Singular History Integral for Creep Rate of Concrete
Publication: Journal of Engineering Mechanics
Volume 109, Issue 3
Abstract
A uniaxial constitutive equation describing the deviations from the linear principle of superposition of aging concrete at constant moisture content and temperature is presented. Both the creep increase (flow) at high stress and the stiffening (adaptation) due to low sustained compressive stress are modeled, the latter being of principal interest. The constitutive equation expresses the creep rate as a history integral with a singular kernel involving the time lag of creep strain. The integral has the property that the strain response is proportional to the stress history but depends nonlinearly on the stress history when nonproportional stress histories are superposed. The double power law for aging creep is a special limiting case. The constitutive relation is also explained in terms of the rate‐process (activation energy) theory for the rate of bond ruptures causing creep. For structural creep problems a corresponding step‐by‐step integration algorithm which correctly captures the asymptotic properties of the integral is also developed. A good agreement with test data from the literature is achieved.
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References
1.
Bažant, Z. P., “Mathematical Models for Creep and Shrinkage of Concrete,” Creep and Shrinkage of Concrete Structures, Chapter 7, Z. P. Bažant and F. H. Wittmann, eds., John Wiley and Sons, Inc., London, England, 1982.
2.
Bažant, Z. P., “Numerical Determination of Long‐range Stress History from Strain History in Concrete,” Materials and Structures (RILEM), Vol. 5, 1972, pp. 135–141.
3.
Bažant, Z. P., “Theory of Creep and Shrinkage in Concrete Structures: A Précis of Recent Developments,” Mechanics Today, Vol. 2, Pergamon Press, New York, N.Y., 1975, pp. 1–93.
4.
Bažant, Z. P., “Thermodynamics of Solidifying or Melting Viscoelastic Material,” Journal of the Engineering Mechanics Division, ASCE, Vol. 105, No. EM6, Proc. Paper 15041, Dec., 1979, pp. 933–952.
5.
Bažant, Z. P., “Viscoelasticity of Solidifying Porous Material—Concrete,” Journal of the Engineering Mechanics Division, ASCE, Vol. 103, No. EM6, Proc. Paper 13432, Dec., 1977, pp. 1049–1067.
6.
Bažant, Z. P., and Kim, S.‐S., “Nonlinear Creep of Concrete—Adaptation and Flow,” Journal of the Engineering Mechanics Division, ASCE, Vol. 105, No. EM3, Proc. Paper 14654, June, 1979, pp. 429–446.
7.
Bažant, Z. P., and Osman, E., “Double Power Law for Basic Creep of Concrete,” Materials and Structures, Vol. 9, Paris, France, 1976, pp. 3–11.
8.
Bažant, Z. P., and Panula, L., “Practical Prediction of Creep and Shrinkage of Concrete,” Materials and Structures, RILEM, Paris, France, Parts I and II, Vol. 11, No. 68, 1978, pp. 307–328;
Parts III and IV, Vol. 11, No. 69, 1978, pp. 415–434;
Parts V and VI, Vol. 12, No. 72, 1979, pp. 169–183.
9.
Bažant, Z. P., and Tsubaki, T., “Weakly Singular Integral for Creep Rate of Concrete,” Mechanics Research Communications, Vol. 7, No. 5, 1980, pp. 335–340.
10.
“Finite Element Analysis of Reinforced Concrete Structures,” by the Structural Division Committee on Finite Element Analysis of P.C. Structures, A. Nilson, Chmn., Time‐Dependent Effects, ASCE Special Publications, 1982.
11.
Glasstone, S., Laidler, K. J., and Eyring, H., The Theory of Rate Processes, McGraw‐Hill Book Co., Inc., New York, N.Y., 1941.
12.
Hanson, J. A., “A 10‐Year Study of Creep Properties of Concrete,” Concrete Laboratory Report No. SP‐38, United States Bureau of Reclamation, Denver, Colo., 1953.
13.
Kimishima, H., and Kitahara, H., “Creep and Creep Recovery of Mass Concrete,” Technical Report C‐64001, Central Research Institute of Electric Power Industry, Tokyo, Japan, Sept., 1964.
14.
Komendant, G. J., Polivka, M., and Pirtz, D., “Study of Concrete Properties for Prestressed Concrete Reactor Vessels; Part II, Creep and Strength Characteristics of Concrete at Elevated Temperatures,” Report No. UC SESM 76‐3, Structures and Materials Research, Department of Civil Engineering, University of California, Berkeley, Calif., Apr., 1976.
15.
Krausz, A. S., and Eyring, H., Deformation Kinetics, John Wiley and Sons, Inc., New York, N.Y., 1975.
16.
Mamillan, M., “A Study of the Creep of Concrete,” RILEM Bulletin No. 3, Réunion Internationale des Laboratoires d'Essais et de Recherches sur les Matériaux et les Constructions, Paris, France, 1959, pp. 15–33.
17.
Mullick, A. K., “Effect of Stress‐History on the Microstructure and Creep Properties of Maturing Concrete,” thesis presented to the University of Calgary, at Alberta, Canada, in 1972, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
18.
Polivka, M., Pirtz, D., and Adams, R. F., “Studies of Creep in Mass Concrete,” Proceedings, American Concrete Institute SP‐6, Symposium on Mass Concrete, 1963, pp. 257–285.
19.
Roll, R., “Long‐Time Creep‐Recovery of Highly Stressed Concrete Cylinders,” Proceedings, American Concrete Institute SP‐9, Symposium on Creep, Detroit, Mich., 1964, pp. 115–128.
20.
Ross, A. D., “Creep of Concrete under Variable Stress,” Proceedings, American Concrete Institute Journal, Vol. 54, 1958, pp. 739–758.
21.
Straub, F., and Wittmann, F. H., “Activation Energy and Activation Volume of Compressive and Tensile Creep of Hardened Cement Paste,” Proceedings, Conference on Hydraulic Cement Pastes: Their Structure and Properties, Sheffield, England, 1976, pp. 227–230.
22.
Wittmann, F. H., “Bestimmung Physikalischer Eigenschaften des Zementsteins,” Deutscher Ausschuss für Stahlbeton, Heft 232, W. Ernst & Sohn, West Berlin, Germany, 1974.
23.
Wittmann, F. H., “Creep and Shrinkage Mechanisms,” Creep and Shrinkage in Concrete Structures, by Z. P. Bažant and F. H. Wittmann, eds., John Wiley and Sons, Inc., London, England, 1982, pp. 129–162.
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Copyright © 1983 ASCE.
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Published online: Aug 1, 1983
Published in print: Aug 1983
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