Meso-scale analyses of size effect in brittle materials using DEM

The paper describes numerical meso-scale results of a size effect on strength, brittleness and fracture in brittle materials like concrete. The discrete element method (DEM) was used to simulate the size effect during quasi-static splitting tension with the experimental-based meso-structure. The two-dimensional (2D) calculations were carried out on concrete cylindrical specimens with two diameters wherein two different failure modes occurred (quasi-brittle and very brittle with the snap-back instability). Concrete was modelled as a random heterogeneous 4-phase material composed of aggregate particles, cement matrix, interfacial transitional zones and macro-voids, based on x-ray micro-CT-images of the real concrete meso-structure. Attention was paid to the effect of the different specimen diameter on both the strength, brittleness and fracture pattern. Each internal energy component was analyzed in the fracture process zone and beyond it, and compared for the different post-peak behaviour of concrete. The evolutions of the number of broken contacts, coordination number, crack displacements and normal contact forces were also shown. Of specific interest was the fracture initiation and formation of two different failure modes. Next, the 2D DEM results of a size effect for 4 different specimen diameters were directly compared with corresponding experiments from the research literature. The experimental size effect was realistically reproduced in numerical calculations, i.e. the concrete strength and ductility decreased with increasing concrete specimen diameter. The calculated decreasing strength approached an asymptote with increasing cylindrical specimen diameter within the considered specimen size range.