Predictive modelling of rainfall-induced rockfall: a copula-based approach

Rockfall is a significant natural hazard threatening infrastructure and public safety, often intensified by extreme weather, particularly rainfall. Understanding the relationship between rockfall volumes and rainfall is crucial for effective rockfall risk management. This study develops a copula-based joint distribution model to examine the dependence between rockfall volume and accumulated rainfall. The methodology is applied to two sub-vertical rock faces in a coal mine in Australia. The dataset considers rainfall accumulation over one day, two days, three days, and one week before each rockfall event. Analysis indicates a stronger nonlinear than linear dependency, with Pearson correlation coefficients between 0.25 and 0.45, and Kendall's tau coefficients ranging from 0.44 to 0.57. Marginal distributions for rockfall volume and rainfall were assessed via a statistical goodness-of-fit test. A copula-based joint probability is developed to compute the conditional probability of rockfall volume given specific rainfall amounts. Appropriate copula functions are selected based on dependency strength and fit statistics. Validation against observed volumes and linear regression confirmed the model's robustness: about 92% of observed volumes fell within the 90th percentile of predicted values. Results highlight the effectiveness of the novel predictive approach to inform engineering decisions under accumulated rainfall conditions.