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A new Delaunay triangulation-based approach to characterize the pore network in granular materials

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Abstract

The ability of granular materials to retain fine particles transported within their void space by seepage flow depends strongly on the geometric characteristics of their pore network (pore sizes and constriction sizes). Hence, characterizing the pore network of a granular assembly obtained by means of a micro-tomography scanning or a numerical discrete simulation is of great importance in assessment of its filtration efficiency. Here, we determine characteristics of the pore network of virtual samples composed of spherical particles simulated by using the DEM. A new criterion is proposed to merge neighboring tetrahedra issued from the weighted Delaunay triangulation. To do so, we extend the concept of inscribed void sphere, initially defined for each tetrahedron, to each polyhedral sub-domain constituted of merged tetrahedra. This inscribed void sphere fits the best the void space within the sub-domain. Flat tetrahedra are first eliminated by a primary merging procedure taking into account two basic geometric conditions required for each pore. Adjacent sub-domains are then merged depending on the level of overlap between their inscribed void spheres. The pore size distributions and constriction size distributions (CSD) of granular samples with different grain size distributions obtained with the new merging criterion are compared to those given by two other criteria often used in the literature. The new criterion allows us to reduce greatly the inherent subjectivity in characterizing the granular pore network and to remediate the drawbacks of the two considered criteria in the literature. Moreover, CSDs given by these different criteria tend to converge for gap-graded and widely graded materials. The CSDs obtained with the new merging criterion are used to estimate the controlling constriction sizes \(D_c^*\) of the considered samples, and the estimated values of \(D_c^*\) are compared to Kenney and Lau’s empirical rule.

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Acknowledgements

The authors would like to acknowledge Prof. Eric Vincens and Dr. Feda Seblany at Ecole Centrale de Lyon for valuable discussion about the \(\mathrm {L}_1\) and \(\mathrm {L}_2\) criteria and for having provided some data so that the authors could validate the implementation of these criteria in their own code. This work was partially supported by Cedre program of the French and Lebanese scientific cooperation (Grant No. 40188UD).

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  1. GeM Institute, University of Nantes, 58 Rue Michel Ange, BP 420, 44606, Saint-Nazaire Cedex, France

    Ngoc-Son Nguyen, Habib Taha & Didier Marot

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  1. Ngoc-Son Nguyen
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  2. Habib Taha
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  3. Didier Marot
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Correspondence to Ngoc-Son Nguyen.

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Nguyen, NS., Taha, H. & Marot, D. A new Delaunay triangulation-based approach to characterize the pore network in granular materials. Acta Geotech. 16, 2111–2129 (2021). https://doi.org/10.1007/s11440-021-01157-1

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