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

Abstract

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.

Numerical prediction of gas migration properties in Callovo‐Oxfordian (COx) argillite using morpho‐mathematical operations

“…However, a single L c morphological model shows a limited pore size range around L c . This issue has been treated by an union of K independent excursions with diverse properties . The union is given as …”

“…This issue has been treated by an union of K independent excursions with diverse properties. 22,23 The union is given as…”

“…More importantly, this method is no longer restricted by defined objects thus pore structure is generated with random shapes. This idea has been applied for the pore space reconstruction of concrete or cement paste . Based on the generated model, using morpho‐mathematical operations (erosion, dilation, morphological opening, geodesic reconstruction), image filtering and purely geometric analysis are conducted for 2 purposes: (1) describe the gas invasion process, predict the gas entry pressure and the gas breakthrough pressure, and verify whether the capillary induced breakthrough is possible in COx argillite with gas pressure lower than the fracture threshold; (2) describe the water imbibition process and predict the residual gas saturation.…”

Numerical Prediction of Gas Breakthrough in Boom Clay

“…An excursion E is defined by a threshold t where Gaussian random field f(x) takes its values above t: Figure 2 illustrates the excursion result. In fact, the defined threshold t governs the volume fraction of excursion and the correlation length L of random field assigns a certain characteristic length-scale thus represents the average pore size in the generated excursion [10]. In other words, a single excursion is not able to comprise the large interval of pore size of Boom clay between 10nm and 1000nm.…”

“…This method can not only build randomly shaped pore structure, but can also respect the experimental PSD. It has been used to simulate pore space of concrete [10] and COx argillite [11]. Based on the generated model, purely image analyses are conducted using morpho-mathematical operations.…”