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  • 1
    Electronic Resource
    Electronic Resource
    Similarity solutions for granular avalanches of finite mass with variable bed friction (1989)
    Springer
    Continuum mechanics and thermodynamics 1 (1989), S. 239-265 
    Details
    ISSN: 1432-0959
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract This paper continues a series of studies on the plane flow of a pile of cohesionless granular material down a rough inclined plane. Internal and basal friction laws are assumed to obey the Mohr-Coulomb yield criterion but in contrast to previous investigations the angle of friction at the bottom of the pile is considered to depend on the position or on the velocity or on both. Similarity, i.e. shape preserving solutions are constructed. The depth of the pile and the profile of the total minus the centre of mass velocity are determined analytically, but the total length and the position of the centre of mass are calculated numerically. If the basal friction angle is constant, the centre of mass moves with constant acceleration and the length of the pile extends monotonically. These motions change, when the angle of friction varies along the pile — the length of the pile may extend, contract or remain stationary and the centre of mass motion may decelerate or even reach steady state. Eight special cases are exhibited which demonstrate the influence of the friction law on the speed and spread of the pile.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01125776
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Ping-pong ball avalanche at a ski jump (1998)
    Springer
    Archive for history of exact sciences 1 (1998), S. 51-56 
    Details
    ISSN: 1432-0657
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Natural Sciences in General
    Notes: Abstract Three dimensional granular flow experiments were carried out on a ski jump with 300,000 ping-pong balls. Since the air drag was a large effect, the flow arrived at a steady state within a short distance. The terminal velocities attained showed a remarkable increase with the number of released balls. In addition, the flow formed a distinct head and tail structure, which has often been observed in large-scale geophysical flows in nature. Similarity analysis is used to show that the experiment corresponds to a natural snow avalanche that runs for several kilometers. Video cameras positioned above the flow allowed the measurement of the location and the distance of a single ball, which finally led to the particle velocity profiles. The static pressure depression measurements in and above the flow showed the air velocity profiles and suggested the strong interaction between the balls and the surrounding fluid(air). Computer simulation of 3-dimensional, inhomogeneous two-phase flows that uses the DEM for the particles and the Reynolds-averaged Navier Stokes equations for the fluid are currently in progress.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/PL00010911
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  • 3
    Electronic Resource
    Electronic Resource
    Two-dimensional spreading of a granular avalanche down an inclined plane Part I. theory (1993)
    Springer
    Acta mechanica 100 (1993), S. 37-68 
    Details
    ISSN: 1619-6937
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary This paper is concerned with the motion of an unconfined finite mass of a granular material released from rest on an inclined plane. The granular mass is treated as a frictional Coulomb-like continuum with a Coulomb-like basal friction law. Depth averaged equations are deduced from the three-dimensional dynamical equations by scaling the equations and imposing the shallowness assumption that the moving piles are long and wide but not deep. Several distinguished limits for small depth to length and depth to width ratios can be analysed. We develop an approximate theory based upon the full dynamical equations parallel to the inclined plane and imposed hydrostatic pressure conditions perpendicular to it. The resulting model equations are then applied to construct either yet simpler model equations or else solutions for particular cases. In a first application the transverse distributions of the velocity fields and of the depth profile are prescribed, while representative values of these functions (such as the cross sectional averages or maxima) as functions of time and the downhill coordinate are left unspecified. For these quantities evolution equations are obtained from a lateral averaging of the vertically averaged equations. In a second application approximate similarity solutions of the spatially two-dimensional equations are derived. The depth and velocity profiles for the moving mass are determined in analytical form, and the evolution equation for the total length and the total width of the pile is integrated numerically. A parameter study illustrates the performance of the model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01176861
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  • 4
    Electronic Resource
    Electronic Resource
    Similarity solutions for a Voellmy model of snow avalanches with finite mass (1990)
    Springer
    Acta mechanica 82 (1990), S. 99-127 
    Details
    ISSN: 1619-6937
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary This paper, though independently written, continues an analysis of similarity solutions for the two-dimensional flow of a mass of cohesionless granular material down rough, flat and curved beds, see Savage and Nohguchi [12], Nohguchi, Hutter and Savage [7]. The basal friction force is assumed to be composed of a Mohr-Coulomb type component with a bed friction angle that is position dependent plus a viscous Voellmy-type resistive stress, that is proportional to the velocity squared. This granular flow model is conjectured to adequately model the motion and dispersion of flow avalanches of snow whose air borne powder component can be ignored. The depth and velocities relative to those of the centre of mass of the moving pile are determined analytically, and it is shown that the pile has a parabolic cap shape and the difference velocity varies linearly with distance from the centre of mass. The length and the position and velocity of the centre mass are calculated numerically. We explicitly show: (i) Existence of a rigid body motion of the moving pile requires either a variable bed friction angle or a bed with gradually varying bed inclination angle or both. (ii) A model avalanche with no Voellmy-type resistive drag on a plane bed will accelerate for ever. (iii) Along a plane bed the centre of mass can reach a final equilibrium speed only when the Voellmy type drag is accounted for and the basal friction angle varies with position. (iv) Along curved beds rigid body motions of the moving pile are possible with accelerating, decelerating and steady centre of mass motions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01173741
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Similarity solutions for avalanches of granular materials down curved beds (1988)
    Springer
    Acta mechanica 75 (1988), S. 153-174 
    Details
    ISSN: 1619-6937
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary The present paper investigates similarity solutions for the two-dimensional flow of a mass of cohesionless granular material down rough curved beds having gradually varying slopes. The work is relevant to the motion of rockfalls and loose snow flow avalanches. The depth and velocity profiles for the moving mass are determined in analytical form and the evolution equation for the total length of the pile is integrated numerically using a Runge-Kutta technique. Although similarity solutions can occur for general bed shapes (as long as the curvature is small), specific computations are performed here for two families of bed profiles, one which is in the shape of a circular arc and the other in which the slope decays exponentially with downstream distance. The pile of granular material starts from rest, initially accelerates and then decelerates, finally coming to rest as a result of bed friction and the gradually decreasing bed slope. Depending upon the frictional parameters, the shape of the bed and the initial depth to length of the pile, it is found that the variation of total length with time can exhibit different behaviours. The pile can grow monotonically, it can asymptote to a constant length, it can grow to a maximum and then decrease or it can decrease to a minimum and then increase with time. Furthermore, there are regions in parameter space for which the pile moves as a rigid body either for the whole time of travel or for portions of it.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01174633
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    Paper (German National Licenses)
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