Entrainment of bed material by Earth-surface mass flows: review and reformulation of depth-integrated theory

Reviews of Geophysics
By:  and 



Earth-surface mass flows such as debris flows, rock avalanches, and dam-break floods can grow greatly in size and destructive potential by entraining bed material they encounter. Increasing use of depth-integrated mass- and momentum-conservation equations to model these erosive flows motivates a review of the underlying theory. Our review indicates that many existing models apply depth-integrated conservation principles incorrectly, leading to spurious inferences about the role of mass and momentum exchanges at flow-bed boundaries. Model discrepancies can be rectified by analyzing conservation of mass and momentum in a two-layer system consisting of a moving upper layer and static lower layer. Our analysis shows that erosion or deposition rates at the interface between layers must in general satisfy three jump conditions. These conditions impose constraints on valid erosion formulas, and they help determine the correct forms of depth-integrated conservation equations. Two of the three jump conditions are closely analogous to Rankine-Hugoniot conditions that describe the behavior of shocks in compressible gasses, and the third jump condition describes shear traction discontinuities that necessarily exist across eroding boundaries. Grain-fluid mixtures commonly behave as compressible materials as they undergo entrainment, because changes in bulk density occur as the mixtures mobilize and merge with an overriding flow. If no bulk density change occurs, then only the shear-traction jump condition applies. Even for this special case, however, accurate formulation of depth-integrated momentum equations requires a clear distinction between boundary shear tractions that exist in the presence or absence of bed erosion.

Additional publication details

Publication type Article
Publication Subtype Journal Article
Title Entrainment of bed material by Earth-surface mass flows: review and reformulation of depth-integrated theory
Series title Reviews of Geophysics
DOI 10.1002/2013RG000447
Volume 53
Year Published 2015
Language English
Publisher American Geophysical Union
Publisher location Washington, D.C.
Contributing office(s) Volcano Science Center
Description 32 p.
First page 1
Last page 32
Online Only (Y/N) N
Additional Online Files (Y/N) N