Forecast of time-of-instability in rocks under complex stress conditions using spatial precursory AE response rate

The precursory response rate with the relationship of the time-reversed Omori law can characterize the damage acceleration behavior in the approach to the local instability of rocks. In the present study, the precursory acoustic emission (AE) response rate obtained by the local spatial AE events is employed to forecast the time-of instability of sandstone under biaxial and true triaxial compression. The phase of damage acceleration of rocks is first identified retrospectively based on the mechanical properties and the spatio-temporal AE evolution characteristics. The precursory AE event rate charactering the power-law acceleration behavior in the vicinity of instability point is qualitatively recalculated by the spatial AE events in the damage localization bands determined by the AE localization technique. The precursory time series of spatial AE event rate are adopted to pseudo-prospectively predict the time-of-instability according to the relationship of the time-reversed Omori law. The accurate forecast, being both more precise and less biased, is achieved as the fitted data subsets continuously update towards the instability point. The forecast accuracy based on the spatial AE response rate is higher than that based on the temporal AE response rate. Furthermore, the forecast accuracy obtained by using the pseudo prospective way is higher than that obtained by using the retrospective way.