Showing papers by "Zdenek P. Bazant published in 1974"

Rate-type creep law of aging concrete based on maxwell chain

Abstract: It is shown that the linear creep law of concrete can be characterized, with any desired accuracy, by a rate-type creep law that can be interpreted by a Maxwell chain model of time-variable viscosities and spring moduli. Identification of these parameters from the test data is accomplished by expanding into Direchlet series the relaxation curves, which in turn are computed from the measured creep curves. The identification has a unique solution if a certain smoothing condition is imposed upon the relaxation spectra. The formulation is useful for the step-by-step time integration of large finite element systems because it makes the storage of stress history unnecessary. For this purpose a new, unconditionally stable numerical algorithm is presented, allowing an arbitrary increase of the time step as the creep rate decays. The rate-type formulation permits establishing a correlation with the rate processes in the microstructure and thus opens the way toward rational generations to variable tempeature and water content. The previously developed Kelvin-type chain also permits such a correlation, but its identification from test data is more complicated.

Creep and Shrinkage Law for Concrete at Variable Humidity

Abstract: The drying creep effect is modeled by a nonlinear coupling between two types of hidden stresses, those in solids and those in (hindered adsorbed) water. Material parameters, as functions of pore humidity, of equivalent hydration period, and of relaxation time, are identified from the existing test data, using an optimization algorithm based on a least-square criterion and coupled with a finite element program for strain and stress history in a drying concrete cylinder. The ratios in which pore humidity modifies the creep parameters are found to be nearly the same for all concretes. Realistic estimates of stresses induced by shrinkage and by drying creep are also reached. The formulation is also extended to variable temperature. The success in fitting the data corroborates the underlying irreversible therodynamic theory of the creep mechanism, and especially confirms that creep at working stress levels is caused primarily by the diffusion of solids which, in turn, is facilitated by the presence of water and is nonlinearly accelerated by its migration.

Stiffness Method for Curved Box Girders at Initial Stress

Abstract: A method of analysis of the global behavior of long curved or straight single-cell girders with or without initial stress is presented. It is based on thin-wall beam elements that include the modes of longitudinal warping and of transverse distortion of cross section. Deformations due to shear forces and transverse bimoment are included, and it is found that the well-known spurious shear stiffness in very slender beams is eliminated by virtue of the fact that the interpolation polynomials for transverse displacements and for longitudinal displacements (due to rotations and warping) are linear and quadratic, respectively, and an interior mode is used. The element is treated as a mapped image of one parent unit element and the stiffness matrix is in integration in three dimensions, which is numerical in general, but could be carried out explicitly in special cases. Numerical examples of deformation of horizontally curved bridge girders, and of lateral buckling of box arches, as well as straight girders, validate the formulation and indicate good agreement with solutions by other methods.

Thermoviscoelasticity of aging concrete

Abstract: Assuming constant water content, linear stress range, and temperatures between 2°C and 80–100°C, creep of aging concrete at normal and elevated varying (or constant) temperatures, a phenomenon of importance for nuclear reactor vessels, is formulated by a rate-type creep law with hidden stresses based on Maxwell chain model of time-variable properties. Dependence of the creep rate upon temperature is expressed with the help of activation energies which, in general, may be different for the individual Maxwell units in the chain. Introducing the equivalent hydration period, acceleration of aging due to temperature rise is formulated by means of the activation energy of hydration. It is demonstrated that all of the pertinent more extensive data available in the literature can be fitted satisfactorily by the method described. However, no set of data for one concrete available at present is complete enough to assure unique solution to the problem of identification of material parameters from data.