Showing papers by "Zdenek P. Bazant published in 1977"

Stochastic process for extrapolating concrete creep

Abstract: Creep of concrete is modeled as a process with independent increments of locally gamma distribution. The process is transformed to a stationary gamma process. The mean prediction agrees with the deterministic double power law established previously. Infinite divisibility of the increment distribution is assumed. This is justified by additivity of deformations and of stresses, and also by considerations of the microscopic mechanism of creep, assuming creep to be due to migrations of widely spaced solid particles along micropore passages whose length is statistically distributed. The treatment of creep as a stochastic process allows extracting considerable information from measurements even on one specimen, although a greater number of specimens is preferable. The main use of the model is in extrapolation of short time creep data into long times, and calculation of confidence limits. Methods of determining process parameters from creep test data are given. Monte Carlo simulations demonstrate reasonable agreement with test data.

Viscoelasticity of Solidifying Porous Material-Concrete

Abstract: The form of the age effect on linear creep and elasticity is established by treating the hydrating cement paste as a variable composite in which the volume fraction of solid grows while the material creeps under load. The formulation rests on three hypotheses: (1)The average strains in microelements solidified at various times are equal; (2)the properties of solidified matter (cement gel) are time-invariant; (3)the rate of migrations of solid particles causing creep in cement gel depends on the mean length of migration passages at the time of load application. The first hypothesis allows eliminating the microstresses from a system of two integral equations set up to relate stress and strain histories. A new form of the creep function is deduced, expressing the aging effect in terms of the growth of volume of cement gel and the increase of the migration passage length. It is shown that the double power law is obtained as a special case when the growth of gel volume is negligible, and a generalization consistent with growing gel volume is suggested and compared with creep data.

Densification and hysteresis of sand under cyclic shear

Abstract: The accumulation of inelastic strain due to the irreversible rearrangement of grain configurations associated with deviatoric strains is characterized by a nondecreasing material variable, termed the rearrangement measure; this variable, in turn, forms the basis of an intrinsic time scale and other related variables termed the densification measure and distortion measure. The shear modulus is identified to be a function of the mean normal stress and the second invariant of the strain deviator. In contrast with empirical methods, the material behavior is described herein by a constitutive law that satisfies all invariance requirements of continuum mechanics; thus, this law should, in principle, be generally applicable, including the cases of nonsinusoidal loadings with varying amplitudes, general multiaxial stress states, and nonproportional stress component histories. In addition, the law automatically exhibits hysteretic damping and is fully continuous, i.e., it contains no inequalities, such as those used in plasticity to distinguish unloading.

Prediction of hysteresis of reinforced concrete members

Abstract: The endochronic theory for inelasticity and failure, previously established, is used to predict the response of reinforced concrete beams in cyclic bending at large strains. Cross sections are assumed to remain plain and are subdivided in slices. Existing bending theories must be enhanced by inclusion of transverse normal strain as a third variable, in addition to curvature and transverse shear angle. The forces in stirrups bring concrete under confining hydrostatic pressure, and, according to endochronic theory, this greatly increases ductility and strength and suppresses strain-softening. The theory is applicable to any history of bending moment, shear force, and axial force, and allows the necessary cross-sectional area of stirrups to be calculated. It is most remarkable that a number of test data have been correctly predicted without having to adjust any of the material parameters determined previously from tests of plain concrete. The endochronic theory represents not merely a descriptive model, but a prediction method.

Constitutive law for nonlinear creep of concrete

Abstract: Endochronic theory, previously proposed and verified for multiaxial time-independent experimental data, is extended to nonlinear long-time creep at high stress and is compared with available uniaxial creep data. The extension is based on a Maxwell chain model, each unit of which is characterized by its own intrinsic time, an independent variable whose increments depend both on time and strain increments. The dependence on the latter involves the previously determined hardening and softening functions. Aging is included and the previously established Maxwell chain model for low-stress creep with aging is obtained as a special case. The theory also describes the decrease of strength with load duration when the compression is high, gives an increase when the compression is low, and yields the additional inelastic strain accumulation due to cyclic load. An effective and numerically stable algorithm for timestep integration of structural response, permitting the time steps to be increased with the load duration, is presented.