21 Apr 2021

21 Apr 2021

Review status: this preprint is currently under review for the journal SE.

Investigating Spatial Heterogeneity within Fracture Networks using Hierarchical Clustering and Graph Distance Metrics

Rahul Prabhakaran1,2, Giovanni Bertotti1, Janos Urai3, and David Smeulders2 Rahul Prabhakaran et al.
  • 1Department of Geoscience and Engineering, Delft University of Technology, Delft, the Netherlands
  • 2Department of Mechanical Engineering, Eindhoven University of Technology, the Netherlands
  • 3Structural Geology, Tectonics and Geomechanics, RWTH Aachen University, Aachen, Germany

Abstract. We investigate the spatial variation of 2D fracture networks digitized from the well-known Lilstock limestone pavements, Bristol Channel, UK. By treating fracture networks as spatial graphs, we utilize a novel approach combining graph similarity measures and hierarchical clustering to identify spatial clusters within fracture networks and quantify spatial variation. We use four graph similarity measures: fingerprint distance, D-measure, NetLSD, and portrait divergence to compare fracture graphs. The technique takes into account both topological relationship and geometry of the networks and is applied to three large fractured regions consisting of nearly 300,000 fractures spread over 14,200 sq.m. The results indicates presence of spatial clusters within fracture networks with that vary gradually over distances of tens of metres. One region is not influenced by faulting but still displays variation in background fracturing. Variation in fracture development in the other two regions are interpreted to be primarily influenced by proximity to faults that gradually gives way to background fracturing. Comparative analysis of the graph similarity-derived clusters with fracture persistence measures indicate that there is a general correspondence between patterns; however, additional variations are highlighted that is not obvious from fracture intensity and density plots. The proposed method provides a quantitative way to identify spatial variations in fracture networks which can be used to guide stochastic and geostatistical approaches to fracture network modelling.

Rahul Prabhakaran et al.

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on se-2021-45', Anonymous Referee #1, 11 May 2021
    • AC1: 'Reply on RC1', Rahul Prabhakaran, 28 Jul 2021
  • RC2: 'Comment on se-2021-45', David Sanderson, 21 May 2021
    • AC2: 'Reply on RC2', Rahul Prabhakaran, 28 Jul 2021

Rahul Prabhakaran et al.

Data sets

Data Supplement: Fracture Subgraphs from the Lilstock Pavement, Bristol Channel, UK Rahul Prabhakaran, Giovanni Bertotti, Janos L Urai, David Smeulders

Rahul Prabhakaran et al.


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Short summary
Rock fractures are organized as networks with spatially varying arrangements. Owing to networks' influence on bulk rock behavior, it is important to quantify network spatial variation. We utilize an approach where fracture networks are treated as spatial graphs. By combining graph similarity measures with clustering techniques, spatial clusters within large-scale fracture networks are identified and organized hierarchically. The method is validated on a dataset with nearly 300,000 fractures.