Determination of Avalanche Dynamics Friction Coefficients from Measured Speeds

An avalanche dynamics model, appropriate for complex terrain, for real avalanche paths was developed by Perla, Cheng and McClung in 1980. The model has two friction terms, one for sliding friction which is independent of speed, and one for turbulent friction which is proportional to V2, where V is the centre-of-mass speed along the incline. By introducing speed maxima for avalanches, along with start and stop reference positions, it is possible to determine the the two constant friction coefficients for the model. When this is done, it is found that speed data often exceed a model speed limit implied by the application of V = 0 at the start and stop positions. This effect is illustrated by analytic solutions of the relevant equations, as well as numerical solutions for actual avalanche paths. Some limitations and properties of the fundamental modelling are outlined and suggestions given for future use of such models.

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Calculations of Avalanche Friction Coefficients from Field Data

Journal of Glaciology ◽

10.3189/s0022143000010650 ◽

1980 ◽

Vol 26 (94) ◽

pp. 109-119 ◽

Cited By ~ 1

Author(s):

M. Martinelli ◽

T. E. Lang ◽

A. I. Mears

Keyword(s):

Internal Friction ◽

Field Data ◽

Sliding Friction ◽

Surface Friction ◽

Kinetic Friction ◽

Friction Coefficients ◽

Turbulent Friction ◽

Coefficient Of Sliding Friction ◽

Avalanche Dynamics ◽

Slow Moving

AbstractThe friction coefficients needed to solve Voellmy’s avalanche-dynamics equations and as input to the numerical, finite-difference computer program AVALNCH are calculated from case studies. The following coefficients of internal friction v and of surface friction f worked well for program AVALNCH: for midwinter dry snow v = 0.5 to 0.55 m2/s and f = 0.5 to 0.55; for hard slab v = 0.7 to 0.8 m2/s and f = 0.7 to 0.8; for fresh, soft slab v = 0.4 to 0.5 m2/s and f = 0.4 to 0.5. The program predicted run-out distance well for a variety of conditions but performed less well in cases of sharp, adverse grade in the run-out zone. For the Voellmy approach, large design-size avalanches required turbulent friction coefficients ξ of 1200 to 1600 m/s2 and kinetic friction coefficients of 0.15. Two hard-slab avalanches, a slow-moving,wet-slab avalanche, and a soft-slab avalanche that ran through scattered mature timber required ξ of 700 to800 m/s2 and μ of 5/V when V is velocity in m/s. The coefficient of sliding friction for a hard-slab avalanchethat encountered damp snow in the run-out zone was computed directly from movies to be 0.35, 0.43, and 0.32 for three measured sections of the run-out zone.

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Calculations of Avalanche Friction Coefficients from Field Data

Journal of Glaciology ◽

10.1017/s0022143000010650 ◽

1980 ◽

Vol 26 (94) ◽

pp. 109-119 ◽

Cited By ~ 20

Author(s):

M. Martinelli ◽

T. E. Lang ◽

A. I. Mears

Keyword(s):

Internal Friction ◽

Field Data ◽

Sliding Friction ◽

Surface Friction ◽

Kinetic Friction ◽

Friction Coefficients ◽

Turbulent Friction ◽

Coefficient Of Sliding Friction ◽

Avalanche Dynamics ◽

Slow Moving

AbstractThe friction coefficients needed to solve Voellmy’s avalanche-dynamics equations and as input to the numerical, finite-difference computer program AVALNCH are calculated from case studies. The following coefficients of internal frictionvand of surface frictionfworked well for program AVALNCH: for midwinter dry snowv =0.5 to 0.55 m2/s andf= 0.5 to 0.55; for hard slabv =0.7 to 0.8 m2/s andf =0.7 to 0.8; for fresh, soft slabv= 0.4 to 0.5 m2/s and f = 0.4 to 0.5. The program predicted run-out distance well for a variety of conditions but performed less well in cases of sharp, adverse grade in the run-out zone. For the Voellmy approach, large design-size avalanches required turbulent friction coefficients ξ of 1200 to 1600 m/s2and kinetic friction coefficients of 0.15. Two hard-slab avalanches, a slow-moving,wet-slab avalanche, and a soft-slab avalanche that ran through scattered mature timber required ξ of 700 to800 m/s2and μ of 5/V whenVis velocity in m/s. The coefficient of sliding friction for a hard-slab avalanchethat encountered damp snow in the run-out zone was computed directly from movies to be 0.35, 0.43, and 0.32 for three measured sections of the run-out zone.

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The influence of vertical density and velocity distributions on snow avalanche runout

Annals of Glaciology ◽

10.3189/172756410791386409 ◽

2010 ◽

Vol 51 (54) ◽

pp. 200-206 ◽

Cited By ~ 2

Author(s):

Ashok K. Keshari ◽

Deba P. Satapathy ◽

Amod Kumar

Keyword(s):

Flux Distribution ◽

Numerical Solutions ◽

Model Parameters ◽

Dynamics Model ◽

Turbulent Friction ◽

One Dimensional ◽

Variation Diminishing ◽

Flow Features ◽

Vertical Density ◽

Two Fluid

AbstractA one-dimensional avalanche dynamics model accounting for vertical density and velocity distributions is presented. Mass and momentum flux distribution factors are derived to incorporate the effect of density and velocity variations within the framework of depth-integrated models. Using experiments of avalanche flows on an inclined snow chute at Dhundhi, Manali, India, we conceptualize snow flow rheology as a Voellmy fluid where the distribution of internal shearing is given by a Newtonian fluid (NF) or Criminale–Ericksen–Filbey fluid (CEFF). Then the generalized mass and momentum distribution factors are computed for these two fluid models for different density stratifications. Numerical solutions are obtained using a total variation diminishing Lax–Friedrichs (TVDLF) finite-difference method. The model is validated with the experimental results. We find that the flow features of the chute experiments are simulated well by the model. The velocities and runout distances are obtained for the Voellmy model with both NF and CEFF extensions for various input volumes, and the optimum values of the model parameters, namely, coefficients of dynamic and turbulent friction, are determined.

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Observed Maximum Run-Out Distance of Snow Avalanches and the Determination of the Friction Coefficients µ and ξ

Journal of Glaciology ◽

10.3189/s0022143000010662 ◽

1980 ◽

Vol 26 (94) ◽

pp. 121-130 ◽

Cited By ~ 6

Author(s):

Othmar Buser ◽

Hans Frutiger

Keyword(s):

Extreme Values ◽

Field Observations ◽

Snow Avalanches ◽

Hazard Maps ◽

Friction Coefficients ◽

Avalanche Hazard ◽

Long Run ◽

Avalanche Dynamics ◽

Very High

AbstractTo fix the limits of different hazards in the avalanche-hazard maps one uses criteria pertaining to avalanche dynamics. These criteria are at present the velocity and the run-out distance of a given avalanche for a given place. In 1955 A. Voellmy published his theory of avalanche dynamics which has widely been used in practical map preparation. Since 1962 his equations have also been used by the Eidg. Institut für Schnee- und Lawinenforschung (EISLF) to calculate avalanche pressures and run-out distances. Furthermore B. Salm (EISLF) developed another equation for the calculation of run-out distances in 1978. Both the equations of Voellmy and of Salm contain two friction coefficients, µ and ξ. Little is known about them and opinions, even among specialists, differ on what values should be given to them.This paper presents field observations on very long run-out distances. These observations are used to calculate values for pairs of µ and ξ. For avalanche zoning, only extreme values are of interest, i.e. very low values for µ and very high values for ξ. For the calibration of those coefficients, ten avalanches from the winters 1915–16, 1967–68, 1974–75, and 1977–78 have been used. Those avalanches occurred during heavy and intense snowfalls. For those avalanches, the pair µ= 0.155, ξ = 1 120 m/s2 was found for the Voellmy equation and the pair µ = 0.157, ξ =1 067 m/s2 for the Salm equation. These values only partially agree with those used up to date by EISLF. It is recommended for example that for extreme flowing avalanches (newly fallen snow, soft slabs) the pair µ = 0.16,ξ = 1 360 m/s2 be used.

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Observed Maximum Run-Out Distance of Snow Avalanches and the Determination of the Friction Coefficients µ and ξ

Journal of Glaciology ◽

10.1017/s0022143000010662 ◽

1980 ◽

Vol 26 (94) ◽

pp. 121-130 ◽

Cited By ~ 52

Author(s):

Othmar Buser ◽

Hans Frutiger

Keyword(s):

Extreme Values ◽

Field Observations ◽

Snow Avalanches ◽

Hazard Maps ◽

Friction Coefficients ◽

Avalanche Hazard ◽

Long Run ◽

Avalanche Dynamics ◽

Very High

AbstractTo fix the limits of different hazards in the avalanche-hazard maps one uses criteria pertaining to avalanche dynamics. These criteria are at present the velocity and the run-out distance of a given avalanche for a given place. In 1955 A. Voellmy published his theory of avalanche dynamics which has widely been used in practical map preparation. Since 1962 his equations have also been used by the Eidg. Institut für Schnee- und Lawinenforschung (EISLF) to calculate avalanche pressures and run-out distances. Furthermore B. Salm (EISLF) developed another equation for the calculation of run-out distances in 1978. Both the equations of Voellmy and of Salm contain two friction coefficients,µandξ. Little is known about them and opinions, even among specialists, differ on what values should be given to them.This paper presents field observations on very long run-out distances. These observations are used to calculate values for pairs ofµandξ. For avalanche zoning, only extreme values are of interest, i.e. very low values forµand very high values forξ. For the calibration of those coefficients, ten avalanches from the winters 1915–16, 1967–68, 1974–75, and 1977–78 have been used. Those avalanches occurred during heavy and intense snowfalls. For those avalanches, the pairµ= 0.155,ξ= 1 120 m/s2was found for the Voellmy equation and the pairµ= 0.157,ξ=1 067 m/s2for the Salm equation. These values only partially agree with those used up to date by EISLF. It is recommended for example that for extreme flowing avalanches (newly fallen snow, soft slabs) the pairµ= 0.16,ξ= 1 360 m/s2be used.

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New Equation for Predicting Pipe Friction Coefficients Using the Statistical Based Entropy Concepts

Entropy ◽

10.3390/e23050611 ◽

2021 ◽

Vol 23 (5) ◽

pp. 611

Author(s):

Yeon-Woong Choe ◽

Sang-Bo Sim ◽

Yeon-Moon Choo

Keyword(s):

Friction Coefficient ◽

Accurate Determination ◽

Mean Velocity ◽

Friction Coefficients ◽

Flow Discharge ◽

Comparison Results ◽

Flow Loss ◽

Key Variables ◽

New Equation

In general, this new equation is significant for designing and operating a pipeline to predict flow discharge. In order to predict the flow discharge, accurate determination of the flow loss due to pipe friction is very important. However, existing pipe friction coefficient equations have difficulties in obtaining key variables or those only applicable to pipes with specific conditions. Thus, this study develops a new equation for predicting pipe friction coefficients using statistically based entropy concepts, which are currently being used in various fields. The parameters in the proposed equation can be easily obtained and are easy to estimate. Existing formulas for calculating pipe friction coefficient requires the friction head loss and Reynolds number. Unlike existing formulas, the proposed equation only requires pipe specifications, entropy value and average velocity. The developed equation can predict the friction coefficient by using the well-known entropy, the mean velocity and the pipe specifications. The comparison results with the Nikuradse’s experimental data show that the R2 and RMSE values were 0.998 and 0.000366 in smooth pipe, and 0.979 to 0.994 or 0.000399 to 0.000436 in rough pipe, and the discrepancy ratio analysis results show that the accuracy of both results in smooth and rough pipes is very close to zero. The proposed equation will enable the easier estimation of flow rates.

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A numerical study of the interaction between unsteay free-stream disturbances and localized variations in surface geometry

Journal of Fluid Mechanics ◽

10.1017/s0022112089003113 ◽

1989 ◽

Vol 209 ◽

pp. 285-308 ◽

Cited By ~ 35

Author(s):

R. J. Bodonyi ◽

W. J. C. Welch ◽

P. W. Duck ◽

M. Tadjfar

Keyword(s):

Numerical Solutions ◽

Free Stream ◽

Stokes Equations ◽

Numerical Study ◽

Navier Stokes ◽

Surface Geometry ◽

Navier Stokes Equations ◽

S Waves ◽

Tollmien Schlichting

A numerical study of the generation of Tollmien-Schlichting (T–S) waves due to the interaction between a small free-stream disturbance and a small localized variation of the surface geometry has been carried out using both finite–difference and spectral methods. The nonlinear steady flow is of the viscous–inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier–Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of the T–S waves generated by the interaction between the free-stream disturbance and the surface distortion, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the T–S waves.

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Parameter Study of Offset Press Cylinder Based on Sliding Friction

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.174.299 ◽

2010 ◽

Vol 174 ◽

pp. 299-302 ◽

Cited By ~ 1

Author(s):

Hai Yan Zhang ◽

He Ping Hou ◽

Jun Feng Si ◽

Xiao Yu Chen

Keyword(s):

Contact Area ◽

Sliding Friction ◽

Accurate Determination ◽

Rolling Process ◽

Elastic Cylinder ◽

Parameter Study ◽

Cylinder Radius ◽

Printing Quality ◽

Dot Gain

In the contact area of offset, a relative slide occurs between the surface of plate cylinder and blanket cylinder, which changes the print image and influences the printing quality. The relative slide in the cylinders’ rolling process is investigated, and the determination rule of cylinders’ geometric parameters of offset press is proposed. The results show that the relative slide is minimization under the condition that the compression of elastic cylinder radius is 0.2 times bigger than that of rigid cylinder radius, and the deformation of print image and dot gain both are minimization. The results provide theoretical direction for accurate determination of cylinder radius of offset press.

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New cosmological solutions in hybrid metric-Palatini gravity from dynamical symmetries

Modern Physics Letters A ◽

10.1142/s0217732321501005 ◽

2021 ◽

pp. 2150100

Author(s):

Andronikos Paliathanasis

Keyword(s):

Conservation Laws ◽

Integrable Systems ◽

Functional Form ◽

Analytic Solutions ◽

Momentum Conservation ◽

Field Equations ◽

Dynamical Symmetries ◽

Cosmological Solutions ◽

Liouville Integrable

We investigate the existence of Liouville integrable cosmological models in hybrid metric-Palatini theory. Specifically, we use the symmetry conditions for the existence of quadratic in the momentum conservation laws for the field equations as constraint conditions for the determination of the unknown functional form of the theory. The exact and analytic solutions of the integrable systems found in this study are presented in terms of quadratics and Laurent expansions.

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