Fluid Percolation in a Porous Material - Application to Construction Pathology

Percolation theory has been a constantly evolving field of research for over 40 years, with applications ranging from theoretical aspects in mathematics and the physical sciences, through the connectivity of geological features, to applications in fields as diverse as construction, the spread of disease, telecommunications and forest fires.

New models and concepts continue to be developed both for theoretical aspects and for various applications to flow phenomena in porous media.

This article follows this line of research, making contributions to the understanding of contaminant percolation and propagation mechanisms.

The mechanisms of contamination are close to the theory of fluid percolation in a porous medium, following preferential pathways that depend on the overall accessible porosity, the average size of clusters, and the strength of contacts between elements of various clusters (which depends on the probability of contacts or barrier defects).

In a medium, we speak of the geometric complexity of porosity, and of the porosity accessible to the percolating fluid. The medium can be characterized by its intrinsic porosity, and that accessible to the fluid, but also by the power of communication or connection between elementary pores, or clusters.

Formal analysis of a structure with this morphological (pores and clusters) and topological (connections between pores) complexity enables a generalized approach to percolation in 3 dimensions, but also to contamination as a function of the main parameters of accessible porosity, cluster distribution and contact cases.

One of the first objectives of this work is to characterize the behavior laws of a contamination process in a porous medium, or population composed of clusters, and to approach critical situations as a function of the overall accessible porosity. $\left(p\right)$ which depends on the average distribution of the population in a containment or non-containment situation, as well as on the communication power. $\left(\beta \right)$ which depends on the probability of contact between members of different clusters.

There are two types of application, particularly in the construction industry. Those concerning precautions against external contaminants (possibly contaminated water, carbon dioxide), where the mechanism needs to be approached to determine the risks of diffusion, and those concerning repair techniques.

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