H33G-01 13:40h
Computing Granular Avalanches Over Complex Topography
Rapid Granular mass movement phenomena such as snow avalanches, rock avalanches and debris flows are natural phenomena that occur in mountainous areas throughout the world. Whereas the physical understanding of their release is quite complex, depend of many very different parameters and hence difficult to understand, the understanding of motion and stopping is less difficult and is investigated in this work using numerical simulations. Savage and Hutter (1989) proposed a one-dimensional continuum model for the numerical simulation of dry granular mixtures. It assumes an incompressible shallow flow behaviour and that the flowing mass behaves as a Mohr-Coulomb plastic material when yielding. This was extended by Gray et al. (1998) and Iverson & Denlinger on multi dimensions and by Iverson & Denlinger (2001) and Savage & Iverson (2003) for rapid two-phase flow phenomena. In this paper we are presenting a new numerical model approach for the solution of the Iverson & Denlinger equations in the case of dry rapid granular flows, with the following characteristics: - it solves the conservation laws for rapid dry granular flows. - it operates on unstructured triangular grids in the finite volume context. - it works with a dynamic adaptive grid strategy. - it operates with a higher order approximate Riemann solver and a new source term balancing technique. - it operates in a parallelized environment. We tested the numerical model against several numerical testproblems and laboratory experiments such as: - the classical lake at rest problem; - a dry granular flow down an inclined chute; - a dry granular flow down an inclined plane with and without a flow diverting obstacle; - a dry granular flow down an unregular laboratory topography .
http://lhewww.epfl.ch/
H33G-02 13:55h
Coupling between basal shear stresses and internal stresses plays a crucial role in granular avalanches
Models of granular avalanches commonly assume that basal shear stresses obey some type of friction rule (for example, the Coulomb rule), but that internal stresses are the same as those in an ideal, frictionless fluid. These assumptions lead to depth-integrated momentum-conservation equations that are essentially identical to those of standard shallow-water theory. Although the simplicity of these equations is appealing, omission of internal friction is inconsistent with the persistent contact between solid fragments and with measurements of laboratory avalanches that cross rugged, irregular, three-dimensional terrain (e.g., Iverson et al., JGR 109, 2004, doi:10.1029/2003JF000084). These inconsistencies have little consequence if avalanches traverse only planar or nearly planar terrain, because such terrain does not produce strong variations in accelerations and accompanying reaction forces. Moreover, effects of the inconsistencies can be camouflaged if an avalanche model is tuned to fit the observed distribution of an avalanche deposit, rather than tested against detailed experimental data. We demonstrate the importance of internal friction in granular avalanches by comparing experimental data to model predictions that assume Coloumb friction governs basal shear stresses, but with internal deviatoric stresses that are either absent or governed by the Coulomb rule. We also demonstrate how local accelerations produced by deflection of avalanches by rugged topography produces strong variations in both basal shear stresses and internal stresses. Forces produced by basal shear stress are coupled to forces generated by internal friction, and this coupling determines the way the flow interacts with terrain. The clear importance of internal stresses indicates that models that neglect them do not offer a sound basis for interpreting avalanche deposits or for forecasting the behavior of future avalanches in the process of hazards evaluation.
http://vulcan.wr.usgs.gov/Projects/MassMovement
H33G-03 14:10h
Particle size segregation in geophysical mass flows
Particle size segregation by kinetic sieving is a fundamental feature of many geophysical mass flows, which gives rise to the formation of inversely-graded layers. Shear within the flow then tends to transport the large particles to the front of the avalanche and the small particles to the rear. If the large particles experience more resistance to motion than the small particles, an instability is generated in which the small particles push the large particles to the side to form lateral levees. This is responsible for the generation of fingers and lobes, which are commonly observed in debris-flows and pyroclastic deposits. Despite its fundamental importance there has been very little theoretical work on modelling the kinetic sieving process. In this paper a simple continuum model is derived which allows the particles to segregate within any three-dimensional incompressible geophysical mass flow model. Some simple exact solutions for steady uniform flows are then constructed to illustrate the capabilities of the model.
H33G-04 14:25h
Numerical Modelling of the Formation of Levees in Granular Flow Deposits: a way to Investigate the Hidden Part of the Flow law
Debris avalanches regularly cause large amounts of human and material damages. Their numerical simulation should provide a useful tool for investigating, within realistic geological contexts, the dynamics and the stopping phase of these flows and for improving the risk assessment of such natural hazards. The major difficulty in modelling debris avalanches is linked to the behavior of such granular materials. The flow law describing the steady flow of granular materials over an inclined plane has been determined empirically in recent experimental studies. However, the behavior at small Froude number (near the destabilization or near the stopping phase) is still an open question. We present here an unique framework where this part of the flow law can be investigated: the modelling of levees on the border of an unconfined granular flow. Recent experiments have shown the appearance of lateral static zones on each border of a granular flow over an inclined plane with a constant input flux. Furthermore, the deposit obtained after cutting the supply exhibit a levee/channel morphology similar to that observed on pyroclastic flow deposits. These results are simulated here numerically providing insights into the formation of these static zones and of the morphology of the deposit. These features are shown to be closely linked to the behavior of the flow law at small Froude number providing a unique tool to investigate the behavior of granular materials near the destabilisation and/or stopping phase.
H33G-05 14:40h
Estimation of a Stopping Criterion for Geophysical Granular Flows Based on Numerical Experimentation
Inundation area may be the most important factor for mitigation of natural hazards related to avalanches, debris flows, landslides and pyroclastic flows. Run-out distance is the key parameter for inundation because the front deposits define the leading edge of inundation. To define the run-out distance, it is necessary to know when a flow stops. Numerical experiments are presented for determining a stopping criterion and exploring the suitability of a Savage-Hutter granular model for computing inundation areas of granular flows. The TITAN2D model was employed to run numerical experiments based on the Savage-Hutter theory. A potentially reasonable stopping criterion was found as a function of dimensionless average velocity, aspect ratio of pile, internal friction angle, bed friction angle and bed slope in the flow direction. Slumping piles on a horizontal surface and geophysical flows over complex topography were simulated. Several mountainous areas, including Colima volcano (MX), Casita (Nic.), Little Tahoma Peak (WA, USA) and the San Bernardino Mountains (CA, USA) were used to simulate geophysical flows. Volcanic block and ash flows, debris avalanches and debris flows occurred in these areas and caused varying degrees of damage. The areas have complex topography, including locally steep open slopes, sinuous channels, and combinations of these. With different topography and physical scaling, slumping piles and geophysical flows have a somewhat different dependence of dimensionless stopping velocity on power-law constants associated with aspect ratio of pile, internal friction angle, bed friction angle and bed slope in the flow direction. Visual comparison of the details of the inundation area obtained from the TITAN2D model with models that contain some form of viscous dissipation point out weaknesses in the model that are not evident by investigation of the stopping criterion alone.
http://www.gmfg.buffalo.edu
H33G-06 14:55h
Dynamic Modeling of Landslides That Entrain Material From the Path
Numerical modeling of rapid landslide motion is receiving worldwide attention and could eventually become a routine component of quantitative landslide risk assessment. A number of models have been proposed and some are already being used in practice. Most model flow over a non-erodible bed and suppose that flow resistance is governed by intrinsic material properties that remain constant for the duration of motion and can be predicted in advance. In reality, landslides interact with different surficial materials along their paths, which may fail under rapid loading. Entrainment of this material increases the volume of a landslide, alters its composition and consequently influences its mobility and the extent of its potential impact area. This is an important characteristic of rapid landslides at any scale, from debris avalanches and debris flows, which can derive most of their volume by entrainment, to rock slides and rock avalanches, whose mobility may be governed by a thin basal layer containing eroded path material. A new continuum model has been developed at the University of British Columbia that accounts for volume and basal rheology changes due to material entrainment. Based on an existing model, DAN, it uses a meshless, depth-averaged, Lagrangian numerical method adapted from Smoothed Particle Hydrodynamics. This unique method allows the simulation of motion across complex 3-D terrain without requiring the input of a pre-defined path and permits large deformations of the landslide without mesh distortion problems. Mass and momentum transfer between the landslide and the erodible bed are governed by an empirical erosion rate. The user can implement a change in resistance at the initiation of entrainment. Although quite simple, the model has produced accurate simulations of several real landslides involving significant increases in volume. Comparative analyses have shown that these events could not be reproduced without accounting for entrainment. As a result, we propose that material entrainment capabilities should be incorporated into any numerical model intended for practical landslide hazard analysis.
H33G-07 15:10h
Study of the Collapse and Spreading of a Granular Mass Using Discrete Numerical Simulation
Natural catastrophic flows often involve a discrete solid phase made of rocks and unconsolidated soils. The granular nature of the material, and the complex phenomena it implies, are a source of great difficulties in the modelling of the flow dynamics and rheology. In this perspective, the study of simple dry granular flows is of paramount interest. In addition the use of Discrete Element Methods to simulate collections of grains makes way for new insights into the behaviour of granular material. We present here the results of a series of 2D numerical simulations of gravity-driven collapse and spreading of a granular mass. The relationship between the runout distance and the initial geometrical characteristics of the mass (namely the initial height and width) is established and compared to experimental data. The relevance of a Coulombic friction model for the sideways flow of the granular matter is shown when relating the runout distance to the kinetic energy of the flow. A corresponding coefficient of friction for the material is computed with respect to different grains properties. However, the effective friction of the flow, measured as the ratio of the initial height to the runout distance, is shown to depend also on the initial geometry of the mass. The relation between the effective friction, the properties of the grains and the initial geometry is established. These results are discussed in terms of the mobility of natural flows.
H33G-08 15:25h
New scaling law for the runout of large rock avalanches: from the laboratory to the field
Large rock avalanches are commonly described by their relative runout length, defined as the ratio of the runout distance to the fall height. This quantity shows a tendency to increase with volume from a value of about 2 at volumes smaller than $10^5 m^3$ to values larger than 10 for volume in excess of 1$km^3$. However attempts to scale the runout length with the initial volume are not satisfying, as this "scaling law" exhibits extremely large scatter, the origin of which remains controversial. We report in this paper the results of laboratory experiments aimed at understanding the parameters controlling the runout length of a rock avalanche in a simple "cliff-collapse" geometry. The experiment consists of a sudden release a pile of dry granular material which is then allowed to spread on an horizontal surface. Both the runout length and the morphology of the resulting deposit are investigated as a function of the volume released, the initial aspect ratio of the granular pile, the spreading surface properties and the bead size. Two different flow geometries (linear or axisymmetric) are considered. Our main result is that the runout length varies only with the aspect ratio of the initial granular pile and is independent of the volume released. The same approach is then applied to image analysis of the landslides localized along the walls of the Valles Marineris Canyon on Mars. The runout of the Valles Marineris landsides do not scale with their volume but with an estimate of the initial aspect ratio of the mobilized rock mass (before collapsing), exhibiting a much better collapse of the data than the "classical" approach. The results of these two separate investigations suggests that the "classical" approach is not applicable, at least in the case of a cliff collapse where the rock mass spreads along a small slope.