Random Lattice-Particle Simulation of Statistical Size Effect in Quasi-Brittle Structures Failing at Crack Initiation

The modeling of statistical size effect of concrete structures that fail at crack initiation is studied, with special attention to the interaction between the autocorrelation length and the size of the failure zone. The mechanical failure of concrete is modeled by a network of axial springs with degrading stiffness. The heterogeneity of concrete is idealized by spatial variation of the tensile strength and fracture energy. As an example, the direct tensile test in plane stress, with the size range of 1:20, is simulated. Furthermore, simulations of a four-point bending test with varying bending span are compared to the experimental results reported in the literature. The interaction of the autocorrelation length and the size of the failure zone is identified as a key parameter for the modeling of statistical size effect.