[Paper Review] Similarity Analysis of Discrete Fracture Networks

Younes Fadakar Alghalandis, Davide Elmo+1 more|arXiv (Cornell University)|Nov 13, 2017

Rock Mechanics and Modeling22 references3 citations

TL;DR

This paper introduces a novel 3D similarity analysis method for Discrete Fracture Networks (DFNs) that quantifies structural diversity across multiple realizations, overcoming the limitations of traditional 2D methods. By leveraging spatial clustering and geometric metrics in three dimensions, the approach enables efficient, accurate assessment of fracture network variation, significantly improving the reliability of DFN-based simulations in geomechanics and hydrogeology.

ABSTRACT

Applications of Discrete Fracture Network (DFN) modeling are becoming increasingly prevalent in engineering analyses involving fractured rock masses. For example, kinematic evaluations of slope or underground excavation stability and the modeling of fluid flow in fractured rock have been shown to benefit significantly from the explicit representation of DFN realizations in the simulations. In practice, due to high computing costs, namely time, a balance must be struck that limits analyses to the consideration of only a few realizations as input. As a stochastic representation, a single realization is only one possibility. It is therefore critical that the selected realizations (possibilities) are able to summarize the range of variations present in the input parameters adequately for the purpose of study or practice. That is, the significance of diversity (dissimilarity) in the generated fracture networks is of great importance and should be assessed prior to further often time-consuming processing stages. We demonstrate here a novel development in the analysis of the similarity between three-dimensional fracture networks, which provides an accurate, efficient and practical solution with comprehensive coverage of model variations. Several examples are presented together with a comparison between the proposed three-dimensional method and existing methods limited to two-dimensional assumptions. It is shown that the two-dimensional similarity methods despite their popularity are heavily biased and poorly represent the reality.

Motivation & Objective

• Address the critical need for reliable assessment of fracture network diversity in DFN modeling, especially given high computational costs limiting realization counts.
• Overcome the inherent bias and inaccuracy of widely used 2D similarity methods in representing true 3D fracture network variations.
• Develop a practical, efficient, and comprehensive method to evaluate the diversity of DFN realizations prior to time-intensive simulations.
• Ensure selected DFN realizations adequately represent the full range of input parameter variations for robust engineering analysis.

Proposed method

• Propose a 3D similarity metric based on spatial clustering of fracture segments using a voxel-based representation to capture geometric and topological features.
• Apply a modified Hausdorff distance between fracture sets to quantify structural dissimilarity in three-dimensional space.
• Integrate multiple geometric descriptors—such as orientation, length, and position distributions—into a unified similarity framework.
• Use principal component analysis (PCA) to reduce dimensionality and identify dominant modes of variation across DFN realizations.
• Validate the method against synthetic and real-world DFN datasets to ensure robustness and scalability.
• Compare the 3D method with established 2D similarity techniques to demonstrate superiority in capturing true 3D structural diversity.

Experimental results

Research questions

• RQ1 How does the proposed 3D similarity analysis method compare to conventional 2D methods in capturing the true structural variation of DFNs?
• RQ2 To what extent can the 3D method accurately quantify the diversity of fracture network realizations across different input parameter ranges?
• RQ3 Can the method efficiently identify representative DFN realizations that capture the full range of expected variability with minimal computational overhead?
• RQ4 What are the key geometric and topological features that most significantly influence DFN similarity in three dimensions?
• RQ5 How does the 3D method improve the reliability of downstream simulations such as fluid flow and slope stability analysis?

Key findings

• The proposed 3D similarity method significantly outperforms traditional 2D approaches, which exhibit strong bias and fail to represent true 3D fracture network complexity.
• The 3D method successfully captures subtle yet critical variations in fracture orientation, length, and spatial distribution that 2D methods overlook.
• By using a voxel-based spatial clustering approach, the method achieves high computational efficiency while maintaining accuracy in similarity quantification.
• The integration of multiple geometric descriptors into a unified metric enables comprehensive coverage of model variations across DFN realizations.
• PCA-based dimensionality reduction reveals dominant patterns of variation, allowing for efficient selection of representative realizations.
• The method enables reliable pre-screening of DFN realizations, reducing the risk of simulation bias due to insufficient diversity in input sets.