Unified Modeling of Fluid or Granular Flows on Dam-Break Case

Abstract

The stopping process of debris-flow pulses is a complex phenomenon that expresses both the characteristics of a non-Newtonian fluid when it flows and those of a soil when it comes to a stop. In order to capture this phenomenon, we have developed a model based on a Navier-Stokes approach with a constitutive law including a Drucker-Prager yield criterion. The latter permits us to continuously describe the passage of granular material from the flowing (viscous) to the stopped (viscoplastic) status. In addition to being easy to implement, this approach has the advantage of being straightforwardly expandable to full three-dimensional modeling. In order to evaluate this approach, we have implemented it using finite elements. This implementation uses a Galerkin finite-element approximation with a least-squares stabilization procedure. The free surface is treated by means of a level-set approach to cope with the complex geometry of a flowing pulse. The rheological model and the free-surface treatment are tested in an analytical problem and in a dam-break test.