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.

Micromechanics Model for Creep of Anisotropic Clay

Abstract: Clays frequently possess a fabric with a preferred particle orientation and the creep properties of such clays are therefore anisotropic. A two-dimensional microstructural model to describe this creep response is developed. The model is based on a triangular cell of three particles sliding over each other at a rate predicted by rate-process theory. Equating the rate of energy dissipation within the cell to that of the macroscopic continuum leads to the determination of the tangential viscosity matrix and the matrix of the nonviscous stress components, both of which are stress dependent. The anisotropic creep viscosity parametres then are obtained by a statistical averaging procedure based on the probability density of the particle orientation distribution, as determined by x-ray diffraction. The resulting model is able to predict the directional differences in the creep rate and the stress dependence of creep in clays with anisotropic fabric. Undrained creep tests were conducted on specimens cut in various directions from both isotropically and anisotropically consolidated kaolinite samples.

Imbricate continuum and progressive fracturing of concrete and geomaterials

Abstract: After giving an overview of the recent results at Northwestern University on mathematical models for fracturing heterogeneous materials, the lecture addresses the problem of a continuum model for strain-softening. In a classical, local continuum, strain-softening leads to unrealistic unstable response, such that failure localizes into a layer of vanishing thickness and occurs at vanishing energy dissipation. While the classical nonlocal continuum does not resolve the problem, solution is found in the form of a new type of nonlocal continuum, called the imbricate continuum, which represents the limiting case of a system of overlapping (imbricated) finite elements of a certain fixed characteristic size that is a material property.

Reinterpretation of Karihaloo's size effect analysis for notched quasibrittle structures

Abstract: Karihaloo recently published an analytical study of the size effect in concrete based on large-size asymptotic approximations of the cohesive crack model. From this analysis, he concluded that the nominal strength can be determined only for sizes above a certain lower bound, large enough to invalidate, at least for concrete, all the existing experimental methods based on size effect measurements, such as the size effect method of Bažant or the general bilinear fit method of Planas, Guinea and Elices. The purpose of this paper is to show that this conclusion is misleading, and to explain why.

Viscoplasticity of Normally Consolidated Clays

Abstract: A constitutive law is developed to model the behavior of normally consolidated isotropic cohesive soils under multidimensional stress or strain paths. This law represents the endochronic form of viscoplasticity and involves a number of material variables that are defined in terms of semi-empirical expressions and model: (1)Strain softening and hardening; (2)densification and dilatancy; (3)frictional aspects; and (4)strain rate dependence of the response. Furthermore, by considering saturated soils as two-phase media, the model accounts for the development of pore pressures due to the volumetric strain in the solid skeleton. Data reported in the literature are used to demonstrate the applicability of the approach, and approximate correlations between material parameters are established to predict the stress-strain-pore response of normally consolidated clays.

Nonlinear Creep Buckling of Reinforced Concrete Columns

Abstract: This model accounts not only for the rapid increase of creep at high compressive stress (flow) but also for the decrease of creep observed for subsequent load increments after a long period of low sustained compressive stress (adaptation). A simply supported column is analyzed for typical load histories: sustained loading; short-time loading to failure; and sustained load followed by short-time loading to failure. Numerical results confirm that the flow nonlinearity makes the column fail in a finite time and the adaptation nonlinearity makes the response to the short-time load applied after a long period of a low sustained load stiffer. Also, there is a substantial difference in the column strength for the same load duration depending upon the loading history, especially the ratio of constant sustained load (dead load) and short-time load (live load) and their durations. This could be taken into account in setting the safety factors for columns subjected to dead and live loads of various ratios.

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.