Computation of Probability Distribution of Strength of Quasibrittle Structures Failing at Macrocrack Initiation

journal article - other

English

Engineering structures must be designed for an extremely low failure probability, i.e. Pf < 10-6. To determine the structural strength corresponding to such a low failure probability, a physical model of the probability distribution of structural strength is required. Recent study showed that the strength distribution of quasibrittle structures, which fail at the macro-crack initiation from one representative volume element (RVE), can be statistically modeled as a finite chain of RVEs. It has been further demonstrated that, based on atomistic fracture mechanics and a statistical multi-scale transition model, the strength distribution of each RVE can be approximately described by a Gaussian distribution, onto which a Weibull tail is grafted from the far-left end a point of the probability of about 10-4 to 10-3. The model implies that the strength distribution of quasibrittle structures depends on the structure size, varying from the Gaussian distribution modified by a far-left Weibull tail for small-size structures to the Weibull distribution for large-size structures. Compared to the classical Weibullian strength distribution, which is limited to perfectly brittle structures, the grafted Weibull-Gaussian distribution makes the calculation of strength distribution of quasibrittle structures much more complicated. This paper presents two methods of computing the strength distribution of quasibrittle structures: 1) for structures with a simple stress field, an approximate closed-form expression of the strength distribution is proposed based on the Taylor series expansion of the grafted Weibull-Gaussian distribution, and 2) for structures with a complicated stress field, a random RVE placement method is developed based on the centroidal Voronoi tessellation. Through some numerical examples including three-point and four point bend beams as well as a 2D model of Malpassets dam, it is shown that the strength distribution calculated by the proposed approximated analytical formulation agrees well with that calculated by the numerical methods such as the random placement method as well as a previously proposed nonlocal boundary method.

Finite weakest link model; Strength statistics; Representative volume element; Structural safety; Fracture; Concrete structures; Composites

LE, J.; ELIÁŠ, J.; BAŽANT, Z.

2012

15. 7. 2012

USA

0733-9399

Journal of Engineering Mechanics

138

7

United States of America

888

899

12