Granular Avalanches on Complex Topography

Abstract

The Savage-Hutter theory for the one-dimensional gravity driven free-surface flow of cohesionless granular materials down inclines (Savage & Hutter, 1989) and curved beds (Savage & Hutter, 1991) was generalised to two-dimensions by Hutter et al. (1992) and Greve et al. (1994). Savage & Hutter (1991) introduced a simple curvilinear coordinate system Oxz with the x coordinate parallel to, and the z component normal to, the local one-dimensional chute geometry. In the two-dimensional theories a similar coordinate system Oxyz was adopted with a lateral (or cross slope) coordinate y perpendicular to the x, z coordinates. Thus, the curvilinear surface z = 0 followed a quasi one-dimensional chute topography, with down slope but no cross slope variation. Agreement between experiments performed on such a chute and the predicted two-dimensional spreading of these uncon-fined granular avalanches was extremely good (Koch et al., 1994). Recently the theory has been generalised (Gray et al., 1996) to allow for shallow down and cross slope variation in the basal chute geometry. In this paper a comparison is made between the theoretical predictions and experimental results from two chutes with complex down and cross slope topography.