Statistical Modeling of Near-Surface Aggregate Size Distributions in Concrete

This study presents a distribution-optimized mesostructure estimation method for statistically modeling near-surface aggregate size distributions in concrete by optimizing the spatial arrangement of polydisperse spherical aggregates with respect to formwork boundaries. The approach is based on minimizing the deviation between a generated cumulative aggregate volume function and an idealized linear target function corresponding to a constant area fraction along the specimen depth. To enable efficient computation for systems containing a large number of aggregates, grain size groups derived from the grading curve are represented using symmetric Beta distributions, allowing each group to be described by a single shape parameter. The resulting optimization problem is solved using a derivative-free Powell algorithm. The method inherently captures wall effects, leading to a migration of smaller aggregates toward the specimen boundaries to compensate for the geometric constraints of bigger aggregates. Experimental validation was performed for a single concrete mixture and specimen geometry by determining the depth-dependent mean bulk density of a concrete cube using incremental surface grinding combined with high-resolution 3D laser scanning. The optimized mesostructure shows strong agreement with measured density profiles for the investigated specimen. While the validation is limited to a single mixture and geometry, the results indicate that the proposed method is a computationally efficient approach for incorporating wall effects into mesoscale concrete models. Furthermore, increasing aggregate volume fractions intensify the near-surface accumulation of fine particles.