Prediction of landslide failure time based on moving average convergence and divergence coupling with Bayesian updating method

Predicting landslide failure time is a critical issue in geotechnical engineering. Traditional methods often rely on the empirical power law of material failure to deterministically predict this time, which depends heavily on the accurate selection of precursor time series and the precise identification of the onset of the acceleration (OOA) deformation stage. In this paper, we present an innovative approach that couples the Moving Average Convergence and Divergence (MACD) method with the Bayesian update method, and derive a new model for calculating landslide failure time. The MACD method is employed to divide creep landslide displacement into three distinct deformation stages, accurately pinpointing the OOA point. Following this, we introduce the novel calculation model to analyze landslide displacement time series after the OOA point. Finally, the Bayesian update method, combined with the Markov Chain Monte Carlo (MCMC) method, is employed to probabilistically predict landslide failure time. Taking the Wolongsi, Xintan and Dexing Open-pit mine landslides as examples, the proposed method is employed to divide the three deformation stages and predict the landslide failure time. Moreover, the predicted failure time is in good agreement with the actual failure time, indicating the proposed model's ability to accurately predict landslide failure time.