Crack Shear in Concrete: Crack Band Microflane Model
Publication: Journal of Structural Engineering
Volume 110, Issue 9
Abstract
The crack band model is applied to the problem of crack shear in concrete. The constitutive law for concrete within the crack band is provided by the microplane model, in which the microstrains on weak planes of various orientations (the microplanes) are assumed to conform to the same macroscopic strain tensor, and the microstresses from all the microplanes are superimposed. Due to the neglect of shear stiffness on individual microplanes, the material behavior is completely characterized by the relation between the normal stress and strain for each microplane. To simulate crack shear, the law for unloading contribution on the microplanes after previous tensile strain‐softening is important, since the shear stresses resisting crack shear, as well as the normal confining stresses and crack dilatancy, result from compression along lines inclined with regard to the crack plane. A satisfactory agreement with the existing results from shearing tests of cracked concrete blocks (i.e., aggregate interlock tests) is achieved. Since the same type of model was previously shown capable of modeling strain‐softening in direct tensile tests, fracture of notched specimens, and deflections of cracked reinforced beams, the present model appears to have a general applicability. It can be applied to the shearing of cracks only partially formed (a system of distinct discontinuous cracks still in the strain softening stage), to cracks that are being produced simultaneously with shearing, to crack shear when the direction of shearing within the crack plane rotates, and to shearing of concrete intersected by cracks of various directions. Thus, the model appears suitable for general finite element programs.
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References
1.
Albrecht, J., and Collatz, L., “Zur numerischen Auswertung mehrdimensionaler Integrate,” Zeitschrift für Angewandte Mathematik und Mechanik, Band 38, Heft 1/2, Jan.–Feb., pp. 1–15.
2.
Batdorf, S. B., and Budiansky, B., “A Mathematical Theory of Plasticity Based on the Concept of Slip,” NACA TN1871, Apr., 1949.
3.
Bažant, Z. P., “Instability, Ductility and Size Effect in Strain‐softening of Concrete,” Journal of the Engineering Mechanics Division, ASCE, Vol. 102, Paper 12042, No. EM2, Apr., 1976, pp. 331–334.
4.
Bažant, Z. P., “Crack Band Model for Fracture of Geomaterials,” Fourth International Conference on Numerical Methods in Geomechanics, Z. Eisenstein, ed., Vol. 3, University of Alberta, Edmonton, Canada, 1982, pp. 1137–1152.
5.
Bažant, Z. P., “Microplane Model for Strain‐Controlled Triaxial Behavior,” Mechanics of Engineering Materials, C. S. Desai and R. H. Galagher, eds., Chapter 3, John Wiley & Sons, London, England, 1984, pp. 45–59.
6.
Bažant, Z. P., and Cedolin, L., “Finite Element Modeling of Crack Band Propagation,” Journal of Structural Engineering, ASCE, Vol. 109, No. ST1, Paper 17618, Jan., 1983, pp. 69–92.
7.
Bažant, Z. P., and Gambarova, P. G., “Rough Cracks in Reinforced Concrete,” Journal of the Structural Division, ASCE, Vol. 106, No. ST4, Paper 15330, Apr., 1980, pp. 819–842.
8.
Bažant, Z. P., and Oh, B. H., “Efficient Numerical Integration on the Surface of a Sphere,” Report, Center for Concrete and Geomaterials, Northwestern University, Evanston, Ill., 1982.
9.
Bažant, Z. P., and Oh, B. H., “Model of Weak Planes for Progressive Fracture of Concrete and Rock,” Report No. 83‐2/448m, Center for Concrete and Geomaterials, Northwestern University, Evanston, Ill., Feb., 1983.
10.
Bažant, Z. P., and Oh, B. H., “Crack Band Theory for Fracture of Concrete,” Materials and Structures, (RILEM, Paris), Vol. 16, No. 94, July–Aug., 1983, pp. 155–177.
11.
Bažant, Z. P., and Oh, B. H., “Microplane Model for Fracture Analysis of Concrete Structures,” Proceedings of the Symposium on the Interaction of Nonnuclear Munitions with Structures, C. A. Ross, ed., U.S. Air Force Academy, Colorado Springs, McGregor & Werner, Inc., Washington, D.C., May, 1983.
12.
Bažant, Z. P., and Oh, B. H., “Deformations of Progressively Cracking Reinforced Concrete Beams,” American Concrete Institute Journal, Vol. 81, 1984, pp. 268–278.
13.
Bažant, Z. P., and Panula, L., “Statistical Stability Effects in Concrete Failure,” Journal of the Engineering Mechanics Division, ASCE, Vol. 104, Paper 14074, No. EMS, Oct., 1978, pp. 1195–1212.
14.
Daschner, F., and Kupfer, H., “Versuche zur Schubkraftübertragung in Rissen von Normal‐und Leichtbeton,” Bauingenieur 57, 1982, pp. 57–60.
15.
Eleiott, A. F., “An Experimental Investigation of Shear Transfer Across Cracks in Reinforced Concrete,” thesis presented to Cornell University, at Ithaca, N.Y., in 1974, in partial fulfillment of the requirements for the degree of Master of Science.
16.
Entov, V. M., and Yagust, V. I., “Experimental Investigation of Laws Governing Quasi‐static Development of Macrocracks in Concrete,” Mechanics of Solids (translated from Russian), Vol. 10, No. 4, 1975, pp. 87–95.
17.
Evans, R. H., and Marathe, M. S., “Microcracking and Stress‐Strain Curves for Concrete in Tension,” Materials and Structures, (Paris), No. 1, Jan.–Feb., 1968, pp. 61–64.
18.
Fardis, M. N., and Buyukozturk, O., “Shear Transfer Model for Reinforced Concrete,” Journal of the Engineering Mechanics Division, ASCE, Vol. 105, No. EM2, Paper 14507, Apr., 1979, pp. 255–276.
19.
Gambarova, P. G., “On Aggregate Interlock Mechanism in Reinforced Concrete Plates with Extensive Cracking,” Final Report of the IASBE Colloquium on Advanced Mechanics of Reinforced Concrete, Delft, The Netherlands, June, 1981, pp. 99–120.
20.
Heilmann, H. G., Hilsdorf, H. H., and Finsterwalder, K., “Festigkeit und Verformung von Beton unter Zugspanungen,” Deutscher Ausschuss für Stahlbeton, Heft 203, W. Ernst & Sohn, West Berlin, Germany, 1969.
21.
Houde, J., and Mirza, M. S., “Investigation of Shear Transfer Across Cracks by Aggregate Interlock,” Research Report No. 72‐06, Département de Génie Civil, Division des Structures, Ecole Polytéchnique de Montréal, Montréal, Canada, 1972.
22.
Hughes, B. P., and Chapman, G. P., “The Complete Stress‐Strain Curve for Concrete in Direct Tension,” Bulletin RILEM, No. 30, 1966, pp. 95–97.
23.
Laible, J. P., White, R. N., and Gergely, P., “Experimental Investigation of Seismic Shear Transfer Across Cracks in Concrete Nuclear Containment Vessels,” Special Publication SP53, American Concrete Institute, 1977, pp. 203–226.
24.
Mattock, A. H., “The Shear Transfer Behaviour of Cracked Monolithic Concrete Subject to Cyclically Reversing Shear,” Report SM 74‐4, Department of Civil Engineering, University of Washington, Seattle, Wash., Nov., 1974.
25.
McLaren, A. D., “Optimal Numerical Integration on a Sphere,” Mathematics of Computation, Vol. 17, 1963, pp. 361–383.
26.
Pande, G. N., and Sharma, K. G., “Multi‐laminate Model of Clays—A Numerical Evaluation of the Influence of Rotation of the Principal Stress Axes,” Report, Department of Civil Engineering, University College of Swansea, U.K., 1982;
see also Proceedings, Symposium on Implementation of Computer Procedures and Stress‐Strain Laws in Geotechnical Engineering, C. S. Desai and S. K. Saxena, eds., Acorn Press, Durham, N.C., Aug., 1981, pp. 575–590.
27.
Pande, G. N., and Xiong, W., “An Improved Multi‐laminate Model of Jointed Rock Masses,” Proceedings, International Symposium on Numerical Models in Geomechanics, R. Dungar, G. N. Pande, and G. A. Studer, eds., Balkema, Rotterdam, The Netherlands, 1982, pp. 218–226.
28.
Paulay, T., and Loeber, P. J., “Shear Transfer by Aggregate Interlock,” Special Publication SP42, American Concrete Institute, 1974, pp. 1–15.
29.
Paulay, T., Park, R., and Phillips, M. H., “Horizontal Construction Joints in Cast‐in‐Place Reinforced Concrete,” Special Publication SP42, American Concrete Institute, 1974, pp. 599–616.
30.
Petersson, P. E., “Fracture Energy of Concrete: Method of Determination,” Cement and Concrete Research, Vol. 10, 1980, pp. 78–89,
and “Fracture Energy of Concrete: Practical Performance and Experimental Results,” Cement and Concrete Research, Vol. 10, 1980, pp. 91–101.
31.
Rashid, Y. R., “Analysis of Prestressed Concrete Pressure Vessels,” Nuclear Engineering and Design, Vol. 7, No. 4, Apr., 1968, pp. 334–344.
32.
Reinhardt, H. W., and Walraven, J. C., “Crack in Concrete Subject to Shear,” Journal of the Structural Division, ASCE, Vol. 108, Paper 16802, Jan., 1982, pp. 207–224.
33.
Rüsch, H., and Hilsdorf, H., “Deformation Characteristics of Concrete under Axial Tension,” Voruntersuchungen, Bericht Nr. 44, Munich, Germany, May, 1963.
34.
Stroud, A. H., Approximate Calculation of Multiple Integrals, Prentice Hall, Englewood Cliffs, N.J., 1971, pp. 296–302.
35.
Taylor, G. I., “Plastic Strain in Metals,” Journal of Inst. Metals, Vol. 62, 1938, pp. 307–324.
36.
Walraven, J. C., and Reinhardt, H. W., “Theory and Experiments on the Mechanical Behavior of Cracks in Plain and Reinforced Concrete Subjected to Shear Loading,” HERON Journal, Vol. 26, No. 1A, Department of Civil Engineering, University of Technology, Delft, The Netherlands, 1981.
37.
Wecharatana, M., and Shah, S. P., “Slow Crack Growth in Cement Composites,” Journal of the Structural Division, ASCE, Vol. 108, Paper 17181, June, 1982, pp. 1400–1413.
38.
Zienkiewicz, O. C., and Pande, G. N., “Time‐Dependent Multi‐laminate Model of Rocks—A Numerical Study of Deformation and Failure of Rock Masses,” International Journal of Numerical and Analytical Methods in Geomechanics, Vol. 1, 1977, pp. 219–247.
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Published In
Journal of Structural Engineering
Volume 110 • Issue 9 • September 1984
Pages: 2015 - 2035
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Copyright © 1984 ASCE.
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Published online: Sep 1, 1984
Published in print: Sep 1984
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