Technical Papers
Feb 25, 2023

Determination of Double-K Fracture Parameters of Concrete Using Bottom-Notched Splitting Test

Publication: Journal of Materials in Civil Engineering
Volume 35, Issue 5

Abstract

A new fracture test method—the bottom-notched splitting (BNS) test—is proposed in this study to determine the double-K fracture parameters of concrete. In the BNS test, the concrete cube with a preset crack on the bottom surface is subjected to a line compressive load on the top surface. Numerical analyses are first carried out to simulate the stress distributions along the ligament and crack opening profiles of the BNS specimens. Then, the fitting expressions of the stress intensity factor and the crack center opening displacement are derived based on the linear elastic fracture mechanics. A series of BNS tests and three-point bending (TPB) tests with different ratios of the preset crack length to the specimen height are conducted to determine the double-K fracture parameters of the concrete. The results indicate that the preset cracks in the BNS tests could initiate and propagate throughout the whole cross-sections of the concrete cubes. By substituting the obtained initial fracture loads, maximum loads, and critical crack center opening displacements in the BNS tests into the fitting expressions, the double-K fracture parameters could be determined. By comparing with the TPB tests, the BNS tests proved to be an effective method to determine the double-K fracture parameters of concrete. The BNS tests are convenient to operate and can reduce the damage risk of the preset cracks. Meanwhile, they also would be appropriate for assessing the fracture properties of existing concrete structures in service because the cubes can be easily obtained from the samples core-drilled from existing concrete structures.

Get full access to this article

View all available purchase options and get full access to this article.

Data Availability Statement

Some or all data, models, or codes that support the findings of this study are available from the corresponding author upon reasonable request.

Acknowledgments

The authors gratefully acknowledge the financial support of the National Natural Science Foundation of China under the Grants NSFC 52179123 and NSFC 51878117.

References

Bakour, A., and M. B. Ftima. 2022. “Investigation of fracture properties and size effects of mass concrete using wedge splitting tests on large specimens.” Eng. Fract. Mech. 259 (Jan): 108144. https://doi.org/10.1016/j.engfracmech.2021.108144.
Bažant, Z. P., and M. T. Kazemi. 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.
Bažant, Z. P., and M. T. Kazemi. 1991. “Size dependence of concrete fracture energy determined by RILEM work-of-fracture method.” Int. J. Fract. 51 (2): 121–138. https://doi.org/10.1007/BF00033974.
Bhowmik, S., and S. Ray. 2019. “An experimental approach for characterization of fracture process zone in concrete.” Eng. Fract. Mech. 211 (Apr): 401–419. https://doi.org/10.1016/j.engfracmech.2019.02.026.
Cifuentes, H., and B. L. Karihaloo. 2013. “Determination of size-independent specific fracture energy of normal- and high-strength self-compacting concrete from wedge splitting tests.” Constr. Build. Mater. 48 (Nov): 548–553. https://doi.org/10.1016/j.conbuildmat.2013.07.062.
Dong, W., Z. Wu, and X. Zhou. 2013a. “Calculating crack extension resistance of concrete based on a new crack propagation criterion.” Constr. Build. Mater. 38 (Jan): 879–889. https://doi.org/10.1016/j.conbuildmat.2012.09.037.
Dong, W., W. Yuan, B. Zhang, and H. Zhong. 2022. “Energy-based fracture criterion of rock-concrete interface considering viscoelastic characteristics.” J. Eng. Mech. 148 (2): 04021155.
Dong, W., X. Zhou, and Z. Wu. 2013b. “On fracture process zone and crack extension resistance of concrete based on initial fracture toughness.” Constr. Build. Mater. 49 (Dec): 352–363. https://doi.org/10.1016/j.conbuildmat.2013.08.041.
Dong, W., X. Zhou, and Z. Wu. 2016. “Fracture mechanisms of rock-concrete interface: Experimental and numerical.” J. Eng. Mech. 142 (7): 04016040.
Gao, S., L. Qi, Y. Zhu, and W. Wang. 2022. “Effect of notch depth ratio on mode I and mixed mode I-II fracture properties of engineered cementitious composites (ECC).” Int. J. Solids Struct. 236–237 (Feb): 111363. https://doi.org/10.1016/j.ijsolstr.2021.111363.
Guan, J., X. Hu, and Q. Li. 2016. “In-depth analysis of notched 3-p-b concrete fracture.” Eng. Fract. Mech. 165 (Oct): 57–71. https://doi.org/10.1016/j.engfracmech.2016.08.020.
Guan, J., Q. Li, Z. Wu, S. Zhao, W. Dong, and S. Zhou. 2015. “Minimum specimen size for fracture parameters of site-casting dam concrete.” Constr. Build. Mater. 93 (Jun): 973–982. https://doi.org/10.1016/j.conbuildmat.2015.05.060.
Hall, E., B. Pulatsu, E. Erdogmus, and B. Skourup. 2022. “Compression, tension, and fracture energy properties of compressed cement-stabilized earth blocks.” J. Archit. Eng. 28 (1): 06021005. https://doi.org/10.1061/(ASCE)AE.1943-5568.0000524.
Hillerborg, A., M. Modéer, and P. E. Petersson. 1976. “Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements.” Cem. Concr. Res. 6 (6): 773–781. https://doi.org/10.1016/0008-8846(76)90007-7.
Hu, S., X. Zhang, and S. Xu. 2015. “Effects of loading rates on concrete double-K fracture parameters.” Eng. Fract. Mech. 149 (Nov): 58–73. https://doi.org/10.1016/j.engfracmech.2015.09.027.
Hu, X., and F. H. Wittmann. 1990. “Experimental method to determine extension of fracture-process zone.” J. Mater. Civ. Eng. 2 (1): 15–23. https://doi.org/10.1061/(ASCE)0899-1561(1990)2:1(15).
Ince, R. 2010. “Determination of concrete fracture parameters based on two-parameter and size effect models using split-tension cubes.” Eng. Fract. Mech. 77 (12): 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 (Mar): 100–114. https://doi.org/10.1016/j.engfracmech.2011.11.026.
Kumar, S., and S. V. Barai. 2009. “Determining double-K fracture parameters of concrete for compact tension and wedge splitting tests using weight function.” Eng. Fract. Mech. 76 (7): 935–948. https://doi.org/10.1016/j.engfracmech.2008.12.018.
Lacidogna, G., G. Piana, and A. Carpinteri. 2019. “Damage monitoring of three-point bending concrete specimens by acoustic emission and natural frequency analysis.” Eng. Fract. Mech. 210 (Feb): 203–211. https://doi.org/10.1016/j.engfracmech.2018.06.034.
Lei, B., H. Li, J. Zuo, H. Liu, M. Yu, and G. Wu. 2021. “Meso-fracture mechanism of Longmaxi shale with different crack-depth ratios: Experimental and numerical investigations.” Eng. Fract. Mech. 257 (Nov): 108025. https://doi.org/10.1016/j.engfracmech.2021.108025.
Li, Q., J. Guan, Z. Wu, W. Dong, and S. Zhou. 2015. “Fracture behavior of site-casting dam concrete.” ACI Mater. J. 112 (1): 11–20.
Li, X., Z. Wu, J. Zheng, and A. Alahdal. 2016. “Effect of loading rate on bond behavior of deformed reinforcing bars in concrete under biaxial lateral pressures.” J. Struct. Eng. 142 (6): 04016027. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001479.
Li, X., Z. Wu, J. Zheng, H. Liu, and W. Dong. 2018. “Hysteretic bond stress-slip response of deformed bars in concrete under uniaxial lateral pressure.” J. Struct. Eng. 144 (6): 04018041. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002031.
Lu, Y., and Z. Li. 2012. “Study of the relationship between concrete fracture energy and AE signal energy under uniaxial compression.” J. Mater. Civ. Eng. 24 (5): 538–547. https://doi.org/10.1061/(ASCE)MT.1943-5533.0000418.
Ouyang, C., B. Mobasher, and S. P. Shah. 1990. “An R-curve approach for fracture of quasi-brittle materials.” Eng. Fract. Mech. 37 (4): 901–913. https://doi.org/10.1016/0013-7944(90)90087-W.
Ožbolt, J., J. Bošnjak, and E. Sola. 2013. “Dynamic fracture of concrete compact tension specimen: Experimental and numerical study.” Int. J. Solids Struct. 50 (25–26): 4270–4278. https://doi.org/10.1016/j.ijsolstr.2013.08.030.
Pradhan, S., S. Kumar, and S. V. Barai. 2020. “Impact of particle packing method of design mix on fracture behavior of concrete: Critical analysis.” J. Mater. Civ. Eng. 32 (4): 04020045. https://doi.org/10.1061/(ASCE)MT.1943-5533.0003138.
Qing, L., and Y. Cheng. 2018. “The fracture extreme theory for determining the effective fracture toughness and tensile strength of concrete.” Theor. Appl. Fract. Mech. 96 (Aug): 461–467. https://doi.org/10.1016/j.tafmec.2018.06.009.
Qing, L., M. Dong, and J. Guan. 2018. “Determining initial fracture toughness of concrete for split-tension specimens based on the extreme theory.” Eng. Fract. Mech. 189 (Feb): 427–438. https://doi.org/10.1016/j.engfracmech.2017.11.011.
Ruiz, G., J. J. Ortega, R. C. Yu, S. Xu, and Y. Wu. 2016. “Effect of size and cohesive assumptions on the double-K fracture parameters of concrete.” Eng. Fract. Mech. 166 (Oct): 198–217. https://doi.org/10.1016/j.engfracmech.2016.09.001.
Shah, S. P. 1990. “Determination of fracture parameters (KsIC and CTODc) of plain concrete using three-point bend tests.” Mater. Struct. 23 (6): 457–460. https://doi.org/10.1007/BF02472029.
Shi, Z. H. 2004. “Numerical analysis of mixed-mode fracture in concrete using extended fictitious crack model.” J. Struct. Eng. 130 (11): 1738–1747. https://doi.org/10.1061/(ASCE)0733-9445(2004)130:11(1738).
Shi, Z. H., M. Ohtsu, M. Suzuki, and Y. Hibino. 2001. “Numerical analysis of multiple cracks in concrete using the discrete approach.” J. Struct. Eng. 127 (9): 1085–1091. https://doi.org/10.1061/(ASCE)0733-9445(2001)127:9(1085).
Tang, T., Z. P. Bažant, S. Yang, and D. Zollinger. 1996. “Variable-notch one-size test method for fracture energy and process zone length.” Eng. Fract. Mech. 55 (3): 383–404. https://doi.org/10.1016/0013-7944(96)00030-6.
Wang, B., X. Hu, and P. Lu. 2020. “Modelling and testing of large-scale masonry elements under three-point bending—Tough and strong nacre-like structure enlarged by a factor of 20,000.” Eng. Fract. Mech. 229 (Apr): 106961. https://doi.org/10.1016/j.engfracmech.2020.106961.
Wu, Z., H. Rong, J. Zheng, and W. Dong. 2013. “Numerical method for mixed-mode I-II crack propagation in concrete.” J. Eng. Mech. 139 (11): 1530–1538.
Wu, Z., H. Rong, J. Zheng, F. Xu, and W. Dong. 2011. “An experimental investigation on the FPZ properties in concrete using digital image correlation technique.” Eng. Fract. Mech. 78 (17): 2978–2990. https://doi.org/10.1016/j.engfracmech.2011.08.016.
Xu, S., and H. W. Reinhardt. 1999a. “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. https://doi.org/10.1023/A:1018668929989.
Xu, S., and H. W. Reinhardt. 1999b. “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 (2): 151–177. https://doi.org/10.1023/A:1018740728458.
Xu, S., and H. W. Reinhardt. 2000. “A simplified method for determining double-K fracture parameters for three-point bending tests.” Int. J. Fract. 104 (2): 181–209. https://doi.org/10.1023/A:1007676716549.
Yuan, W., W. Dong, B. Zhang, and H. Zhong. 2021. “Investigations on fracture properties and analytical solutions of fracture parameters at rock-concrete interface.” Constr. Build. Mater. 300 (3): 124040. https://doi.org/10.1016/j.conbuildmat.2021.124040.
Zhang, X., and S. Xu. 2011. “A comparative study on five approaches to evaluate double-K fracture toughness parameters of concrete and size effect analysis.” Eng. Fract. Mech. 78 (10): 2115–2138. https://doi.org/10.1016/j.engfracmech.2011.03.014.
Zhao, Z., S. Kwon, and S. P. Shah. 2008. “Effect of specimen size on fracture energy and softening curve of concrete: Part I. Experiments and fracture energy.” Cem. Concr. Res. 38 (8): 1049–1060. https://doi.org/10.1016/j.cemconres.2008.03.017.

Information & Authors

Information

Published In

Go to Journal of Materials in Civil Engineering
Journal of Materials in Civil Engineering
Volume 35Issue 5May 2023

History

Received: Jan 28, 2022
Accepted: Aug 24, 2022
Published online: Feb 25, 2023
Published in print: May 1, 2023
Discussion open until: Jul 25, 2023

Permissions

Request permissions for this article.

Authors

Affiliations

Wenyan Yuan [email protected]
Doctoral Student, State Key Laboratory of Coastal and Offshore Engineering, Dalian Univ. of Technology, Dalian 116024, PR China. Email: [email protected]
Professor, State Key Laboratory of Coastal and Offshore Engineering, Dalian Univ. of Technology, Dalian 116024, PR China (corresponding author). Email: [email protected]
Binsheng Zhang [email protected]
Professor, Dept. of Civil Engineering and Environmental Management, School of Computing, Engineering and Built Environment, Glasgow Caledonian Univ., Glasgow G4 0BA, UK. Email: [email protected]
Master’s Student, State Key Laboratory of Coastal and Offshore Engineering, Dalian Univ. of Technology, Dalian 116024, PR China. Email: [email protected]

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

  • Experimental Study on Dynamic Fracture Properties of Concrete under Small Eccentricity Loading, Journal of Materials in Civil Engineering, 10.1061/JMCEE7.MTENG-17503, 36, 8, (2024).

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share