  A theoretical scaling law for the size effect of the strength of brittle
materials is presented. To some extend, it can be seen as an extension of the
well known Weibull law. For that a correlated Random Fields is used to model
the heterogeneities of the material. Thanks to recent results on the geometry
of excursion sets, one can analytically compute the whole probability
distribution function for the strength of a structure of a given size. Then,
using this PDF, the structural strength associated to any failure probability
can be derived.
