Probabilistic Modeling for Cementitious Materials Based on Data of Nanoindentation

Abstract

By introducing probabilistic modeling approaches, the interface transition zone (ITZ) and the bulk paste (BP) of concrete are investigated on the basis of the nanoindentation results, especially with respect to the relationship between the microstructure and mechanical properties of cementitious materials. The investigation of the probability density function (PDF) of the random field for nanoindentation properties revealed that the same properties of the ITZ and the BP usually yield the same PDF, which was elaborated from different points of view. Specifically, a log-normal distribution was best for nanoindentation hardness, whereas the Weibull distribution and gamma distribution were much more suitable for the nanoindentation modulus of both the ITZ and the BP. According to the comparative study of the correlation structure, both the ITZ and BP obeyed the exponential correlation structure associated with a first-order autoregressive process, and basically exhibited a similar scale of fluctuation. Furthermore, the scales of fluctuation were found to be directly related to the clinker size and the distance between clinkers. Our work provides a new approach to stochastically modeling cementitious materials, where the content of hydration products controls the mean values of nano-properties, the indentation property dominates the PDF, and the nano-topological structure governs the correlation structure.