Mathematical Modeling for Disrupted Material Flows Modelación matemática para flujos de material desagregado

Abstract

As an alternative to conventional methods for slope stability analysis, this paper presents a literature review of procedures to model the disaggregated material flows that start from the continuum mechanics (Eulerian approach), conservation of mass and momentum, from which select the methodology proposed by Iverson & Denünger m 2001. Ibis methodology assumes the mixing behavior of a Newtonian fluid and solid whose functional interaction is represented by Coulomb. The momentum equation is simplified in such a way that can generate an analytical solution to which was performed a sensitivity analysis according to each of the input parameters. The results of the sensitivity analysis show a general behavior of the model which tends to a constant speed after a very long time and never stops as an effect of assuming an angle of the flow path and other parameters are constant. The simplified model can be used for the stepwise calculation of the speed and the displacement of the center of mass. Also, this simplified method can be used as input for nsk assessment by disaggregated material flows. The most ímportant parameters in the model are the slope angle, bed friction angle and the fraction of pore pressure, as they determine the slope stability. In case the slope is moved most influencmg variable is the dynamic viscosity and the thickness of flow, as they cause which the flow has a change in the acceleration from the beginning.