A BLOCK-BASED THEORETICAL-MODEL SUITED TO GRAVITATIONAL SLIDING

An original theoretical model has been devised to simulate mass flow o ver hill slopes due to gravitational sliding. The sliding mass is disc retized into a sequence of contiguous blocks which are subjected to gr avitational forces, to bottom friction and to surface resistance stres ses that are generally negligible for subaerial flows, but are relevan t for submarine slides. The blocks interact with each other while slid ing down the hill flanks because of internal forces that dissipate mec hanical 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 i nstantaneous distance between the block centers of mass, which is a me asure of the deformation experienced by the blocks: the functional dep endence includes three parameters, namely the interaction intensity <( lambda)over bar>, the deformability parameter sigma and the shape para meter gamma, by means of which a wide range of interaction types can b e fully accounted for. The time integration is performed numerically b y solving the equations for the block velocities and positions at any time ti by means of the block accelerations at the previous time t(i-1 ), and by subsequently updating the block accelerations, which allows to proceed iteratively to the following times. The model has been test ed against laboratory results available from literature and by means o f several numerical experiments involving a simplified geometry both f or the sliding body and the basal surface, with the purpose of clarify ing the influence of the model parameters on the slide dynamics. The m odel improves the performance of the existing kinematic models for sli des, moreover preserving an equivalent numerical simplicity. Future ap plications and possible improvements of this model are suggested.