Quantitative investigation on the heterogeneity of deformation fields in sandstone pre-existing cracks during damage evolution

The inherently heterogeneous microstructures of rocks lead to heterogeneity of the deformation distribution within the rock volume. In this study, experiments were conducted on red sandstone specimens with four different pre-existing crack inclinations stressed under uniaxial loading to investigate these features. Acoustic emission and digital image correlation techniques were used to confirm the damage process and obtaining deformation fields, respectively. The results showed that the heterogeneity of the deformation fields in the rock specimens amplifies with increasing stress magnitude, i.e., the displacement field heterogeneity shows two dense bands around the pre-existing crack, and the strain field heterogeneity shows localized regions with a numerical difference (quantified by the normalized standard deviation) and spatial concentration (quantified by the spatial correlation coefficient). The variations in the normalized standard deviation and spatial correlation coefficient were closely related to the damage process. The normalized standard deviation presented four evolution stages: relatively constant low value, steady growth, significant growth, and high rate growth. The spatial correlation coefficient changed from increasing at a relatively constant rate to increasing at a gentle rate and finally increasing rapidly. The evolution rate along with the strain showed two sharp fluctuations. The first could be used as precursor information of the damage. Finally, we confirmed the feasibility of the damage variable obtained from the heterogeneous deformation indicators used to calibrate or form damage evolution laws.