Document Type : Original Research Paper

Authors

• Mohammad Reza Zeerak ¹
• Mohammad Fatehi Marji ²
• Manouchehr Sanei ²
• Mehdi Najafi ²
• Abolfazl Abdollahipour ³

¹ Department of Mining and Metallurgical Engineering, Yazd University, Yazd, Iran,

² Department of Mining and Metallurgical Engineering, Yazd University, Yazd, Iran

³ School of Mining Engineering, College of Engineering, University of Tehran, Tehran, Iran

Abstract

The Extended Finite Element Method (XFEM) is a leading computational approach for studying crack growth in rocks, as it can effectively model complex crack paths and discontinuities without the need for re-meshing. In this context, XFEM is particularly well-suited for simulating the development of hydraulic fractures. XFEM is employed to investigate crack initiation, propagation, and aperture size in rock formations, with validation using a Boundary Element Method (BEM)-based approach. Three scenarios are analyzed for crack orientation and interaction in: single cracks at  and  crack displacement behavior at  and  multiple cracks at  and . Displacement in the vertical direction (U2) and stress distribution around the crack tip in the S22 direction are examined to understand fracture mechanics parameters. The findings highlight that crack at higher angles, such as , exhibit more straightforward propagation, while those at or beyond  often require additional stress to continue growing. The comparison between XFEM and BEM results confirms the reliability of the numerical approach, demonstrating strong agreement in predicting fracture behavior in rock materials. The results provide deeper insights into fracture evolution, stress intensity factors, and fracture toughness in geological media. These simulations advance computational fracture mechanics, contributing to optimizing hydraulic fracturing techniques for improved efficiency and safety in subsurface formations. This study is limited to 2D geometries and isotropic materials, potentially missing 3D heterogeneous subsurface complexities. Future work could explore 3D models, anisotropy, and fluid pressure/thermal effects to improve crack growth predictions.

Keywords

• Extended Finite Element Method
• Hydraulic Fracturing
• Crack formation
• Boundary Element Method
• Rock Fractures

Main Subjects

• Rock Mechanics