Isaac Newton Institute  Abstracts

Navigation
INI Home Page
GPF Program
GPFW02 Workshop

THE ROLE OF INTERNAL STRESSES IN THE FLOW OF GRANULAR AVALANCHES
 30/10/03

Roger P. Denlinger, (US Geological Survey) roger@usgs.gov

Understanding the flow of granular debris is prerequisite to assessment and
mitigation of debris flow and avalanche hazards. As part of a research
team working toward more realistic hazard assessments, I formulated a
finitevolume model to solve equations describing depthaveraged granular
flow in an earthcentered coordinate system. The equations assume Coulomb
resistance to flow, both internally and from basal sliding, and include the
effects of variable vertical acceleration. Horizontal mass and momentum
flux between cells is determined using highresolution methods borrowed
from shock wave research, and this flux is combined with the vertical
momentum equation to determine corresponding velocities in three dimensions
(3D). Subsequently, these velocities are used to determine (3D) stresses
in the flowing material using finiteelement methods. Detailed comparisons
of the model output with laboratory experiments of the flow of sand
demonstrate the efficacy of the model and illustrate the role that internal
stresses play in the flow of granular debris.
The role of internal deviatoric stresses, derived from the friction
between grains or fragments in continuous contact, is significant in all of
our comparisons with experminents. Replacement of deviatoric stresses with
isotropic stresses (by neglecting intergranular friction) will yield
different results for collapse of a sand cylinder to form a cone, for
release of sand from a hopper, for flow of sand in a channel, or for
deposition of sand at the base of a slope. In collapse of a cylinder, the
forces driving outward flow are reduced by intergranular friction and
consequently are less than obtained assuming isotropic stress states.
Neglect of intergranular friction results in higher lateral accelerations
and a flatter cone. Similarly, release of material on a slope is affected
by the same mechanisms: for a uniform slope and any variation in basal
friction or support, more material is mobilized and accelerates faster (as
a result of higher lateral stresses) in the case of an isotropic
formulation that ignores intergranular friction. As sand flows down a
channel, its behavior continues to depend upon internal stresses within the
flow. For example, in comparisons with an experiment using an irregular
channel that has a shallow midchannel ridge, model flows will not be
completely divided by the ridge (as observed), but tend to flow over the
ridge when intergranular friction and the stress it generates is ignored.
As the sand comes to rest at the base of a slope, an isotropic formulation
for internal stresses produces a more rounded deposit with shallower slopes
as a result of higher velocities during transport. These comparisons show
that internal stresses play a crucial role in many aspects of the flow and
deposition of granular debris, one that should not be eliminated in the
interests of model efficiency or simplification.

