Multigene Genetic Programming Based Prediction of Concrete Fracture Parameters of Unnotched Specimens

M. R. Sudhir, M. Beulah

Abstract


This study explores the fracture energy of notched and unnotched concrete specimens subjected to the classical three-point bend test, instantiating a gradational step in the continued development of concrete fracture mechanics. An experimental campaign involving 18 notched test specimens and nine unnotched specimens of three different grades of concrete, an examination of the existing literature models for unnotched specimens, and a novel Multigene Genetic programming (MGGP) based concrete fracture energy model for unnotched specimens are integral to this study. As a salient result, the multiple approaches to quasi-brittle materials adopted in the study, highlighted the criticality of the determination of fracture energy, tensile strength and characteristic length for the crack width study. The failure modes of notched and unnotched specimens were found to be similar. The reported literature has mainly focused on a limited number of fracture energy influencing parameters. Therefore, six impact parameters have been chosen and incorporated into the present study to provide a more acceptable explanation of concrete fracture behaviour. A sensitivity analysis of the parameters and an error analysis of the model undertaken have established the accuracy and robustness of the developed MGGP model.

 

Doi: 10.28991/CEJ-2023-09-02-011

Full Text: PDF


Keywords


Concrete; Fracture Parameters; Notched and Unnotched Specimens; Multigene Genetic Programming.

References


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.

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.

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.

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.

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.

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.

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.

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.

Mehta, P. K. (1986). Concrete. Structure, properties and materials. Prentice Hall, Hoboken, United States.

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.

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.

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.

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.

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.

Bazzant, Z. P., & Planas, J. (1998). Fracture and size effect in concrete and other quasibrittle materials. CRC Press, Boca Raton, United States.

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.

Østergaard, 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.

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.

Hoover, C. G., P. Bažant, 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.

Hoover, C. G., & Bažant, 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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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).

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.

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.

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.

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.

JCI-S-001e2003. (2003). Method of Test for Fracture Energy of Concrete by Use of Notched Beam. Japan Concrete Institute, Tokyo, Japan.

Hanson, N. W., & Kurvits, O. A. (1965). Instrumentation for Structural Testing. Development Bulletin, 0144, 1-91.

Bažant, 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.

Bažant, Z. P., & Planas, J. (2019). Fracture and Size Effect in Concrete and Other Quasibrittle Materials. Routledge, New York, United States. doi:10.1201/9780203756799.

Darwin, D., Barham, S., Kozul, R., & Luan, S., (2001). Fracture Energy of High-Strength Concrete. ACI Materials Journal, 98(5), 410-417.

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.

IS456-2000 (2000) Indian Standard Plain and Reinforced Concrete Code of Practice. Bureau of Indian Standards, New Delhi, India.

CEB-FIP Model Code. (2010). Final Draft. Federation Internationale Du Béton, Bulletins 65 & 66, Lausanne, Switzerland.

ACI 318-19. (2022). Building Code Requirements for Structural Concrete and Commentary. American Concrete Institute (ACI), Michigan, United States.

ACI 363R-92. (1997). State of the art report on high strength concrete. American Concrete Institute (ACI), Michigan, United States.

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.

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.

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.

Comité Euro-International du Béton, (1990). CEB-FIP Model Code 1990. Thomas Telford, London, United Kingdom.

Bažant, 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.

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.

Strauss, A., Zimmermann, T., Lehký, D., Novák, D., & Keršner, 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.

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.

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.

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.

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.


Full Text: PDF

DOI: 10.28991/CEJ-2023-09-02-011

Refbacks

  • There are currently no refbacks.




Copyright (c) 2023 Sudhir M R, Beulah M

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
x
Message