Mechanistic Modeling of Strength Distribution of Quasibrittle Structures and Its Implication for Structural Reliability

Abstract

This paper reviews a recently developed finite weakest link model of strength of quasibrittle structures, which fail under controlled load at macro-crack initiation from one representative volume element (RVE). The probability distribution of RVE strength is derived from the transition state theory and a hierarchical multi-scale transition model. The model predicts that the strength distribution of quasibrittle structures depends on the structure size and geometry, transitioning from a predominantly Gaussian distribution to a Weibull distribution as the structure size increases. By further considering the load randomness, it is shown that the size dependence of the strength distribution directly leads to a strong size effect on the Cornell reliability index. Through asymptotic matching, approximate size effect equations can be constructed for both the nominal and central safety factors. The important role of size effect in the reliability analysis of large-size structures is demonstrated through the analysis of the failure of the Malpasset Dam.