Numerical and Experimental Investigation of a Correlation Model to Describe Spatial Variability of Concrete Properties

The heterogeneous character of concrete results in spatial variation of its material properties. Random field models are often used to account for this effect. Due to the large scatter on the correlation lengths suggested in literature, tests could be performed to determine the most appropriate correlation model and corresponding correlation length. Subsequently, different techniques can be employed to fit an analytical model to the experimental semivariogram, resulting in the most appropriate correlation model and corresponding correlation length. However, the resulting correlation lengths can largely depend on the experimental design. In this work, the effect of several parameters and choices to be made by an engineer in deriving the correlation model based on experimental data from destructive tests has been investigated. It was found that the curve-fitting method generally leads to better estimates of the scale of fluctuation compared to the maximum likelihood method. Moreover, there is a clear benefit of applying a bootstrapping procedure to the experimental data to estimate the covariance matrix adopted in the fitting procedures as well as to estimate the uncertainty related to the estimated parameters. When a measurement error is suspected to be present and cannot be neglected, the nugget should be estimated together with the variance and the scale of fluctuation. Furthermore, the Gaussian correlation model was found to be the most robust choice, even if the actual correlation model is not Gaussian. The latter was confirmed for actual experimental data on the material properties of concrete, in which a linear model was found to fit the data best but the Gaussian model provided comparable results.