The interaction between rapid

granular flows and braking mounds:

an experimental study

at a range of physical scales

Kristín Martha Hákonardóttir1�2, Tómas Jóhannesson1,

Andrew J. Hogg2, Martin Kern3, Felix Tiefenbacher3

November 1, 2004

1The Icelandic Meteorological Office, Bústaðavegur 9, IS-150, Reykjavík,

Iceland.

2Centre for Environmental & Geophysical Flows, School of Mathematics,

University of Bristol, BS8 1TW Bristol, England.

3Swiss Federal Institute for Snow and Avalanche Research,

Flüelastrasse 11, CH-7260 Davos Dorf, Switzerland.

Abstract

The scale dependence of the interaction between supercritical granular

flows and relatively low obstacles, in which the flow is launched directly

1

over the obstacles, is studied experimentally. Series of laboratory exper-

iments at several physical scales using different granular materials were

conducted. The experiments suggest that the flow dynamics around the

obstacles are governed, to leading order, by the geometry of the obstacles

and the large-scale properties of the flowing avalanche, measured by the

Froude number, rather than the micro-scale properties of the granular cur-

rent. Small-scale laboratory experiments may therefore be useful tools to

study the retarding effect of natural-scale protection measures against dry-

snow avalanches and may provide guidance on their design.

1 Introduction

Braking mounds are defense structures designed to retard snow avalanches. They

have widely been used for protection against dense, wet-snow avalanches, but

have also been built to retard dry-snow avalanches. Their effect on large dry-snow

avalanches is the focus of this study. Braking mounds are typically arranged in

rows perpendicular to the direction of the avalanche flow. Several rows of braking

mounds are sometimes positioned upstream of a catching dam in order to slow the

avalanche down before it hits the dam and thereby reduce the height of the dam

that is required to stop the avalanche. At present, there exist no widely accepted

guidelines for the design of such structures. Braking mounds have often been de-

signed with a conical shape, since that is the most convenient and economic shape

of such structures constructed from loose materials. The height of the mounds is

typically a few times the depth of the dense core of a dry-snow avalanche (see

e.g. McClung and Schaerer (1993)).

2

Laboratory experiments to study the retarding effect of avalanche braking

mounds were undertaken during 1999–2001, as a part of the design of braking

mounds above the town Neskaupstaður, eastern Iceland (Tómasson and others,

1998). Figure 1 shows a photograph of one of the mounds. The experiments are

described by Hákonardóttir and others (2003c). The experiments were scaled so

that the Froude number of the flow matched that realised in naturally occurring

avalanches, thus maintaining dynamical similarity with the dense core of large

dry-snow avalanches. In this context the Froude number is defined as

Fr�upg�h

� (1)

whereu is the flow speed,g� � gcosψ is the normal component of the gravita-

tional acceleration,ψ is the slope of the terrain, andh is the flow depth. Observa-

tions suggest that the dense core of a natural dry-snow avalanche is supercritical

(Fr� 1) with a Froude number in the range 5–10 (Issler, 2003).

These experiments revealed a number of interesting aspects of the interaction

of high Froude number, granular flow with mounds of a height that is just a few

times the flow depth. These include: the formation of a coherent airborne jet

launched from the top of the obstacle; a complicated three-dimensional structure

of the flow as the particulate current was deflected vertically and laterally; and

considerable mixing of streams, that were deflected from adjacent obstacles. The

airborne jets followed parabolic paths through the air before landing back on the

ground. Formation of such airborne jets has important practical consequences for

the use of multiple rows of defense structures to retard avalanches. Spacing be-

tween the rows must be chosen sufficiently large so that snow launched from the

3

first row of mounds does not jump over subsequent rows farther down the slope.

Furthermore, the experiments showed that one row of steep mounds with a height

approximately twice the flow depth, can shorten the run-out of the avalanche be-

yond the obstacles by 30–40%. Hákonardóttir and others (2003c) concluded that

the shortening of the run-out was brought about by irregularities and mixing of the

flow caused by the presence of the mounds. The retarding effect of the mounds

would thereby depend to a large degree on the exact geometry and layout of the

mounds. The experimental observations were finally used to deduce the optimal

geometry and layout of braking mounds for maximum retardation of the flow.

The experiments reported here extend the work of Hákonardóttir and oth-

ers (2003c) and Faug and others (2003) and collate series of experiments that have

either appeared as technical reports, short papers or have remained unpublished

(see references in §2). Experiments with identical obstacle setups were conducted

at four different length-scales, using either small glass particles or snow, in or-

der to investigate whether Froude number scaling would be sufficient to maintain

dynamical similarity in the interaction, and thereby confirm the findings of the ear-

lier laboratory experiments regarding the optimal geometry and layout of braking

mounds. The experimental results reported here have been used to formulate the

first systematic ideas regarding the design of avalanche braking mounds (Jóhan-

nesson and Hákonardóttir, 2003).

The study starts with a brief description of the experimental setup (§2) and de-

sign (§3). The experimental results are reported in §4. The throw angle (defined

as the angle at which the airborne jets leave the obstacles) and the dissipation

of kinetic energy at the upstream face of the obstacles are studied in §4.2.1 and

4

the relative run-out shortening by different mound and dam setups are reported in

§4.2.2. Finally in §5, some general conclusions are drawn regarding the interac-

tion of natural-scale, dry-snow avalanches with braking mounds.

2 Experimental setup

In the experiments, particles were instantaneously released down an inclined chute

to form a rapid granular flow. The flow interacted with obstacles close to the end

of the upper most section of the chute, see Figure 2. The chutes consisted of two

or more planar sections, where the upper most section was steep (� 40�) and the

lower most section was almost horizontal (� 10�). The chutes ranged in length

and width from 3 to 34 m and 0.2 to 2.5 m, respectively. Table 1 summarizes the

dimensions of the different experimental chutes.

The original experimental series, Ballotini (i), was conducted on a chute of dy-

namic friction angle 21�0��0�5�, in Bristol, UK. Ballotini (ii) was carried out on a

smaller chute of dynamic friction angle 17�5��0�5� situated in Reykjavík, Iceland

and Ballotini (iii) at a larger chute of dynamic friction angle 20��1� at the Swiss

Federal Institute of Snow and Avalanche Research (SLF) in Davos, Switzerland.

Experiments with snow were conducted on a 34 m long chute on Weissfluhjoch,

above Davos, also owned by SLF (see Tiefenbacher and Kern (2004) for a detailed

description). The Ballotini (ii) and (iii) series are described by Hákonardóttir and

others (2001) and experiments with wet snow are described by Hákonardóttir and

others (2003b) and (2003d).

The particles within the flows varied from small, almost spherical and approx-

5

imately uniformly sized glass beads (ballotini) to both wet and granular, and dry

and powdery snow. A few experiments were additionally conducted on the 10 m

long chute at SLF, using coarse, angular sand. Those experiments will only be

mentioned briefly in §4.2.2. The ballotini beads had a mean diameter of 90µm,

bulk density of 1600 kg m�3 and an internal friction angle of approximately 22�.

The wet and dry flowing snow had densities and particle sizes in the range 350–

400 kg m�3 and 0.002–0.1 m, and 250–350 kg m�3 and 0.001–0.1 m, respectively.

All the obstacles but the conical mounds had a planar upstream face normal

to the experimental chutes. The obstacles spanned different proportions of the

chutes and were of varying heights and widths as will be described in §3.

2.1 Experiments with dry granular flows

The progression of the flows down the chutes and the interaction with the obstacles

were recorded using video cameras recording at a rate of 25 frames per second.

The speed of the flow front was measured by video analysis, while the surface

speed of the interior of the flow was measured by tracking tracer particles in the

flow. High speed cameras were additionally used for measurements of internal

speeds of the flows in Ballotini (i) and Ballotini (iii). The experimental chute in

Davos, where the Ballotini (iii) experiments were conducted, was also equipped

with optical velocity sensors at the basal surface of the upper section of the chute.

Basal velocity measurements of the flows were obtained through cross correlation

of the signals from the sensors and could be compared with the surface and interior

velocity measurements (see McElwaine and Tiefenbacher (2003) for a description

6

of the sensors and the measurement technique).

The maximum flow depth on the chutes was measured by fixing a gate in

the flow path at a known distance from the base of the chutes. The height of

the gate above the base was then increased systematically until all of the current

(following the flow head) flowed under the gate without touching it. The internal

friction angle was measured by building up a cone of particles on a horizontal

plane and repeatedly measuring the height and the diameter of the cone. The

dynamic bed friction angle was determined by tilting a plane with a thin layer of

moving material until the angle at which the layer stopped was found.

The flows came to rest on the lower section of the chutes, where the run-out

length and deposit thickness were measured.

2.2 Experiments with snow

Snow experiments were conducted during two weeks in the winters 2002 and

2003. Air temperature in the mountain during the experimental week in 2002 was

approximately 0�C and the snow was granular and wet. During the experiments

in 2003, temperature at Weissfluhjoch was on average�15�C and the snow was

fine, dry and powdery.

A volume of approximately 5 m3 of snow was shovelled manually onto the

chute behind a lock gate. After the release of the gate, the snow flowed down

the chute and carried on down the mountainside until arresting on the ski slope

underneath. Rubber bars were placed on the base of the chute between the lock

gate and the barriers to agitate the flow. The progression of the avalanches down

7

the chute was recorded using two video cameras, each recording 25 frames per

second.

The flow depth was measured from video footage of the experiments. Flow

speed at different locations upstream and downstream of the obstacles was ob-

tained through cross correlation of signals from optical sensors (McElwaine and

Tiefenbacher, 2003). A row of basal velocity sensors and an array of sensors at the

side of the chute were positioned just upstream of the obstacles and another row

of basal sensors was positioned downstream from the obstacles, see Figure 2b.

Due to lack of space on the mountainside at Weissfluhjoch, it was not possible

to build a run-out section which was long enough for the flow to come to rest

on the chute and thus compare the effect of different mound and dam geometries

by measurements of the run-out. The flow speed upstream of the obstacles and

downstream of the point where the jets landed were measured instead, using the

optical velocity sensors. The difference in the measured speed downstream of the

landing point of the jets allowed for comparison of the retarding effect between

the different mound and dam setups.

3 Experimental design

The experiments were scaled with the Froude number, such that the flow depth

and the flow speed squared were reduced by factors of 10 to 1000 relative to those

of the dense core of a large, natural dry-snow avalanche, while maintaining an

approximately constant Froude number, Fr� 10.

A number of different configurations of the obstacles were tested in the initial

8

experimental series, Ballotini (i), which is reported by Hákonardóttir and others

(2003c). These experiments indicated an importance of a steep upstream face of

the obstacles for obtaining maximum retarding effect. The experiments further

revealed that many narrow mounds were more effective in retarding the flow than

fewer and wider mounds blocking the same proportion of the flow path (60%) and

than a dam spanning the entire width of the flow path, if the height of the obstacles

was up to twice the depth of the flow.

Experiments with a few carefully chosen obstacle configurations were re-

peated at different scales in order to study the scale dependence of the experi-

mental results summarized above. The run-out shortening in a configuration of

a few wide mounds, termed ‘datum mounds’ (DM) was compared to the run-out

reduction of: more and narrower mounds (NM) blocking the same proportion of

the flow path; conically shaped mounds (CM) blocking a similar proportion of

the flow path; and a continuous dam (Dam). The height of the obstacles was sys-

tematically changed in all of the setups, such that the obstacles had a height that

was one to five times the depth of the flow, while the aspect ratio of the mounds

(here defined as the ratio between the height and width of a mound) and the ob-

structed proportion of the flow path were kept fixed. Trajectories of jets which

were launched over continuous dams were analysed and throw angles and energy

dissipation at the upstream dam faces were studied. The different obstacle setups

are sketched in Figure 3 and listed in Table 2.

The barriers were positioned close to the upstream edge of the lower chute

section in the Ballotini (ii) and (iii) series. This section was inclined at an angle

of approximately 10� to the horizontal in order to maintain similarity in the slope,

9

between experiments and mounds in run-out zones of natural snow avalanches.

In the original series, Ballotini (i), the mounds were positioned on a curved metal

sheet, inclined at 30� to the horizontal, connecting the two chute sections smoothly.

The mounds were positioned on a slope of 32� in the snow experiments. In all of

the experimental series, the inclination of the upper chute section was chosen such

that the current had a Froude number of the order 10, except in the experiments

on the Weissfluhjoch snow chute, where it was not possible to obtain such high

Froude numbers, as will be discussed in the following section (§4.1).

4 Results

4.1 Flow description

Flow properties in the different experimental series are listed in Table 3. The

experiments with snow differed from the dry granular experiments in that the snow

mass contained both fine grains and larger snow lumps and the wetness of the

snow changed between individual experiments. The wetter flows were in general

thicker and slower than the dry ones. The Froude numbers in these experiments

were in the range 3–6, varying with each experimental run, depending on the

condition of the snow. These were the highest Froude numbers that could be

realised with the experimental setup and they were somewhat lower than those of

large, natural dry-snow avalanches. When the snow was released it extended 5 to

6 m behind the lock gate. After the release, the avalanche spread longitudinally

on the chute and had a length of approximately 8 m before reaching the mounds.

10

The dry granular currents (ballotini) had a relatively dilute and agitated head,

followed by a denser and thinner, body which flowed almost steadily with a close

to constant speed and depth. Finally there was a significantly thinner and slower

tail.

The duration of each avalanche was approximately 2 s, of which the steady

flow phase lasted for just under 1 s in all the experiments (including the snow

experiments). The ratio between the flow depth and the length of the flow was

thus much smaller for the snow than the ballotini currents, leading to a more

‘impulsive’ event rather than the approximately steady flow which was observed

in the experiments at the smaller scales.

It was difficult to measure the flow depth and speed upstream of the obstacles

that were positioned just downstream of the break in the slope (see Figure 2a).

Instead the flow speed and depth were measured at the downstream end of the

upper chute section. The distance from the break in the slope to the obstacles

was approximately five times the flow depth, chosen such that the current would

have fully changed its direction without having thickened and slowed down sig-

nificantly before hitting the obstacles. Since the connection between the two chute

sections was not perfectly smooth, the flow slowed down and thickened slightly

before reaching the obstacles. From video recordings of the flows, it was possible

to obtain an upper bound on the flow depth upstream of the obstacles. The maxi-

mum estimated flow depth was 0.007 m for Ballotini (ii) and 0.03 m for Ballotini

(iii). The minimum flow speed directly upstream of the obstacles was estimated

using an expression of mass conservation and assuming that the bulk density of

the flow did not change,u0h0 � u1h1. Hereu0 andh0 are the flow speed and depth

11

just upstream of the break in the slope andu1 andh1 are the flow speed and depth

directly upstream of the obstacles.

4.2 Interaction between the flow and the obstacles

4.2.1 Trajectory of the airborne jet

It was observed in all of the experiments that on reaching the obstacles, a stream

of particles was projected from their top to form a coherent jet. During a fraction

of a second of the interaction, the airborne jet established a quasi-steady shape

that persisted while the bulk of the flow passed over the barrier until the source

of particles from the chute waned. Images from the video recordings of the ex-

periments showed that the airborne jets followed parabolic paths described by the

equation

z � x tan�θ�ψ�� 12

gx2

ju2j2 sec2�θ�ψ�� (2)

whereg is gravitational acceleration,ψ is the slope of the chute,x andz are spatial

coordinates measured horizontally and vertically from the top of the obstacle,ju2jis the throw speed andθ is the throw angle of the jet (see Figure 4). The parameters

that define the geometry of the semi-steady jet are thus the throw angle,θ, and the

speed,ju2j. These were calculated indirectly for experiments with dams by fitting

a least squares parabola through the middle of each observed jet trajectory.

The throw angles are plotted in Figure 5a for the different experimental series.

The curves approximately collapse onto a single curve to within experimental

error. The figure shows that the throw angles steepen as the height of the dams

12

increases relative to the flow depth and approach the full angle of the upstream

dam face (here 90�). This is consistent with the theoretical deflection of a fluid

jet in the absence of gravitational acceleration and with no energy dissipation at

the obstacle. (See Hákonardóttir and others (2003a) for a detailed study of the

deflection of a granular jet.)

Flow interacting with braking mounds is deflected laterally as well as forming

coherent jets over individual mounds. The jets projected directly over the mounds

may be expected to behave as jets over dams. Jets of this sort have also been

observed when supercritical water flow interacts with mounds (Gerodetti, 1985).

The other parameter determining the size and shape of the jet is the throw

speed,ju2j. Following the approach of Hákonardóttir and others (2003c), its de-

pendence on the dimensionless dam height is studied below by simple consid-

erations of the flow energetics. A point mass approach is applied and the ratio

between the mechanical energy of the flow as the jet takes off from the top of a

dam and just before interacting with the dam is approximately given by

N2 �ju2j2

ju1j2�2gH cosψ� (3)

Hereju1j is the flow speed just before the interaction andju2j is the speed of the

jet as it is launched from the top of the obstacle,g is gravitational acceleration and

H cosψ is the vertical rise of the flow when it passes over the obstacle. Mechanical

energy is conserved in the interaction if the ratio equals unity (N2 � 1) and kinetic

energy is solely converted into gravitational potential energy. The square root of

this ratio is plotted in Figure 5b as a function of the dimensionless dam height.

The plot shows that kinetic energy is dissipated at the upstream dam faces (N � 1)

13

and that the dissipation increases as the height of the dams increases relative to

the flow depth. The results at all four length scales are consistent with each other

to within experimental error. A difference in the dissipation between ballotini and

wet and dry snow is not noticeable (bearing in mind the large error bars associated

with the snow experiments) even though the materials have very different material

properties, such as coefficients of restitution, cohesion and particle shape. The

efficiency of dams, 1�N2, can be estimated from the plot as approximately 50%

for dams with a height of 2 to 3 times the flow depth. Further experiments with

snow and other materials at larger physical scales are needed to further test these

findings.

4.2.2 Retarding effect of different obstacle setups

The leading edge run-out of the flow,L, relative to the undisturbed run-out of

the control flow (no obstacles in the flow path),Lcont , is plotted in Figure 6 as a

function of the dimensionless height of the obstacles in the flow path. The run-

out was measured from the upstream obstacle face. It was reproducible in all the

experiments and is listed in Table 3 for the control flows. The experimental data

approximately overlap and thereby confirm the findings of the earlier experiments

[Ballotini (i)] regarding the optimal design of braking mounds for maximum retar-

dation of the flow. As expected, the run-out shortens as the height of the obstacles

in the flow path increases. Mounds lead to a larger run-out reduction than dams

for obstacles with a height up to twice the flow depth. Many narrow mounds are

more efficient than fewer and wider mounds (for a constant proportion of the flow

path blocked by mounds) and the conical mounds are least effective.

14

The ratioL�Lcont provides no information about the effect that the obstacles

have upon the distribution of the deposited particles, since it measures only the

reduction in run-out of the leading edge. Therefore, the distance of the centre of

mass downstream of the obstacles relative to that measured without obstacles was

also calculated. It was found that this ratio was less thanL�Lcont . However the

same obstacle configurations were most and least effective at reducing the run-out

of the centre of mass, namely narrow mounds were most effective and conical

mounds least effective.

Faug and others (2003) have also studied the run-out shortening of rapid sand

and ballotini flows by relatively low catching dams. They found that the run-out

reduction for both sand and ballotini collapsed onto a single curve which also

coincides with the curve which is plotted in Figure 6a.

Additional experiments using coarse sand as the experimental material were

conducted at the 10 m long chute at SLF. It was observed that obstacles (dams and

mounds) in the flow path led to a larger shortening of the leading edge run-out

relative to the undisturbed run-out than was observed in the ballotini experiments.

These experiments are not described here in any detail since the flows were rel-

atively shallow, attaining depths of approximately only 10 particle diameters and

can therefore not be directly compared to the ballotini and snow flows (see Ta-

ble 3).

The retarding effect of different obstacle setups in the experiments with snow

was analysed by plotting the ratio of flow speed upstream of the obstacles,ju1j,to the flow speed downstream of the landing point of the jet,ju4j, see Figures 4

and 7. The analysis was only carried out for the dry-snow experiments due to

15

technical problems with the velocity sensors during the wet-snow experiments.

The speedju4j was measured close to the end of the 25� chute section, a few

metres downstream from the landing point of the jets (see Figure 2b). The fact that

the jets landed on a considerable slope, may have led to a subsequent acceleration

of the flow before the speed was measured. The retarding effect of the mound and

dam setups may therefore be larger than Figure 7 indicates, had the jets landed

on low inclines on which the flows would decelerate and stop, as in the other

laboratory experiments. One may, nevertheless, conclude from Figure 7 that the

mounds are at least as effective in retarding the avalanche flow as a continuous

dam of the same height (whenH�h1� 2). Figure 8 shows a dry-snow avalanche

being deflected over and around two braking mounds at the Weissfluhjoch snow

chute.

5 Discussion and conclusions

The interaction of supercritical granular flows with mounds and dams with a

height comparable to the depth of the approaching flow has been investigated.

Similar dynamical behaviour was observed across a range of physical scales. This

similarity and the nature of the interaction were observed to depend on the follow-

ing factors: the Froude number of the flow; the height of the obstacles relative to

the flow depth; the aspect ratio of the obstacles; and the blocked proportion of the

flow path. The similarity is most clearly evident in the same type of mound setups

being the most effective at reducing the run-out distances of the flows for all the

materials at all experimental scales. The trajectories of the jets and the dynamics

16

of the interaction are relatively insensitive to the exact value of the Froude num-

ber, since similar observations are made for the snow flows with Froude numbers

in the range 3–6 and for the dry granular currents with Froude numbers of order

10.

The experiments confirm the findings of earlier experiments of Hákonardót-

tir and others (2003c) regarding the optimal shape and layout of steep braking

mounds for maximum retardation of granular flows. Therein the following con-

clusions were deduced: a mound height of 2–3 times the flow depth is sufficient

to obtain essentially full retarding effect; the aspect ratio of the mounds should be

chosen close to one; and the mounds should be placed close together for maxi-

mum interaction between laterally deflected material from adjacent mounds. It is

interesting to note that this is almost the same geometry as was found to be most

effective for ‘baffle blocks’ in hydraulic stilling basins (Peterka, 1984). The most

effective baffle blocks for water flows with Froude numbers in the range 8–12 had

a height that was 2–2.5 times the upstream flow depth; the transverse width of

the blocks and the spacing between them was 0.75 times their height; and steep

upstream faces, normal to the bottom of the stilling basin, with relatively sharp

corners, were important for effective energy dissipation, whereas the geometry of

the downstream part of the blocks was of little importance.

Photographic images of the experiments show more spreading of the leading

edge of the jets than of the flow immediately following. This effect may indicate

entrainment of air into the leading edge of the jets or pressure differences as the

flow front displaces the air. The jet trajectories were best modelled by assuming

that air resistance was negligible. Larger-scale experiments with water show, on

17

the other hand, that between 0 and 30% of the initial mechanical energy of a water

jet may be lost during the jump (USBR, 1984; Novak and others, 1989; Hager,

1992). Similarly, air drag may be expected to become significant in avalanche

flow at natural scales and energy loss due to air drag will then affect the length of

the jump (Jóhannesson and Hákonardóttir, 2003).

It is interesting to note that a similar relative dissipation of the mechanical en-

ergy of both snow and ballotini flows was found at the upstream faces of continu-

ous dams for the same dam height to flow depth ratio but at very different physical

scales. The experimental series is limited, however, and further experiments using

snow, and dams with different frictional properties are needed to corroborate these

findings. The dissipation of mechanical energy in interactions of this sort can be

shown to be independent of material properties to leading order, if the obstacles

are sufficiently high so that a jump in flow depth and speed (termed ‘granular

jump’) occurs upstream of the obstacles (Gray and others, 2003; Hákonardót-

tir, 2004). Hákonardóttir (2004) used classical theory of hydraulic jumps (see

e.g. Whitham (1999)), supported by experimental observations of granular flows,

to show that the obstacles need to be at least nine times as high as the depth of

the approaching flow for such a granular/hydraulic jump to form for Fr� 10.

Mounds are, however, usually designed with a height to flow depth ratio of under

4. Granular jumps do therefore not form in the interaction with such low mounds,

and the whole flow is launched directly over the mounds as reported. The experi-

ments nevertheless suggest that, similarly to granular jumps, the dynamics of the

interaction is governed to leading order by the geometry of the obstacles and the

large-scale properties of the granular currents.

18

Mounds with a layout based on these experimental results have recently been

constructed above Neskaupstaður in eastern Iceland. Figure 1 shows one of the

mounds. The mounds have an aspect ratio close to one and a steep and planar

upstream face. The geometry of these mounds is thus different from the more

common conical shape of avalanche braking mounds.

6 Acknowledgements

The experiments described in the paper were carried out with support from the

Icelandic Avalanche Fund. KMH acknowledges the financial support of the Uni-

versity of Bristol and the Icelandic Research Fund for Graduate Students. The

authors would like to thank everyone who took part in shovelling snow at Weiss-

fluhjoch.

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21

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22

List of Figures

1 Photograph of a braking mound above Neskaupstaður, Iceland. A

person is standing in front of the mound.. . . . . . . . . . . . . . 29

2 Schematic side-view of the experimental chutesa in Bristol (Bal-

lotini (i)), Reykjavík (Ballotini (ii)) and Davos (Ballotini (iii)) and

b at Weissfluhjoch (Snow). The inclination of each section of the

Weissfluhjoch chute is given on the figure relative to the horizon-

tal. The position of optical velocity sensors is indicated with thick

arrows. The basal sensors are denoted by BS and SA stands for

the sensor array which was positioned at the side of the chute. . . 30

3 Schematic plan-view of the different obstacle setups. DM stands

for datum mounds, NM stands for narrow mounds and CM stands

for conical mounds. . . . .. . . . . . . . . . . . . . . . . . . . . 31

4 Schematic diagram of a supercritical granular current jumping

over a dam with an upstream face normal to the base of the ex-

perimental chute. . . . . .. . . . . . . . . . . . . . . . . . . . . 31

5 a The throw angle,θ, as a function of the dimensionless dam

height,H�h1. The curve shows the theoretical deflection of an

inviscid, fluid jet.b The square root of the ratio of the mechanical

energy of the flow at the top of a continuous dam to the mechanical

energy just before interacting with the dam,N � ju2j�pju1j2�2gH cosψ,

as a function of the dimensionless dam height. In Ballotini (ii) and

Ballotini (iii), the obstacles were positioned on the lower chute

section, just downstream of a break in the slope. The points on the

graph correspond to measurements of the flow speed and depth,u0

andh0, on the upper chute section, upstream of the break in the

slope. The error bars indicate the flow depth directly upstream

of the obstacles,h1, estimated from video recordings of the flows

and the flow speed,u1, estimated from mass balance. . . . . . . . 32

6 The leading edge run-out,L, relative to the leading edge run-out of

the undisturbed control flow,Lcont , measured from the upstream

face of the obstacles, as a function of the dimensionless obsta-

cle height for experiments witha dams andb mounds. A line

is drawn through the datum mound experiments (DM), while the

narrow and conical mounds are presented with points. The higher

point corresponds to conical mounds (CM) while the lower point

corresponds to narrow mounds (NM) in each experimental series. 33

24

7 The ratio between the flow speed in the dry-snow experiments

at the upper and lower sensors on the Weissfluhjoch chute (see

Figure 2) as a function of the dimensionless obstacle height. Each

point is an average of two experiments. A line is drawn through

the points of the dam experiments to distinguish them from the

mound experiments. . . . .. . . . . . . . . . . . . . . . . . . . . 34

8 Photograph of a 0.3 m deep, dry-snow avalanche being deflected

over and around two 0.6 m high mounds at the Weissfluhjoch snow

chute. . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

25

List of Tables

1 Dimensions of the different experimental chutes according to Fig-

ure 2. *The obstacles in Ballotini (i) were positioned close to

the downstream end of the upper chute section on a curved metal

sheet connecting the two sections smoothly. . . . . .. . . . . . . 37

2 Geometry of the different obstacle setups:H is the height of an

obstacle; # stands for the number of obstacles on the experimental

chute;B is the width of an obstacle; andA� is the proportion of

the width of the chute that is blocked by mounds. The setup of

datum mounds is denoted by DM, NM stands for narrow mounds,

CM for conical mounds and Dam for obstacles spanning the entire

width of the experimental chute. . . . .. . . . . . . . . . . . . . 37

3 Flow characteristics in each experimental series are listed. The

mass of particles released in each experimental series,M, the re-

sulting flow speed,u, and depth,h, of the quasi-steady flow phase,

along with the undisturbed run-out,Lcont , measured from the up-

stream face of the obstacles, the ratio of the flow depth to the

particle diameter,h�d, and the Froude numbers of the flows, Fr.

*The stars indicate measurements of flow speed and depth directly

upstream of the obstacles (h1, u1), while non-starred entries are

measurements just upstream of the break in the slope (h0, u0). . . 38

27

Figure 1:

29

b1

b1

a Laboratory chutes

ψ0

Row of mounds

Plan-view

ψ1

ll

b0 b0

D

D

B

Lock gate

Rubber mats

Lock gate

b Snow chute at Weissfluhjoch

Obstacles

10.0m

10.0m

6.1 m

4.2m

3.5 m

45 �

45 �

32 �

25�

8�

0.6m

BS

BSSA

Snow

Figure 2:

30

DM

NM

B

b1

CM

Dam

Figure 3:

g

u1

h1

x

z

u2θ

ψ

H

u4

Figure 4:

31

0

20

40

60

80

Ballotini (i)Ballotini (ii)Ballotini (iii)

Wet snowDry snow

Theoryθ

���

a

0

0.2

0.4

0.6

0.8

0 1 2 3 4 5 6

Ballotini (i)Ballotini (ii)Ballotini (iii)

Wet snowDry snow

N

b

H�h1

Figure 5:

32

0

0.2

0.4

0.6

0.8

1

Ballotini (i)Ballotini (ii)Ballotini (iii)

L

�

L con

ta Dams

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6 7 8

Ballotini (i): DMCM/NM

Ballotini (ii): DMCM/NM

Ballotini (iii): DMCM/NM

L

�

L con

t

b Mounds

H�h1

Figure 6:

33

0

0.2

0.4

0.6

0.8

0 1 2 3 4 5 6

DamsMounds

ju 4

j�j

u 1

j

H�h1

Figure 7:

34

Figure 8:

35

Series l (m) D (m) b0 (m) b1 (m) ψ0 (�) ψ1 (�)

Ballotini (i) 3.0 - 0.3 0.5 37, 30* 10

Ballotini (ii) 1.5 0.025 0.2 0.3 43 14

Ballotini (iii) 5 0.15 0.5 0.8 45 10

Snow � 20 0.6 2.5 2.5 45 32, 25, 8

Table 1:

Series Setup H (m) # A� H�B

Ballotini DM 0.005, 0.01, 0.03 3 0.6 0.08, 0.17, 0.5

(i) NM 0.05, 0.07 3 0.6 0.83, 1.17

Dam 0.005, 0.01, 0.03, 0.05 1 1.0 small

Ballotini DM 0.005, 0.01, 0.015 12, 6, 4 0.6 0.5

(ii) NM 0.01 12 0.6 1.0

CM 0.01 10 0.5 0.5

Dam 0.005, 0.01, 0.015, 0.02 1 1.0 small

Ballotini DM 0.025, 0.05 6, 3 0.6 0.5

(iii) NM 0.05 6 0.6 1.0

CM 0.05 5 0.5 0.5

Dam 0.025, 0.05, 0.10 1 1.0 small

Snow DM 0.4 2 0.48 0.67

wet/dry NM 0.6 2 0.48 1.0

Dams 0.4, 0.6 1 1.0 small

Table 2:

37

Series M (kg) u (m s�1� h (m) Lcont (m) h�d Fr

Ballotini (i) 6 2�8�0�1* 0�01�0�0005* 2�00�0�02 100 10*

Ballotini (ii) 2 2�7�0�1 0�006�0�001 1�22�0�01 60 13

Ballotini (iii) 50 5�0�0�1 0�0225�0�002 3�90�0�025 225 13

Wet snow 1500–2000 7�5�1�0* 0�3�0�1* – 3–150 3–6*

Dry snow 1500–2000 6�5�1�0* 0�2�0�05* – 2–200 5*

Table 3:

38