Evolution of the damage precursor based on the felicity effect in shale

Damage precursors during hydraulic fracturing in shale gas reservoirs may be better understood if the deformation, failure, and acoustic emission (AE) characteristics under cyclic loading are known. Therefore, the purpose of this paper is to investigate the quantitative damage based on the Felicity effect under constant stress lower limit uniaxial cyclic loading-unloading rates (0.5, 1.0, 1.5, 2.0, and 2.5 kN/s). Variations in the b-value and the spatiotemporal evolution of cumulative AE were also used to observe how shale fractures formed. The findings reveal that during the unloading stage, there are many cumulative AE events when the stress level is low (<= 1.50 kN/s) but that this number drops significantly when the stress level increases above (>2.0 kN/s). The AE amplitude, AE counts, and cumulative AE energy of each cycle in a loading-unloading test show an increasing trend, but the rate increases in the last cycle. During the whole process of loading and unloading, the Kaiser effects were present in the 3rd cycle at stress levels (<= 1.5 kN/s). Still, the Felicity effect appeared in the 2nd and 1st cycles during 2.0 and 2.5 kN/s cyclic loading. The Kaiser effect occurs in the linear elastic stage, while the Felicity effect occurs in the crack initiation and crack damage stage. Furthermore, the Felicity ratio (FR) variations during shale deformation and failure can be divided into four phases: (Phase I = 1.01 >= FR > 0.89), (Phase II = 0.89 >= FR > 0.48), (Phase III = 0.48 >= FR > 0.23), and (Phase IV = FR <= 0.23). The b-value is relatively higher under the loading rate below (<= 1.50 kN/s), indicating an increase in the number of small AE events. In contrast, the fact that the b-value is relatively smaller under the loading rate above (>2.0 kN/s) indicates that, the number of large AE events increases the number of cracks and fractures. These findings provide important design references for damaged precursors during hydraulic fracturing in shale gas reservoirs.