Taking the heterogeneity character of concrete into account, this paper presents an equivalent probabilistic model for failure study of concrete in which the heterogeneity of concrete is considered by assuming that the material properties conform to the Weibull distribution law and by using mesoscale mesh of finite elements. The study is divided into three parts. In the first part, a spatial correlation length factor is developed into the Weibull distribution formula so that the spatial correlation of local continuity of material properties can be considered. The second part presents a series of numerical analyses for investigating the size effect of self-compacting concrete (SCC) based on the equivalent probabilistic model, and a comparison is made between the simulation results and compression test measurements for illustrating the size effect on uniaxial compression strength and failure pattern of the SCC concerned. It is shown that the numerical model can provide reasonable predictions in the analysis of the size effect of SCC. In the final part, as an engineering application of the presented model, the damage and fracture behavior of the Koyna gravity dam during the 1967 earthquake are analyzed. Influences of concrete parameters on the crack pattern and failure modes of the dam prototype during the event are discussed. DOI: 10.1061/(ASCE)MT.1943-5533.0000179. (C) 2011 American Society of Civil Engineers.