Further Development (Probabilistic Approach)
Percolation of fluid in a porous material - Application to the pathology of constructions

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C7304 V2 Article

Further Development (Probabilistic Approach)
Percolation of fluid in a porous material - Application to the pathology of constructions

Author : Fouad BOUYAHBAR

Publication date: July 10, 2026 | Lire en français

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3. Further Development (Probabilistic Approach)

3.1 Combinatorics of Clusters

The complexity of the previous approach (which requires multiple simulations) can be addressed by a combinatorial count of clusters within a given grid.

Ergodicity allows us to consider the distribution of clusters within a single grid as related to the porosity distribution in the actual material.

Random grid generation allows us to introduce a probability distribution governing whether cells are open or closed.

The probability that a cell chosen at random from a grid is open is, of course, equal to p (the material’s intrinsic porosity).

The objective is to determine the probability of cluster formation around or originating from the specified cell.

Its neighboring cells (4 in total)...

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