Computational modeling of concrete requires an accurate geometrical model of the mesostructure, which consists of high volume fractions of aggregate particles embedded in a cement matrix. Crushed rock aggregates may be modeled as random polytopes, which are placed in the volume cell using algorithms based on the Random Sequential Adsorption (RSA) method. However, the RSA algorithm is computationally expensive for high volume fractions, and cannot realize very high volume fractions [1]. We propose an algorithm to efficiently generate high volume fractions based on the overlap removal method of Williams and Philipse [2]. To obtain synthetic aggregates, we generate random polytopes matching experimentally obtained aggregate size distributions. Combining both approaches, we investigate realizable aggregate volume fractions and effective properties of concrete mesostructures. [1] V. Holla, G. Vu, J. J. Timothy, F. Diewald, C. Gehlen, G. Meschke, Computational Generation of Virtual Concrete Mesostructures, Materials, Vol. 14 (14), 3782, 2021. [2] S. R. Williams, A. P. Philipse Random packings of spheres and spherocylinders simulated by mechanical contraction, Physical Review E, Vol. 67 (5), 051301, 2004.