Creep and shrinkage of concrete

When a deformation is suddenly imposed and held constant, creep causes relaxation of critically produced elastic stress.

The difference, called the drying creep or Pickett effect (or stress-induced shrinkage), represents a hygro-mechanical coupling between strain and pore humidity changes.

At low pore humidities (<75%), shrinkage is caused by a decrease of the disjoining pressure across nano-pores less than about 3 nm thick, filled by adsorbed water.

It is caused partly by chemical volume changes, but mainly by self-desiccation due to loss of water consumed by the hydration reaction.

The gel forms particles of colloidal dimensions, weakly bound by van der Waals forces.

The constitutive material model in the equations that follow is not the only one available but has at present the strongest theoretical foundation and fits best the full range of available test data.

In service, the stresses in structures are < 50% of concrete strength, in which case the stress–strain relation is linear, except for corrections due to microcracking when the pore humidity changes.

is replaced by the bulk and shear compliance functions: At high stress, the creep law appears to be nonlinear (Fig.

(this condition is required to prevent the principle of superposition from giving non-monotonic recovery curves after unloading which are physically objectionable).

of evaporable (i.e., not chemically bound) water per unit volume of concrete, a physically realistic constitutive relation may be based on the idea of microprestress

The microprestress is produced as a reaction to chemical volume changes and to changes in the disjoining pressures acting across the hindered adsorbed water layers in nanopores (which are < 1 nm thick on the average and at most up to about ten water molecules, or 2.7 nm, in thickness), confined between the C-S-H sheets.

(4) to be generalized as A crucial property is that the microprestress is not appreciably affected by the applied load (since pore water is much more compressible than the solid skeleton and behaves like a soft spring coupled in parallel with a stiff framework).

One physical cause of aging is that the hydration products gradually fill the pores of hardened cement paste, as reflected in function

The explanation is that the microstress peaks relax with age, which reduces the number of creep sites and thus the rate of bond breakages.

= coordinate vector) may be approximately considered as uncoupled from the stress and deformation problem and may be solved numerically from the diffusion equation

-values at various points are incompatible, the calculation of the overall shrinkage of structures as well as test specimens is a stress analysis problem, in which creep and cracking must be taken into account.

For finite element structural analysis in time steps, it is advantageous to convert the constitutive law to a rate-type form.

1 then disappear from the constitutive law, the history being characterized by the current values of the internal state variables (the partial strains or stresses of the Kelvin or Maxwell chain).

Conversion to a rate-type form is also necessary for introducing the effect of variable temperature, which affects (according to the Arrhenius law) both the Kelvin chain viscosities and the rate of hydration, as captured by

Compared to the point-wise constitutive equation, the algebraic expressions for such average characteristics are considerably more complicated and their accuracy is lower, especially if the cross section is not under centric compression.

The following approximations have been derived and their coefficients optimized by fitting a large laboratory database for environmental humidities

These high uncertainties can be drastically reduced by updating certain coefficients of the formulae according to short-time creep and shrinkage tests of the given concrete.

A fully rational prediction of concrete creep and shrinkage properties from its composition is a formidable problem, far from resolved satisfactorily.

Underestimation of multi-decade creep has caused excessive deflections, often with cracking, in many of large-span prestressed segmentally erected box girder bridges (over 60 cases documented).

Non-uniformity of creep and shrinkage, caused by differences in the histories of pore humidity and temperature, age and concrete type in various parts of a structures may lead to cracking.

The creep effects are particularly important for prestressed concrete structures (because of their slenderness and high flexibility), and are paramount in safety analysis of nuclear reactor containments and vessels.

At high temperature exposure, as in fire or postulated nuclear reactor accidents, creep is very large and plays a major role.

(1) can be used but in that form the variations of humidity and temperature with time cannot be introduced and the need to store the entire stress history for each finite element is cumbersome.

To this end, the creep properties in each sufficiently small time step may be considered as non-aging, in which case a continuous spectrum of retardation moduli of Kelvin chain may be obtained from

This way the creep analysis problem gets converted to a series of elastic structural analyses, each of which can be run on a commercial finite element program.