2016/07/19 by Ernesto Estrada, Estrada, Ernesto, Matthew Sheerin +1
Computer Science · Engineering · Physics and Astronomy · #Advanced Clustering Algorithms Research #Complex Network Analysis Techniques #FOS: Physical sciences #Geophysics (physics.geo-ph) #Rock Mechanics and Modeling #Topological and Geometric Data Analysis #Underground infrastructure and sustainability
paper · pdf · doi:10.48550/arxiv.1607.06678
openalex publication_date 2016/07/19 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
We propose a new model to account for the main structural characteristics of\nrock fracture networks (RFNs). The model is based on a generalization of the\nrandom neighborhood graphs to consider fractures embedded into rectangular\nspaces. We study a series of 29 real-world RFNs and find the best fit with the\nrandom rectangular neighborhood graphs (RRNGs) proposed here. We show that this\nmodel captures most of the structural characteristics of the RFNs and allows a\ndistinction between small and more spherical rocks and large and more elongated\nones. We use a diffusion equation on the graphs in order to model diffusive\nprocesses taking place through the channels of the RFNs. We find a small set of\nstructural parameters that highly correlates with the average diffusion time in\nthe RFNs. We found analytically some bounds for the diameter and the algebraic\nconnectivity of these graphs that allow to bound the diffusion time in these\nnetworks. We also show that the RRNGs can be used as a suitable model to\nreplace the RFNs in the study of diffusion-like processes. Indeed, the\ndiffusion time in RFNs can be predicted by using structural and dynamical\nparameters of the RRNGs. Finally, we also explore some potential extensions of\nour model to include variable fracture apertures, the possibility of long-range\nhops of the diffusive particles as a way to account for heterogeneities in the\nmedium and possible superdiffusive processes, and the extension of the model to\n3-dimensional space.\n