Stochastic Fracture Simulation and Size Effect for Notched Concrete Beams

This paper proposes a stochastic fracture simulation method based on the phase field model, incorporating variability in the critical energy release rate and tensile strength. Experimental data from notched concrete beams are used to validate the proposed method. The simulated crack propagation paths, load versus crack mouth opening displacement curves, and nominal strengths demonstrate the anticipated variability. Furthermore, an asymptotic weakest-link Weibull model is proposed to characterize the nominal strength. The weakest-link effect gradually becomes dominant, resulting in a decrease in nominal strength as the normalized beam depth increases. The threshold normalized beam depth can be determined when the proposed model asymptotically approaches the weakest-link model. The results indicate that the proposed model fits two sets of nominal strength data reported in the literature quite well. The size effect on nominal strength depends on the notch-to-depth ratio and becomes more pronounced as the variability in nominal strength increases.