Oscillatory finite-time singularities in rockbursts
Forecasting violent rockbursts remains a formidable challenge due to significant uncertainties involved. One major uncertainty arises from the intermittency of rock failure processes, typically characterised by a series of progressively shorter quiescent phases punctuated by sudden accelerations, rather than a smooth continuous progression towards the final breakdown. This non-monotonic evolution of rock mass deformation complicates rockburst prediction, challenging conventional time-to-failure models that often assume a smooth power law accelerating behaviour. Here, we introduce a generalised time-to-failure model called log-periodic power law singularity (LPPLS) model to effectively capture the intermittent dynamics of damage and rupture processes in rock leading up to violent rockbursts. We perform parametric and nonparametric tests on 11 historical rockburst events at three underground mines, documenting empirical evidence and providing theoretical arguments to demonstrate the significance of log-periodic oscillatory power law finite-time singularities. Log-periodicity in these rockburst events is likely driven by the interaction of subparallel propagating cracks, the diffusion of stress-triggering processes, or the interplay between stress drop and stress corrosion. Our results and insights obtained have significant implications for not only understanding but also forecasting rockbursts, as recognising and characterising log-periodicity can help transform intermittency from traditionally perceived noise into valuable predictive information.