In order to investigate the fracture behavior of concrete mesostructure and reveal the inner failure mechanisms which are hard to obtain from experiments, we develop a 3D numerical model based on the Voronoi tessellation and cohesive elements. Specifically, the Voronoi tessellation is used to generate the aggregates, and the cohesive elements are applied to the interface transition zone (ITZ) and the potential fracture surfaces in the cement matrix. Meanwhile, the mechanical behavior of the fracture surfaces is described by a modified constitutive which considers the slips and friction between fracture surfaces. Through comparing with the experiments, the simulated results show that our model can accurately characterize the fracture pattern, fracture propagation path, and mechanical behaviors of concrete. In addition, we found that the friction on the loading surfaces has a significant effect on the fracture pattern and the strength of concrete. The specimens with low-friction loading surfaces are crushed into separate fragments whereas those with high-friction loading surfaces still remain relatively complete. Also, the strength of concrete decreases with the increase of the specimen height in the high friction-loading surfaces condition. Further, the energy analysis was applied to estimate the restraint impact of loading surfaces restraint on the compressive strength of concrete. It shows that the proportion of the friction work increases with the increase of the restraint degree of loading surfaces, which finally causes a higher compressive strength. Generally, based on the proposed model, we can characterize the complicated fracture behavior of concrete mesostructure, and estimate the inner fracture mode through extracting and analyzing the energies inside the cohesive elements.

The mechanical behavior of concrete under biaxial loading condition (especially biaxial compression) is one of the most important indexes to evaluate the quality of concrete. To study the mechanical behavior of concrete under biaxial compression at mesoscale, we adopted our recently developed 3D numerical model based on Voronoi tessellation and cohesive elements. A constitutive model considering the friction effect is used in the model to characterize the fracture behavior of all potential fracture surfaces inside the concrete. A series of numerical experiments with different biaxial compression stress ratios were carried out. It was found that with the increase of the biaxial compression ratio, the proportion of energy increment caused by friction stress increases. The effect of inner friction coefficient on the biaxial relative strength was also investigated, and this kind of study is hard to be carried out through laboratory experiments. The results show that the inner friction coefficient has a great influence on the biaxial relative strength of concrete, and there is a positive correlation between these two parameters. Based on the above rules, a conservative biaxial relative compression strength envelope is obtained by setting the inner friction coefficient as zero.