Spatial modeling of concrete strength based on data

Structural verification of concrete structures relies on an underlying probabilistic model of the concrete strength. This concrete strength exhibits a spatial variability, which is of particular relevance in existing concrete structures, for which the strength is assessed based on samples. To accurately account for the spatial variability of the concrete material, a random field modeling approach can be adopted, which includes a spatial correlation function. Unfortunately, the available literature on spatial variability of concrete strength is not sufficient to make an educated choice of this correlation function. In this paper, we propose a hierarchical Bayesian random field model, that enables learning the parameters of a selected correlation function with in-situ spatially distributed measurements of the concrete strength. We propose a correlation function that accounts for the composite nature of the material through distinguishing micro-scale and meso-scale variability. The predictive spatial distribution of the proposed random field model given the spatial data is then obtained through an analytical random field update, resulting in a non-homogeneous random field model with log-Student's t-marginal distribution. The proposed approach provides an effective means to employ in-situ measurements for updating verification predictions of concrete structures. We apply our approach to two case studies on chamber walls of ship locks, where measurements of the concrete strength are available from core samples.