Analysis of 3D scale and size effects in numerical concrete

Size effect on strength of quasi-brittle materials like concrete, ice and rock, in the literature often referred as geomaterials, has been an issue of discussion over the last three decades. Size effect investigations have been carried out either by experiments or through numerical simulations. Usually mechanical properties of specimens of different sizes (volumes) are investigated. Most commonly, specimens are scaled two-dimensionally. In a numerical study, fracture experiments were investigated subjected to 3point bending. Here, concrete prisms are scaled in all three dimensions. As numerical model a 3D beam lattice model was used, which has proven to be quite suitable for simulating fracture experiments of concrete. Samples are modeled with regular lattices with inclusion of the concrete heterogeneity. The aggregate content Pk and the aggregate geometry can vary. The aggregates shapes can be either ideal spherical, crushed or oval shaped. For building an ideal spherical aggregate distribution, a computer program is used. In case of non-spherical aggregates, a different approach, which is described in Chapter 4, is adopted: Small real concrete prisms containing aggregates with high density (like marble) are scanned directly by means of X-ray tomography and the resulting 3D images are implemented into the 3D lattice. Without the availability of huge computing facilities and parallel solvers, fracture simulation with 3D models and size effect investigation can not be done. Even with state-of-the-art computing facilities at the time the simulations were conducted, the size range from the smallest to the largest specimen was limited to 1:8. There were also other constraints: specimen sizes are rather small and the ratio of the specimen size and largest aggregate diameter D/dmax is for some sizes small (with D/dmax < 3). Numerical results of the size effect analyses are presented in Chapters 5 to 7. Dependent which aggregate shapes are used in the mixture, the fracture behaviour differs. Regardless of aggregate content and shape, size effect on bending strength can be found in all cases. However, the calculated slopes in