Shiva P. Pudasaini

Rapid shear flows of dry granular masses down curved and twisted channels

This paper presents a two-dimensional depth-integrated theory for the gravity-driven free-surface flow of a granular avalanche over an arbitrarily but gently curved and twisted topography which is an important extension of the original Savage & Hutter theory. In contrast to previous extensions the present coordinate system is based on a reference curve with curvature and torsion. Its derivation was necessary because real avalanches are often guided by rather curved and twisted valleys or more general slopes. The aim is to gain fundamental insight into the effects of non-uniform curvature and torsion, using an orthogonal coordinate system that rotates with torsion, and find an analytic description of flow avalanches. We present a set of model equations which comprises nonlinear hyperbolic partial differential equations for the space and time evolution of the granular pile height and the depth-averaged streamwise velocity distribution of a finite mass of granulates. The emerging theory is believed to be capable of predicting the flow of dense granular materials over moderately curved and twisted channels of general type.

Rapid flow of dry granular materials down inclined chutes impinging on rigid walls

We performed laboratory experiments of dry granular chute flows impinging an obstructing wall. The chute consists of a 10cm wide rectangular channel, inclined by 50° relative to the horizontal, which, 2m downslope abruptly changes into a horizontal channel of the same width. 15l of quartz chips are released through a gate with the same width as the chute and a gap of 6cm height, respectively. Experiments are conducted for two positions of the obstructing wall, (i) 2m below the exit gate and perpendicular to the inclined chute, and (ii) 0.63m into the horizontal runout and then vertically oriented. Granular material is continuously released by opening the shutter of the silo. The material then moves rapidly down the chute and impinges on the obstructing wall. This leads to a sudden change in the flow regime from a fast moving supercritical thin layer to a stagnant thick heap with variable thickness and a surface dictated by the angle of repose typical for the material. We conducted particle image velocimet...

The Savage–Hutter avalanche model: how far can it be pushed?

The Savage–Hutter (SH) avalanche model is a depth-averaged dynamical model of a fluid-like continuum implementing the following simplifying assumptions: (i) density preserving, (ii) shallowness of the avalanche piles and small topographic curvatures, (iii) Coulomb-type sliding with bed friction angle δ and (iv) Mohr–Coulomb behaviour in the interior with internal angle of friction φ≥δ and an ad hoc assumption reducing the number of Mohrs circles in three-dimensional stress states to one. We scrutinize the available literature on information regarding these assumptions and thus delineate the ranges of validity of the proposed model equations. The discussion is limited to relatively large snow avalanches with negligible powder snow component and laboratory sand avalanches starting on steep slopes. The conclusion of the analysis is that the SH model is a valid model for sand avalanches, but its Mohr–Coulomb sliding law may have to be complemented for snow avalanches by a second velocity-dependent contribution. For very small snow avalanches and for laboratory avalanches starting on moderately steep and bumpy slopes it may not be adequate.

Velocity measurements in dry granular avalanches using particle image velocimetry technique and comparison with theoretical predictions

Velocity and depth are crucial field variables to describe the dynamics of avalanches of sand or soil or snow and to draw conclusions about their flow behavior. In this paper we present new results about velocity measurements in granular laboratory avalanches and their comparison with theoretical predictions. Particle image velocimetry measurement technique is introduced and used to measure the dynamics of the velocity distribution of free surface and unsteady flows of avalanches of non-transparent quartz particles down a curved chute merging into a horizontal plane from initiation to the runout zone. Velocity distributions at the free surface are determined and in one case also at the bottom from below. Also measured is the settlement of the avalanche in the deposit. For the theoretical prediction we consider the model equations proposed by Pudasaini and Hutter [J. Fluid Mech. 495, 193 (2003)]. A nonoscillatory central differencing total variation diminishing scheme is implemented to integrate these mode...

Some exact solutions for debris and avalanche flows

Exact analytical solutions to simplified cases of nonlinear debris avalanche model equations are necessary to calibrate numerical simulations of flow depth and velocity profiles on inclined surfaces. These problem-specific solutions provide important insight into the full behavior of the system. In this paper, we present some new analytical solutions for debris and avalanche flows and then compare these solutions with experimental data to measure their performance and determine their relevance. First, by combining the mass and momentum balance equations with a Bagnold rheology, a new and special kinematic wave equation is constructed in which the flux and the wave celerity are complex nonlinear functions of the pressure gradient and the flow depth itself. The new model can explain the mechanisms of wave advection and distortion, and the quasiasymptotic front bore observed in many natural and laboratory debris and granular flows. Exact time-dependent solutions for debris flow fronts and associated velocity...

Rapid motions of free-surface avalanches down curved and twisted channels and their numerical simulation.

This paper presents a new model and discussions about the motion of avalanches from initiation to run-out over moderately curved and twisted channels of complicated topography and its numerical simulations. The model is a generalization of a well established and widely used depth-averaged avalanche model of Savage & Hutter and is published with all its details in Pudasaini & Hutter (Pudasaini & Hutter 2003 J. Fluid Mech. 495, 193–208). The intention was to be able to describe the flow of a finite mass of snow, gravel, debris or mud, down a curved and twisted corrie of nearly arbitrary cross-sectional profile. The governing equations for the distribution of the avalanche thickness and the topography-parallel depth-averaged velocity components are a set of hyperbolic partial differential equations. They are solved for different topographic configurations, from simple to complex, by applying a high-resolution non-oscillatory central differencing scheme with total variation diminishing limiter. Here we apply the model to a channel with circular cross-section and helical talweg that merges into a horizontal channel which may or may not become flat in cross-section. We show that run-out position and geometry depend strongly on the curvature and twist of the talweg and cross-sectional geometry of the channel, and how the topography is shaped close to run-out zones.

A two‐phase mechanical model for rock‐ice avalanches

Rock-ice avalanche events are among the most hazardous natural disasters in the last century. In contrast to rock avalanches, the solid phase (ice) can transform to fluid during the course of the rock-ice avalanche and fundamentally alter mechanical processes. A real two-phase debris flow model could better address the dynamic interaction of solid (rock and ice) and fluid (water, snow, slurry, and fine particles) than presently used single-phase Voellmy- or Coulomb-type models. We present a two-phase model capable of performing dynamic strength weakening due to internal fluidization and basal lubrication and internal mass and momentum exchanges between the phases. Effective basal and internal friction angles are variable and correspond to evolving effective solid volume fraction, friction factors, volume fraction of the ice, true friction coefficients, and lubrication and fluidization factors. Benchmark numerical simulations demonstrate that the two-phase model can explain dynamically changing frictional properties of rock-ice avalanches that occur internally and along the flow path. The interphase mass and momentum exchanges are capable of demonstrating the mechanics of frontal surge head and multiple other surges in the debris body. This is an observed phenomenon in a real two-phase debris flow, but newly simulated here by applying the two-phase mass flow model. Mass and momentum exchanges between the phases and the associated internal and basal strength weakening control the exceptional long runout distances, provide a more realistic simulation especially during the critical initial and propagation stages of avalanche, and explain the exceptionally high and dynamically changing mobility of rock-ice avalanches.

Avalanching granular flows down curved and twisted channels: Theoretical and experimental results

Depth evolution and final deposits play a crucial role in the description of the dynamics of granular avalanches. This paper presents new and important results on the geometric deformation and measurements of avalanche depositions in laboratory granular flows and their comparisons with theoretical predictions through some benchmark problems for flows down curved and twisted channels merging into a horizontal plane. XY-table and analoglaser sensor are applied to measure geometries of deposited masses in the fanlike open transition and runout zones for different granular materials, different channel lengths, and different channel mouths in the runout zone. The model equations proposed by Pudasaini and Hutter [“Rapid shear flows of dry granular masses down curved and twisted channels,” J. Fluid Mech. 495, 193 (2003)] are used for theoretical prediction. We show that geometric parameters such as curvature, twist and local details of the channel play a crucial role in the description of avalanching debris and ...

Landslide-generated tsunami and particle transport in mountain lakes and reservoirs

Abstract Gravitational mass flows may generate tsunamis as they hit water bodies such as oceans, reservoirs or mountain lakes. Upon impact, they can generate tremendous particle-laden or debris flows and floods. Rapidly cascading waves down mountain slopes can trigger debris flows or floods, potentially causing huge damage to civil structures and endangering life. Here we apply a general two-phase mass flow model (Pudasaini, 2012), and present three-dimensional (3-D), high-resolution simulations for a real two-phase debris impacting a fluid reservoir. An innovative formulation provides an opportunity, within a single framework, to simulate simultaneously the sliding two-phase debris/landslide, reservoir, debris impact at reservoir, water-wave generation, propagation and mixing, and separation between solid and fluid phases. The results demonstrate formation and propagation of very special solid and fluid structures in the reservoir, propagation of submarine debris, turbidity currents, and complex interactions between the subaerial debris, surface tsunami and submarine debris waves. Our results reveal that the submerge timescaling for a deformable two-phase debris deviates substantially from the same for a non-deformable solid. These results substantially increase our understanding of 3-D complex multiphase systems/flows. This allows for the proper modeling of landslide/debris-induced mountain tsunami, dynamics of turbidity currents and highly concentrated sediment transports in Himalayan and Alpine slopes and channels, with associated applications to engineering, environmental and hazard-mitigation plans.

Buoyancy induced mobility in two-phase debris flow

This paper shows that buoyancy enhances mobility in two-phase debris flow with an analysis based on the generalized two-phase debris flow model proposed by Pudasaini [1]. The model (the most generalized two-phase flow model to date) incorporates many essential physical phenomena, including solid-volume-fraction-gradient-enhanced non-Newtonian viscous stress, buoyancy, virtual mass and a generalized drag force. We find a strong coupling between the solid- and the fluid-momentum transfer, where the solid normal stress is reduced by buoyancy, which in turn diminishes the frictional resistance, enhances the pressure gradient, and reduces the drag on the solid component. This leads to higher flow mobility. Numerical results show that the model can adequately describe the dynamics of buoyancy induced mobility in two-phase debris flows, and produces observable geometry of flowing mass in the run-out zone. The results presented here are consistent with the physics of the flow.