Predicting Fracture Network Development in Crystalline Rocks

Jessica Mcbeck,J M Aiken,B Cordonnier,F Renard,Y Ben-Zion

doi:10.1007/s00024-021-02908-7

Abstract

The geometric properties of fractures influence whether they propagate, arrest, or coalesce with other fractures. Thus, quantifying the relationship between fracture network characteristics may help predict fracture network development, and perhaps precursors to catastrophic failure. To constrain the relationship and predictability of fracture characteristics, we deform eight one centimeter tall rock cores under triaxial compression while acquiring in situ X-ray tomograms. The tomograms reveal precise measurements of the fracture network characteristics above the spatial resolution of 6.5 µm. We develop machine learning models to predict the value of each characteristic using the other characteristics, and excluding the macroscopic stress or strain imposed on the rock. The models predict fracture development more accurately in the experiments performed on granite and monzonite, than the experiments on marble. Fracture network development may be more predictable in these igneous rocks because their microstructure is more mechanically homogeneous than the marble, producing more systematic fracture development that is not strongly impeded by grain contacts and cleavage planes. The varying performance of the models suggest that fracture volume, length, and aperture are the most predictable of the characteristics, while fracture orientation is the least predictable. Orientation does not correlate with length, as suggested by the idea that the orientation evolves with increasing differential stress and thus fracture length. This difference between the observed and expected relationship between orientation and length highlights the influence of mechanical heterogeneities and local stress perturbations on fracture growth as fractures propagate, link, and coalesce.

Highlights

Mechanical weaknesses, such as fractures, control the macroscopic strength of brittle solids (Griffith, 1924)
Consistent with the idea that increasing differential stress should increase the length of fractures and change the fracture orientation (Fig. 2c), the models that predict the fracture orientation depend on the length (Fig. 6)
We develop the models to predict fracture network characteristics using other characteristics, without knowledge of the macroscopic stress or strain imposed on the rock

Summary

Introduction

Mechanical weaknesses, such as fractures, control the macroscopic strength of brittle solids (Griffith, 1924). Depending on how the fractures propagate, arrest, coalesce, and localize, the evolving fracture network may lead to catastrophic, systemsize failure. In experiments on granite with in situ acquisition of X-ray tomograms during deformation (e.g., CartwrightTaylor et al, 2020; McBeck et al, 2020), the fracture networks develop from small, isolated fractures to system-spanning, connected networks (Fig. 1). In these experiments, increasing differential stress, rD, localizes fracture development first toward the top portion of the core (Fig. 1).

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