Influence of particle density on 3D size effects in the fracture of (numerical) concrete

In this paper, three-dimensional beam lattice models are extended and used for simulating size effects on strength of 3-point bending fracture experiments on concrete. At the meso-level concrete is schematized as a three-phase material, consisting of aggregate particles, cement matrix and the bond zone, which separates these two phases. Displacement-controlled 3-point bending experiments are simulated varying the particle density Pk (Pk = 0%, 15%, 35% and 55%) and the specimen size, which is scaled in all three dimensions in a range of 1:8 (volume range 1:512), containing between 15,703 and 7,448,373 lattice elements. The numerical analyses show particle density dependent scaling behaviour of strength. For very low (0%) and high (55%) particle density, scaling comes close to classical Weibull theory; for intermediate densities a significantly different power emerges caused by stable pre-critical crack growth leading to hardening.