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Showing papers by "Zdenek P. Bazant published in 1999"


Journal ArticleDOI
TL;DR: A broad review of the problem of size effect or scaling of failure can be found in this paper, where the main results of Weibull statistical theory of random strength are briefly summarized, and its applicability and limitations described.
Abstract: The article attempts a broad review of the problem of size effect or scaling of failure, which has recently come to the forefront of attention because of its importance for concrete and geotechnical engineering, geomechanics, arctic ice engineering, as well as for designing large load-bearing parts made of advanced ceramics and composites, e.g. for aircraft or ships. First, the main results of Weibull statistical theory of random strength are briefly summarized, and its applicability and limitations described. In this theory as well as plasticity, elasticity with a strength limit, and linear elastic fracture mechanics (LEFM), the size effect is a simple power law, because no characteristic size or length is present. Attention is then focused on the deterministic size effect in quasibrittle materials which, because of the existence of a nonnegligible material length characterizing the size of the fracture process zone, represents the bridging between the simple power-law size effects of plasticity and of LEFM. The energetic theory of quasibrittle size effect in the bridging region is explained, and then a host of recent refinements, extensions and ramifications are discussed. Comments on other types of size effect, including that which might be associated with the fractal geometry of fracture, are also made. The historical development of the size-effect theories is outlined, and the recent trends of research are emphasized.

300 citations


Journal ArticleDOI
TL;DR: In this paper, a mathematical model is established for chloride penetration in saturated concrete, which takes into account various influential parameters such as water-to-cement ratio, curing time, types of cement, and aggregate content.
Abstract: A mathematical model is established for chloride penetration in saturated concrete. The model takes into account various influential parameters such as water-to-cement ratio, curing time, types of cement, and aggregate content. Two material models are developed for binding capacity and chloride diffusivity, which have a dominant effect on the chloride diffusion process. The chloride binding capacity is modeled by means of the chloride adsorption isotherm. The chloride diffusivity is modeled by a composite material theory in which concrete is considered as a two-phase material with the cement paste as one phase and the aggregate as another. To take into account the effect of aggregate content, the three-phase model for diffusivity of a two-phase composite developed by Christensen is used. The diffusivity for cement paste is characterized by the Kozeny-Carman model as modified by Martys et al. The influences of temperature and chloride ion concentration are also handled in the model. The model prediction agrees quite well with available test results.

245 citations


Journal ArticleDOI
TL;DR: In this article, a macroscopic material model for rapidly heated concrete is developed, which accounts explicitly for the dehydration of concrete and its cross-effects with deformation (chemomechanical couplings) and temperature (chemothermal couplings).
Abstract: This paper and its companion paper present the main results of an assessment of the fire in the Channel Tunel (the “Chunnel”), which destroyed a part of the concrete tunnel rings by thermal spalling. The study seeks (1) to evaluate the effect of thermal damage (loss of elastic stiffness) and thermal decohesion (loss of material strength) upon the stress state and cracking at a structural level; and (2) to check whether restrained thermal dilatation can explain the thermal spalling observed during the fire. In the present paper, a macroscopic material model for rapidly heated concrete is developed. It accounts explicitly for the dehydration of concrete and its cross-effects with deformation (chemomechanical couplings) and temperature (chemothermal couplings). The thermal decohesion is considered as chemoplastic softening within the theoretical framework of chemoplasticity. Furthermore, kinetics of dehydration, dimensional analysis, and thermodynamic equilibrium considerations show that a unique thermal dehydration function exists that relates the hydration degree to the temperature rise, provided that the characteristic time of dehydration is much inferior to the characteristic time of structural heat conduction. The experimental determination of the thermal dehydration function from in-situ measurements of the elastic modulus versus furnace temperature rise is shown from experimental data available from the chunnel concrete. Finally, by way of an example, the proposed constitutive model for rapidly heated concrete is combined with the three-parameter William-Warnke criterion extended to isotropic chemoplastic softening.

208 citations


Journal ArticleDOI
TL;DR: In this article, the results of reduced-scale failure tests of simply supported four-point-bend beams of different sizes, containing lapped bond splices of smooth (undeformed) longitudinal reinforcing bars, are reported.
Abstract: The results of reduced-scale failure tests of simply supported four-point-bend beams of different sizes, containing lapped bond splices of smooth (undeformed) longitudinal reinforcing bars, are reported. The tests consist of two groups, with splices located either in the midspan region with a uniform bending moment, or in one of the end regions with a uniform shear force. The specimens were made of microconcrete with a maximum aggregate size of 4.76 mm. Beams of three different heights (50 mm, 100 mm, and 200 mm) were tested. The beams were geometrically similar in three dimensions, and even the bar diameters and cover thicknesses were scaled in proportion. The reinforcement ratio was 0.31%. The results reveal the existence of a significant size effect, which can be approximately described by the size effect law previously proposed by Bazant. The size effect is found to be stronger for splices without any spiral than for splices confined by a spiral, and stronger for splices in the maximum shear force region of a beam than for splices in the maximum bending moment region. Generalization of the existing formula of Orangun and colleagues is proposed and recommended for design. Although the formula provides a safer alternative to the existing approach, further testing is needed for better calibration. The size effect on the nominal bond strength implied by the development length provisions of the current and previous American Concrete Institute code is discussed and shown to be inadequate.

34 citations


Journal ArticleDOI
TL;DR: In this article, a tube-squash test was proposed to evaluate the ductile shear and deviatoric deformation of steel-alloyed concretes at hydrostatic pressures of approximately 125 MPa.
Abstract: In this study, a new type of concrete test, called the tube-squash test, that achieves, without fracturing under high pressures, enormous shear and deviatoric strains is developed. Tubes 76.2 mm and 63.5 mm in diameter, with wall thicknesses of 14.22 mm and 12.7 mm, made of highly ductile steel alloy, are filled with concrete. After curing, they are squashed in a high-capacity compression testing machine to half their original length, forcing the tubes to bulge. Normal and high-strength concretes at hydrostatic pressures of approximately 125 MPa are found to be remarkably ductile, capable of sustaining shear angles over 70 deg (1.225 rad) without visually detectable cracks or voids, though significant distributed mechanical damage does take place. Tests of cores drilled out from squashed tubes show that, after such enormous deformation, the concrete still retains approximately 25-35% of its initial uniaxial compression strength and initial stiffness and approximately 10-20% of its initial split-cylinder tensile strength. What makes the tube-squash test meaningful is the development of a relatively simple method of test results analysis that avoids solving the inverse nonlinear finite strain problem with finite elements despite high nonuniformity of the strain field. Approximate stress-strain diagrams of concrete at such large shear angles and strains are obtained by finite strain analysis of the middle cross section utilizing the measured lateral expansion, axial shortening, and bulge profile. The finite strain triaxial plastic constitutive law of the steel alloy needs to be determined first, and a method to do that is also formulated. Approximate stress-strain diagrams and internal friction angles of concrete are deduced from the test without making any hypotheses about its constitutive equation. Tests of tubes filled by hardened portland cement paste and cement mortar, as well as tubes with a snugly fitted limestone insert, show similar ductile shear strains and residual strengths.

19 citations


Journal ArticleDOI
TL;DR: In this article, the size effect on the nominal strength of steel-concrete composite beams caused by shear failures of connectors such as welded studs is analyzed by two different approaches: fracture type analysis of the energy release caused by propagation of the zone of failed connectors along the beam; and a direct solution of the load-deflection diagrams from the differential equations of beam bending theory.
Abstract: The size effect on the nominal strength of steel-concrete composite beams caused by shear failures of connectors such as welded studs is analyzed by two different approaches: (1) In this paper (Part I) by a fracture type analysis of the energy release caused by propagation of the zone of failed connectors along the beam; and (2) in a companion paper (Part II) by a direct solution of the load-deflection diagrams from the differential equations of beam bending theory The former can capture the large size asymptotic size effect and yields simple formulas suitable for design, whereas the latter can provide the solution for small beam sizes for which the connector failure zone is not much shorter than the span The force-slip diagram of the connectors exhibits postpeak softening, which engenders an energetic size effect on the nominal strength of the connector If the connectors are geometrically scaled with the beam, the size effect in the shear failure of connectors (mesoscale) is superimposed on the size e

16 citations


Journal ArticleDOI
TL;DR: In this article, the authors defined the ductility of an elastic structure with a growing crack as the ratio of the additional load-point displacement that is caused by the crack at the moment of loss of stability under displacement control to the elastic displacement at no crack at peak load.
Abstract: The ductility of an elastic structure with a growing crack may be defined as the ratio of the additional load-point displacement that is caused by the crack at the moment of loss of stability under displacement control to the elastic displacement at no crack at the moment of peak load. The stability loss at displacement control is known to occur when the load-deflection curve of the whole structural system with the loading device (characterized by a spring) reaches a snapback point. Based on the known stress intensity factor as a function of crack length, the well-known method of linear elastic fracture mechanics is used to calculate the load-deflection curve and determine the states of snapback and maximum loads. An example of a notched three-point bend beam with a growing crack is analyzed numerically. The ductility is determined and its dependence of the structure size, slenderness, and stiffness of the loading device is clarified. The family of the curves of ductility versus structure size at various loading device stiffnesses is found to exhibit at a certain critical stiffness a transition from bounded single-valued functions of D to unbounded two-valued functions of D. The method of solution is general and is applicable to cracked structures of any shape. The flexibility (force) method can be adapted to extend the ductility analysis to structural assemblages provided that the stress intensity factor of the cracked structural part considered alone is known. This study leads to an improved understanding of ductility, which should be useful mainly for design against dynamic loads.

7 citations


Journal ArticleDOI
TL;DR: In this article, the authors present an energy analysis of the size effect of composite beams and give a solution by integrating the differential equations of beam bending theory, coupled with a softening force-slip law for the interface.
Abstract: After presenting an energy analysis of size effect in the first part of this study, the second part gives a solution by integrating the differential equations of beam bending theory, coupled with a softening force-slip law for the interface. This analysis is more accurate than the previous energy analysis but does not yield simple explicit formulas for the size effect. The results generally support the simple conclusion from energy analysis. They do not disagree with the available limited experimental evidence; however, measurements of size effect in geometrically scaled composite beams seem unavailable. Further tests are needed.

6 citations


01 Jan 1999
TL;DR: In this paper, the authors discuss the problem of formulation and evaluation of a prediction model for creep and shrinkage of concrete, and propose three criteria: (1) after optimizing its coefficients, the model should be capable of providing close fits of the individual test data covering a broad range of times, ages, humidities, thicknesses etc.
Abstract: The paper discusses the problem of formulation and evaluation of 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 complete existing data bank easy. However, statistics based on the data bank are insufficient. There are three further criteria : (1) After optimizing its coefficients, the model should be capable of providing close fits of the individual test data covering a broad range of times, ages, humidities, thicknesses, etc. ; (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, high ages at loading, large thicknesses etc. The last criterion is very important because good long-time predictions can be achieved only through updating based on short-time data for the given particular concrete. Various aspects of the B3 and GZ models recently considered by ACI Committee 209, as well as some aspects of the CEF-FIP model, are briefly analyzed in the light of these criteria, clarifying the way to move ahead.

5 citations