Meso-scale modeling of concrete: A morphological description based on excursion sets of Random Fields

In view of the significant impact of thin scale heterogeneities in regards with the macroscopic response of concrete (and generally speaking of heterogeneous materials), a particular effort is dedicated to morphological representation and modeling. The development of a model based on spatially correlated random functions (Random Fields) is proposed in this article. It is shown how the stationary ergodic property coupled with the spatial structure of correlated Random Fields can efficiently address the problematic when submitted to a threshold process. Recent mathematical results Adler (2008) give accurate ways to analytically control the resulting morphology, both geometrically and topologically speaking. The generalized aspect of this framework has to be seen here as the ability of the model to represent different kind of morphologies such as matrix/inclusion, opened or closed porosity. With such features, heterogeneous material can be represented at different scales. By expanding a rather abstract formula given by Adler (2008), the authors aim at spreading this point of view with a “ready for use” framework. Furthermore, by addressing common issues such as, reaching high volume fraction with disconnected topologies and representing grain size distributions, solutions to adapt it to cementitious materials are given.