Showing papers by "Zdenek P. Bazant published in 2008"

Comprehensive Database on Concrete Creep and Shrinkage

Abstract: The authors present a further enlargement of the first large database created in 1978 at Northwestern University, comprising 490 shrinkage tests and 621 creep tests. The 1993 RILEM database, which contains 426 shrinkage tests and 518 creep tests, is significantly extended by this database. More realistic creep prediction model verification and calibration for design will be made possible through this new, conveniently computerized database, provided that there is employment of a proper unbiased statistical technique which compensates for inevitable strong statistical bias in data distribution. The database can be downloaded from http://www.iti.northwestern.edu free of charge.

Unbiased Statistical Comparison of Creep and Shrinkage Prediction Models

Abstract: This paper addresses the problem of selecting the most realistic creep and shrinkage prediction model, important for designing durable and safe concrete structures Statistical methods of standard and several nonstandard types and a very large experimental database have recently been used to compare and rank the existing prediction models, but conflicting results have been obtained by various investigators This paper attempts to overcome this confusion It introduces data weighting required to eliminate the bias due to improper data sampling in the database, and then examines Bazant and Baweja's Model B3, the ACI model, the CEB model, and two of Gardner's models The statistics of prediction errors are based strictly on the method of least squares, which is the standard and the only statistically correct method, dictated by the maximum likelihood criterion and the central limit theorem of the theory of probability, as well as the requirement of noncorrelation of errors Several nonstandard statistical methods that have recently been invented to evaluate creep and shrinkage models are also examined and their deficiencies are pointed out The ranking of the models that ensues from the least-square regression statistics is shown to be quite different from the rankings obtained by the nonstandard statistics

Minimizing Statistical Bias to Identify Size Effect from Beam Shear Database

Abstract: A broad database can be used to statistically calibrate a design formula capturing the size effect on shear strength of reinforced concrete beams without stirrups. This database, however, can have a bias of two types: 1) most data points are crowded in the small size range; and 2) the means of the subsidiary influencing parameters, such as the steel ratio and shear-span ratio are very different within different intervals of beam size or beam depth. The database must be properly filtered to minimize the second type of bias. To this end, the size range is first subdivided into intervals of constant size ratio. Then, in each size interval, a computer program progressively restricts the range of influencing parameters both from above and from below, until the mean of the influencing parameter values remaining in that interval attains about the same value in all the size intervals. The centroids of the filtered shear strength data within the individual size interval are found to exhibit a rather systematic trend. Giving equal weight to each interval centroid overcomes the first bias. The centroids can be closely matched by bivariate least-square regression using Bazant’s size effect law. This purely statistical inference of minimized bias also supports the previous fracture-mechanics-based conclusion that, for large sizes, the bi-logarithmic size effect plot must terminate with the asymptotic slope of –1/2. Similar filtering of the database gives further evidence for the previous empirical observation that the shear strength of beams is approximately proportional to the 3/8-power of the longitudinal reinforcement ratio. The proposed statistical procedure can be used to improve the calibration of formulas in concrete design codes.

Size effect on strength and lifetime distributions of quasibrittle structures implied by interatomic bond break activation

Abstract: Engineering structures such as aircrafts, bridges, dams, nuclear containments and ships, as well as computer circuits, chips and MEMS, should be designed for failure probability < 10 to 10 per lifetime. However, the safety factors required to ensure it are still determined empirically, even though they represent much larger and much more uncertain corrections to deterministic calculations than do the typical errors of modern computer analysis of structures. Bažant and Pang recently developed (and presented at previous ECF) a new theory for the cumulative distribution function (cdf) for the strength of quasibrittle structures failing at macro-fracture initiation, and offered its simplified justification in terms of thermally activated inter-atomic bond breaks. Presented here is a refined justification of this theory based on fracture mechanics of atomic lattice cracks advancing through the lattice by small jumps over numerous activation energy barriers on the surface of the free energy potential of the lattice. For the strength of the representative volume element (RVE) of material, simple statistical models based on chains and bundles are inadequate and a model consisting of a hierarchy of series and parallel couplings is adopted. The theory implies that the strength of one RVE must have a Gaussian cdf, onto which a Weibullian (or power-law) tail is grafted on the left at the failure probability of about 10 to 10. A positive-geometry structure of any size can be statistically modeled as a chain of RVEs. With increasing structure size, the Weibullian part of the cdf of structural strength expands from the left tail and the grafting point moves into the Gaussian core, until eventually, for a structure size exceeding about 10 equivalent RVEs, the entire cdf becomes Weibullian. Relative to the standard deviation, this transition nearly doubles the distance from the mean to the point of failure probability 10. Contrary to recent empirical models, it is found that the strength threshold must be zero. This finding and the size effect on cdf has a major effect on the required safety factor. The theory is further extended to model the lifetime distribution of quasibrittle structures under constant load (creep rupture). It is shown that, for quasibrittle materials, there exists a strong size effect on not only the structural strength but also the lifetime, and that the latter is stronger. Like the cdf of strength, the cdf of lifetime, too, is found to change from Gaussian with a remote power-law tail for small sizes, to Weibullian for large sizes. Furthermore, the theory provides an atomistic justification for the powerlaw form of Evans’ law for crack growth rate under constant load and of Paris’ law for crack growth under cyclic load. For various quasibrittle materials, such as industrial and dental ceramics, concrete and fibrous composites, it is finally demonstrated that the proposed theory correctly predicts the experimentally observed deviations of strength and lifetime histograms from the classical Weibull theory, as well as the deviations of the mean size effect curves from a power law.

Mechanics based statistical prediction of structure size and geometry efiects on safety factors for composites and other quasibrittle materials

Abstract: For a rational determination of safety factors, it is necessary to establish the probability density distribution function (pdf) of the structural strength. For perfectly ductile and perfectly brittle materials, the proper pdf’s of the nominal strength of structure are known to be Gaussian and Weibullian, respectively, and are invariable with structure size and geometry. However, for quasibrittle materials, many of which came recently to the forefront of attention, the pdf has recently been shown to depend on structure size and geometry, varying gradually from Gaussian pdf with a remote Weibull tail at small sizes to a fully Weibull pdf at large sizes. This recent result is reviewed, and then mathematically extended in two ways: 1) to a mathematical description of structural lifetime as a function of applied (time-invariable) nominal stress, and 2) to a mathamatical description of the statistical parameters of the pdf of structural strength as a function of structure size and shape. Experimental veriflcation and calibration is relegated to a subsequent journal article.

Size Effect on Strength of Hybrid Metal-Composite Joints

Abstract: Metal-composite joints are common in composite structures made up of conventional steel parts and advanced polymer composite parts, e.g., in hybrid ship hulls. Correct prediction of the size effect on the strength of the joints is important for the extrapolation of the small-scale laboratory testing results to full size joints, for ensuring an efficient and reliable design. In this study, the size effect on the strength of metal-composite joints is analyzed theoretically, numerically and experimentally. The analytical formulation of the size effect is asymptotically anchored at the large size limit by the linear elastic fracture mechanics (LEFM), which exhibits a singularity with a complex exponent. Numerical analysis with cohesive fracture model is used to design the specimens to be tested, and also to analyze the experimental results to be reported at the conference. Preliminary results from the ongoing experimental studies are also presented. Both computational and analytical methods indicate that the fracture must initiate from the inner steel-composite edges. The experimental findings confirmed that indeed the fracture initiates in the inner steel-composite edges. To determine the size effect law that spans all sizes, the energy release rate is determined numerically and used in the sense of equivalent LEFM. Initial findings indicate that the size effect on the strength of hybrid joints is of the LEFM type.