Size effect on reliability indices and safety factors of quasibrittle structures

Many modern engineering structures are made of brittle heterogenous (quasibrittle) materials, such as concrete, composites, and tough ceramics. Recent studies have shown that the strength distribution of quasibrittle structures varies from a Gaussian distribution modified by a power-law tail to a Weibull distribution as the structure size increases, and such size dependence can be well captured by a finite weakest link model. This paper investigates the implication of the size-dependent strength distribution on the reliability-based analysis and design of quasibrittle structures by considering a linear failure limit state. The size effect on the statistical properties of structural strength directly leads to a size-dependent Cornell index, which could give a reasonable estimation of the failure risk in some cases. To improve the prediction of the structural failure risk, the size dependence of the strength distribution is further incorporated into the computation of the Hasofer-Lind index, where it is shown that the transformation method for the non-Gaussian random structural strength is dependent on the structure size and geometry. By assuming that the applied load follows a Gaussian distribution, approximate size effect equations are developed for the central and nominal safety factors through asymptotic matching. The proposed formulation of the size effect on reliability indices and safety factors is applied to analyze the failure of the Malpasset arch dam.