Among many contributing factors, the load range, number of load cycles and specimen geometry (including configuration and size) are three major variables for fatigue failure. Most existing statistical fatigue models deal with only one or two of these three variables. According to the statistical distribution of microcracks with respect to their size and spatial location, a weakest-link probabilistic model for fatigue failure is established to incorporate the combined effect of load range, number of load cycles and specimen size. The model reveals a compound parameter of load range and number of load cycles reminiscent of the empirical formulae of fatigue stress-life curve and its correlation with another compound parameter of cumulative failure probability and specimen size. Four sets of published fatigue test data are adopted to validate the model.

The well established consensus that cleavage fracture is preceded by plastic deformation in structural steels implies that plastic yielding is the threshold stress state for a volume element to incur cleavage fracture. An accurate compliance with this consensus underlies the normalisation of cumulative cleavage fracture probability and the justification of constraint effect on cleavage fracture. These understandings lead to the proposal of a framework for statistical modelling of cleavage fracture in structural steels. The framework takes the spatial microcrack distribution into account to formulate the cumulative failure probability model that allows for a pertinent physical interpretation of Weibull statistics, and derives the fracture probability of an elemental volume in conformity with the yielding condition from a set of commonly adopted microcrack size or strength distributions. Alternative approaches to calibrating model parameters are suggested based on frequency analysis of brittle particles as cleavage initiators and on statistical analysis of cleavage fracture stress. The strict adherence to plastic yielding as a prerequisite to cleavage fracture also reveals the probabilistic nature of notch brittleness and ductile-to-brittle transition behaviour.

A procedure for non‐proportional size scaling of the strength of concrete based on the weakest‐link statistics is proposed to synchronize strength data from specimens of different geometries and different loading modes. The procedure relies on proportional size scaling of strength to determine the parameters of the statistical model and often on finite element analysis to calculate the coefficient of the equivalent strength. The approach for non‐proportional size scaling is capable to synchronize the uniaxial strength data of concrete from uniaxial tensile specimens and 3‐point bending specimens, or the biaxial tensile strength data of circular plates in different loading mode. The non‐transference of the uniaxial strength data to the biaxial strength data is unclear in its mechanism but possibly due to the variation of statistical distribution of microcracks with stress states in different specimens.