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This paper presents a stochastic analysis of the size effect on the nominal strength of quasibrittle structures with a large preexisting notch. This type of scaling behavior has been extensively studied within a deterministic framework. Little attention is paid to stochastic analysis, which is essential for reliability-based analysis and design of engineering structures. Stochastic finite element simulations are performed to study the failure of geometrically similar beams of different sizes. The numerical analysis uses a continuum damage model, in which the tensile strength and fracture energy are modeled by homogeneous random fields. Different correlation lengths are considered as a parametric study. The analysis yields the size effects on the mean and coefficient of variation (CoV) of the nominal structural strength. It is shown that the size effect on the mean strength agrees well with the Bazant size effect model. The simulation predicts a strong size effect on the CoV of the nominal strength. Small-, intermediate-, and large-size asymptotes are derived analytically for the scaling behavior of the strength CoV. Based on these asymptotes, an approximate scaling equation is proposed for the CoV of nominal strength. The effect of the correlation length on the simulated failure behavior is discussed. [ABSTRACT FROM AUTHOR]

Anchored by the theory of extreme value statistics, Weibull distribution is the most widely used mathematical model for strength distribution of brittle structures. In a series of recent studies, a finite weakest-link model was developed for strength distribution of quasi-brittle structures, and the classical Weibull distribution was shown to represent the large-size asymptote of the model. By employing a length scale, the finite weakest-link model is capable of capturing correctly the size effects on both the probability distribution and the mean value of structural strength. However, the connection of this length scale with the basic material properties is still missing. This study investigates the relationship between the length scale of the finite weakest-link model and the material length scales by analyzing the size effect on the mean structural strength. The mathematical form of this relationship is derived through dimensional analysis. To validate the model, a set of mean size effect curves is obtained through stochastic simulations, which use a nonlinear constitutive model involving both the Irwin characteristic length and the crack band width. The internal length scale of the weakest-link model is determined by optimum fitting of the benchmark size effect curves in the small-size range. Furthermore, the effect of stress field on this internal length scale is studied by considering three different loading configurations. The present analysis reveals the importance of the mean size effect analysis for the calibration of finite weakest-link model. [ABSTRACT FROM AUTHOR]