Simple approximation to bottom friction for Bingham fluid depth integrated models

Catastrophic gravity driven flows such as debris flows, mud flows, and flow slides cause major economic damage and loss of human life. Numerical models are important prediction tools which can help to design contention, channeling, and routing structures. Their accuracy is limited by that of the rheological model they implement. Bingham models provide a reasonable good compromise between accuracy and simplicity, and they have been frequently used to describe the rheology of hyperconcentrated flows, mudflows, and debris flows. Their use in depth integrated models presents a difficulty. In order to obtain the bottom friction term, one has to obtain the roots of a third order polynomial. This paper describes a depth integrated model for flows of Bingham fluids. Bottom friction is obtained using an approximation which provides good accuracy and saves 20% of CPU time.