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

Analytical link between structural strength size effect and material random heterogeneity