Particle Bed 3D Printing (PB3DP) by Selective Cement Application (SCA) is an additive manufacturing (AM) technique, where cement is locally activated by spraying water onto packed particles, enabling the creation of free-form construction parts. Due to the layer-wise application of material, the method can result in anisotropy, heterogeneity, or even defects. Unlike in conventional construction, this remains a challenge due to the lack of experience in evaluating the effect of possible defects. Combined with the brittle failure behavior typical of mineral-based materials, these attributes must be considered for the structural application of PB3DP-SCA parts. Therefore, a digital qualification process is essential. Computed tomography (CT), enables high resolution scanning and in-depth microstructural investigations of AM parts. In addition to spatial geometry, the CT-scan provides voxelwise grayscale values - called Hounsfield unit - which can be related to the material density, and thus to the mechanical properties. This enables characterization of both spatial defects and material heterogeneity from a single CT-scan. Coupled with recent advancements of the finite cell method (FCM), the direct simulation of phase field fracture on CT-scans has been made possible. To this end, an experimental series was conducted to obtain a material law relating Hounsfield unit to the material properties of hardened cement paste with varying water / cement (w/c) ratios - the most influential parameter affecting concrete density. A phase-field approach was employed to analyze fracture processes at the microscale, capturing material inhomogeneity on a voxel level. The high resolution of the data leads to significant memory demands and increased computational complexity. To address this issue, a moment fitting procedure was adapted to represent material properties accurately for each cell, while avoiding voxelwise integration. This approach reduces computational time, without sacrificing information of individual voxels. This talk presents the methodology as well as recent results.