An integrated experimental and numerical study of size effect on the mode I fracture toughness of rock

Abstract

Rock is a typical quasi-brittle and heterogeneous material that shows the apparent size effect of mode I fracture toughness (KIc). To further explore the mechanism of the size effect on the KIc of rocks, a novel experimental procedure, i.e., combining a semi-circular bend test with a small-scale direct tension test, is conducted to determine the KIc and fracture process zone (FPZ) length of rock specimens of various sizes. Meanwhile, the four-dimensional lattice spring model (4D-LSM), incorporating a cohesive zone model (CZM) and the modified Mohr–Coulomb strength criterion for bond fracturing, is adopted to interpret these experimental results. After a detailed comparison between experimental and numerical results, we conclude that the size effect is dominated by the softening zone size of the mesoscale grain bond’s constitutive behaviour, rather than other mechanical parameters of rock, e.g., tensile strength, cohesion, and internal friction angle. Without introducing the size-dependent constitutive model into the discrete numerical model but only using a softening model for the mesoscale grain bond, we have successfully reproduced the change in KIc values and FPZ length of the rock specimens of various sizes with high goodness-of-it for the Bazant size effect curve, which indicates that the discrete numerical model can sufficiently reproduce or interpret the size effect in the KIc of rocks.