Keywords: failure probability, nonlinear fracture mechanics, random fields, safety and reliability, size effect, stochastic finite element method, Latin hypercube sampling, Weibull theory.

The paper describes different methodologies to capture both reliability and size effect of concrete structures. Structural reliability modeling based on classical random variables approach, Weibull theories and stochastic finite element method using random fields is briefly summarized with respect to capturing statistical size effect. The transition from deterministic to statistical size effect, research development and roles of approaches are illustrated using the well known problem of modulus of rupture. The theoretical achievements are well supported by experimental test data. Finally the possibilities of probabilistic treatment of complex fracture mechanics problems using the combination of feasible type of Monte Carlo simulation and nonlinear fracture mechanics computational modeling are presented. This new and promising interdisciplinary effort is illustrated by statistical and reliability analysis of particular problems.

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