Showing papers by "Zdenek P. Bazant published in 2000"

Microplane Model M4 for Concrete. I: Formulation with Work-Conjugate Deviatoric Stress

Abstract: The first part of this two-part study presents a new improved microplane constitutive model for concrete, representing the fourth version in the line of microplane models developed at Northwestern University. The constitutive law is characterized as a relation between the normal, volumetric, deviatoric, and shear stresses and strains on planes of various orientations, called the microplanes. The strain components on the microplanes are the projections of the continuum strain tensor, and the continuum stresses are obtained from the microplane stress components according to the principle of virtual work. The improvements include (1) a work-conjugate volumetric deviatoric split—the main improvement, facilitating physical interpretation of stress components; (2) additional horizontal boundaries (yield limits) for the normal and deviatoric microplane stress components, making it possible to control the curvature at the peaks of stress-strain curves; (3) an improved nonlinear frictional yield surface with plasticity asymptote; (4) a simpler and more effective fitting procedure with sequential identification of material parameters; (5) a method to control the steepness and tail length of postpeak softening; and (6) damage modeling with a reduction of unloading stiffness and crack-closing boundary. The second part of this study, by Caner and Bazant, will present an algorithm for implementing the model in structural analysis programs and provide experimental verification and calibration by test data.

Creep and shrinkage prediction model for analysis and design of concrete structures: model b3

Abstract: This paper presents a model for the characterization of concrete creep and shrinkage in design of concrete structures (Model B3), which is simpler, agrees better with the experimental data and is better theoretically justified than the previous models. The prediction model B3 is calibrated by a computerized databank comprising practically all the relevant test data obtained in various laboratories throughout the world. The effect of concrete composition and design strength on the model parameters is the main source of error of the model. A method to reduce this error by updating one or two model parameters on the basis of short time creep tests is given. The updating of model parameters is particularly important for high strength concretes and other special concretes containing various admixtures, super plasicizers, water-reducing agents and pozzolanic materials. This new model allows a more realistic assessment of the creep and shrinkage effects in concrete structures, which significantly affect the durability and long time serviceability of civil engineering infrastructure.

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...

Fracturing Rate Effect and Creep in Microplane Model for Dynamics

Abstract: The formulation of microplane model M4 (in Parts I and II) is extended to rate dependence. Two types of rate effect in the nonlinear triaxial behavior of concrete are distinguished: (1) rate dependence of fracturing (microcrack growth) associated with the activation energy of bond ruptures, and (2) creep (or viscoelasticity). Short-time linear creep (viscoelasticity) is approximated by a nonaging Maxwell spring-dashpot model calibrated so that its response at constant stress will be tangent to the compliance function of model B3 for a time delay characteristic of the problem at hand. An effective explicit algorithm for step-by-step finite-element analysis is formulated. The main reason that the rate dependence of fracturing must be taken into account is to simulate the sudden reversal of post-peak strain softening into hardening revealed by recent tests. The main reason that short-time creep (viscoelasticity) must be taken into account is to simulate the rate dependence of the initial and unloading stiffnesses. Good approximations of the rate effects observed in material testing are achieved. The model is suitable for finite-element analysis of impact, blast, earthquake, and short-time loads up to several hours duration.

Probabilistic nonlocal theory for quasibrittle fracture initiation and size effect. i: theory

Abstract: The nonlocal generalization of Weibull theory previously developed for structures that are either notched or fail only after the formation of a large crack is extended to predict the probability of failure of unnotched structures that reach the maximum load before a large crack forms, as is typical of the test of modulus of rupture (flexural strength). The probability of material failure at a material point is assumed to be a power function (characterized by the Weibull modulus and scaling parameter) of the average stress in the neighborhood of that point, the size of which is the material characteristic length. This indirectly imposes a spatial correlation. The model describes the deterministic size effect, which is caused by stress redistribution due to strain softening in the boundary layer of cracking with the associated energy release. As a basic check of soundness, it is proposed that for quasibrittle structures much larger than the fracture process zone or the characteristic length of material, the probabilistic model of failure must asymptotically reduce to Weibull theory with the weakest link model. The present theory satisfies this condition, but the classical stochastic finite-element models do not, which renders the use of these models for calculating loads of very small failure probabilities dubious. Numerical applications and comparisons to test results are left for Part II.

Energetic-Statistical Size Effect in Quasibrittle Failure atCrack Initiation

Abstract: The size effect on the nominal strength of quasibrittle structures failing at crack initiation, and particularly on the modulus of rupture of plain concrete beams, is analyzed. First, an improved deterministic formula is derived from the energy release caused by a boundary layer of cracking (initiating fracture process zone) whose thickness is not negligible compared with beam depth. To fit the test data, a rapidly converging iterative nonlinear optimization algorithm is developed. The formula is shown to give an excellent agreement with the existing test data on the size effect on the modulus of rupture of plain concrete beams. The data range, however, is much too limited; it does not cover the extreme sizes encountered in arch dams, foundations, and retaining walls. Therefore, it becomes necessary to extrapolate on the basis of a theory. For extreme sizes, the Weibull type statistical effect of random material strength must be incorporated into the theory. Based on structural analysis with the recently developed statistical nonlocal model, a generalized energetic-statistical size effect formula is developed. The formula represents asymptotic matching between the deterministic-energetic formula, which is approached for small sizes, and the power law size effect of the classical Weibull theory, which is approached for large sizes. In the limit of infinite Weibull modulus, the deterministic-energetic formula is recovered. Data fitting with the new formula reveals that, for concrete and mortar, the Weibull modulus is approximately equal to 24 rather than 12, the value widely accepted so far. This means that, for extreme sizes, the nominal strength (modulus of rupture) decreases, for two-dimensional (2D) similarity, as the -1/12 power of the structure size, and for 3D similarity, as the -1/8 power (whereas the -1/4 power has been assumed thus far). The coefficient of variation characterizing the scatter of many test results for one shape and one size is shown not to give the correct value of Weibull modulus because the energetic size effect inevitably intervenes. The results imply that the size effect at fracture initiation must have been a significant contributing factor in many disasters (for example, those of Malpasset Dam, Saint Francis Dam and Schoharie Creek Bridge.)

Probabilistic nonlocal theory for quasibrittle fracture initiation and size effect. ii: application

Abstract: The nonlocal probabilistic theory developed in Part I is applied in numerical studies of plain concrete beams and is compared to the existing test data on the modulus of rupture. For normal size test beams, the deterministic theory is found to dominate and give adequate predictions for the mean. But the present probabilistic theory can further provide the standard deviation and the entire probability distribution (calculated via Latin hypercube sampling). For very large beam sizes, the statistical size effect dominates and the mean prediction approaches asymptotically the classical Weibull size effect. This is contrary to structures failing only after the formation of a large crack, for which the classical Weibull size effect is asymptotically approached for very small structure sizes. Comparison to the existing test data on the modulus of rupture demonstrates good agreement with both the measured means and the scatter breadth.

Microplane Constitutive Model and Metal Plasticity

Abstract: The microplane model is a versatile constitutive model in which the stress-strain relations are dermed in tenns of vectors rather than tensors on planes of all possible orientations, called the microplanes, representative of the microstructure of the material. The microplane model with kinematic constraint has been successfully employed in the modeling of concrete, soils, ice, rocks, fiber composites and other quasibrittle materials. The microplane model provides a powerful and efficient numerical tool for the development and implementation of constitutive models for any kind of material. The paper presents a review of the background from which the microplane model stems, highlighting differences and similarities with other approaches. The basic structure of the microplane model is then presented, together with its extension to fmite strain defonnation. Three microplane models for metal plasticity are introduced and discussed. They are compared mutually and with the classical Jrflow theory for incremental plasticity by means of two examples. The first is the material response to a nonproportional loading path given by uniaxial compression into the plastic region followed by shear (typical of buckling and bifurcation problems). This example is considered in order to show the capability of the microplane model to represent a vertex on the yield surface. The second example is the 'tube-squash' test of a highly ductile steel tube: a finite element computation is run using two microplane models and the Jrflow theory. One of the microplane models appears to predict more accurately the final shape of the deformed tube, showing an improvement compared to the J2-flow theory even when the material is not SUbjected to abrupt changes in the loading path direction. This review article includes 114 references.

Criteria for Rational Prediction of Creep and Shrinkage of Concrete

Abstract: This paper examines various basic questions in formulating and evaluating a prediction model for creep and shrinkage of concrete. Verification by comparisons to a few subjectively selected data sets is no longer justifiable because computers have made statistical comparisons to the existing internationally accepted comprehensive data bank very easy. Yet, there are three criteria to be considered: 1) After optimizing its coefficients, the prediction model should be capable of providing close fits of the individual test data covering a broad range of times, ages, humidities, thicknesses; 2) the model should have a rational, physically justified theoretical basis; and 3) should allow good and easy extrapolation of the short time tests into long times, at high ages of loading, large thicknesses etc.

Compressive failure, large-strain ductility and size effect in concrete: Microplane model

Abstract: The paper presents applications of the microplane model for concrete in finite element analyses performed to investigate two aspects of the compressive behavior of concrete. The first aspect is the ductile response, observed under extreme pressures, and the second aspect is the quasibrittle response, exhibited under normal pressures. Pressures high enough to induce ductile response are developed, for instance in impact events, and the ductile properties of concrete at high pressures can be observed in the "tube-squash" test, conceived at Northwestern University, in which concrete is cast inside a thick steel tube. In such a test the confinement provided by the steel tube allows concrete to achieve very large deviatoric strains (with shear angles up to 70°), retaining integrity, without visible damage. The axial compression of the tube filled with concrete is reproduced with a finite strain, finite element analysis, proving the capability of the microplane model for concrete to capture accurately the behavior of concrete under extreme pressures. In conditions of normal confinement, concrete exhibits quasi brittle behavior in compression, resulting in a significant size effect in the compressive failure of 'concrete structures. Finite element simulations of the compressive failure of reduced-size columns show good agreement with the structural response observed experimentally. For the latter analysis, the microplane constitutive law is employed adopting the crack band model. Zdenek P. BaZant, and Michele Brocca.