Zdenek P. Bazant

Bio: Zdenek P. Bazant is an academic researcher from Northwestern University. The author has contributed to research in topics: Creep & Fracture mechanics. The author has an hindex of 82, co-authored 301 publications receiving 20908 citations. Previous affiliations of Zdenek P. Bazant include École Polytechnique Fédérale de Lausanne & Rensselaer Polytechnic Institute.

Bayesian Statistical Prediction of Concrete Creep and Shrinkage

Abstract: In present design practice, the statistical approach is used for strength but not for deformations, including creep and shrinkage. However, predicting concrete creep properties from design strength and concrete composition involves a large uncertainty, much larger than that of strength. It is shown that by carrying out some short-time creep measurements, even rather limited ones, the uncertainty can be drastically reduced, and extrapolation of short-time measurements can be made much more reliable. This is accomplished by developing a Bayesian approach to creep prediction. Prior information consists of the coefficient of variation of deviations from the creep law for concrete in general, as determined in a recent statistical analysis of the numerous creep data that exist in literature. This information is combined, according to Bayes' theorem, with the probability of a given concrete's creep values to yield the posterior probability distribution of the creep values for any load duration and age at loading. Only a linear creep case is considered, and a normal distribution of errors is assumed for the given concrete as well as for the prior information. To demonstrate and verify the method developed, various creep data reported in literature are considered. Predictions made on the basis of only a part of the test data are compared with the rest of the data, and very good agreement is found. The effects of various amounts of measured data, and of various degrees of uncertainty in the prior information, are also illustrated. The present approach is recommended for concrete structures for which the creep deflections, creep-induced cracking, or creep buckling are of special concern, e.g., nuclear reactor vessels and containments, certain very large bridges, shells, or building frames.

Compression Failure of Quasibrittle Material: Nonlocal Microplane Model

Abstract: The previously presented constitutive model of microplane type for nonlinear triaxial behavior and fracture of concrete is used in nonlocal finite element analysis of compression failure in plane strain rectangular specimens. For specimens with sliding rigid platens there is a bifurcation of the loading path at the beginning of postpeak softening; a symmetric (primary) path exists but the actual (stable) path is the nonsymmetric (secondary) path, involving an inclined shear‐expansion band that consists of axial splitting cracks and is characterized by transverse expansion. The secondary path is indicated by the first eigenvalue of the tangent stiffness matrix but can be more easily obtained if a slight nonsymmetry is introduced into the finite element model. In specimens with bonded rigid platens there is no bifurcation; they fail symmetrically, by two inclined shear‐expansion bands that consist of axial splitting cracks. The transverse expansion produces transverse tension in the adjacent material, which...

Easy-to-Compute Tensors With Symmetric Inverse Approximating Hencky Finite Strain and Its Rate

Abstract: It is shown that there exist approximations of the Hencky (logarithmic) finite strain tensor of various degrees of accuracy, having the following characteristics: (1) The tensors are close enough to the Hencky strain tensor for most practical purposes and coincide with it up to the quadratic term of the Taylor series expansion; (2) are easy to compute (the spectral representation being unnecessary) ; and ( 3 ) exhibit tension-compression symmetry (i.e., the strain tensor of the inverse transformation is minus the original strain tensor). Furthermore, an additive decomposition of the proposed strain tensor into volumetric and deviatoric (isochoric) parts is given. The deviatoric part depends on the volume change, but this dependence is negligible for materials that are incapable of large volume changes. A general relationship between the rate of the approximate Hencky strain tensor and the deformation rate tensor can be easily established.

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.

New method of analysis for slender columns

Abstract: The paper presents a simple new method to calculate column-interaction diagrams, which takes into account slenderness effects. The method consists of a simple incremental loading algorithm that traces the load-deflection curve at constant eccentricity of the axial load. The column failure is defined for design purposes as the peak of the diagram of axial load versus midlength bending moment at constant load eccentricity. The tangent modulus load is found to be apporximately equal to the peak load of column with load eccentricity 0.01 of the cross-sectional thickness and represents a lower bound for the maximum loads at still smaller eccentricities. Strain irreversibility at unloading can be taken into account but its effect is very small. The method is compared with the ACI moment magnification method and with the CEB Model column method based on moment-curvature relations. The agreement with the CEB method is very close, but with respect to the ACI method there are large discrepancies.

Theoretical stress strain model for confined concrete

Abstract: A stress‐strain model is developed for concrete subjected to uniaxial compressive loading and confined by transverse reinforcement. The concrete section may contain any general type of confining steel: either spiral or circular hoops; or rectangular hoops with or without supplementary cross ties. These cross ties can have either equal or unequal confining stresses along each of the transverse axes. A single equation is used for the stress‐strain equation. The model allows for cyclic loading and includes the effect of strain rate. The influence of various types of confinement is taken into account by defining an effective lateral confining stress, which is dependent on the configuration of the transverse and longitudinal reinforcement. An energy balance approach is used to predict the longitudinal compressive strain in the concrete corresponding to first fracture of the transverse reinforcement by equating the strain energy capacity of the transverse reinforcement to the strain energy stored in the concret...

Crack band theory for fracture of concrete

Abstract: A fracture theory for a heterogenous aggregate material which exhibits a gradual strain-softening due to microcracking and contains aggregate pieces that are not necessarily small compared to structural dimensions is developed. Only Mode I is considered. The fracture is modeled as a blunt smeard crack band, which is justified by the random nature of the microstructure. Simple triaxial stress-strain relations which model the strain-softening and describe the effect of gradual microcracking in the crack band are derived. It is shown that it is easier to use compliance rather than stiffness matrices and that it suffices to adjust a single diagonal term of the complicance matrix. The limiting case of this matrix for complete (continuous) cracking is shown to be identical to the inverse of the well-known stiffness matrix for a perfectly cracked material. The material fracture properties are characterized by only three parameters—fracture energy, uniaxial strength limit and width of the crack band (fracture process zone), while the strain-softening modulus is a function of these parameters. A method of determining the fracture energy from measured complete stres-strain relations is also given. Triaxial stress effects on fracture can be taken into account. The theory is verified by comparisons with numerous experimental data from the literature. Satisfactory fits of maximum load data as well as resistance curves are achieved and values of the three material parameters involved, namely the fracture energy, the strength, and the width of crack band front, are determined from test data. The optimum value of the latter width is found to be about 3 aggregate sizes, which is also justified as the minimum acceptable for a homogeneous continuum modeling. The method of implementing the theory in a finite element code is also indicated, and rules for achieving objectivity of results with regard to the analyst's choice of element size are given. Finally, a simple formula is derived to predict from the tensile strength and aggregate size the fracture energy, as well as the strain-softening modulus. A statistical analysis of the errors reveals a drastic improvement compared to the linear fracture theory as well as the strength theory. The applicability of fracture mechanics to concrete is thus solidly established.