Abstract
A simple theoretical approach is used to obtain expressions for the dependence of a number of physical properties of concrete upon the physical properties of its constituents and the aggregate volume concentration. It is assumed that concrete approximates to a two phase material consisting of aggregate particles dispersed in a cement matrix and it is shown that the theory is in reasonable agreement with some Young's modulus, creep and shrinkage measurements made on concrete.
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Abbreviations
- k,k m andk a :
-
bulk moduli of the composite, matrix and aggregate respectively
- k h :
-
bulk modulus of a composite containing pores in place of the aggregate particles
- E, E m and E a :
-
Young's moduli of the composite, matrix and aggregate
- ν, ν m and ν a :
-
Poisson's ratios of the composite, matrix and aggregate
- C, C m and C a :
-
volumetric shrinkages or volumetric thermal contractions of the composite, matrix and aggregate
- C g :
-
volumetric shrinkage of the cement gel
- T, T m and T a :
-
volumetric thermal expansions of the composite, matrix and aggregate
- α, α m and α a :
-
linear coefficients of thermal expansion for the composite, matrix and aggregate
- P:
-
applied hydrostatic stress
- P m :
-
average hydrostatic stress in the matrix
- P a :
-
hydrostatic stress in the aggregate
- ΔP:
-
P a −P m
- σ:
-
applied compressive stress
- σ m :
-
average stress in the matrix
- σ a :
-
average stress in the aggregate
- D a :
-
aggregate volume concentration
- D u :
-
volume concentration of the unhydrated cement in the cement paste
- V m :
-
volumetric strain induced in the matrix by P m
- V a :
-
volumetric strain induced in the aggregate by P m
- dV m :
-
volumetric strain induced in the matrix by an applied hydrostatic stress −ΔP
- dV a :
-
volumetric strain induced in the aggregate by an applied hydrostatic stress ΔP
- dV:
-
average volumetric strain induced in the composite by shrinkage
- t :
-
time
- ε and ε m :
-
average longitudinal strains in the composite and matrix
- ε mt :
-
creep or total strain in a matrix specimen at timet
- a :
-
a constant at a given timet
- τ:
-
change in temperature
References
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Hobbs, D.W.—Stress-strain behaviour of a number of coal measure rocks. To be published in Colliery Guard.
Hansen, T.C.—Influence of aggregate and voids on the modulus of elasticity of concrete, cement mortar and paste. J. Am. Concr. Inst. vol. 62, 1965, pp. 193–;216.
Counto, U.J.—The effect of the elastic modulus of the aggregate on the elastic modulus, creep and creep recovery of concrete. Mag. Concr. Res. vol. 16, 1964, pp. 129–;138.
Hobbs, D.W.—Stress-strain-time behaviour of a number of coal measure rocks. Int. J. Rock. Mech. Min. Sci., vol. 7, 1970, pp. 149–;170.
Pickett, G..—Effect of aggregate on shrinkage of concrete and a hypothesis concerning shrinkage. Vol. 52, 1956, pp. 581–;590.
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Hobbs, D.W. The dependence of the bulk modulus, Young's modulus, creep, shrinkage and thermal expansion of concrete upon aggregate volume concentration. Mat. Constr. 4, 107–114 (1971). https://doi.org/10.1007/BF02473965
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DOI: https://doi.org/10.1007/BF02473965