Analytical and approximate expressions predicting post-failure landslide displacement using the multi-block model and energy methods

A multi-block sliding model has been proposed in order to simulate the actual geometry of landslides and their rotation with displacement. The governing equation of motion was formulated with the force equilibrium approach and solved by numerical integration in terms of time. The present work derives the formulation of the multi-block model based on another perspective, the energy conservation principle. This approach, in contrast to the force equilibrium approach, has the ability to derive analytical equations predicting the distance moved of masses sliding with resistance exhibiting both cohesional and frictional components. The most general geometry, where analytical solution predicting post-failure displacement can be obtained, is considered. Then, and as this equation is complex, a simple special case geometry is considered in order to derive easy-to-apply simple expressions which predict post-failure landslide displacement in terms of soil resistance and geometric parameters of the sliding mass. The accuracy of this approximate for general geometries expression is validated by extensive parametric analyses.