Granular avalanches across irregular three‐dimensional terrain: 1. Theory and computation

Abstract

[1] To establish a theoretical basis for predicting and interpreting the behavior of rapid mass movements on Earth's surface, we develop and test a new computational model for gravity-driven motion of granular avalanches across irregular, three-dimensional (3-D) terrain. The principles embodied in the model are simple and few: continuum mass and momentum conservation and intergranular stress generation governed by Coulomb friction. However, significant challenges result from the necessity of satisfying these principles when deforming avalanches interact with steep and highly variable 3-D terrain. We address these challenges in four ways. (1) We formulate depth-averaged governing equations that are referenced to a rectangular Cartesian coordinate system (with z vertical) and that account explicitly for the effect of nonzero vertical accelerations on depthaveraged mass and momentum fluxes and stress states. (2) We compute fluxes of mass and momentum across vertical cell boundaries using a high-resolution finite volume method and Roe-type Riemann solver. Our algorithm incorporates flux difference splitting, an entropy correction for the flux, and eigenvector decomposition to embed the effects of driving and resisting forces in Riemann solutions. (3) We use a finite element method and avalanche displacements predicted by Riemann solutions to compute Coulomb stresses conjugate to the displacements in 3-D stress space. (4) We test the model output against analytical solutions, a sand cone conceptual experiment, and (in a companion paper) data from detailed laboratory experiments. Model results illustrate a complex interplay of basal traction and internal stress, and they successfully predict not only the gross behavior but also many details of avalanche motion from initiation to deposition.

Mechanism of the Donghekou landslide triggered by the 2008 Wenchuan earthquake revealed by discrete element modeling

“…However, a continuous method demonstrates the advantage of representing the complex geometry of a rock avalanche in this way (Crosta et al, 2006). Refined numerical solutions and a Coulomb-like behavior have been successfully derived for landslides (Iverson and Denlinger, 2001;Iverson and Vallance, 2001;Denlinger and Iverson, 2004), which often involve heterogeneous granular materials such as rocks and debris that may fall, topple or slide (Cruden and Varnes, 1996). For numerical models, many researchers have adopted discrete element methods to analyze landslides (Campbell et al, 1995;Poisel and Roth 2004;Poisel et al, 2005;Staron, 2007;Peng, 2008;Tang et al, 2009aTang et al, , b, 2013.…”

An equivalent fluid/equivalent medium approach for the numerical simulation of coastal landslides propagation: theory and case studies

“…Some particular mechanisms, which play a major role in subaqueous mass movements, can be taken into account by using the EFEM approach, such as hydroplaning (Mohrig et al, 1998;Harbitz et al, 2003; and glide blocks (De Blasio et al, 2006a;Engvik et al, 2006). These mechanisms, which are considered to be effective only for high-speed mass movements, imply a drastic reduction in the basal friction of the landslide that is due to the presence of a water layer, which is trapped between the landslide and the slope.…”

Correction to “Experimental study of bedrock erosion by granular flows”

“…Iverson and Vallance [2001] used the angle of surface inclination in their expression for intergranular normal stress on planes at depth, because the surface slope determines the pressure gradient driving the flow. To address irregular topography, Denlinger and Iverson [2004] included the influence of changes in z momentum due to topographic variations. They defined total vertical acceleration, Figure 2.…”