Generalized failure law for landslides, rockbursts, glacier breakoffs, and volcanic eruptions

Catastrophic failures have momentous impact in many scientific and technological fields but remain challenging to understand and predict. One key difficulty lies in the burstiness of rupture phenomena, which typically involve a series of progressively shorter quiescent phases punctuated by sudden bursts, rather than a smooth continuous progression. This seemingly erratic pattern challenges the conventional power law assumption of continuous scale invariance. Here, we propose a generalized material failure law based on the log-periodic power law, which better captures the discrete scale invariance inherent in intermittent rupture dynamics. Our method's superiority is demonstrated through testing on 109 historical geohazard events, including landslides, rockbursts, glacier breakoffs, and volcanic eruptions. The results indicate that our method is general and robust, offering significant potential to forecast catastrophic failures.