The task of predicting the structural performance of concrete, including its damage and failure, is very practical one and it has led to a number of innovative models and modeling approaches. The limitations of traditional fracture mechanics to properly capture quasi-brittle behavior of concrete is one of the driving forces behind the development of advanced modeling approaches. These models must balance the incorporation of material features that dictate the concrete behavior with the computational tractability, because in the end, models should not only serve to improve scientific understanding of the underlying phenomena, but most importantly to solve practical problems. The available advanced models range from modified continua in which the heterogeneity is modeled via spatially varying properties to discrete models in which the material representation is better tied to the physical microstructure and the micromechanical phenomena that produce quasi-brittle behavior. The last about two decades has seen a gradual rise in discrete models that use discontinuous representations of the quasi-brittle material. The particle-based discrete models resolving the mesoscale features (individual large mineral grains) seem to provide the best balance between affordable computational complexity and the amount of captured structural redistribution effects associated with inelastic effect in heterogeneous materials such as concrete. The advantage of discrete models is the possibility to use vectorial-based constitutive law for individual interfaces instead of full tensorial description needed in standard continuum-based models. The triaxial stress redistribution effects with complicated phenomena such as anisotropic damage are automatically captured by the resolution of material mesoscale with the involved interactions between material bonds described by interface-like constitutive laws. The marriage of the tractable vectorial description with structural effects is the key to success in matching diverse mechanisms in a wide range of loading scenarios. The particle-based discrete model used in the present work reproduces the material integrity via mechanical components (links) each representing the connection between a pair of two adjacent mineral grains. A phenomenological interface model is used to lump the inter-aggregate interaction into a single interface constitutive law. This constitutive model must respond reasonably also under cyclic loading.