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.

Compression failure of quasibrittle materials and size effect

Abstract: The paper presents a model for size effect in the failure of columns or other compression made members made of quasibrittle materials such as concretes, rocks, or composites. The size effect is explained by energy release due to transverSe propagation of a band of axial splitting cracks. The microslabs of the material between the splitting cracks are considered to buckle and undergo post-critical deflections. The failure condition is based on the equality of the energy released from the uncracked elastic member and the energy consumed by the axial splitting cracks in the band. The analysis leads to a closed-form expression relating the nominal strength of the structure and the structures characteristic size. The resulting formulation is compared to the test results on model reinforced concrete columns reported previously by Bazant and Kwon (1994). Satisfactory match of the test data is achieved. INTRODUCTION In a number of previous studies, it has been shown that structures made of quasibrittle materials such as concrete, rock or composites, exhibit a significant size effect (BaZant, 1993a). The nominal strength of structure is not constant, as predicted for materials following yield or strength failure criteria, but decreases with an increasing size of structure. The size effect is due to fracture or damage phenomena, particularly the fact that these modes of material failure are governed by energy release and consume a certain amount of energy which is a material property. Previous work has demonstrated that such size effect exists in various tensile and shear failures, including diagonal shear failure of reinforced concrete beams, torsional failure, punching shear failure, pullout of bars and anchors, and others. In a recent work (BaZant, 1993b), a theoretical argument has been presented showing that a deterministic size effect due to energy release should also exist in compression failures in which the energy release depends on the structure size, for example reinforced concrete columns. The general formulation of the size effect for compression failures has been presented, however, detailed formulas for the size effect ha.ve not been derived

Box Girder Bridge Deflections: Why is the Initial Trend Deceptive?

Abstract: Current analysis methods for deflection of long-span prestressed concrete box girder bridges can result in incorrect long-term predictions of deflection. The effects of creep and shrinkage are usually analyzed assuming uniformed coefficients over the entire cross section of the box girder. To accurately predict long-term deflections, the diffusion nature of drying must be realistically reflected in the creep and shrinkage predictions model.

Does Strength Test Satisfying Code Requirement for Nominal Strength Justify Ignoring Size Effect in Shear

Abstract: The ACI 318 Code has not adopted size effect provisions for beams of depths up to 1 m, invoking a recent test in which the strength of such a beam was almost equal to the nominal strength required by the Code and was much larger than the strength obtained after applying the strength reduction factor. This paper criticizes the use of this test to justify ignoring size effect in shear. If numerous tests of 1 m (40 in.) deep beams with different shear spans and steel ratios, made of different concretes and under different hygro-thermal conditions, could be carried out, the beam strength would exhibit a similar statistical scatter, with approximately the same coefficient of variation, as the strength of beams up to 0.2 m (8 in.) deep, for which there are numerous test results in the database. Based on this expected scatter, it is shown that neglecting the size effect for beams up to 1 m (40 in.) deep is likely to increase the expected frequency of failures from approximately 1 in a million to approximately 1 in a thousand when the beam depth increases from 0.2 to 1 m (8 to 40 in.). These findings indicate the need to introduce the size effect into the ACI 318 Code for all beam sizes.

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.