Growth of three-dimensional fractures, arrays, and networks in brittle rocks under tension and compression

Abstract

Concurrent growth of multiple fractures in brittle rock is a complex process due to mechanical interaction effects. Fractures can amplify or shield stress on other fracture tips, and stress field perturbations change continuously during fracture growth. A three-dimensional, finite-element based, quasi-static growth algorithm is validated for mixed mode fracture growth in linear elastic media, and is used to investigate concurrent fracture growth in arrays and networks.Growth is governed by fracture tip stress intensity factors, which quantify the energy contributing to fracture extension, and are validated against analytical solutions for fractures under compression and tension, demonstrating that growth is accurate even in coarsely meshed domains. Isolated fracture geometries are compared to wing cracks grown in experiments on brittle media. A novel formulation of a Paris-type extension criterion is introduced to handle concurrent fracture growth. Fracture and volume-based growth rate exponents are shown to modify fracture interaction patterns. A geomechanical discrete fracture network is generated and examined during its growth, whose properties are the direct result of the imposed anisotropic stress field and mutual fracture interaction. Two-dimensional cut-plane views of the network demonstrate how fractures would appear in outcrops, and show the variability in fracture traces arising during interaction and growth.

Permeability of Three‐Dimensional Numerically Grown Geomechanical Discrete Fracture Networks With Evolving Geometry and Mechanical Apertures

“…A detailed overview and validation of fracture growth using the methodology presented herein, implemented in C++ in the Imperial College Geomechanics Toolkit, is given in Thomas et al (). The method is based on linear elastic fracture mechanics theory and grows fractures quasi‐statically in distinct growth steps, starting from an initial distribution of flaws in a three‐dimensional volumetric domain (Growth Step 0).…”

“…Flow and equivalent permeability analysis at each growth step is performed during postprocessing after growth (section ). The present work focuses on linear elastic tensile deformation and Darcy flow, and in other work the ICGT has also been applied to compressive stresses (Thomas et al, ), friction and contact (Nejati et al, ), and coupled thermohydromechanics (Salimzadeh et al, ).…”

“…Near the tip, the first terms of the Williams series are dominant, providing an expression for the singular stress field near the tip. Thomas et al () validated DC for fractures under tension and compression for all three SIF modes within the present implementation of the method.…”

“…Two‐dimensional networks consistently underestimate the connectivity and permeability of three‐dimensional networks (Lang et al, ). Mechanical interaction between fractures can increase or decrease stress along different parts of a fracture's tip, depending on their relative location and the orientation of stress, with significant implications for three‐dimensional growth patterns (Thomas et al, , ).…”

“…The present work makes significant progress toward realistic fracture network generation through the use of a three‐dimensional, finite element‐based fracture growth simulator (Paluszny & Zimmerman, ; Paluszny et al, ). Thomas et al () validated fracture growth under tension and compression, and describe the advanced computational framework enabling the generation of geomechanical DFNs (GDFNs). In contrast to Poisson or pseudo‐mechanical DFNs, these networks are generated by continually evaluating deformation of the volumetric domain and tracking the resulting changes in the network geometry.…”