1778
NOTE / NOTE
Relationships between size and velocity for
particles within debris flows
Adam B. Prochaska, Paul M. Santi, and Jerry D. Higgins
Abstract: Estimation of the impact forces from boulders within a debris flow is important for the design of structural mitigation elements. Boulder impact force equations are most sensitive to the inputs of particle size and particle velocity. Current guidelines recommend that a design boulder should have a size equal to the depth of flow and a velocity equal to that
of the flow. This study used video analysis software to investigate the velocities of different sized particles within debris
flows. Particle velocity generally decreased with increasing particle size, but the rate of decrease was found to be dependent on the abilities of particles to rearrange within debris flows.
Key words: debris flow, boulder, velocity, impact force, design.
Résumé : L’estimation des forces d’impact des boulders à l’intérieur d’un écoulement de débris est important pour la
conception d’éléments structuraux de comfortement. Les équations de la force d’impact de boulders sont très sensibles aux
intrants de dimension et de vélocité de la particule. Les règles courantes recommandent que, pour fin de conception, un
boulder devrait avoir une dimension égale à la profondeur de l’écoulement et une vélocité égale à celle de l’écoulement.
La présente étude a utilisé une analyse avec un logiciel de vidéo pour étudier les vélocités de différentes dimensions de
particules à l’intérieur des écoulements de débris. La vélocité de la particule décroı̂t généralement avec l’accroissement de
la dimension de la particule, mais on a trouvé que le taux de diminution dépendait des capacités des particules à se réarranger à l’intérieur des écoulements de débris.
Mots-clés : écoulement de débris, boulder, vélocité, force d’impact, conception.
[Traduit par la Rédaction]
Introduction
Estimation of the potential boulder impact forces from a
debris flow is important for the design of structural mitigation elements. Equations for the estimation of boulder impact forces (Hungr et al. 1984; VanDine 1996; Lo 2000) are
most sensitive to the inputs of particle size and particle velocity. Design guidelines recommend using a design boulder
equal in size to the depth of flow that is traveling at the velocity of the flow (Hungr et al. 1984; Lo 2000). This study
used Vernier Software and Technology’s Logger Pro 3.2
software to analyze the velocities of over 200 different sized
particles within eight debris-flow video segments to investigate the practicality of this guideline.
Previous studies have also used video analysis to investigate debris flows (Inaba et al. 1997; Arattano and Grattoni
Received 6 September 2007. Accepted 15 August 2008.
Published on the NRC Research Press Web site at cgj.nrc.ca on
16 December 2008.
A.B. Prochaska,1,2 P.M. Santi, and J.D. Higgins. Colorado
School of Mines, Department of Geology and Geological
Engineering, 1516 Illinois Street, Golden, CO 80401, USA.
1Corresponding
author (e-mail:
aprochaska@rjh-consultants.com).
2Present address: 11131 W 17th Ave. #106, Lakewood, CO
80215, USA.
Can. Geotech. J. 45: 1778–1783 (2008)
2000; Ikeda and Hara 2003; Inaba and Itakura 2003; Lavigne et al. 2003; Tecca et al. 2003; Zhang and Chen 2003).
However, these studies did not investigate the velocity distribution among different sized particles within debris flows.
Data sources
Eight debris-flow video segments were analyzed to investigate the relationships between variously sized particles
within the flow and their respective velocities. These video
segments will be referred to as videos A through H, as described below.
Video A: Devore Heights, California. This debris flow
emanated from Devore Canyon on 25 December 2003
and was recorded by a local resident as it flowed along
Greenwood Avenue. This video can be viewed at http://
www.usgs.gov/homepage/science_features/
debris_flow_ca.asp. The analyzed portion of the video
was from 0:10 to 0:17 (minutes:seconds).
Video B through video F: These videos were obtained
from Costa and Williams (1984) and J. Costa (no date;
Subaerial debris flows. Video, U.S. Geological Survey,
Water Resources Division, Vancouver, Washington) and
depict debris flows from China, Japan, New Zealand, California, Washington, and Utah. The analyzed portions of
the video by Costa and Williams (1984) were from 6:20
doi:10.1139/T08-088
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2008 NRC Canada
Prochaska et al.
Fig. 1. Images from (a) video A and (b) video G.
1779
Fig. 2. Images from (a) video D and (b) video E.
(a)
(a)
(b)
(b)
to 6:27 (video B) and 6:27 to 6:32 (video C). The analyzed portions of the video from J. Costa were from 1:19
to 1:22 (video D), 1:34 to 1:37 (video E), and 2:13 to
2:24 (video F).
Video G: US Forest Service video (USFS 1997) documenting a debris flow that occurred in Whitney Creek
near Mount Shasta, California in August 1997. The analyzed portion of this video was from 1:12 to 1:13.
Video H: U.S. Geological Survey video (no date; Debris
flow of 9/92 in Nagano Pref./Debris flows in the Urakawa R. 1980–1984. Video, U.S. Geological Survey,
Golden, Colo.) depicting debris flows within the Urakawa
River, Japan. The analyzed portion of this video was
from 35:50 to 36:20.
Representative images of analyzed portions from videos A
and G are shown in Figs. 1a and 1b, respectively. Analyzed
portions of these flows consisted primarily of a fluid matrix
material with very little interaction among the larger particles. Representative images of the flows from videos D
and E are shown in Figs. 2a and 2b, respectively. The motions analyzed in these video segments were those of dry
boulders on the flow surface; no interstitial matrix material
was observed between the individual analyzed particles.
Representative images from videos B, C, and H are shown
in Figs. 3a, 3b, and 3c, respectively. These flows had qualitative compositions that were intermediate between those
shown in Figs. 1 and 2. These flows had high boulder concentrations similar to the flows shown in Fig. 2 with highly
fluid interstitial matrix materials similar to those shown in
Fig. 1. A representative image from video F is shown in
Fig. 4. This video segment was of a viscous, steep-sided,
slowly flowing debris-flow front.
Methods
Videos (VHS and digital formats) were obtained that depict the motion of variously sized particles within debris
flows. Relevant sections of VHS tapes were converted to
digital formats using Pinnacle Studio Plus (Ver. 11) and a
Dazzle DVD recorder. The video analysis tool within the
Logger Pro software was used to investigate the velocities
of individual particles within the digital videos.
Logger Pro software allows its user to manually track a
particle’s motion as a digital video is advanced frame-byframe. For a user-defined scale and coordinate system,
elapsed time and the x- and y-coordinates of the tracked particle are tabulated for each video frame. As the videos did not
contain objects of known size from which to reference the
scales, a large boulder or other easily identifiable landmark
was set to an arbitrary distance of unity for each video segment. Within the videos, the origin of the coordinate system
was set at the upstream edge of each analyzed particle at the
beginning of the analyzed time segment. As the video was
advanced, the position of the downstream edge of the particle
in each video frame was tracked. The x- and y-coordinates of
the initial analyzed frame (i.e., the distance from the upstream edge to the downstream edge of the particle) were
used to identify the relative particle sizes. The particle velocities were calculated as
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2008 NRC Canada
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Can. Geotech. J. Vol. 45, 2008
Fig. 3. Images from (a) video B, (b) video C, and (c) video H.
Fig. 4. Image from video F.
(a)
(b)
were sufficiently minimized during the normalization of the
velocities (as discussed subsequently).
Individual particles were analyzed for as long as their unimpeded flow could be followed in the videos. Analysis
times for the different video segments ranged from 0.3 to
10.7 s, or from 6 to 161 video frames. Analyzed video segments were also chosen so as to avoid any panning, zooming, or unsteadiness within the video.
Plots were made of particle velocity versus particle size.
Due to the arbitrary scales used for each video segment,
magnitudes of size and velocity were relative. Thus, both
velocity and size were normalized by the highest respective
values within each video so that the maximum relative size
and velocity were both unity.
(c)
Results
Figure 5 shows the results of relative particle velocity versus relative particle size for the eight analyzed video segments. The figure sections (a) through (h) correspond to
video A through video H, respectively, as described in the
‘‘Data sources’’ section.
Linear regressions were performed on the particle velocity
versus particle size data shown in Fig. 5. Table 1 shows the
regression results for these data.
Discussion
½1
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ðxf xi Þ2 þ ðyf yi Þ2
v¼
tf ti
where v is particle velocity, xf is the particle’s x-coordinate
in the final analysis frame, xi is the particle’s x-coordinate in
the initial analysis frame, yf is the particle’s y-coordinate in
the final analysis frame, yi is the particle’s y-coordinate in
the initial analysis frame, tf is the video time at the final
analysis frame, and ti is the video time at the initial analysis
frame.
Equation [1] provides only an approximation of particle
velocity, as it neglects three-dimensional motion and the effects of camera perspective. However, for distant particles
with approximately parallel paths, we feel that these effects
The analyzed video segments did not include absolute
scales from which the sizes of particles could be ascertained.
However, based upon reference items, such as vegetation
present within the videos, we estimate that the largest of the
analyzed particles had sizes between 2 and 3 m, and the majority of the analyzed particles were between 0.5 and 1.5 m
in size. In the majority of the analyzed debris flows, the
largest transported particles were less than one-third of the
flow depth. Transportation of particles up to and even larger
than the depth of flow was observed in video A and video
G. However, the largest of these particles moved substantially slower than the flow by rolling and sliding along the
bottom of the channel.
The low P-values in Table 1 indicate that for five of the
eight analyzed video segments (videos A, D, E, G, and H),
the regressions of particle velocity versus particle size would
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Prochaska et al.
1781
1.00
(a)
Relative particle velocity
Relative particle velocity
Fig. 5. Relative particle velocity versus relative particle size for the eight analyzed video segments. Figure sections (a) through (h) correspond to videos A through H, respectively.
Video A:
Greenwood
0:10 – 0:17
0.75
0.50
0.25
0.00
0.00
0.25
0.50
0.75
1.00
1.00
0.75
0.50
0.25
0.00
0.00
0.25
Video C: Costa and
Williams (1984)
6:27 – 6:32
0.75
0.50
0.25
0.00
0.00
0.25
0.50
0.75
Relative particle velocity
Relative particle velocity
(c)
1.00
1.00
Relative particle velocity
Relative particle velocity
0.75
0.50
0.25
Video E: Costa, 1:34 – 1:37
0.25
0.50
0.75
0.75
0.50
0.25
Video D: Costa, 1:19 – 1:22
0.00
0.00
0.25
0.50
0.75
1.00
1.00
0.75
0.50
0.25
Video F: Costa
2:13 – 2:24
0.00
0.00
0.25
Relative particle velocity
Relative particle velocity
(g)
0.50
Video G: USFS
(1997) 1:12 – 1:13
0.00
0.00
0.25
0.50
0.75
Relative particle size
0.50
0.75
1.00
Relative particle size
0.75
0.25
1.00
(f)
Relative particle size
1.00
1.00
Relative particle size
(e)
0.00
0.00
0.75
(d)
Relative particle size
1.00
0.50
Relative particle size
Relative particle size
1.00
Video B: Costa and
Williams (1984)
6:20 – 6:27
(b)
1.00
1.00
(h)
0.75
0.50
0.25
0.00
0.00
Video H: USGS
35:50 – 36:20
0.25
0.50
0.75
1.00
Relative particle size
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Can. Geotech. J. Vol. 45, 2008
Table 1. Linear regression results for the relative particle velocity versus relative particle size data.
Flow
Video
Video
Video
Video
Video
Video
Video
Video
A: Greenwood Avenue 0:10–0:17
B: Costa and Williams (1984) 6:20–6:27
C: Costa and Williams (1984) 6:27–6:32
D: Costa (no date) 1:19–1:22
E: Costa (no date) 1:34–1:37
F: Costa (no date) 2:13–2:24
G: USFS (1997) 1:12–1:13
H: USGS (no date) 35:50–36:20
Figure
5a
5b
5c
5d
5e
5f
5g
5h
Slope
–0.50
–0.49
–0.56
–0.71
–0.25
0.09
–0.74
–0.55
Slope SEa
0.15
0.24
0.29
0.08
0.09
0.22
0.14
0.13
Intercept
0.63
0.71
0.68
1.01
0.92
0.53
0.98
0.96
Intercept SEa
0.07
0.10
0.14
0.05
0.05
0.14
0.08
0.06
R2
0.21
0.18
0.16
0.80
0.25
0.01
0.61
0.34
P-value
0.002
0.054
0.069
0.000
0.008
0.671
0.000
0.000
a
Standard error.
be considered statistically significant at a level of significance of 0.05. At a level of significance of 0.10, the regressions of particle velocity versus particle size would be
considered statistically significant for all of the analyzed
video segments except for one (video F). Thus, for the debris flows depicted in these videos, there is a statistically
significant decrease in particle velocity as the particle size
increases. The following paragraphs discuss these trends in
the context of the flows’ qualitative compositions.
The analyzed flow from video F did not exhibit a statistically significant trend between particle velocity and particle
size (Table 1). Figure 5f shows that for this flow, a wide
range of velocities was observed for any given particle size.
We attribute this to the strength of the matrix material and
the concentration of boulders within this flow, which would
have effectively reduced the ability of an individual particle
to leave its position within the flow. Thus, the localized velocities within the flow would have controlled the velocities
of the individual particles.
The analyzed particles from videos D and E (Fig. 2) had
statistically significant decreases in particle velocity with increasing particle size at a level of significance of 0.05. The
flow of these particles would be controlled by Coulomb friction, and the low confining stress present at the surface of
the flow would allow for these particles to readily rearrange.
We believe that smaller particles could more easily meander
their way through fortuitous openings along the flow surface
and thus would have higher velocities, which is confirmed
in Figs. 5d and 5e.
The analyzed particles from videos A and G (Fig. 1) had
statistically significant decreases in particle velocity with increasing particle size at a level of significance of 0.05. Due
to the fluid matrix material and the low concentration of
boulders, we believe that individual particles were able to
travel at velocities that were unimpeded by frictional interactions among particles or by a highly viscous matrix material. This is shown in Figs. 5a and 5g.
The analyzed particles from videos B, C, and H (Fig. 3)
had statistically significant (at a significance level of 0.10)
decreases in particle velocity as particle sizes increased
(Table 1), but the trends for videos B and C were less significant than the trends for the flows shown in Figs. 1 and
2. Thus, the combination of a high boulder concentration
and fluid matrix material somewhat reduced the abilities of
the particles to rearrange.
Figures 5a, 5b, 5c, 5d, 5g, and 5h show good agreement
in that the largest analyzed particles traveled with velocities
of only 20% to 40% of those of the highest velocity, smaller
particles. From Figs. 5e and 5f, the largest particles in videos E and F had velocities that were 60% to 70% of the
fastest particles. Figures 5e and 5f (as well as Figs. 5b and
5c) contain data from debris-flow fronts that were analyzed.
Regressions of particle size versus velocity for these four
figures also had the highest P-values (Table 1), meaning
that the decreases in velocity as particle sizes increased
were less statistically significant for these flows. This may
indicate that particle velocities near the front of a debris
flow could be less dependent on particle sizes than they are
in subsequent flow phases.
It has been recognized by previous researchers that boulders within a debris flow will advance towards and accumulate at the flow front (e.g., Takahashi 1980; Iverson 1997;
Yamagishi et al. 2003). The results from this study, where
larger particles were found to travel slower than smaller
ones, are not meant to contradict this phenomenon. All of
the analyzed particles were much larger than the debrisflow matrix materials, and thus would be expected to advance towards the fronts of the flows. The results indicate,
however, that smaller boulders on the flow surface may advance to the flow front faster than larger boulders on the
flow surface. It is likely that the smaller analyzed boulders
were traveling at the maximum (surface) velocity of the
flows, while larger boulders were traveling at velocities
closer to the mean flow velocity that occurs at greater
depths. The results of larger particles having lower velocities are in agreement with previous qualitative results.
Kang (1997) reported that large particles within a debris
flow were observed to travel at velocities lower than that of
the flow. Genevois et al. (2000) found that velocities of
frontal boulders were lower than instantaneous surface velocities due to frictional resistance. Iverson (2003) reported
that large particles at debris-flow fronts move primarily by
sliding and rolling rather than by flowing.
Summary and conclusions
Logger Pro software was used to analyze the velocities of
different sized particles within debris flows. The velocities
of different sized particles were found to be dependent on
the ability of individual particles to rearrange, based on
flow composition and rheology. Particle velocities decreased
with increasing particle size on the surface of granular flows
where no matrix material was present among boulders and
for fluid flows where few large-particle interactions occurred. For flows that contained a high concentration of
boulders within a viscous matrix, no statistically significant
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Prochaska et al.
trend was found between particle velocity and particle size.
Flows with high concentrations of boulders within fluid matrix materials showed trends intermediate to those previously
mentioned.
Acknowledgements
This work has been funded by the US Department of Education through a Graduate Assistance in Areas of National
Need (GAANN) Fellowship, award #P200A060133. Computer software was purchased with a generous donation by
the Halliburton Foundation. Thanks to Lynn Highland of
the U.S. Geological Survey for providing debris-flow videos. Thanks also to Chris Kelso of the Colorado School of
Mines Physics Department for providing Logger Pro software and to Shauna Gilbert of the Colorado School of Mines
for technical support.
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