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- Giving to Math

Event Type:

Applied Mathematics and Computation Seminar

Date/Time:

Friday, January 30, 2015 - 12:00 to 13:00

Location:

KEAR 112

Event Link:

Guest Speaker:

Institution:

USGS

Abstract:

The ultimate mobility of a landslide can be strongly contingent on feedback mechanisms in the early stages of motion which influence the frictional resistance of a granular-fluid mixture. An initial failure can lead to runaway acceleration and extensive runout, or, conversely, a stabilizing slump. This distinction is strongly dependent on initial sediment material properties, such as porosity, permeability and fluid content. Traditional slope-stability models attempt to quantify initial force balances of sediment masses, but they do not address the fate of a failing mass. Traditional debris-flow runout models often begin with unrealistic initial force balances and friction coefficients in order to match an observed event. We have developed a mathematical model with the aim of simulating landslides and debris flows, seamlessly from initiation to deposition. The depth-averaged model is a two-phase granular-fluid model borrowing from principles of fluid mechanics, granular mechanics and soil mechanics. The result is a nonconservative hyperbolic system of five PDEs, similar to other St. Venant (shallow water) models for free-surface flows (tsunamis, flooding, etc.). These problems present similar mathematical and computational challenges.

I will describe the mathematical model and computational software that we have developed for these problems. As a case study, simulations of the 2014 Oso, Washington, disaster will be presented. Implications of initial sediment porosity and landslide liquefaction will be described.