Showing papers by "Zdenek P. Bazant published in 2006"

Reliability, Brittleness, Covert Understrength Factors, and Fringe Formulas in Concrete Design Codes

Abstract: The paper analyzes the reliability consequences of the fact that the current design codes for concrete structure contain covert (or hidden) understrength (or capacity reduction) factors. This prevents distinguishing between different combinations of separate risks due to the statistical scatter of material properties, the error of the design formula, and the degree of brittleness of failure mode, and also makes any prediction of structural reliability (or survival probability) impossible. The covert formula error factor is implied by the fact that the design formula was calibrated to pass not through the mean but through the fringe (or periphery, margin) of the supporting experimental data. The covert material randomness factor is the ratio of the reduced concrete strength required for design to the mean of the strength tests. As a remedy, the covert understrength factor of design formula should be made overt, its coefficient of variation (based on the supporting test data) should be specified, and the type of probability distribution (e.g., Gaussian or Weibull) indicated (which then also implies the probability cutoff). Alternatively, the code could give the mean formula, specify its coefficient of variation and type of distribution, and either prescribe the probability cutoff or overtly declare the understrength factor. The mean of strength tests required for quality control should be figured out from the required design strength on the basis of a specified probability cutoff and the coefficient of variation of these tests. Furthermore, it is proposed that the currently used empirical understrength factor, which accounts mainly for the risks of structural brittleness (or lack of ductility), should be based on the expected maximum kinetic energy that could be imparted to the structure. The reliability integral taking into account the randomness of both the load and structural resistance is generalized for the case of multiple (statistically independent) understrength factors. Finally, it is pointed out that the currently assumed proportionality of the tensile and shear strengths to the square root of compressive strength of concrete is realistic only for the mean, but grossly underestimates the scatter of tensile and shear strengths.

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.

Statistical Mechanics of Safety Factors and Size Effect in Quasibrittle Fracture

Abstract: Throughout most of the 20th century, it was widely believed that the size effect on structural strength has a purely statistical origin, explained by extreme value statistics based on the weakest link model, and described by Weibull statistical theory of random strength. However, beginning with the first suggestions made already in the early 1970s, it gradually transpired that, in quasibrittle materials (i.e. heterogeneous brittle materials with a non-negligible fracture process zone), the mean size effect is essentially deterministic, stemming from energy release caused by stress redistribution in a structure prior to maximum load. The quasibrittle energetic scaling bridges three simple asymptotic power-law scalingsthose of linear elastic fracture mechanics, plasticity, and Weibull theory. Renormalization group transformation does not suffice to handle the transitional nature of this quasibrittle size effect, often spanning several orders of magnitude of size. As is now widely accepted, quasibrittle materials including concrete, rock, tough ceramics, sea ice, snow slabs and composites exhibit major size effects on the mean structural strength that are largely or totally deterministic in nature, being caused by stress redistribution and energy release associated with stable propagation of large fractures or with formation of large zones of distributed cracking.