A Block-Based Theoretical Model Suited to Gravitational Sliding

An original theoretical model has been devised to simulate mass flow over hill slopes due to gravitational sliding. The sliding mass is discretized into a sequence of contiguous blocks which are subjected to gravitational forces, to bottom friction and to surface resistance stresses that are generally negligible for subaerial flows, but are relevant for submarine slides. The blocks interact with each other while sliding down the hill flanks because of internal forces that dissipate mechanical energy and produce a momentum exchange between the individual blocks, yet conserving the total momentum of the mass. Internal forces are expressed in terms of interaction coefficients depending on the instantaneous distance between the block centers of mass, which is a measure of the deformation experienced by the blocks: the functional dependence includes three parameters, namely the interaction intensity ¯λ, the deformability parameter σ and the shape parameter γ, by means of which a wide range of interaction types can be fully accounted for. The time integration is performed numerically by solving the equations for the block velocities and positions at any time ti by means of the block accelerations at the previous time ti-1, and by subsequently updating the block accelerations, which allows to proceed iteratively to the following times. The model has been tested against laboratory results available from literature and by means of several numerical experiments involving a simplified geometry both for the sliding body and the basal surface, with the purpose of clarifying the influence of the model parameters on the slide dynamics. The model improves the performance of the existing kinematic models for slides, moreover preserving an equivalent numerical simplicity. Future applications and possible improvements of this model are suggested.