Technical Papers
Jan 18, 2013

Numerical Method for Mixed-Mode I–II Crack Propagation in Concrete

Publication: Journal of Engineering Mechanics
Volume 139, Issue 11

Abstract

A crack-propagation criterion is proposed in this paper for mixed-mode I–II fracture in concrete. In this criterion, crack propagation is initiated when the difference between the stress-intensity factor at the crack tip caused by the external force and that by the cohesive stress satisfies the crack-initiation equation. On the basis of this criterion, a numerical method is developed to simulate mixed-mode I–II crack propagation in concrete. To verify the criterion, three sets of experimental data are selected: one is obtained from the self-conducted test and the other two are collected from the literature. The numerical results show that the calculated load versus crack-mouth opening and sliding displacement curves and crack trajectories are in good agreement with experimental results. Therefore, once the mode I initial cracking toughness, elastic modulus, fracture energy, possion’s ratio, and tensile strength of concrete are available, the whole mixed-mode I–II fracture process in concrete can be predicted with reasonable accuracy.

Get full access to this article

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

Acknowledgments

The financial support from the National Natural Science Foundation with Grant Nos. 50878036 and 51121005 and the National Basic Research Program (973 Program) with Grant No. 2009CB623200, of the People’s Republic of China, is greatly acknowledged.

References

Anderson, T. L. (2004). Fracture mechanics: Fundamentals and applications, CRC Press, Boston.
Arrea, M., and Ingraffea, A. R. (1982). “Mixed-mode crack propagation in mortar and concrete.” Rep. No. 81-113, Dept. of Structural Engineering, Cornell Univ., Ithaca, NY.
Barpi, F., and Valente, S. (2000). “Numerical simulation of prenotched gravity dam models.” J. Eng. Mech., 126(6), 611–619.
Bažant, Z. P., and Oh, B. H. (1983). “Crack band theory for fracture of concrete.” Mater. Struct., 16(3), 155–177.
Beer, F. P., and Johnston, E. R. (1981). Mechanics of material, McGraw Hill, New York.
Bocca, P., Carpinteri, A., and Valente, S. (1991). “Mixed mode fracture of concrete.” Int. J. Solids Struct., 27(9), 1139–1153.
Carpinteri, A., and Massabó, R. (1997). “Reversal in failure scaling transition of fibrous composites.” J. Eng. Mech., 123(2), 107–114.
Carpinteri, A., Valente, S., Ferrara, G., and Imperato, L. (1992). “Experimental and numerical fracture modeling of a gravity dam.” Fracture mechanics of concrete structures, Elsevier, New York, 351–360.
Carter, B. J., Chen, C. S., Ingraffea, A. R., and Wawrzynek, P. A. (1997). “A topology based system for simulating 3D crack growth in solid and shell structures.” Proc., 9th Int. Congress on Fracture ICF9, Elsevier, Sydney, Australia.
Dias-da-Costa, D., Alfaiate, J., Sluys, L. J., and Júlio, E. (2010). “A comparative study on the modelling of discontinuous fracture by means of enriched nodal and element techniques and interface elements.” Int. J. Fract., 161(1), 97–119.
Dolbow, J., Moës, N., and Belytschko, T. (2000). “Discontinuous enrichment in finite elements with a partition of unity method.” Finite Elem. Anal. Des., 36(3–4), 235–260.
Du, X. H., Duan, Y. L., and Wang, G. L. (2005). “Numerical analysis of fracture in gravity dam.” J. Hydraul. Eng., 36(9), 1–10 (in Chinese).
Erdogan, F., and Sih, G. C. (1963). “On the crack extension in plates under plane loading and transverse shear.” J. Basic Eng., 85(4), 519–525.
Foote, R. M. L., Mai, Y. W., and Cotterell, B. (1986). “Crack growth resistance curves in strain-softening materials.” J. Mech. Phys. Solids, 34(6), 593–607.
Guo, Z. K., Kobayashi, A. S., and Hawkins, N. M. (1994). “Mixed modes I and II concrete fracture: an experimental analysis.” J. Appl. Mech., 61(4), 815–821.
Hillerborg, A., Modeer, M., and Petersson, P. E. (1976). “Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements.” Cement Concr. Res., 6(6), 773–782.
Hillerborg, A., and Rots, J. (1989). “Crack opening and numerical modelling.” Fracture mechanics of concrete structures, L. Elfgren, ed., Chapman & Hall, London, 128–146.
Ingraffea, A. R. (1990). “Case studies of simulation of fracture in concrete dams.” Eng. Fract. Mech., 35(1–3), 553–564.
Kim, H. G. (2003). “Interface element method: Treatment of non-matching nodes at the ends of interfaces between partitioned domains.” Comput. Methods Appl. Mech. Eng., 192(15), 1841–1858.
Kumar, R., and Nayak, G. C. (1994). “Numerical modeling of tensile crack propagation in concrete dams.” J. Struct. Eng., 120(4), 1053–1074.
Li, S., Thouless, M. D., Waas, A. M., Schroeder, J. A., and Zavattieri, P. D. (2005). “Use of a cohesive-zone model to analyze the fracture of a fiber-reinforced polymer-matrix composite.” Compos. Sci. Technol., 65(3–4), 537–549.
Li, V. C., and Liang, E. (1986). “Fracture processes in concrete and fiber reinforced cementitious composites.” J. Eng. Mech., 112(6), 566–586.
Lohrasbi, A. R., and Attarnejad, R. (2008). “Crack growth in concrete gravity dams based on discrete crack method.” Am. J. Eng. Appl. Sci., 1(4), 318–323.
Mai, Y. W. (2002). “Cohesive zone and crack-resistance (R)-curve of cementitious materials and their fibre-reinforced composites.” Eng. Fract. Mech., 69(2), 219–233.
Ohtsu, M., Kaminaga, Y., and Munwam, M. C. (1999). “Experimental and numerical crack analysis of mixed-mode failure in concrete by acoustic emission and boundary element method.” Construct. Build. Mater., 13(1–2), 57–64.
Petersson, P. E. (1981). “Crack growth and development of fracture zones in plain concrete and similar materials.” Technical Rep. TVBM-1006, Div. of Building Materials, Lund Univ., Lund, Sweden.
Plizzari, G. A. (1997). “LEFM applications to concrete gravity dams.” J. Eng. Mech., 123(8), 808–815.
Plizzari, G., Waggoner, F., and Saouma, V. E. (1995). “Centrifuge modeling and analysis of concrete gravity dams.” J. Struct. Eng., 121(10), 1471–1479.
RILEM 50-FMC Draft Recommendation. (1985). “Determination of the fracture energy of mortar and concrete by means of three-point bend tests on notched beams.” Mater. Struct., 18(4), 287–290.
Saleh, A. L., and Aliabadi, M. H. (1995). “Crack growth analysis in concrete using boundary element method.” Eng. Fract. Mech., 51(4), 533–545.
Shi, Z. H. (2004). “Numerical analysis of mixed-mode fracture in concrete using extended fictitious crack model.” J. Struct. Eng., 130(11), 1738–1747.
Unger, F. J., Eckardt, S., and Konke, C. (2007). “Modelling of cohesive crack growth in concrete structures with the extended finite element method.” Comput. Methods Appl. Mech. Eng., 196(41–44), 4087–4100.
Walter, H., Gerstle, W. H., and Xie, M. (1992). “FEM modeling of fictitious crack propagation in concrete.” J. Struct. Eng., 118(2), 416–432.
Wittmann, F. H., and Hu, X. Z. (1991). “Fracture process zone in cementitious materials.” Int. J. Fract., 51(1), 3–18.
Xu, S. L., and Reinhardt, H. W. (1999). “Determination of double-K criterion for crack propagation in quasi-brittle fracture, II: Analytical evaluating and practical measuring methods for three-point bending notched beams.” Int. J. Fract., 98(2), 151–177.
Yang, Z. J., and Chen, J. F. (2004). “Fully automatic modelling of cohesive discrete crack propagation in concrete beams using local arc-length methods.” Int. J. Solids Struct., 41(3–4), 801–826.
Zhang, J., and Victor, C. L. (2004). “Simulation of crack propagation in fiber-reinforced concrete by fracture mechanics.” Cement Concr. Res., 34(2), 333–339.

Information & Authors

Information

Published In

Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 139Issue 11November 2013
Pages: 1530 - 1538

History

Received: May 13, 2012
Accepted: Jan 16, 2013
Published online: Jan 18, 2013
Published in print: Nov 1, 2013

Permissions

Request permissions for this article.

Authors

Affiliations

Professor, State Key Laboratory of Coastal and Offshore Engineering, Dalian Univ. of Technology, Dalian 116024, P. R. China (corresponding author). E-mail: [email protected]
Hua Rong
Ph.D. Student, State Key Laboratory of Coastal and Offshore Engineering, Dalian Univ. of Technology, Dalian 116024, P. R. China.
JianJun Zheng
Professor, School of Civil Engineering and Architecture, Zhejiang Univ. of Technology, Hangzhou 310014, P. R. China.
Wei Dong, Ph.D.
Lecturer, State Key Laboratory of Coastal and Offshore Engineering, Dalian Univ. of Technology, Dalian 116024, P. R. China.

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

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