Landslide Modeling Basing on Probability Theory of Renewal Processes

This report is aimed at showing that the model based on random process theory, i.e. the renewal process model, is suitable for predicting the time of landslide activation and obtaining its dynamic parameters. The model deals with a geologically-uniform area, where landslide activation results from local factors, such as storm rainfall, depergelation (melting permafrost), and others. Using the theory of limit distribution of random renewal processes after a long time, we obtain the following mathematical equations: (1) the probability distribution of landslide activation cycle and its mathematical expectation obtained from the probability distribution of last activation time of the given area; (2) the probability distribution and the most probable time of next future landslide activation (forecast) from probability distribution of landslides last activation time within the given area. The proposed approach minimizes the duration of the monitoring series necessary for landslide forecasting.