Mapping internal stress field in deforming rocks using synchrotron high-energy X-ray diffraction

Abstract

Understanding the mechanisms controlling brittle rock failure at the grain to sub-grain scale is a fundamental challenge in geosciences. Recent advances in triaxial compression and dynamic shock experiments combined with dynamic X-ray microtomography provide unparalleled insights into the 3D strain field evolution within deforming rocks. However, these methods do not accurately predict the heterogeneous internal stress field prior to failure, which is crucial for predicting microfracture initiation and propagation, leading to macroscopic failure. In the past decade, efforts have focused on developing synchrotron X-ray diffraction techniques leveraging the high penetrative capacity of hard X-rays from the last generations of synchrotron light sources. These techniques offer spatially resolved information on crystal phase orientation and elastic strain within a 3D volume. The local orientation and elastic strain tensor is reconstructed grain-by-grain, with precision down to approximately 10-3 radian for orientation and 10-4 for strain. Stress is then calculated using Hooke's law for anisotropic materials and the elastic constants of the crystal phases. We employed 3D X-ray diffraction to investigate the internal stress field evolution in a rock core sample deformed under triaxial compression in the Hades apparatus. A 5mm-diameter core of Berea sandstone was subjected to axial step loading under constant radial stress of 10 MPa, reaching brittle failure at around 90 MPa differential stress. Elastic strain of individual quartz grains were measured at different load steps, and elastic stresses were calculated, providing maps of the internal strain and stress field in the sample. Results reveal progressive elastic shortening of quartz grains parallel to the compression axis and elongation in orthogonal directions due to the Poisson’s effect. Reorientation of principal stress components is also observed with increasing axial stress, which tend to align with the macroscopic stress field. Internal stresses distribution varies within a range of ca. 300 MPa, suggesting local stress amplifications occurred interpreted as force chains, potentially favoring crack nucleation. This experiment is among the first ones to characterize in-situ the stress distribution in a natural rock under compressive loading, and demonstrates the potential of synchrotron diffraction techniques for investigating strain and stress in geological materials.