Numerical issues in computing inundation areas over natural terrains using Savage-Hutter theory

When characterizing geologic natural hazards, specifically granular flows including pyroclastic flows, debris avalanches and debris flows, perhaps the most important factor to consider is the area of inundation. One of the key parameters demarcating the leading edge of inundation is the run-out distance. To define the run-out distance, it is necessary to know when the flow stops. Numerical experiments are presented for determining a stopping criterion and exploring the suitability of the Savage-Hutter theory for computing inundation areas of granular flows. The stopping criterion is a function of dimensionless average velocity, pile aspect ratio and internal and bed friction angle and can be implemented on either a global (entire flow) or local (small areas of the flow) level. Slumping piles on a horizontal surface, and geophysical flows over complex topography were simulated. Mountainous areas, such as Colima volcano, Mexico; Casita, Nicaragua; Little Tahoma Peak, USA, and the San Bernardino Mountains, USA, were used as test regions. These areas have combinations of steep, open slopes and sinuous channels. Because of differences in topography and physical scaling, slumping piles in the laboratory and geophysical flows in natural terrain must be scaled differently to determine a reasonable dimensionless relationship for the stopping criterion.