We present large-scale simulations of microcracking initiation and propagation using a continuum mechanics description in realistic, voxel-based microstructures of heterogeneous quasi-brittle materials obtained from CT imaging techniques. The phase field method is used to describe the evolution of the complex microcracks networks in both uniaxial tension and compression of a sub-volume of a lightweight concrete, where all pores and sand grains are explicitly described. A description of the meshing techniques for such complex voxel-based models is provided, and a convergence study of the tensile failure strength with respect to the sample size is carried out. Such large-scale simulations have high potential to be used either within recent concurrent multiscale methods or in approaches combining in-situ experiments with 3D imaging techniques and simulations for inverse identification of microstructural damage models.