Fracture Size Effect: Review of Evidence for Concrete Structures
Publication: Journal of Structural Engineering
Volume 120, Issue 8
Abstract
The paper reviews experimental evidence on the size effect caused by energy release due to fracture growth during brittle failures of concrete structures. The experimental evidence has by now become quite extensive. The size effect is verified for diagonal shear failure and torsional failure of longitudinally reinforced beams without stirrups, punching shear failure of slabs, pull‐out failures of deformed bars and of headed anchors, failure of short and slender tied columns, double‐punch compression failure and for part of the range also the splitting failure of concrete cylinders in the Brazilian test. Although much of this experimental evidence has been obtained with smaller laboratory specimens and concrete of reduced aggregate size, some significant evidence now also exists for normal‐size structures made with normal‐size aggregate. There is also extensive and multifaceted theoretical support. A nonlocal finite element code based on the microplane model is shown to be capable of correctly simulating the existing experimental data on the size effect. More experimental data for large structures with normal‐size aggregate are needed to strengthen the existing verification and improve the calibration of the theory.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Bažant, Z. P., and Oh. (1983). “Crack band theory for fracture of concrete.” Mat. and Struct., Paris, France, 93(16), 155–177.
2.
Bažant, Z. P. (1984). “Size effect in blunt fracture: concrete, rock, metal.” J. Engrg. Mech., ASCE, 110(4), 518–535.
3.
Bažant, Z. P., and Kim, J. K. (1984). “Size effect in shear failure of longitudinally reinforced beams.” J. Am. Concrete Inst., 81(5), 456–468.
4.
Bažant, Z. P. (1986). “Mechanics of distributed cracking.” Appl. Mech. Rev., Vol. 39, 675–705.
5.
Bažant, Z. P. (1987). “Fracture energy of heterogeneous materials and similitude.” Proc., SEM‐RILEM Int. Conf. on Fracture of Concrete and Rock, S. P. Shah and S. E. Swartz, eds., Houston, 390–402.
6.
Bažant, Z. P., and Cao, Z. (1987). “Size effect in punching shear failure of slabs.” ACI Struct. J., Vol. 84, 44–53.
7.
Bažant, Z. P., and Sun, H.‐H. (1987). “Size effect in diagonal shear failure: influence of aggregate size and stirrups.” ACI Mat. J., 84(4), 259–272.
8.
Bažant, Z. P., and Prat, P. C. (1988). “Microplane model for brittle‐plastic material. Parts I and II.” J. Engrg. Mech., ASCE, 114(10), 1672–1702.
9.
Bažant, Z. P., and Sener, S. (1988). “Size effect in pullout tests.” ACI Mat. J., Vol. 85, 347–351.
10.
Bažant, Z. P., Sener, S., and Prat, P. (1988). “Size effect tests of torsional failure of plain and reinforced concrete beams.” Mat. and Struct., Paris, France, 21, 425–430.
11.
Bažant, Z. P., and Lin, F.‐B. (1988). “Nonlocal smeared cracking model for concrete fracture.” J. Engrg. Mech., ASCE, Vol. 114, 2493–2510.
12.
Bažant, Z. P., and Ožbolt, J. (1990). “Nonlocal microplane model for fracture, damage, and size effect in structures.” J. Engrg. Mech., ASCE, 116(11), 2485–2504.
13.
Bažant, Z. P., and Xi, Y. (1991). “Statistical size effect in quasibrittle structures.” J. Engrg. Mech., ASCE, 117(11), 2609–2640.
14.
Bažant, Z. P., Tabbara, M. T., Kazemi, M. T., and Pijaudier‐Cabot, G. (1990). “Random particle model for fracture of aggregates and fiber composites.” J. Engrg. Mech., ASCE, 116(8), 1686–1705.
15.
Bažant, Z. P., and Kazemi, M. T. (1991). “Size effect on diagonal shear failure of beams without stirrups.” ACI Struct. J., Vol. 88, 268–276.
16.
Bažant, Z. P., and Cedolin, L. (1991). Stability of structures: elastic, inelastic, fracture and damage theories. Oxford University Press, New York, N.Y.
17.
Bažant, Z. P., and Kwon, Y. W. (1991). “Size effect in failure of short or slender reinforced concrete columns.” Struct. Engrg. Rep. 91‐12‐/457s, Dept. of Civ. Engrg., Northwestern University, Evanston, Ill.
18.
Bažant, Z. P., Kazemi, M. T., Hasegawa, T., and Mazars, J. (1991) “Size effect in Brazilian split‐cylinder tests: measurements and fracture analysis.” ACI Mat. J., 88(3), 325–332.
19.
Bažant, Z. P. (1992). “New nonlocal damage concept based on micromechanics of crack interactions.” Rep. 92‐7/C457 n, Dept. of Civ. Engrg., Northwestern University, Evanston, Ill.; also J. Engrg. Mech., ASCE, 120(3), 593–617 (1994).
20.
Bhal, N. S. (1968). “Über den Einfluβ der Balkenhohe auf die Schubtragfähtigkeit von einfeldrigen Stahlbetonbalken mit und ohne Schubbewehrung,” doctoral thesis, Unversität Stuttgart, Stuttgart, Germany.
21.
Bocca, P., Carpinteri, A., and Valente, S. (1990). “Size effect in mixed mode crack propagation: softening and snap‐back analysis.” Engrg. Fracture Mech., 35, 159–70.
22.
Carpinteri, A. (1982). “Notch‐sensitivity and fracture testing of aggregate materials.” Engrg. Fracture Mech., 16(14), 467–481.
23.
Carpinteri, A. (1986). Mechanical damage and crack growth in concrete. Martinus Nijhoff Publishers, Dordrecht, The Netherlands.
24.
Červenka, V., Pukl, R., and Eligehausen, R. (1990). “Computer simulation of anchoring technique in reinforced concrete beams.” Proc., Int. Conf. Computer Aided Analysis and Design of Concrete Struct.; Part I, N. Bićanić et al., eds., Pineridge Press, Swansea, Wales, 1–21.
25.
Chana, P. S. (1981). “Some aspects of modeling the behavior of reinforced concrete under shear loading.” Tech. Rep. No. 543, Cement and Concrete Assoc., Wexham Springs.
26.
de Borst, R. (1991). “Continuum models for discontinuous media.” Proc., Int. RILEM/ESIS Conf.; Fracture Processes in Concrete, Rock and Ceramics, Noordwijk, The Netherlands, 601–618.
27.
de Borst, R., and Rots, J. G. (1989). “Occurrence of spurious mechanisms in computations of strain softening solids.” Engrg. Comp., 6, 272–280.
28.
Eligehausen, R., Fuchs, W., and Mayer, B. (1988). “Load‐bearing behaviour of anchor fastenings in tension.” Betonwerk + Fertigteil Technik, 12(Part 1), 826–832, 1(Part 2), 29–35.
29.
Eligehausen, R., Fuchs, W., Ick, U., Mallée R., Reuter, M., Schimmelpfenning, K., and Schmal, B. (1991). “Tragverhalten von Kopfbolzenverankerung bei zentrischer Zugbeanspruchung.” Bauingenieur, Berlin, Germany (in German).
30.
Eligehausen, R., and Sawade, G. (1989). “A fracture mechanics based description of the pull‐out behavior of headed studs embedded in concrete.” Fracture mechanics of concrete structures—RILEM report, L. Elfgren, ed., Chapman and Hall, London, England, 263–280.
31.
Eligehausen, R., and Ožbolt, J. (1990). “Size effect in anchorage behavior.” Proc., 8th European Conf. on Fracture Behaviour and Design of Mat. and Struct., Torino, Italy, 2671–2677.
32.
Eligehausen, R., and Ožbolt, J. (1992). “Size effect in concrete structures.” Application of fracture mechanics to reinforced concrete, A. Carpinteri, ed., Elsevier Applied Science, Torino, Italy, 17–44.
33.
Eligehausen, R., Bouška, P., Červenka, V., and Pukl, R. (1992). “Size effect of the concrete cone failure load of anchor bolts,” FramCoS 1, Z. P. Bažant, ed., Elsevier Applied Science, Breckenridge, 517–525.
34.
Gogotsi, G. A., Groushevski, Y. L., and Strelov, K. K. (1978). “The significance of non‐elastic deformation in the fracture of heterogeneous ceramic materials.” Ceramuqia Int., 4(3), 113–118.
35.
Heilmann, H. G. (1969). “Beziehungen zwischen Zug‐ und Druckfestigkeit des Betons.” Beton, Berlin, Germany, 2, 68–72 (in German).
36.
Hawkins, N. M. (1985). “The role of fracture mechanics in conventional reinforced concrete design.” Proc., NATO Advanced Res. Workshop on Application of Fracture Mechanics to Cementious Composites, held at Northwestern University, Evanston, Ill., S. P. Shah, ed., Martinus Nijhoff Publishers, Boston, Mass., 639–666.
37.
Hillerborg, A., Modéer, M., and Petersson, P. E. (1976). “Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements.” Cement and Concrete Res., Vol. 6, 773–782.
38.
Hillerborg, A. (1985). “The theoretical basis of a method to determine the fracture energy of concrete.” Mat. and Struct., Paris, France, 18(106), 291–296.
39.
Hillerborg, A. (1989). “Fracture mechanics and the concrete codes.” Fracture mechanics: applications to concrete; ACI‐SP118, V. Li and Z. P. Bažant, eds., American Concrete Institute (ACI), Detroit, Mich., 157–170.
40.
Homeny, J., Darroudi, T., and Bradt, R. G. (1980). “J‐integral measurements of the fracture of 50% aluminia refractories.” J. Am. Ceramic Soc., 63(5–6), 326–331.
41.
Hsu, T. T. C. (1968). “Torsion of structural concrete—plain concrete rectangular sections.” Torsion of structural concrete (SP‐18), American Concrete Institute (ACI), Detroit, Mich., 203–238.
42.
Humphreys, R. (1957). “Torsional properties of prestressed concrete.” Struct. Engr., London, England, 35(6), 213–224.
43.
Iguro, M., Shioya, T., Nojiri, Y., and Akiyama, H. (1985). “Experimental studies on shear strength of large reinforced concrete beams under uniformly distributed load.” Concrete Library Int., Japan Society of Civil Engineers, Tokyo, Japan, (5), 137–154.
44.
Ingraffea, A. R. (1985). “Fracture propagation in rock.” Mechanics of geomaterials: rocks, concretes, soils, Z. P. Bažant, ed., John Wiley and Sons, Inc., New York, N.Y., 219–258.
45.
Kani, G. N. J. (1967). “How safe are our large reinforced concrete beams?” J. Am. Concrete Inst., 64(3), 128–141.
46.
Leonhardt, F., and Walter, R. (1962). “Beiträge zur Behandlung der Schubprobleme im Stahlbetonbau.” Beton‐ und Stahlbetonbau, Berlin, Germany, (Mar.), 56–64, (Jun.), 141–149 (in German).
47.
Marti, P. (1989). “Size effect in double‐punch tests on concrete cylinders.” ACI Mat. J., 86(6), 597–601.
48.
McMullen, A. E., and Daniel, H. R. (1972). “Torsional strength of longitudinally reinforced concrete members of rectangular cross‐section,” doctoral thesis, West Virginia University, Morgantown, W.Va.
49.
Mihashi, H., and Zaitsev, J. W. (1981). “Statistical nature of crack propagation.” Section 4‐2; Rep. to RILEM TC 50—FMC, F. W. Wittmann, ed., RILEM, Paris, France.
50.
Mihashi, H. (1983). “Chapter 4.3: a stochastic theory for fracture of concrete.” Fracture mechanics of concrete, F. H. Wittman, ed., Elsevier, New York, N.Y., 301–340.
51.
Ožbolt, J., and Eligehausen, R. (1991). “Analysis of reinforced concrete beams without shear reinforcement using nonlocal microplane model.” Proc., Int. RI‐LEM/ESIS Conf., Fracture Processes in Concrete, Rock and Ceramics, Noordwijk, The Nederlands, 919–930.
52.
Ožbolt, J. (1992). “Smeared crack analysis—new nonlocal microcrack interactions approach.” Internal Rep. No. 4/14‐92/19, Institut für Werkstoffe im Bauwesen, Stuttgart University, Stuttgart, Germany.
53.
Ožbolt, J., and Petrangeli, M. (1993). “Improved microplane model for concrete.” Internal Rep. No. 4/17‐93/5, Institut für Werkstoffe im Bauwesen, Stuttgart University, Stuttgart, Germany.
54.
Petersson, P. E. (1981). “Crack growth and development of fracture zones in plain concrete and similar materials.” Rep. TVBM‐1006, Div. of Building Materials, Lund Inst. of Tech., Lund, Sweden.
55.
Petrangeli, M., and Ožbolt, J. (1992). “Smeared crack approaches—material modeling.” Internal Rep. No. 4/15‐92/22, Institut für Werkstoffe im Bauwesen, Stuttgart University, Stuttgart, Germany.
56.
Reinhardt, H. W. (1981a). “Similitude of brittle fracture of structural concrete.” IABSE Colloquium on Adv. in Reinforced Concrete, Delft, The Netherlands, 175–184.
57.
Reinhardt, H. W. (1981b). “Maβtabseinfluβe in Schubversuchen im sicht der Bruchmechanik.” Beton und Stahlbetonbau, Berlin, Germany, 76(1), 19–21 (in German).
58.
Rüsch, H., Haugli, F. R., and Mayer, H. (1962). “Schubversuche an Stahlbeton‐Rechteckbalken mit gleichmäβig verteilter Belastung,” Bull. No. 145, Deutscher Ausschuβ für Stahlbeton, Berlin, Germany, 4–30 (in German).
59.
Rots, J. G. (1988). “Computational modelling of concrete fracture,” doctoral thesis, Delft University of Technology, Delft, The Netherlands.
60.
Rots, J. G. (1992). “Removal of finite elements in strain‐softening analysis of tensile fracture.” FramCoS 1, Z. P. Bažant, ed., Elsevier Applied Science, Breckenridge, 330–338.
61.
Sener, S. (1993). “Size effect in failure of splices of reinforcing bars in concrete.” Rep., Technical University of Ankara, Ankara, Turkey.
62.
Taylor, F. P. J. (1972). “The shear strength of large beams.” J. Struct. Engrg., ASCE, 98, 2473–2490.
63.
van Mier, J. G. M. (1992). “Scaling in tensile and compressive fracture of concrete.” Application of fracture mechanics to reinforced concrete, A. Carpinteri, ed., Elsevier Applied Science, Torino, Italy, 95–136.
64.
Walraven, J. (1978). “The influence of depth on the shear strength of lightweight concrete beams without shear reinforcement.” Stevin Lab. Rep. No. 5‐78‐4, Delft University of Technology, Delft, The Netherlands.
65.
Walraven, J., and Lehwalter, N. (1990). “Einfluβ des Maβtabs in schubbeanspruchten Bauteilen ohne Schubbewehrung,” Beton‐ und Stahlbetonbau 85, Berlin, Germany, 9, 228–232 (in German).
66.
Walraven, J. (1990). “Scale effects in beams with unreinforced webs, loaded in shear.” Progress in Concrete Res; Annu. Rep., Delft University of Technology, Delft, The Netherlands, Vol. 1, 101–112.
67.
Walsh, P. F. (1976). “Crack initiation in plain concrete.” Mag. Concrete Res., Vol. 28, 37–41.
68.
Wittman, F. H., Mihashi, H., and Noumura, H. (1990). “Size effect on fracture energy of concrete.” Engrg. Fracture Mech., 35, 107–115.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 120 • Issue 8 • August 1994
Pages: 2377 - 2398
Copyright
Copyright © 1994 American Society of Civil Engineers.
History
Received: Jan 27, 1992
Published online: Aug 1, 1994
Published in print: Aug 1994
Authors
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.