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.

Pervasiveness of Excessive Segmental Bridge Deflections: Wake-Up Call for Creep

Abstract: An obsolete standard recommendation for creep design led to significant underestimation of the observed 18-year deflections of the Koror-Babeldaob (KB) Bridge in the island nation of Palau. A search for data on similar bridges revealed that 56 other large-span, prestressed concrete, segmentally erected box girders (66 by the time of proof) have been found to exhibit excessive long-time deflections. There are probably many more in existence. The observed deflections give no sign of approaching a finite bound, as implied in the empirical ACI Committee 209, CEB-fib, and GL models for creep. They were found to evolve approximately logarithmically beginning at about 1000 days after span closing. While sufficient data for the finite element creep analysis of these deflections were not obtainable, comparisons with accurate deflection solutions for the KB Bridge showed that the terminal logarithmic deflection trend can be predicted well by a simple extrapolation of the measured 1000-day deflection under the hypothesis of proportionality to the compliance function increment since the time of span closing. Comparisons of the extrapolations according to various creep models show that the underestimation of long-time deflections is much less severe for the theoretically based Model B3 than it is for the three other models, and that the terminal trend is logarithmic. A simple update of this model that gives the same mean terminal trend as the 56 bridges is devised that should allow for improving the durability of segmental bridges.

Microplane model M7 for plain concrete. I: Formulation

Abstract: Mathematical modeling of the nonlinear triaxial behavior and damage of such a complex material as concrete has been a long-standing challenge in which progress has been made only in gradual increments. The goal of this study is a realistic and robust material model for explicit finite-element programs for concrete structures that computes the stress tensor from the given strain tensor and some history variables. The microplane models, which use a constitutive equation in a vectorial rather than tensorial form and are semimultiscale by virtue of capturing interactions among phenomena of different orientation, can serve this goal effectively. This paper presents a new concrete microplane model, M7, which achieves this goal much better than the previous versions M1–M6 developed at Northwestern University since 1985. The basic mathematical structure of M7 is logically correlated to thermodynamic potentials for the elastic regime, the tensile and compressive damage regimes, and the frictional slip regi...

Designing Against Size Effect on Shear Strength of Reinforced Concrete Beams Without Stirrups: I. Formulation

Abstract: The shear failure of reinforced concrete beams is a very complex fracture phenomenon for which a purely mathematical approach is not possible at present. However, detailed modeling of the fracture mechanism is not necessary for establishing the general form of the size effect. The first part of this paper shows that the general approximate mathematical form of the size effect law to be calibrated by experimental data can be deduced from two facts: (1) the failure is caused by cohesive (or quasibrittle) fracture propagation; and (2) the maximum load is attained only after large fracture growth (rather than at fracture initiation). Simple dimensional analysis yields the asymptotic properties of size effect, which are characterized by: (1) a constant beam shear strength vc (i.e., absence of size effect) for sufficiently small beam depths; and (2) the linear elastic fracture mechanics size effect vc ∼ d−1∕2 for very large beam depths d . Together with the recently established small- and large-size second-orde...

Microprestress-solidification theory for concrete creep. ii: algorithm and verification

Abstract: This paper presents a numerical algorithm for the microprestress-solidification theory developed in a companion paper and verifies this theory by comparisons with typical test data from the literature. A model for cracking is incorporated in the algorithm.

Microplane model m4 for concrete: ii. algorithm and calibration

Abstract: This paper represents Part II of a two-part study in which a new improved version of the microplane constitutive model for damage-plastic behavior of concrete in 3D is developed. In Part II, an explicit numerical algorithm for model M4 is formulated, the material parameters of model M4 are calibrated by optimum fitting of the basic test data available in the literature, and the model is verified by comparisons with these data. The data in which strain localization must have occurred are delocalized, and the size effect is filtered out from the data where necessary. Although model M4 contains many material parameters, all but four have fixed values for all types of concretes. Thus the user needs to adjust only four free material parameters to the data for a given concrete, for which a simple sequential identification procedure is developed. If the user's data consist only of the standard compression strength and the strain at uniaxial stress peak, the adjustment is explicit and immediate. Good agreement wi...

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.