Scaling of failure probability of quasibrittle structures with large cracks

In the present paper, a probabilistic generalization of the Type 2 size effect is proposed. The generalization is derived through a large size asymptotic expansion ofLEFMequations combined with aweighted finite weakest-link model, which is justified by the fact that the structure survives if the crack tip location in any of a finite number of representative volume elements (RVE) cannot cause failure. Compared toType 1 failure, the zone of possible crack tip locations of non-negligible probability is much smaller and its extent in dimensionless coordinates decreases as the structure size increases. Consequently, the statistical component of the Type 2 size effect on the mean structural strength is much weaker. Yet, the size has a significant effect on the coefficient of variation of structural strength. An application to the probability distribution of the diagonal shear failure of reinforced concrete beams is demonstrated.