Percolation of fluid in a porous material - Application to the pathology of constructions

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 to fields as diverse as construction, disease spread, telecommunications, and wildfires, as well as the connectivity of geological features.

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

This article is part of this line of research, contributing to the understanding of the mechanisms of percolation and contaminant propagation.

The mechanisms of contamination are closely related to the theory of fluid percolation through a porous medium, following preferential paths that depend on the total 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 the absence of barriers).

In a medium, one would refer to the geometric complexity of the porosity and the porosity accessible to the percolating fluid. The medium can be characterized by its intrinsic porosity and the porosity accessible to the fluid, but also by the strength of communication or connection between the elementary pores or clusters.

The formal analysis of a structure exhibiting this morphological complexity (pores and clusters) and topological complexity (connections between pores) enables a generalized approach to 3-dimensional percolation, as well as to contamination, based on the key parameters of accessible porosity, cluster distribution, and contact scenarios.

One of the primary objectives of this work is to characterize the behavioral laws of a contamination process in a porous medium—or a population composed of clusters— and to analyze critical situations based on the overall accessible porosity (p)—which depends on the average distribution of the population in confined or unconfined conditions—as well as the communication strength (β), which depends on the probability of contact between members of different clusters.

Applications, particularly in the construction industry, fall into two categories: those involving precautions against external contaminants (such as potentially contaminated water or carbon dioxide), where it is necessary to analyze the mechanism to assess diffusion risks; and those involving repair techniques.

In the context of building repair, it may be necessary to inject passivating agents, neutral substances, or resin to prevent contamination risks (such as deterioration caused by internal sulfate reactions in concrete), or even to regenerate damaged porous materials.

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