Abstract
Cracking is an essential feature of the behavior of concrete structures. Even under service loads, concrete structures are normally full of cracks. Clearly, cracking should be taken into account in predicting ultimate load capacity as well as behavior in service.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bazant, Z.P., and Oh. B.H., Crack Band Theory for Fracture of Concrete, Materials and Structures (RILEM, Paris), Vol. 16, pp. 155–177 (1983) (based on [130]).
Bazant, Z.P., and Kim, S.S., Plastic-Fracturing Theory for Concrete, Journal of the Engineering Mechanics Division, ASCE, Vol. 105, No. EM3, Proc. Paper 14653, pp. 407–428 (1979).
Bazant, Z.P., Crack Band Model for Fracture of Geomaterials, Proc., 4th Intern. Conf. on Numerical Methods in Geomechanics, held in Edmonton, Alberta, Canada, ed. by Z. Eisenstein, Vol. 3 (1982), pp. 1137–1152.
Bazant, Z.P., Instability, Ductility and Size Effect in Strain-Softening Concrete, J. of the Engineering Mechanics Division ASCE, Vol. 102, No. EM2, pp. 331–344 - Paper 12042 (1976).
Bazant, Z.P., and Panula, L., Statistical Stability Effects in Concrete Failure, J. of the Engineering Mechanics Division, ASCE, Vol. 104, No. EM5, pp. 1195–1212, Paper 14074 (1978).
Bazant, Z.P., and Cedolin, L., Blunt Crack Band Propagation in Finite Element Analysis, Journal of the Engineering Mechanics Division, ASCE, Vol. 105, No. EM2, Proc. Paper 14529, pp. 297–315 (1979).
Cedolin, L., and Bazant, Z.P., Effect of Finite Element Choice in Blunt Crack Band Analysis, Computer Methods in Applied Mechanics and Engineering, Vol. 24, No. 3, pp. 305–316 (1980).
Rashid, Y.R., Analysis of Prestressed Concrete Pressure Vessels, Nuclear Engng. and Design, Vol. 7, No. 4, pp. 334–344 (1968).
Mindess, S., and Diamond, S., A Preliminary SEM Study of Crack Propagation in Mortar, Cement and Concrete Research, Vol. 10, pp. 509–519 (1980).
Cedolin, L., Dei Poli, S., and Iori, L. Experimental Determination of the Fracture Process Zone in Concrete, Cement and Concrete Research, Vol. 13, pp. 557–567 (1983).
Cedolin, L., dei Poli, S., and Iori, L., Experimental Determination of the Stress–Strain Curve and Fracture Zone for Concrete in Tension, Proc., Int. Conf. on Constitutive Laws for Engineering Materials, ed. by C. Desai, University of Arizona, Tucson (1983).
Barenblatt, G.I., The Formation of Equilibrium Cracks During Brittle Fracture, General Ideas and Hypothesis. Axially–Symmetric Cracks, Prikladnaya Matematika i Mekhanika, Vol. 23, No. 3, pp. 434–444 (1959).
Dugdale, D.S., Yielding of Steel Sheets Containing Slits, J. Mech. Phys. Solids, Vol. 8, pp. 100–108 (1960).
Kfouri, A.P., and Miller, K.J., Stress Displacement, Line Integral and Closure Energy Determinations of Crack Tip Stress Intensity Factors, Int. Journal of Pres. Ves. and Piping, Vol. 2, No. 3, pp. 179–191 (1974).
Kfouri, A.P., and Rice, J.R., Elastic/Plastic Separation Energy Rate for Crack Advance in Finite Growth Steps, in Fracture 1977 (Proc. of the 4th Intern. Conf. on Fracture, held in Waterloo, Ontario, June 1977), ed. by D.M.R. Taplin, University of Waterloo Press, Vol. 1, pp. 43–59 (1977).
Knauss, W.C., On the Steady Propagation of a Crack in a Viscoelastic Sheet: Experiments and Analysis, in The Deformation in Fracture of High Polymers, ed. by H.H. Kausch, Pub. Plenum Press, pp. 501–541 (1974).
Wnuk, M.P., Quasi-Static Extension of a Tensile Crack Contained in Viscoelastic Plastic Solid, Journal of Applied Mechanics, ASME, Vol. 41, No. 1, pp. 234–248 (1974).
Hillerborg, A., Modeer, M., and Petersson, P.E., Analysis of Crack Formation and Crack Growth in Concrete by Means of Fracture Mechanics and Finite Elements, Cement and Concrete Research, Vol. 6, pp. 773–782 (1976).
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, pp. 91–101 (1980).
Suidan, M., and Schnobrich, W.C., Finite Element Analysis of Reinforced Concrete, Journal of the Structural Division, ASCE, Vol. 99, No. ST10, Proc. Paper 10081, pp. 2109–2122 (1973).
Evans, R.H., and Marathe, M.S., Microcracking and Stress–Strain Curves for Concrete in Tension, Materials and Structures (RILEM, Paris), No. 1, Jan.–Feb., pp. 61–64 (1968).
Heilmann, H.G., Hilsdorf, H.H., and Finsterwalder, K., Festigkeit und Verformung von Beton unter Zugspanungen, Deutscher Ausschuss fur Stahlbeton, Heft 203, W Ernst & Sohn, West Berlin (1969).
Rüsch, H., and Hilsdorf, H., Deformation Characteristics of Concrete under Axial Tension, Voruntersuchungen, Bericht Nr. 44, Munich (1963).
Hughes, B.P., and Chapman, G.P., The Complete Stress–Strain Curve for Concrete in Direct Tension, Bulletin RILEM, No. 30, pp. 95–97 (1966).
Petersson, P.E., Crack Growth and Development of Fracture Zones in Plain Concrete and Similar Materials, Doctoral Dissertation, Lund Institute of Technology, Lund, Sweden (1981).
Reinhardt, H.W., and Walraven, J.C., Cracks in Concrete Subject to Shear, J. of the Structural Division ASCE, Vol. 108, No. ST1, Paper 16802, pp. 207–224 (1982).
ASCE State-of-the-Art Report on Finite Element Analysis of Reinforced Concrete, prepared by a Task Committee chaired by A. Nilson, Am. Soc. of Civil Engrs., New York (1982).
Bazant, Z.P., and Gambarova, P., Rough Cracks in Reinforced Concrete, Journal of the Structural Div., Proc. ASCE, Vol. 106, No. ST4, April 1980, pp. 819–842, Paper 15330; Discussion pp. 2579–2581, pp. 1377–1388 (1981).
Bazant, Z.P., and Tsubaki, T., Slip-Dilatancy Model for Cracked Reinforced Concrete, Journal of the Structural Division, ASCE, Vol. 106, No. ST9, Paper No. 15704, pp. 1947–1966 (1980).
Kupfer, H.B., and Gerstle, K.H., Behavior of Concrete under Biaxial Stress, Journal of the Engineering Mechanics Division, ASCE, Vol. 99, No. EM4, Proc. Paper 9917, pp. 853–866 (1973).
Liu, T.C.Y., Nilson, A.H., and Slate, F.O., Biaxial Stress–Strain Relations for Con–crete, Journal of the Structural Division, ASCE, Vol. 98, No. ST5, Proc. Paper 8905, pp. 1025–1034 (1972).
Rosenthal, I., and Glucklich, J., Strength of Plain Concrete under Biaxial Stress, ACI Journal, pp. 903–914 (1970).
Kachanov, L.M., Time of Rupture Process Under Creep Conditions, Izv. Akad, Nauk, SSR, Otd. Tekh, Nauk, No. 8, pp. 26–31 (1958).
Janson, J., and Hult, J., Fracture Mechanics and Damage Mechanics,–A Combined Approach, Journal de Mecanique Appliquee, Vol. 1, No. 1, pp. 69–84 (1977).
Loland, K.E., Continuous Damage Model for Load–Response Estimation of Concrete, Cement and Concrete Research, Vol. 10, pp. 395–402 (1980).
Lorrain, M., On the Application of the Damage Theory to Fracture Mechanics of Concrete, A State-of-the-Art Report, Civil Engineering Department, I.N.S.A., 31077 Toulouse, Cedex, France.
Mazars, Mechanical Damage and Fracture of Concrete Structures, 5th International Conference on Fracture, Edited by D. Francis, Cannes, France, Vol. 4, pp. 1499–1506 (1981).
Arrea, M., Ingraffea, A.R., Mixed–Mode Crack Propagation in Mortar and Concrete, Report No. 81–83, Dept. of Structural Engineering, Cornell University, Ithaca, N.Y., Feb. (1982).
Knott, J.F., Fundamentals of Fracture Mechanics, Butterworths, London, England (1973).
Parker, A.P., The Mechanics of Fracture and Fatigue, E. & F.N. Spon, Ltd. - Methuen, London (1981).
Broek, D., Elementary Engineering Fracture Mechanics, Noordhoff International Publishing, Leyden, Netherlands (1974).
Mindess, S., The Application of Fracture Mechanics to Cement and Concrete: A Historical Review, Chapter I in ‘Fracture Mechanics of Concrete’, ed. by F.H. Wittmann, Elsevier, The Netherlands (1983).
Brown, J.H., Measuring the Fracture Toughness of Cement Paste and Mortar, Magazine of Concrete Research, Vol. 24, No. 81, pp. 185–196 (1972).
Carpinteri, A., Experimental Determination of Fracture Toughness Parameters Klc and JIC for Aggregative Materials, Advances in Fracture Research, (Proc., 5th International Conference on Fracture, Cannes, ed. by D. Francis, Vol. 4, pp. 1491–1498 (1981).
Carpinteri, A., Static and Energetic Fracture Parameters for Rocks and Concretes, Report, Instituto di Scienza delle Costruzioni–Ingegneria, University of Bologna, Italy (1980).
Entov, V.M., and Yagust V.I., Experimental Investigation of Laws Governing Quasi– Static Development of Macrocracks in Concrete,: Mechanics of Solids (translation from Russian), Vol. 10, No. 4, pp. 87–95 (1975).
Gjørv, O.E., Sorensen, S.I., and Arnesen, A., Notch Sensitivity and Fracture Tough–ness of Concrete, Cement and Concrete Research, Vol. 7, pp. 333–344 (1977).
Huang, C.M.J., Finite Element and Experimental Studies of Stress Intensity Factor for Concrete Beams, Thesis Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy, Kansas State University, Kansas (1981).
Kaplan, M.F., Crack Propagation and the Fracture of Concrete, American Concrete Institute Journal, Vol. 58, No. 11 (1961).
Kesler, C.E., Naus, D.J., and Lott, J.L., Fracture Mechanics — Its Applicability to Concrete, International Conference on the Mechanical Behavior of Materials, Kyoto, August (1971).
Mindess, S., Lawrence, F.V., and Kesler, C.E., The J-Integral As a Fracture Criterion for Fiber Reinforced Concrete, Cement and Concrete Research, Vol. 7, pp. 731–742 (1977).
Naus, D.J., Applicability of Linear–Elastic Fracture Mechanics to Portland Cement Concretes, Thesis Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy, University of Illinois at Urbana-Champaign (1971).
Shah, S.P., and McGarry, F.J., Griffith Fracture Criterion and Concrete, Journal of the Engineering Mechanics Division, ASCE, Vol. 97, No. EM6, Proc. Paper 8597, pp. 1663–1676 (1971).
Sok, C., Baron, J., and Francis, D., Mecanique de la Rupture Appliquee au Beton Hydraulique, Cement and Concrete Research, Vol. 9, pp. 641–648 (1979).
Swartz, S.E., Hu, K.K., Fartash, M., and Huang, C.M.J., Stress Intensity Factors for Plain Concrete in Bending — Prenotched Versus Precracked Beams, Report, Department of Civil Engineering, Kansas State University, Kansas (1981).
Walsh, P.F., Fracture of Plain Concrete,: The Indian Concrete Journal, Vol. 46, No. 11, pp. 469, 470, and 476 (1979).
Wecharatana, M., and Shah, S.P., Resistance to Crack Growth in Portland Cement Composites, Report, Department of Material Engineering, University of Illinois at Chicago Circle, Chicago, Illinois (1980).
Bazant, Z.P., and Oh, B.H., Rock Fracture via Stress-Strain Relations, Concrete and Geomaterials, Report No. 82-ll/665r, Northwestern University, Evanston, Illinois (1982); also to appear in ASCE Journal of Engineering Mechanics, Vol. 110 (1984).
Bazant, Z.P., and Cedolin, L., Fracture Mechanics of Reinforced Concrete, Journal of the Engineering Mechanics Division, ASCE, Vol. 106, No. EM6, Proc. Paper 15917, December 1980, pp. 1287–1306; with Discussion and Closure in Vol. 108, EM., pp. 464–471 (1982).
Bazant, Z.P., and Cedolin, L., Finite Element Modeling of Crack Band Propagation, Journal of Structural Engineering, ASCE, Vol. 109, No. ST2, pp. 69–92 (1983).
Flanagan, D.P., and Belytschko, T., A Uniform Strain Hexahedron and Quaderlateral with Orthogonal Hourglass Control, Int. J. for Numerical Methods in Engineering, Vol. 17, pp. 679–706 (1981).
Marchertas, A., Bazant, Z.P., Belytschko, T., and Fistedis, S.H., Extension of HCDA Safety Analysis of Large PCRV Containment Structures, Preprints 4th Intern. Conf. on Struct. Mech. in Reactor Technology, San Francisco, Paper E4/1 (1977).
Marchertas, A.H., Beltyschko, T.B., Bazant, Z.P., Transient Analysis of LMFBR Reinforced/Prestressed Concrete Containment, Trans, 5th Intern, Conf. on Struct. Mech. in Reactor Tech., Vol. H, Paper H4/1, West Berlin, ed. by T.A. Jaeger and B.A. Boley, publ. by North Holland (1979).
Marchertas, A.H., Fistedis, S.H., Bazant, Z.P., and Belytschko, T., Analysis and Application of Prestressed Concrete Reactor Vessels for LMFBR Containment, Nuclear Engng. and Design, Vol. 49 pp. 155–173 (1978).
Building Code Requirements for Reinforced Concrete (ACI Standard 318–377), Am. Concrete Institute, Detroit (1977).
Marchertas, A.H., Kulak, R.F., and Pan, Y.C., Performance of Blunt Crack Approach Within a General Purpose Code, in Nonlinear Numerical Analysis of Reinforced Concrete, ed. by L.E. Schwer, Am. Soc. of Mech. Engrs., New York 1982, (presented at ASME Winter Annual Meeting, Phoenix, pp. 107–123 (1982).
Bžzant, Z.P., Pfeiffer, P., Finite Element Crack Band Analysis, in preparation.
Bažant, Z.P., Pfeiffer, P., Marchertas, A.H., Blunt Crack Band Propagation in Finite Element Analysis for Concrete Structures, Preprints 7th Int. Conf. on Structural Mechanics in Reactor Technology, Chicago (1983).
Rice, J.R., Mathematical Analysis in the Mechanics of Fracture, in Fracture, an Advance Treatise, H. Liebowitz, ed. Vol. 2, Academic Press, New York, N.Y., pp. 191–250 (1968).
Haugeneder, E., A Note of Finite Element Analysis of Blunt Crack Band Propagation, Proc., Intern. Conf. on Constitutive Equations for Engineering Materials, ed. by C. Desai, University of Arizona, Tucson, pp. 561–564 (1983).
Pan, Y.C., Marchertas, A.H., Kennedy, J.M., Finite Element of Blunt Crack Band Propagation, A Modified J–Integral Approach, Preprints, 7th Intern. Conf. on Structural Mechanics in Reactor Technology, Paper H, Chicago (1983).
Rice, J.R., The Localization of Plastic Deformation, Preprints of the 14th IUTAM Congress (Int. Union of Theor. and Appl. Mech.), held in Delft, Netherlands, Edited by W.T. Koiter, North Holland Publishing Co, Amsterdam, pp. 207–220 (1976).
Bazant, Z.P., Tsubaki, T., and Belytschko, T.B., Concrete Reinforcing Net: Safe Design, Journal of the Structural Division, Proc. ASCE Vol. 106, No. ST9, pp. 1899–1906, Paper 15705 (1980).
Bazant, Z.P., and Wahab, A.B., Instability and Spacing of Cooling or Shrinkage Cracks, Journal of the Engineering Mechanics Division, ASCE, Vol. 105, No. EM5, Proc. Paper 14933, pp. 873–889 (1979),
Bazant, Z.P., and Wahab, A.B., Stability of Parallel Cracks in Solids Reinforced by Bars, International Journal of Solids and Structures, Vol. 16, pp. 97–105 (1980).
Branson, D.E., Design Procedures for Computing Deflection, ACI Journal, Vol. 65, No. 9, pp. 730–742 (1968).
Kani, G.N J., Basic Facts Concerning Shear Failure, Part I and Part II, J. of ACI, Vol. 63, No. 6, pp. 675–692 (1966).
Leonhardt, F., and Walther, R., Beitrage zur Behandlung der Schubprobleme im Stahlbetonbau, Beton–u Stahlbetonbau, Vol. 56, No. 12 (1961), Vol. 57, No. 2, 3, 6, 7, 8, (1962), Vol. 58, No. 8, 9 (1963).
Bhal, N.S. Uber den Einfluss der Balkenhohe auf Schubtragfahihkeit von einfeldrigen Stahlbetonbalken mit und ohne Schubbewehrung, Dissertation, Unversitat Stuttgart (1968).
Walraven, J.C., The Influence of Depth on the Shear Strength of Lightweight Concrete Beams without Shear Reinforcement, Stevin Laboratory Report No. 5–78–4, Delft University of Technology (1978).
Taylor, H.P.J., The Shear Strength of Large Beams, J. of the Structural Division ASCE, Vol. 98, pp. 2473–2490 (1972).
Rusch, M., Haugli, F.R., and Mayer, M., Schubversuche an Stahlbeton Rechteckbalken mit Gleichmassig Verteilter Belastung, Deutscher Ausschuss fur Stahlbeton, Heft 145, W. Ernst u. Sohn, West Berlin (1962).
Swamy, R.N., and Qureshi, S.A., Strength, Cracking and Deformation Similitude in Reinforced T–Beams under Bending and Shear, Part I and II, J. of Am. Concrete Inst., Vol. 68, No. 3, pp. 187–195 (1971).
Bazant, Z.P., Kim. J.K., Size Effect in Shear Failure of Longitudinally Reinforced Beams, Am. Concrete Institute Journal Vol. 81 (1984), in press.
Reinhardt, H.W., Masstabeinfluss bei Schubversuchen im Light der Bruchmechanik (Size Effect in Shear Tests in the Light of Fracture Mechanics), Beton-und Stahlbe- tonbau, Vol. 7, No. 1, pp. 19–21 (1981).
Reinhardt, H.W., Similitude of Brittle Fracture of Structural Concrete, Proc. IABSE Colloquium Advanced Mechanics of Reinforced Concrete, Delft, pp. 201–210 (1981).
Bazant, Z.P., Oh, B.H., Deflections of Cracked Reinforced Concrete Beams, Am. Concrete Institute Journal, Vol. 81 (1984), in press.
Bazant, Z.P., Oh, B.H., Spacing of Cracks in Reinforced Concrete, J. of Engng. Mech. ASCE, in press.
Agrawal, G.L., Tulin, L.G., and Gerstle, K.H., Response of Doubly Reinforced Concrete Beams to Cyclic Loading, ACI Journal, Proc. Vol. 63, No. 7, pp. 823–835 (1965).
Bruns, N.H., and Siess, C.P., Plastic Hinging in Reinforced Concrete, J. of the Structural Division ASCE, Vol. 92, No. ST5, pp. 45–64 (1966).
Burns, N.H., and Siess, C.P., Repeated and Reversed Loading in Reinforced Concrete, J. of the Structural Division ASCE, Vol. 92, No. ST5, pp. 65–78 (1966).
Sinha, B.P., Gerstle, K.H., and Tulin, L.G. Response of Singly Reinforced Beams of Cyclic Loading, ACI Journal, Proc. Vol. 61, No. 8, pp. 1021–1038 (1964).
Bazant, Z.P., and Panula, L., Practical Prediction of Time-Dependent Deformations of Concrete, Materials and Structures (RILEM, Paris), Vol. 11, pp. 307–328, 415–434 (1978), Vol. 12, pp. 169–183 (1979).
Hollington, M.R., A Series of Long–Term Tests to Investigate the Deflection of Representative Precast Concrete Floor Components, Technical Report TRA 442, Cement and Concrete Association (London) (1970).
Krafft, J.M., Sullivan, A.M. Boyle. R.W., Effect of Dimensions on Fast Fracture Instability of Notched Sheets, Cranfield Symposium, Vol. I, pp. 8–28 (1961).
Bazant, Z.P., Cedolin, L., Approximate Linear Analysis of Concrete Fracture by R–Curves, Journal of Structural Engineering ASCE, Vol. 110, No. 5T6, June (1984).
Tada, H., Paris, P.C., and Irwin, G.R., The Stress Analysis of Cracks Handbook, Del Research Corp., Hellertown, Pa. (1973).
Wnuk, M., Bazant, Z.P., and Law, E., Stable growth of Fracture in Bottle Aggregate Materials, Theoretical and Applied fracture Mechanics, Vol. 2 (1984) in press.
Bazant, Z.P., Ohtsubo, H., and Aoh, K., Stability and Post-Critical Growth of a System of Cooling or Shrinkage Cracks, International Journal of Fracture, Vol. 15, No. 5., pp. 443–456 (1979).
Chi, M., and Kirstein, A.F., Flexural Cracks in Reinforced Concrete Beams, Journal, American Concrete Institute, Proc., Vol. 54, No. 10, pp. 865–878 (1958).
Clark, A.P., Cracking in Reinforced Concrete Flexural Member, Journal, American Concrete Institute, Proc., Vol. 52, No. 8, pp. 851–862 (1956).
Kaar, P.H., and Mattock, A.H., High Strength Bars as Concrete Reinforcement, Part 4. Control of Cracking, Journal, Portland Cement Association Research and Development Laboratories, Vol. 5, No. 1, pp. 15–38 (1963).
Hognestad, E., High Strength Bars as Concrete Reinforcement, Part 2. Control of Flexural Cracking, Journal, Portland Cement Association Research and Development Laboratories, Vol. 4, No. 1, pp. 46–63 (1962).
Mathey, R.G., And Watstein, D., Effect of Tensile Properties of Reinforcement on the Flexural Characteristics of Beams, Journal, American Concrete Institute, Proc. Vol. 56, No. 12, pp. 1253–1273 (1960).
Bazant, Z.P., and Raftshol, W.J., Effect of Cracking in Drying and Shrinkage Specimens, Cement and Concrete Research, Vol. 12, pp. 209–226 (1982).
Bazant, Z.P., Mathematical Models for Creep and Shrinkage of Concrete, in Creep and Shrinkage in Concrete Structures, ed. by Z.P. Bazant and F.H. Wittmann, J. Wiley & Sons, London, pp. 163–285 (1982).
Bazant, Z.P., and Ohtsubo, H., Stability Conditions for Propagation of a System of Cracks in a Brittle Solid, Mechanics Research Communications, Vol. 4, No. 5, pp. 353–366 (1977).
Lachenbruch, A.H., Journal of Geophysical Research, Vol. 66, p. 4273 (1961).
Lister, C.R.B., Geophysical Journal of the Royal Astronomical Society, Vol. 39, pp. 465–509 (1974).
Bazant, 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, I I. (1983).
Bazant, Z.P., and Oh, B.H., Microplane Model for Fracture Analysis of Concrete Structures, Proc., Symp. on the Interaction of Nonnuclear Munitions with Structures, U.S. Air Force Academy, Colorado Springs, May 1983, ed. by C.A. Ross, publ. by McGregor & Werner, Inc., Wash. D.C.
Taylor, G.I., Plastic Strain in Metals, J. Inst. Metals, Vol. 63, pp. 307–324 (1983).
Batdorf, S.B., and Budiansky, B., A Mathematical Theory of Plasticity Based on the Concept of Slip, NACA TN1871 (1949).
Zienkiewics, O.C., and Pande, G.N., Time–Dependent Multi–laminate Model of Rocks–A Numerical Study of Deformation and Failure of Rock Masses, Int. Journal of Numerical and Analytical Methods in Geomechanics, Vol. 1, pp. 219–247 (1977).
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 Geo technical Engineering, ed. by C.S. Desai and S.K. Saxena, held in Chicago, Aug. 10, 81, Acorn Press, Durham, N.C., pp. 575–590 (1981).
Pande, G.N., and Xiong, W., An Improved Multi-laminate Model of Jointed Rock Masses, Proceedings, International Symposium on Numerical Models in Geomechanics, ed. by R. Dungar, G.N. Pande, and G.A. Studer, held in Zurich, Sept. 1982, Balkema, Rotterdam, 1982, 218–226.
Bazant, Z.P., and Tsubaki, T., Concrete Reinforcing Net: Optimum Slip-Free Limit Design, Journal of the Structural Division, ASCE Vol. 105, No. ST2, Proc. Paper 14344, Feb. 1979, pp. 327–346; Discussion and Closure, pp. 1375–1383 (1981).
Albrecht, J., and Collatz, L., Zur numerischen Auswertung mehrdimensionaler Integrate, Zeitschrift fur Angewandte Mathematik und Mechanik, Band 38, Heft 1/2, Jan./Feb., pp. 1–15.
Bazant, Z.P., and Oh, B.H., Efficient Numerical Integration on the Surface of a Sphere, Report, Center for Concrete and Geomaterials, Northwestern University, Evanston, 111. (1982).
Bazant, Z.P., and Gambarova, P., Crack Shear in Concrete: Crack Band Microplane Model, Journal of Engineering Mechanics ASCE, Vol. 110 (1984), in press.
Paulay, T., and Loeber, P.J., Shear Transfer by Aggregate Interlock, Am. Concr. Inst. Special Publ. SP42, Detroit, pp. 1–15 (1974).
Reinhardt, H.W., and Walraven, J.E., Crack in Concrete Subject to Shear, Journal of the Structural Division ASCE, Vol. 108, pp. 207–224 (1982).
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, Dept of Civil Eng. Delft University of Technology, Delft (1981).
Laible, J.P., White, R.N., and Gergely, P., Experimental Investigation of Shear Transfer across Cracks in Concrete Nuclear Containment Vessels, Am. Concrete Inst., Special Publ. SP53, pp. 203–226 (1977).
Mattock, A.H., The Shear Transfer Behavior of Cracked Monolithic Concrete Subject to Cyclical Reversing Shear, REport SM7404, Dept. of Civil Engng., Univ. of Washington, Seattle (1974).
Paulay, T., Park, R., and Phillips, M.H., Horizontal Construction Joints in Cast–in–Place Reinforced Concrete, in Shear in Reinf. Concrete, Vol. 2, Am. Concrete Inst. Special Publ. SP42, Detroit (1974).
Laible, J.P., White, R.N., and Gergely, P., Experimental Information on Shear Transfer Across Cracks in Concrete Nuclear Containment Vessels, Special Publ. SP53, Am. Concr. Inst., pp. 203–226, Detroit 1977.
Baumann, T., Zur Frage der Netzbewehrung von Flachentragwerken, Der Bauin genieur, Vol. 47, No. 10, pp. 367–377 (1971).
Additional Bibliography
Bazant, Z.P., Mathematical Models for Creep and Shrinkage of Concrete, Chapter 7 in Creep and Shrinkage in Concrete Structures, ed. by Z.P. Bazant and F.H. Wittmann, J. Wiley & Sons, London, pp. 163–256.
Bazant, Z.P., and Oh, B.H., Strain Rate Effect in Rapid Triaxial Loading of Concrete, Vol. 108, pp. 764–782 (1982).
Bazant, Z.P., and Oh, B.H., Concrete Fracture via Stress-Strain Relations, Report No. 81-10/665c, Center for Concrete and Geomaterials, Technological Institute, North-western University, Evanston, 111. (1981).
Bazant, Z.P. and Oh, B.H., Deformation of Cracked Net–Reinforced Concrete Walls, Journal of the Structural Engineering ASCE, Vol. 109, No. ST2, pp. 93–108 (1983).
Bhal, N.S., Uber den Einfluss der Balkenhohe auf Schubtragfahigkeit von einfeldrigen Stahlbetonbalken mit und ohne Schubbewehrung, Dissertation, Universitat Stuttgart (1968).
Building Code Requirements for Reinforced Concrete ACI-318-77, ACI Committee 318, American Concrete Institute, Detroit, Mich. (1977).
CEB-FIP Model Code for Concrete Structures, Comrnite Eurointernational du Beton, CEB Bulletin No. 124/125-E, Paris (1978).
Cedolin, L., and Bazant, Z.P., Fracture Mechanics of Crack Bands in Concrete, Fracture Mechanic Methods for Ceramics, Rocks and Concrete, ed., S.W. Freiman P. Fuller, Am. Soc. for Testing Materials STP745, pp. 221–236 (1981).
Cedolin, L., and Dei Poli, S., Finite Element Studies of Shear Critical R/C Beams, J. of the Engng. Mech. Div., ASCE, Vol. 103, No. EM3, pp. 395–410 (1979).
Cervenka, V., and Gerstle, K.H., Inelastic Analysis of Reinforced Concrete Panels, Publications, Intern. Assoc. for Bridge and Structural Engng., Zurich, Switzerland, Vol. 31, 1971, pp. 31–45 and Vol. 32, pp. 25–79 (1972).
Christensen, R.M., A Rate–Dependent Criterion for Crack Growth, Intern. J. of Fracture, Vol. 15, No. 1, Feb. 1979, pp. 3–21,; disc. Vol. 16, pp. R229-R232, R233 - R237 (1980).
Chudnovsky, A., On the Law of Fatigue Crack Layer Propagation in Polymers, Polymer Engineering and Science, Vol. 22, No. 15, pp. 922–927 (1982).
Chudnovsky, A., Proceedings of NSF Workshop on Damage, held in General Butler State Park in May 1980, University of Cincinnati.
Crisfield, M.A., Local Instabilities in the Non-linear Analysis of Reinforced Concrete Beams and Slabs, Proc., Institution of Civil Engrs. Part 2, Vol. 73, pp. 135–145 (1982).
Crisfield, M.A., Accelerated Solution Techniques and Concrete Cracking, Comp. Methods in Appl. Mech. and Engng. Vol. 30 (1982).
Carpinteri, A., Notch-Sensitivity and Fracture Testing of Aggregate Materials, Engng, Fracture Mechanics, Vol. 16, No. 14, pp. 467–481 (1982).
Ingraffea, A.R., Numerical Modeling of Fracture Propagation, in Rock Fracture Mechanics, ed. by H.P. Rossmanith, publ. by The International Center for Mechanical Sciences, Udine, Italy (1983).
Isida, J., Elastic Analysis of Cracks and Stress Intensity Factors, Baifukan Publishing Col, Japan (1976).
Kachanov, M., Continuum Model of Medium with Cracks, J. of the Engng. Mech. Div. ASCE, Vol. 106, pp. 1039–1051 (1980).
Kachanov, M.L., A Microcrack Model of Rock Inelasticity, Mechanics of Materials, North Holland, Vol. 1, pp. 19–41 (1982).
Kani, G.N.J., Basic Facts Concerning Shear Failure, Part I and Part II, J. of ACI, Vol. 63, No. 6,pp, 675–692 (1966).
Leonhardt, F., and Walther, R., Beitrage nur Behandlung der Schubprobleme im Stahlbeton bau, Beton–u Stahlbetonban, Vol. 56, No. 12 (1961), Vol. 57, No. 2, 3, 6, 7, 8, (1962), Vol. 58, No. 8, 9 (1963).
Marchertas, A.H., Belytschko, T.B., Comparison of Transient PCRV Model Test Results with Analysis, Trans. 5th Int. Conf. on SMiRT, Paper H8/2, Berlin (1979).
Marchertas, A.H., and Belytschko, T.B., Transient Analysis of a PCRV for LMFBR Primary Containments, Special Issue on Mechanics of Applications to Test Breeder Reactor Safety, Nuclear Technology, Vol. 51, No. 3., pp. 433–442 (1980).
Margolin, L.G., Numerical Simulation of Fracture, Proceedings, INtern. Conf. on Constitutive Relations for Engineering Mechanics, ed. by C. Desai, University of Arizona, Tucson, pp. 567–572 (1983).
Mihashi, H., and Zaitzev, J.W., Statistical Nature of Crack Propagation, Chapter 4 in Report of RILEM Techn. Comm. 50–FMC, to appear
Morley, C.T., Yield Criteria for Elements of Reinforced Concrete Slabs, Introductory Report, Colloquium, Plasticity in Reinforced Concrete, Report of the Working Commission, Inter. Assoc. for Bridge and Struct. Engng., Vol. 8, pp. 35–47 (1979).
Nilson, A., Nonlinear Analysis of Reinforced Concrete by Finite Element Method, Am. Concrete Institute Journal, Vol. 65 (1968).
Paris, P.C., Fracture Mechanics in the Elastic Plastic Regime, Flaw Growth and Fatigue, ASTM Special Techn. Publ. 631, Am. Soc. for Testing Materials, Philadelphia, pp. 3–27 (1977).
Park, R., and Paulay, T., Reinforced Concrete Structures, J. Wiley & Sons, New York, (1975).
Paulay, T., and Loeber, P.J., Shear Transfer by Aggregate Interlock Shear in Reinforced Concrete, Special Publications SP-42, American Concrete Institute, Detroit, Mich., pp. 1–15 (1974).
Pietruszczak, S., and Mroz, Z., Finite Element Analysis of Deformation of Strain-Softening Materials, Intern. J. for Numerical Methods in Engineering, Vol. 17, pp. 327–334 (1981).
Rice, J.R., An Examination of the Fracture Mechanics Energy Balance from the Point of View of Continuum Mechanics, Proc. First International Conference on Fracture (held in Sandia) T. Yokobori, et al., eds. Japanese Soc. for Strength and Fracture of Materials, Tokyo, Japan, Vol. 1, pp. 309–340 (1965).
Rice, J.R., Mathematical Analysis in the Mechanics of Fracture, in Fracture an Advance Treatise, H. Liebowitz, ed., Vol. 2, Academic Press, New York, pp. 191–250 (1968).
Rtisch, E.H., Haugh, F.R., and Mayer, M., Schubversuche an Stahlbeton Rechteckbalken mit Gleichmassig verteilter Belastung, Deutscher Ausschuss fur Stahlbeton, Heft 145, W. Ernst & Sohn, West Berlin (1962).
Saouma, V.E., Ingraffea, A.R., and Catalano, D.M., Fracture Thoughness of Concrete-KIC Revisited, J. of the Energy Mech. Div. ASCE, Vol. 108, pp. 1152–1166 (1982).
Seaman, L., Curran, D.R. Shockey, D.A., Computational Models for Ductile and Brittle Fracture, J. of Applied Physica, Vol. 47, No. 11, 1976, pp. 4814–4826 (also L. Seaman, Proceedings, NSF Workshop on Damage and Fracture, Stone Mountain, Nov. 1982, ed. by A. Altun, Georgia Institute of Technology, Atlanta.
Stout, R.B., Deformation and Thermodynamic Response for a Dislocation Model of Brittle Fracture, Engineering Fracture Mechanics, to appear (also Report UCRL–87472, Lawrence Livermore Laboratory, 1982 ).
Stout, R.B., Thigpen, L., and Peterson, L., Modeling the Deformation of Materials Involving Microcracks Kinetics, Report UCRL-85477, Lawrence Livermore National Laboratory, Livermore, Cal., 1981 (to appear in Int. J. of Num. Methods in Geomechanics, 1983).
Stroud, A.H., Approximate Calculation of Multiple Integrals, Prentice Hall, Englewood Cliffs, New Jersey, pp. 296–302 (1971).
Swamy, R,N., and Qureshi, S.A., Strength, Cracking and Deformation Similitude in Reinforced T–Beams under Bending and Shear, Part I and Part II, J. of Am. Concrete Inst., Vol. 68, No. 3, pp. 187–195 (1971).
Taylor, H.P.J., The Shear Strength of Large Beams, J. of the Structural Division ASCE, Vol. 98, pp. 2473–2490 (1972).
Walraven, J.C., The Influence of Depth on the Shear Strength of Lightweight Concrete Beams without Shear Reinforcement,: Stevin Laboratory Report No. 5-78-4, Delft University of Technology (1978).
Watstein, D., and Mathey, R.G., Width of Cracks in Concrete at the Surface of Reinforcing Steel Evaluated by Means of Tensile Bond Specimens, Journal. American Concrete Institute, Proc. Vol. 56, No. 1, pp. 47–56.
Wecharatana, M., and Shah, S.P., Double Torsion Tests for Studying Slow Crack Growth of Portland Cement Mortar, Cement and Concrete Research, Vol, 10, pp. 833–844 (1980).
Wecharatana, M., and Shah, S.P. Slow Crack Growth in Cement Composites, J. of the Structural Division ASCE, Vol. 108, pp. 1400–1413 (1982).
Wittmann, F.H., Mechanics and Mechanisms of Fracture of Concrete, Advances in Fracture Research (Preprints, 5th Intern. Conf. on Fracture, in Cannes, March 1981), Vol. 4, Pergamon Press, Paris, pp. 1467–1487 (1981).
Zaitsev, Y.W., and Wittmann, F.H., Crack Propagation in a Two-Phase Material Such as Concrete, Fracture, 1977 (Proc. 4th Intern. Conf. on Fracture), University of Waterloo, Vol. 3, pp. 1197–1203 (1977).
Zech, B., and Wittmann, F.H., Variability and Mean Value of Strength of Concrete as a Function of Load, Am. Concrete Institute Journal, Vol. 77, No. 5, pp. 358–362 (1980).
Zech, B. and Wittmann, F.H., Influence of Rate of Loading on Strength of Concrete, Manuscript (1981).
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1985 Martinus Nijhoff Publishers, Dordrecht
About this chapter
Cite this chapter
Bažant, Z.P. (1985). Mechanics of fracture and progressive cracking in concrete structures. In: Sih, G.C., DiTommaso, A. (eds) Fracture mechanics of concrete: Structural application and numerical calculation. Engineering Application of Fracture Mechanics, vol 4. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-6152-4_1
Download citation
DOI: https://doi.org/10.1007/978-94-009-6152-4_1
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-009-6154-8
Online ISBN: 978-94-009-6152-4
eBook Packages: Springer Book Archive