A statistical depth-dependent topography model for virtual reconstruction of salt frost scaling in concrete

This study presents the Virtual Reconstruction of Surface Topography (VRoST) model, a novel framework for describing surface scaling of concrete exposed to freeze–thaw and de-icing salt conditions. The model characterizes surface scaling as a stochastic, geometry-driven process governed by the interaction between cementitious matrix erosion and aggregate stability. High-resolution 3D laser scanning is employed to capture the evolving surface topography during freeze–thaw laboratory testing, enabling the derivation of depth distributions and cumulative distribution functions of the scaling damage. Experimental data is coupled with an idealized statistical aggregate-scale geometry model that represents the spatial arrangement of spherical aggregates and the associated border-zone effect. The VRoST model formulates surface scaling as a depth-dependent topography model in which matrix roughness, matrix asymmetry, and aggregate stability evolve as effective depth-conditioned functions of the governing erosion depth and are parameterized separately from the temporal damage evolution. Within the calibration dataset, Quantile–Quantile optimization achieved generally high in-sample agreement between simulated and experimental cumulative distribution functions (R 2 > 0.90). Within the tested mixtures, larger aggregate size groups were associated with increased roughness, broader depth distributions, and greater scaling susceptibility, consistent with ITZ-related damage mechanisms but not constituting independent verification of ITZ degradation. The proposed framework quantitatively links the measured evolution of external surface topography to effective aggregate-scale geometric and statistical descriptors of matrix erosion and aggregate stability. By separating spatial morphology from temporal damage evolution, the framework may enable consistent comparisons of degradation states across different exposure conditions, supporting improved interpretation of laboratory results and their potential transfer to field applications, provided that the depth-conditioned relationships are independently validated.