You may have a look at the literature and seek predictive models that have been applied to landslide susceptibility modeling. Machine learning and statistical approaches are broadly used for this purpose.
Different types of landslides, including rainfall-induced landslides, have been successfully modeled using these techniques.
My past experience with landslides did not use or was not aware of landslide models. There were some researchers at the USFS Pacific Northwest Experiment Station who studied landslides and came up with some indicators. I think Dr. Dennis Harr was one of them. I worked with geologists, soil scientists during my career and we used various physical indicators such as those mentioned in Watershed Restoration after Calamity in my Researchgate. We did what we could to address them, and try to stabilize or if nothing else make them look less obvious, such as with hydromulching. Rainfall is an obvious driver, but the failure potential also involves slope, depth and type of soils, any strike and dips or failure contacts, past disturbances or concentration of surface flow which can be as little as a cattle or animal trail, or as major as road cut or fill slopes with poor attention to the need for frequent drainage. Vegetation removal such as clear cutting of forest or severe wildfire may contribute in some instances, quickly or delayed response as roots decay. Most of my work with landslides was using archaic methods such as aerial photo interpretation or evaluating issues in the field as a road or stream survey. But the tools of today such as LiDAR allow for what might be called a remote field assessment, where roads, trails, ditches, fault indicators, soil cracks, slumps and earth flows, jackstrawed trees, etc. can be seen or at least suggested. Unstable streams that aggrade or degrade may also have some potential in unstable slope or colluvial materials as floods may undercut toe slopes or stream banks. Models if available may help identify hazard zones to be refined with remote sensing and field work.
William has given you a wealth of information. I don't mean to add to it except to say that modelling rainfall induced debris flows etc. has been tried through simulation experiments. The trouble is that rainfall is unpredictable and soil/slope characteristics so variable that modelling is nigh impossible in the natural environment. Frequently, rainfall induced flows and slides are triggered by intense rains of a highly localised nature. For example, I had one flow triggered on a slope upon which few flows had ever occurred, yet on the other side of the valley where 18 flows had over the centuries been reactivated many times. The valley is no more than 500m wide! Clearly the rainfall that day affected only that top corner of the hillside.
Hürlimann, M., Coviello, V., Bel, C., Guo, X., Berti, M., Graf, C., ... & Yin, H. Y. (2019). Debris-flow monitoring and warning: Review and examples. Earth-Science Reviews, 199, 102981. Article Debris-flow monitoring and warning: Review and examples
Machine learning may be a good choice. But my experience is that different machine learning models may have little difference in prediction results. The key lies in the choice of triggering factors. For the landslide induced by rainfall, the research on rainfall lag may be the core to solve the problem of prediction accuracy.
Thanks very much. I understand that when the top soil in the slope is nearly impermeable, surface runoff starts to flow. Also when the soil in the slope is fully saturated, then surface runoff begins. So what triggers the flow lanslide is the question as you mentioned.