s11527-021-01859-8.
[27] Albayrak, G., & Albayrak, U. (2016). Investigation of Ready Mixed Concrete Transportation Problem Using Linear Programming and Genetic Algorithm. Civil Engineering Journal, 2(10), 491–496. doi:10.28991/cej-2016-00000052.
[28] Wu, K., Chen, B., & Yao, W. (2000). Study on the AE characteristics of fracture process of mortar, concrete and steel-fiber-reinforced concrete beams. Cement and Concrete Research, 30(9), 1495-1500. doi:10.1016/S0008-8846(00)00358-6
[29] Ince, R., & Fenerli, C. (2022). Determination of tensile strength of cementitious composites using fracture parameters of two-parameter model for concrete fracture. Construction and Building Materials, 344, 128222. doi:10.1016/j.conbuildmat.2022.128222.
[30] Guan, J. F., Song, Z. K., Yao, X. H., Chen, S. S., Yuan, P., & Liu, Z. P. (2020). Determination of fracture toughness of concrete and rock using unnotched specimens. Gongcheng Lixue/Engineering Mechanics, 37(3), 36–45. doi:10.6052/j.issn.1000-4750.2019.03.0082. (In Chinese).
[31] Ince, R. (2021). Utilization of splitting strips in fracture mechanics tests of quasi-brittle materials. Archive of Applied Mechanics, 91(6), 2661–2679. doi:10.1007/s00419-021-01913-5.
[32] Stephen, S. J., & Gettu, R. (2020). Fatigue fracture of fibre reinforced concrete in flexure. Materials and Structures/Materiaux et Constructions, 53(3), 1–11. doi:10.1617/s11527-020-01488-7.
[33] Daneshyar, A., Ghaemian, M., & Du, C. (2022). A fracture energy–based viscoelastic–viscoplastic–anisotropic damage model for rate-dependent cracking of concrete. International Journal of Fracture, 1–26. doi:10.1007/s10704-022-00685-5.
[34] 50-FMC Draft Recommendation. (1985). Determination of the fracture energy of mortar and concrete by means of three-point bend tests on notched beams. Materials and Structures, 18(4), 287–290. doi:10.1007/bf02472918.
[35] JCI-S-001e2003. (2003). Method of Test for Fracture Energy of Concrete by Use of Notched Beam. Japan Concrete Institute, Tokyo, Japan.
[36] Hanson, N. W., & Kurvits, O. A. (1965). Instrumentation for Structural Testing. Development Bulletin, 0144, 1-91.
[37] BaŠ¾ant, Z. P., Yu, Q., & Zi, G. (2002). Choice of standard fracture test for concrete and its statistical evaluation. International Journal of Fracture, 118(4), 303–337. doi:10.1023/A:1023399125413.
[38] BaŠ¾ant, Z. P., & Planas, J. (2019). Fracture and Size Effect in Concrete and Other Quasibrittle Materials. Routledge, New York, United States. doi:10.1201/9780203756799.
[39] Darwin, D., Barham, S., Kozul, R., & Luan, S., (2001). Fracture Energy of High-Strength Concrete. ACI Materials Journal, 98(5), 410-417.
[40] Rosselló, C., Elices, M., & Guinea, G. V. (2006). Fracture of model concrete: 2. Fracture energy and characteristic length. Cement and Concrete Research, 36(7), 1345–1353. doi:10.1016/j.cemconres.2005.04.016.
[41] IS456-2000 (2000) Indian Standard Plain and Reinforced Concrete Code of Practice. Bureau of Indian Standards, New Delhi, India.
[42] CEB-FIP Model Code. (2010). Final Draft. Federation Internationale Du Béton, Bulletins 65 & 66, Lausanne, Switzerland.
[43] ACI 318-19. (2022). Building Code Requirements for Structural Concrete and Commentary. American Concrete Institute (ACI), Michigan, United States.
[44] ACI 363R-92. (1997). State of the art report on high strength concrete. American Concrete Institute (ACI), Michigan, United States.
[45] Phillips, D. V., & Binsheng, Z. (1993). Direct tension tests on notched and un-notched plain concrete specimens. Magazine of Concrete Research, 45(162), 25–35. doi:10.1680/macr.1993.45.162.25.
[46] Hillerborg, A. R. N. E. (1983). Concrete fracture energy tests performed by 9 laboratories according to a draft RILEM recommendation. Report to RILEM TC50-FMC, Report TVBM-3015, Lund, Sweden.
[47] Hillerborg, A. (1985). Results of three comparative test series for determining the fracture energy GF of concrete. Materials and Structures, 18(5), 407–413. doi:10.1007/BF02472416.
[48] Comité Euro-International du Béton, (1990). CEB-FIP Model Code 1990. Thomas Telford, London, United Kingdom.
[49] BaŠ¾ant, Z. P., Gettu, R., & Kazemi, M. T. (1991). Identification of nonlinear fracture properties from size effect tests and structural analysis based on geometry-dependent R-curves. International Journal of Rock Mechanics and Mining Sciences and, 28(1), 43–51. doi:10.1016/0148-9062(91)93232-U.
[50] Planas, J., Elices, M., & Guinea, G. V. (1992). Measurement of the fracture energy using three-point bend tests: Part 2-Influence of bulk energy dissipation. Materials and Structures, 25(5), 305–312. doi:10.1007/BF02472671.
[51] Strauss, A., Zimmermann, T., Lehkí½, D., Novák, D., & KerŠ¡ner, Z. (2014). Stochastic fracture"mechanical parameters for the performance"based design of concrete structures. Structural Concrete, 15(3), 380-394. doi:10.1002/suco.201300077.
[52] Martin, J., Stanton, J., Mitra, N., & Lowes, L. N. (2007). Experimental testing to determine concrete fracture energy using simple laboratory test setup. ACI Materials Journal, 104(6), 575–584. doi:10.14359/18961.
[53] Khatieb, M. (2016). Experimental evaluation of concrete fracture energy and its dependency on relevant parameters. International Journal of Applied Engineering Research, 11(20), 10348–10352.
[54] Beygi, M. H. A., Kazemi, M. T., Nikbin, I. M., Vaseghi Amiri, J., Rabbanifar, S., & Rahmani, E. (2014). The influence of coarse aggregate size and volume on the fracture behavior and brittleness of self-compacting concrete. Cement and Concrete Research, 66, 75–90. doi:10.1016/j.cemconres.2014.06.008.
[55] Akram, A. (2021). The Overview of Fracture Mechanics Models for Concrete. Architecture, Civil Engineering, Environment, 14(1), 47–57. doi:10.21307/acee-2021-005.
[2] Abdalla, H. M., & Karihaloo, B. L. (2004). A method for constructing the bilinear tension softening diagram of concrete corresponding to its true fracture energy. Magazine of Concrete Research, 56(10), 597–604. doi:10.1680/macr.2004.56.10.597.
[3] Cedolin, L., & Cusatis, G. (2008). Identification of concrete fracture parameters through size effect experiments. Cement and Concrete Composites, 30(9), 788–797. doi:10.1016/j.cemconcomp.2008.05.007.
[4] Raghu Prasad, B. K. (2009). Experimental evaluation of fracture properties of concrete. Interim progress report under collaborative research project between BARC and Indian Institute of Science, Bangalore, India.
[5] Muralidhara, S., Prasad, B. K. R., Eskandari, H., & Karihaloo, B. L. (2010). Fracture process zone size and true fracture energy of concrete using acoustic emission. Construction and Building Materials, 24(4), 479–486. doi:10.1016/j.conbuildmat.2009.10.014.
[6] Skaryński, L., & Tejchman, J. (2010). Calculations of fracture process zones on meso-scale in notched concrete beams subjected to three-point bending. European Journal of Mechanics, A/Solids, 29(4), 746–760. doi:10.1016/j.euromechsol.2010.02.008.
[7] Ince, R., & Cetin, S. Y. (2019). Effect of grading type of aggregate on fracture parameters of concrete. Magazine of Concrete Research, 71(16), 860–868. doi:10.1680/jmacr.18.00095.
[8] Shah, S.P. & Ouyang, C. (1992). Measurement and Modeling of Fracture Processes in Concrete. Materials Science of Concrete. Materials Science of Concrete III, III(I), 243–270, Jan Skalny, United States.
[9] Mehta, P. K. (1986). Concrete. Structure, properties and materials. Prentice Hall, Hoboken, United States.
[10] Hillerborg, A., & Petersson, P. E. (1981). Fracture mechanical calculations, test methods and results for concrete and similar materials. Advances in Fracture Research, 4, 1515-1522.
[11] Mindess, S. (1984). The effect of specimen size on the fracture energy of concrete. Cement and Concrete Research, 14(3), 431–436. doi:10.1016/0008-8846(84)90062-0.
[12] Wittmann, F. H., Roelfstra, P. E., Mihashi, H., Huang, Y. Y., Zhang, X. H., & Nomura, N. (1987). Influence of age of loading, water-cement ratio and rate of loading on fracture energy of concrete. Materials and Structures, 20(2), 103–110. doi:10.1007/BF02472745.
[13] Bazant, Z. P. (2003). Fracture Mechanics of Concrete Structures: Proceedings of the First International Conference on Fracture Mechanics of Concrete Structures (FraMCoS1, 1-5 June 1992, ), Colorado, United States, CRC Press, London, United Kingdom. doi:10.1201/9781482286847.
[14] Hilsdorf, H. K., & Brameshuber, W. (1991). Code-type formulation of fracture mechanics concepts for concrete. International Journal of Fracture, 51(1), 61–72. doi:10.1007/BF00020853.
[15] Bazzant, Z. P., & Planas, J. (1998). Fracture and size effect in concrete and other quasibrittle materials. CRC Press, Boca Raton, United States.
[16] Planas, J., Elices, M., Guinea, G. V., Gómez, F. J., Cendón, D. A., & Arbilla, I. (2003). Generalizations and specializations of cohesive crack models. Engineering Fracture Mechanics, 70(14), 1759–1776. doi:10.1016/s0013-7944(03)00123-1.
[17] í˜stergaard, L., Lange, D., & Stang, H. (2004). Early-age stress-crack opening relationships for high performance concrete. Cement and Concrete Composites, 26(5), 563–572. doi:10.1016/S0958-9465(03)00074-X.
[18] Peterson, P. E. (1980). Fracture energy of concrete: Method of determination. Cement and Concrete Research, 10(1), 79–89. doi:10.1016/0008-8846(80)90054-X.
[19] Hoover, C. G., P. BaŠ¾ant, Z., Vorel, J., Wendner, R., & Hubler, M. H. (2013). Comprehensive concrete fracture tests: Description and results. Engineering Fracture Mechanics, 114, 92–103. doi:10.1016/j.engfracmech.2013.08.007.
[20] Hoover, C. G., & BaŠ¾ant, Z. Z. (2013). Comprehensive concrete fracture tests: Size effects of Types 1 & 2, crack length effect and postpeak. Engineering Fracture Mechanics, 110(281), 281–289. doi:10.1016/j.engfracmech.2013.08.008.
[21] Marí, A., Bairán, J., Cladera, A., Oller, E., & Ribas, C. (2015). Shear-flexural strength mechanical model for the design and assessment of reinforced concrete beams. Structure and Infrastructure Engineering, 11(11), 1399–1419. doi:10.1080/15732479.2014.964735.
[22] Herbrand, M., Stark, A., & Hegger, J. (2019). Size effect in unnotched concrete specimens in bending: An analytical approach. Structural Concrete, 20(2), 660–669. doi:10.1002/suco.201800136.
[23] Chen, Y., Han, X., Hu, X., Wang, B., & Zhu, W. (2019). A strength criterion for size effect on quasi-brittle fracture with and without notch. Proceedings of the 10th International Conference on Fracture Mechanics of Concrete and Concrete Structures. doi:10.21012/fc10.229373.
[24] Khalilpour, S., BaniAsad, E., & Dehestani, M. (2019). A review on concrete fracture energy and effective parameters. Cement and Concrete Research, 120, 294–321. doi:10.1016/j.cemconres.2019.03.013.
[25] Wang, X., Saifullah, H. A., Nishikawa, H., & Nakarai, K. (2020). Effect of water–cement ratio, aggregate type, and curing temperature on the fracture energy of concrete. Construction and Building Materials, 259, 119646. doi:10.1016/j.conbuildmat.2020.119646.
[26] Mobasher, B. (2022). M&S Highlight: Hillerborg (1985), the theoretical basis of a method to determine the fracture energy GF of concrete. Materials and Structures, 55(2), 1–3. doi:10.1617/s11527-021-01859-8.
[27] Albayrak, G., & Albayrak, U. (2016). Investigation of Ready Mixed Concrete Transportation Problem Using Linear Programming and Genetic Algorithm. Civil Engineering Journal, 2(10), 491–496. doi:10.28991/cej-2016-00000052.
[28] Wu, K., Chen, B., & Yao, W. (2000). Study on the AE characteristics of fracture process of mortar, concrete and steel-fiber-reinforced concrete beams. Cement and Concrete Research, 30(9), 1495-1500. doi:10.1016/S0008-8846(00)00358-6
[29] Ince, R., & Fenerli, C. (2022). Determination of tensile strength of cementitious composites using fracture parameters of two-parameter model for concrete fracture. Construction and Building Materials, 344, 128222. doi:10.1016/j.conbuildmat.2022.128222.
[30] Guan, J. F., Song, Z. K., Yao, X. H., Chen, S. S., Yuan, P., & Liu, Z. P. (2020). Determination of fracture toughness of concrete and rock using unnotched specimens. Gongcheng Lixue/Engineering Mechanics, 37(3), 36–45. doi:10.6052/j.issn.1000-4750.2019.03.0082. (In Chinese).
[31] Ince, R. (2021). Utilization of splitting strips in fracture mechanics tests of quasi-brittle materials. Archive of Applied Mechanics, 91(6), 2661–2679. doi:10.1007/s00419-021-01913-5.
[32] Stephen, S. J., & Gettu, R. (2020). Fatigue fracture of fibre reinforced concrete in flexure. Materials and Structures/Materiaux et Constructions, 53(3), 1–11. doi:10.1617/s11527-020-01488-7.
[33] Daneshyar, A., Ghaemian, M., & Du, C. (2022). A fracture energy–based viscoelastic–viscoplastic–anisotropic damage model for rate-dependent cracking of concrete. International Journal of Fracture, 1–26. doi:10.1007/s10704-022-00685-5.
[34] 50-FMC Draft Recommendation. (1985). Determination of the fracture energy of mortar and concrete by means of three-point bend tests on notched beams. Materials and Structures, 18(4), 287–290. doi:10.1007/bf02472918.
[35] JCI-S-001e2003. (2003). Method of Test for Fracture Energy of Concrete by Use of Notched Beam. Japan Concrete Institute, Tokyo, Japan.
[36] Hanson, N. W., & Kurvits, O. A. (1965). Instrumentation for Structural Testing. Development Bulletin, 0144, 1-91.
[37] BaŠ¾ant, Z. P., Yu, Q., & Zi, G. (2002). Choice of standard fracture test for concrete and its statistical evaluation. International Journal of Fracture, 118(4), 303–337. doi:10.1023/A:1023399125413.
[38] BaŠ¾ant, Z. P., & Planas, J. (2019). Fracture and Size Effect in Concrete and Other Quasibrittle Materials. Routledge, New York, United States. doi:10.1201/9780203756799.
[39] Darwin, D., Barham, S., Kozul, R., & Luan, S., (2001). Fracture Energy of High-Strength Concrete. ACI Materials Journal, 98(5), 410-417.
[40] Rosselló, C., Elices, M., & Guinea, G. V. (2006). Fracture of model concrete: 2. Fracture energy and characteristic length. Cement and Concrete Research, 36(7), 1345–1353. doi:10.1016/j.cemconres.2005.04.016.
[41] IS456-2000 (2000) Indian Standard Plain and Reinforced Concrete Code of Practice. Bureau of Indian Standards, New Delhi, India.
[42] CEB-FIP Model Code. (2010). Final Draft. Federation Internationale Du Béton, Bulletins 65 & 66, Lausanne, Switzerland.
[43] ACI 318-19. (2022). Building Code Requirements for Structural Concrete and Commentary. American Concrete Institute (ACI), Michigan, United States.
[44] ACI 363R-92. (1997). State of the art report on high strength concrete. American Concrete Institute (ACI), Michigan, United States.
[45] Phillips, D. V., & Binsheng, Z. (1993). Direct tension tests on notched and un-notched plain concrete specimens. Magazine of Concrete Research, 45(162), 25–35. doi:10.1680/macr.1993.45.162.25.
[46] Hillerborg, A. R. N. E. (1983). Concrete fracture energy tests performed by 9 laboratories according to a draft RILEM recommendation. Report to RILEM TC50-FMC, Report TVBM-3015, Lund, Sweden.
[47] Hillerborg, A. (1985). Results of three comparative test series for determining the fracture energy GF of concrete. Materials and Structures, 18(5), 407–413. doi:10.1007/BF02472416.
[48] Comité Euro-International du Béton, (1990). CEB-FIP Model Code 1990. Thomas Telford, London, United Kingdom.
[49] BaŠ¾ant, Z. P., Gettu, R., & Kazemi, M. T. (1991). Identification of nonlinear fracture properties from size effect tests and structural analysis based on geometry-dependent R-curves. International Journal of Rock Mechanics and Mining Sciences and, 28(1), 43–51. doi:10.1016/0148-9062(91)93232-U.
[50] Planas, J., Elices, M., & Guinea, G. V. (1992). Measurement of the fracture energy using three-point bend tests: Part 2-Influence of bulk energy dissipation. Materials and Structures, 25(5), 305–312. doi:10.1007/BF02472671.
[51] Strauss, A., Zimmermann, T., Lehkí½, D., Novák, D., & KerŠ¡ner, Z. (2014). Stochastic fracture"mechanical parameters for the performance"based design of concrete structures. Structural Concrete, 15(3), 380-394. doi:10.1002/suco.201300077.
[52] Martin, J., Stanton, J., Mitra, N., & Lowes, L. N. (2007). Experimental testing to determine concrete fracture energy using simple laboratory test setup. ACI Materials Journal, 104(6), 575–584. doi:10.14359/18961.
[53] Khatieb, M. (2016). Experimental evaluation of concrete fracture energy and its dependency on relevant parameters. International Journal of Applied Engineering Research, 11(20), 10348–10352.
[54] Beygi, M. H. A., Kazemi, M. T., Nikbin, I. M., Vaseghi Amiri, J., Rabbanifar, S., & Rahmani, E. (2014). The influence of coarse aggregate size and volume on the fracture behavior and brittleness of self-compacting concrete. Cement and Concrete Research, 66, 75–90. doi:10.1016/j.cemconres.2014.06.008.
[55] Akram, A. (2021). The Overview of Fracture Mechanics Models for Concrete. Architecture, Civil Engineering, Environment, 14(1), 47–57. doi:10.21307/acee-2021-005.
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