Showing papers by "Zdenek P. Bazant published in 1985"

Concrete creep at variable humidity: constitutive law and mechanism

Abstract: The previously formulated rate-type aging creep law based on Maxwell chain is generalized to variable humidity and is calibrated by extensive comparisons with test data from the literature. The main object of attention is the Pickett effect, i.e., the apparent increase in creep due to drying simultaneous with loading. This effect is shown to have four sources, in their decreasing order of importance: (1) stress-induced shrinkage, (2) tensile strain softening due to progressive cracking, (3) irreversibility of unloading contraction after tensile strainsoftening, and (4) increase of material stiffness due to aging (hydration). The model, which is a special case of a previously advanced thermodynamic theory, depends on only one hypothesis about the microscopic physical mechanism of creep: The creep rate depends on the magnitude of the flux of microdiffusion of water between the macropores (capillary pores) and the micropores in the cement gel. By assuming this microdiffusion to be infinitely fast, the effect is reduced to a dependence of creep viscosities on the time rate of pore humidity, and this is further shown to be equivalent to stress-induced shrinkage, in which the shrinkage coefficient defining the ratio of the increments of shrinkage strain and pore relative humidity depends on stress. In three dimensions, the shrinkage coefficient thus becomes a tensor. For thermodynamic reasons, there must also exist stress-induced thermal expansion. Although tensile cracking is found to make significant contribution to the Pickett effect, it is far from sufficient to explain in fully. The theory agrees with test data on basic creep, creep of specimens with reduced water content at hygral equilibrium (predried), shrinkage, swelling, and creep at drying under compression, tension, or bending. The strainsoftening model used for tensile cracking is the same as that used previously to fit test data from fracture tests, direct tensile tests, and deflection tests of reinforced beams.

Strain Softening with Creep and Exponential Algorithm

Abstract: A constitutive relation that can describe tensile strain softening with or without simultaneous creep and shrinkage is presented, and an efficient time-step numerical integration algorithm, called the exponential algorithm, is developed. Microcracking that causes strain softening is permitted to take place only within three orthogonal planes. This allows the description of strain softening by independent algebraic relations for each of three orthogonal directions, including independent unloading and reloading behavior. The strain due to strain softening is considered as additive to the strain due to creep, shrinkage and elastic deformation. The time-step formulas for numerical integration of strain softening are obtained by an exact solution of a first-order linear differential equation for stress, whose coefficients are assumed to be constant during the time step but may vary discontinuously between the steps. This algorithm is unconditionally stable and accurate even for very large time steps, and guarantees that the stress is always reduced exactly to zero as the normal tensile strain becomes very large. This algorithm, called exponential because its formulas involve exponential functions, may be combined with the well-known exponential algorithm for linear aging rate-type creep. The strain-softening model can satisfactorily represent the test data available in the literature.

Log Double Power Law for Concrete Creep

Abstract: An improved law of creep of concrete at constant humidity and temperature is proposed. The well-known double power law gives too high a final slope of creep curves compared to available test data. This is remedied by a new formula which exhibits a continuous transition from a power curve to a straight line in the logarithm of creep duration. The straight line has the same slope for all ages at loading, and the higher the age at loading, the longer is the duration at which the transition occurs. The exponent of the initial power curve is higher than that used in the double power law and is much too high in comparison with the existing test results for very short load durations in the dynamic range. This penalty, however, is outweighed by better extrapolation to very long load durations. The new formula significantly restricts the occurrence of divergence of creep curves at various ages at loading but does not eliminate it completely unless closeness of data fit is sacrificed. The new formula also greatly reduces the occurrence of negative values at the end of calculated stress relaxation curves. Extensive statistical analysis of most test data available in the literature reveals a relatively modest improvement in the overall coefficient of variation for the deviations of the formula from test data and a significant improvement for the deviations of the final slope from its measured value. The same improvements were achieved in an earlier study in which the transition from the power law to the logarithmic law was abrupt, with a discontinuity in curvature. The continuity of curvature in the present formulation is desirable for applications in data extrapolation.