GEOMOR-03031; No of Pages 11
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Geomorphology xxx (2009) xxx–xxx
Contents lists available at ScienceDirect
Geomorphology
j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / g e o m o r p h
Field and laboratory investigations of runout distances of debris flows in the
Dolomites (Eastern Italian Alps)
Vincenzo D'Agostino a,⁎, Matteo Cesca a,1, Lorenzo Marchi b,2
a
b
Department of Land and Agro-Forest Environments, University of Padova, Agripolis, Viale dell'Università 16, 35020 Legnaro (Padova), Italy
CNR-IRPI, Corso Stati Uniti 4, 35127 Padova, Italy
a r t i c l e
i n f o
Article history:
Received 22 December 2007
Received in revised form 30 April 2008
Accepted 15 June 2009
Available online xxxx
Keywords:
Alluvial fan
Debris flow
Runout distance
Laboratory flume
Alps
a b s t r a c t
The estimation of runout distances on fans has a major role in assessing debris-flow hazards. Different methods
have been devised for this purpose: volume balance, limiting topographic methods, empirical equations, and
physical approaches. Data collected from field observations are the basis for developing, testing, and improving
predictive methods, while laboratory tests on small-scale models are another suitable approach for studying
debris-flow runout under controlled conditions and for developing predictive equations. This paper analyses the
problem of assessing runout distance, focusing on six debris flows that were triggered on July 5th, 2006 by intense
rainfall near Cortina d'Ampezzo (Dolomites, north-eastern Italy). Detailed field surveys were carried out
immediately after the event in the triggering zone, along the channels, and in the deposition areas. A fine-scale
digital terrain model of the study area was established by aerial LiDAR measurements. Total travel and runout
distances on fans measured in the field were compared with the results of formulae from the literature
(empirical/statistical and physically oriented), and samples of sediment collected from deposition lobes were
used for laboratory tests. The experimental device employed in the tests consists of a tilting flume with an
inclination from 0° to 38°, on which a steel tank with a removable gate was installed at variable distances from the
outlet. A final horizontal plane works as the deposition area. Samples of different volumes and variable sediment
concentrations were tested. Multiple regression analysis was used to assess the length of the deposits as a function
of both the potential energy of the mass and the sediment concentration of the flow. Our comparison of the results
of laboratory tests with field data suggests that an energy-based runout formula might predict the runout
distances of debris flows in the Dolomites.
© 2009 Elsevier B.V. All rights reserved.
1. Introduction
Debris flows are one of the most important formative processes of
alluvial fans under various climatic conditions. They can transport and
deposit large amounts of water and solid material in short time
intervals, creating a major hazard for people and structures.
The assessment of runout distance, i.e. the length travelled on an
alluvial fan by a debris flow from the initiation of the deposits until
their lowest point, is of utmost importance for delineating the areas at
risk from debris flows. Another key parameter in debris-flow studies is
the total travel distance (the distance from the initiation of the debris
flow to the lowest point of deposition). Methods for determining
⁎ Corresponding author. University of Padova, Department of Land and Agro-Forest
Environments, Agripolis, Viale dell'Università 16, 35020 Legnaro (PD), Italy. Tel.: +39
0498272682; fax: +39 0498272686.
E-mail addresses: [email protected] (V. D'Agostino),
[email protected] (M. Cesca), [email protected] (L. Marchi).
1
Tel.: +39 0498272700; fax: +39 0498272686.
2
Tel.: +39 0498295825; fax: +39 0498295827.
debris-flow runout distance and total travel distance can be based on
field data as well as on data generated by physical models. By
combining these two sources of data, a promising approach emerges
for refining the methods for assessing runout distance on alluvial fans.
This paper contributes to the assessment of debris-flow runout
distance on fans and total travel distance by integrating field
measurements and laboratory tests on a tilting plane rheometer. The
study methods were applied to six debris flows of the Dolomites
(eastern Italian Alps). Field surveys and a hydrological analysis made
it possible to assess the principal parameters relevant for the analysis
of runout distance. Samples taken from the debris-flow deposits were
used to analyse the depositional processes on the tilting plane
rheometer; both quasi-static tests of fan formation and dynamic tests
using a flume were carried out. Field data on runout distance and total
travel distance were compared with both empirical–statistical and
dynamic methods for runout assessment, and with predictive
equations developed from the laboratory test.
This paper is divided into seven sections. Section 2 describes the
principal methods available for assessing runout distance and total
travel distance. Section 3 presents the study area, the field surveys, and
the hydrological analysis implemented for assessing the main variables
0169-555X/$ – see front matter © 2009 Elsevier B.V. All rights reserved.
doi:10.1016/j.geomorph.2009.06.032
Please cite this article as: D'Agostino, V., et al., Field and laboratory investigations of runout distances of debris flows in the Dolomites
(Eastern Italian Alps), Geomorphology (2009), doi:10.1016/j.geomorph.2009.06.032
ARTICLE IN PRESS
2
V. D'Agostino et al. / Geomorphology xxx (2009) xxx–xxx
of the debris flows studied. Section 4 reports the results of applying
methods from previously published literature. Section 5 describes the
laboratory tests. Finally, Sections 6 and 7 discuss the results and summarise the conclusions of the study, respectively.
Table 1
Empirical equations used to compute runout distance R and total travel distance L of
debris flows.
Variable
Empirical equation
Authors
Eq.
Runout (R)
R = 8:6ðV tan θu Þ0:42
R = 25V 0:3
R = 15V 1 = 3
−0:26
ðH =LÞmin = tanβmin = 0:20ðAC Þ
Ikeya (1989)a
Rickenmann (1994)b
Rickenmann (1999)
Zimmermann et al.
(1997)
Rickenmann (1999)
(4)
(5)
(6)
(7)
2. Methods for assessing debris-flow runout
Several authors have proposed methods for assessing runout
distances (e.g., Hungr et al., 1984; Cannon, 1989; Bathurst et al., 1997;
Fannin and Wise, 2001; McDougall and Hungr, 2003). Rickenmann
(2005) classifies the methods for predicting the runout distance into
empirical–statistical and dynamic methods. A more detailed classification of the approaches in the literature includes volume balance
approaches, limiting topographic methods, other empirical equations,
physically-oriented methods, and laboratory studies.
a) Volume balance approach
Volume balance methods predict flooded area (A) as a function of
total volume (V):
A = kV
d
ð1Þ
where k and d are empirical coefficients.
Iverson et al. (1998) proposed a method that has received
significant attention; it predicts the valley cross-sectional area and
planimetric area inundated by lahars from lahar volume on the basis of
two semi-empirical equations. Iverson et al. (1998) developed the
equation A = 200 V2/3 using data from 27 lahars at nine volcanoes with
volumes from 8 × 104 to 4 × 109 m3. A similar equation (A = 6.2 V2/3)
was calculated by Crosta et al. (2003) for 116 debris flows in the Italian
Alps. These authors observed that the empirical coefficient k is
predominantly dependent on the characteristics of the debris-flow
material. Berti and Simoni (2007) studied forty debris-flow basins
with metamorphic and sedimentary lithologies in the Italian Alps, with
debris-flow volumes up to 50,000 m3. They confirmed that there was a
significant correlation between flooded area and volume.
b) Limiting topographic methods
Limiting topographic methods are primarily related to the fan slope Sd
or to parameters related to the energy dissipated along the depositional
path (Vandre, 1985; Ikeya, 1989; Burton and Bathurst, 1998).
Ikeya (1989) proposed a limiting topographic method based on fan
slope. The angle after deposition ranged from 2° to 12° with a modal
value between 4° and 6°; the spread channel width ratio (the ratio
between deposition width to channel width upstream of the fan) is,
on average, equal to 5 and generally assumes a value lower than 10.
Vandre (1985) proposed an empirical approach to estimate the
runout distance of a debris flow:
R = ωΔH
ð2Þ
Travel distance
(L)
L = 1:9V 0:16 H 0:83
a
b
(8)
Mathematical rearrangement from the original form (in Bathurst et al., 1997).
Personal communication in Bathurst et al. (1997).
the channel network until possible deposition occurs. The rules applied to
govern debris flow transport and sediment deposition are as follows:
• for slopes greater than 10°, the debris flow continues unconditionally;
• for slopes between 4° and 10°, the debris flow comes to a halt either if
the condition expressed by Eq. (2) is satisfied or upon reaching the 4°
slope; and
• for slopes less than 4°, the debris flow halts unconditionally and
deposits all remaining material.
c) Empirical equations
Empirical equations use variables, such as debris flow volume (V),
potential mass energy (H), fan slope (Sd), upstream gradient (θu),
mean slope angle of the whole path (β), and catchment area (AC), to
predict the runout distance on the fan and the total travel distance.
The mobility ratio (H/L; see notation for symbols), termed the
effective friction angle (Heim, 1882), has been recently applied by a
number of authors (e.g., Corominas, 1996; Toyos et al., 2007) as a
measure of mobility. According to a personal communication of
Takahashi, Bathurst et al. (1997) assumed that H/L = tan β = 0.20,
very close to the minimum value (tan β = 0.19) obtained by
Rickenmann and Zimmermann (1993). The mobility index roughly
correlates with the volume of the flow (Iverson, 1997) and can be used
to approximate the maximum potential runout of debris flows.
Table 1 summarizes some well-known empirical equations used to
assess runout distance and total travel distance. The relationships, Eqs.
(4)–(8), are mainly based on field data and often include the debrisflow volume (V) as an independent variable coupled to morphometric
information (H, Sd = tan θd, θu, β , AC , Fig. 1).
d) Physically-oriented methods
Dynamic methods consider mass, momentum and energy conservation to simulate the propagation of debris flows using 1D or 2D models
(O'Brien et al., 1993; Hungr, 1995; Iverson and Denlinger, 2001; Laigle
et al., 2003). Numerical models may adopt a variety of hypotheses for
solving the motion equations, and take into account different rheological
models of the material involved. Based on a momentum consideration
where R is the runout distance, ΔΗ is the elevation difference between
the initiation point and the point where deposition starts and ω is an
empirical constant. According to Vandre's data, the value of ω is 0.4
(i.e. the runout distance is 40% of the elevation difference ΔH).
A runout criterion based empirically on Eq. (2) was proposed by
Burton and Bathurst (1998). A debris flow stops when the following
condition is met:
Elevation lost
Distance travelled on slopes
N 0:4
on slopes N 10˚
between 4˚ and 10˚
ð3Þ
where travel distances are measured along the slope. The potential
trajectory of the debris flow starts at the initiation point and progresses in
Fig. 1. Idealized debris flow labelled with the parameters involved in the empirical
relationships.
Please cite this article as: D'Agostino, V., et al., Field and laboratory investigations of runout distances of debris flows in the Dolomites
(Eastern Italian Alps), Geomorphology (2009), doi:10.1016/j.geomorph.2009.06.032
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V. D'Agostino et al. / Geomorphology xxx (2009) xxx–xxx
for a flow travelling over a surface with constant slope, the runout length
R can be described by the following theoretical equation developed by
Hungr et al. (1984) and Takahashi (1991):
R=
fuu cosðθu −θd Þ½1 + ðg hu cosθu Þ=ð2u2u Þg2
g ðSf cosθd − sinθd Þ
ð9Þ
where θd = the terrain slope angle along the area of deposition, θu =
the entry channel slope angle, uu = entry velocity, hu = entry flow
depth, and Sf = the friction slope, which is assumed to be constant
along the runout path and accounts only for sliding friction. The model
assumes a constant discharge from upstream and no change in flow
width after the break in slope.
Hungr et al. (1984) assumed the friction slope angle of 10° and
reported a good agreement between observed values of R and those
predicted by Eq. (9) for five debris flows in western Canada. However,
when Eq. (9) is applied to 14 debris flows in Japan using measured flow
quantities (Okuda and Suwa, 1984), better predictions of R are obtained
for Sf =f tan θd (with f = 1.12) rather than arctan (Sf ) = 10°. The
application of Eq. (9) to Swiss debris flows from 1987 (Rickenmann,
2005) also predicts reasonable runout lengths using Sf = 1.08 tan θd,
when observed flow depths are used to estimate the entry velocity uu.
For the back analysis of the Japanese and Swiss data, it was assumed that
the main surge travelled in the existing channel on the fan to the lowest
point of deposition with essentially no change in flow width.
3
flow marks, and deposits. Field monitoring in instrumented areas is an
invaluable way to gather data on debris-flow dynamics (Okuda et al.,1980;
Genevois et al., 2000; Arattano and Marchi, 2008; Hürlimann et al., 2003).
However, field monitoring of debris flows is expensive and timeconsuming, and is only convenient for sites that show both a high
frequency of events and favourable logistical conditions. To overcome
these issues, several authors have used laboratory flumes (small-scale
model experiments) in order to simulate debris-flow deposition
(Mizuyama and Uehara, 1983; Van Steijn and Coutard, 1989; Liu, 1996;
Deganutti et al., 2003; Ghilardi et al., 2003). Quantities such as flow
velocity, the shape of deposits, deposited volume, and grain-size
distribution can be measured and controlled in the laboratory tests.
Problems of scale are relevant for physically simulating these phenomena:
with only a few exceptions (for example the USGS experimental debrisflow flume, 95 m long and 2 m wide; Major, 1997), channels are typically
narrower than 0.5 m and up to a few meters long; the volume of source
material is generally lower than 0.1 m3, and debris mixtures are commonly
restricted to clay, sand, or muddy sand slurries. This notwithstanding, tests
in laboratory flumes make it possible to analyse the relations between
physical variables of debris flows under controlled conditions, and provide
useful data for developing and testing predictive methods.
3. Case study: Fiames debris flows of July 5th, 2006
3.1. Study area
e) Laboratory studies
Post-event surveys allow researchers to detect only debris-flow
features visible after the end of the processes, such as erosional scars,
The debris flow studied in this paper occurred in Fiames, a locality
of the Dolomites (eastern Italian Alps), near the town of Cortina
Fig. 2. Location of the study area with rock basins and debris-flow deposits highlighted.
Please cite this article as: D'Agostino, V., et al., Field and laboratory investigations of runout distances of debris flows in the Dolomites
(Eastern Italian Alps), Geomorphology (2009), doi:10.1016/j.geomorph.2009.06.032
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V. D'Agostino et al. / Geomorphology xxx (2009) xxx–xxx
d'Ampezzo. An intense rainstorm triggered six debris flows in the
afternoon of July 5th, 2006.
Three main morphological units can be identified in the study area
(shown in Fig. 2). Rock basins, composed of dolomite, are present in the
upper part. A thick talus, consisting of particles from silt to boulders (up
to 1–2 m in size), is situated below the rock cliffs (Figs. 3, 4). The lower
part of the slope is occupied by coalescing fans built by debris flows,
whose initiation points are located at the contact between the rock cliffs
and the scree slope (Fig. 4).
The areas of the rock basins range from 0.024 to 0.182 km2, the
maximum elevations are between 1984 and 2400 m a.s.l., and the minimum elevations, which correspond to the initiation areas of the debris
flows, are between 1521 and 1624 m a.s.l. The channel lengths vary
between 110 and 540 m and the mean channel slope between 22° and
28°. The climatic conditions are typical of an alpine environment: the
annual precipitation at Cortina d'Ampezzo ranges between 900 and
1500 mm, with an average of 1100 mm. Snowfall occurs normally from
October to May, and intense summer thunderstorms are common and
constitute a maximum in the seasonal precipitation regime.
3.2. Field surveys
Immediately after the debris flows of July 2006, field surveys were
carried out in the study area. These field surveys made it possible to
measure several features of debris-flow deposits: mean and maximum depth, depths and slopes of deposition lobes, and cross-sections
of the deposits (Fig. 3). Moreover, cross-sections were measured along
the main channel and detailed descriptions of debris-flow initiation
areas were made (Fig. 4). The grain size distribution was assessed:
i) by means of transect-line measurements on the surfaces of terminal
deposition lobes (84% finer than 0.09 m for the finest sample and
0.17 m for the coarsest); ii) by direct measurements of the largest
deposited boulders (1.0 to 1.4 m; intermediate axis); and iii) by
processing photographs of vertical trenches and assessing the
proportion of sediments with diameters finer than 2 cm (estimated
range from 25 to 40% by weight). The boundaries of the debris-flow
deposits were mapped using a hand-held GPS; the other geometric
characteristics were measured using a laser range finder and a tape.
Fig. 4. Debris-flow channel close to the triggering area (basin 3).
LiDAR and photographic data were acquired from a helicopter
flying at an average altitude of 1000 m above ground level during
snow free conditions in October 2006. The flying speed was 80 kn, the
scan angle was 20°, and the scan rate was 71 KHz. The survey design
Fig. 3. Debris-flow deposition area (basin 5).
Please cite this article as: D'Agostino, V., et al., Field and laboratory investigations of runout distances of debris flows in the Dolomites
(Eastern Italian Alps), Geomorphology (2009), doi:10.1016/j.geomorph.2009.06.032
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point density was specified to be greater than 5 points per m2. LiDAR
point measurements were filtered into returns from vegetation and
bare ground using TerrascanTM software classification routines and
algorithms. A comparison between LiDAR and ground GPS elevation
points carried out in a neighbouring basin showed a vertical accuracy
of 0.1 m.
3.3. Event reconstruction
The debris flows of July 5th, 2006 were triggered by an intense
thunderstorm and hailstorm from 6 p.m. to 7 p.m. (Central European
Summer Time). The highest values of rainfall intensity during the
event were 12.5 mm/5 min and 64 mm/h. These values were
measured at a meteorological station located about 1 km from the
study area and are the highest values ever measured at this station
since it began operating in 1984. After the event, many hailstones
covered the slopes for about 2 h. The debris flows blocked the National
Road and a bicycle trail (located on a former railway track) (Fig. 2).
Local low slopes next to the bicycle trail and the National Road helped
slow down and deposit the debris flows.
The debris flows initiated at the outlet of the rock basins by the
mobilization of loose debris into a flow with progressive entrainment
of debris from channel bank erosion and bed scour (Fig. 4). The main
channel stopped (between 1441 and 1553 m a.s.l.) where the slope
angle decreases and the depositional zone starts.
The deposited volume was assessed by subtracting the 5 meter grid
digital terrain model of the deposits (LiDAR data) from the pre-event
topographic surface, fitted from a topographic map at a scale of
1:5000. The results were checked at sample areas in the field and a
vertical accuracy of 0.10 m was inferred.
Water runoff from the rock basins was simulated by means of a
kinematic hydrological model that integrates the US Soil Conservation
Service-Curve Number (SCS-CN) method (Soil Conservation Service,
1956, 1964, 1969, 1971, 1972, 1985, 1993) with a geomorphologic unit
hydrograph (Chow et al., 1988). The SCS-CN method is one of the most
popular methods for assessing direct surface runoff from rainfall data
through a weighted value of the CN parameter of the basin. The
adopted unit hydrograph is extracted from the hypsographic curve by
assuming equivalence between the contour lines and lines with the
same concentration time (Viparelli, 1963). We calculated the
corresponding CN values on the basis of the geological setting and
land use of the six basins upstream of the triggering point (Soil
Conservation Service, 1993). Under normal antecedent moisture
conditions, the obtained CN values are around CN = 85. The second
SCS parametric variable to compute surface runoff involves initial
abstraction, accounting for depression storage, interception, and
infiltration before runoff begins. Its value was set to 10% of potential
maximum retention (directly expressed by the CN) following the
suggestion of Aron et al. (1977) and the assumption of Gregoretti and
Dalla Fontana (2008) in the hydrologic modelling of headwater basins
of the Dolomites. The concentration time was evaluated as the ratio
between the main channel length and the flow velocity along the
slopes (assumed to be equal to 2 m/s).
Subsequently, the following relation was adopted for assessing
debris-flow discharge from the water flood discharge (Takahashi, 1978):
Qd =
Qw
c
1−ce
ð10Þ
Table 2
Basin area AC, deposited volume V, planimetric flooded area A, mean thickness h (volume V
divided by the area of deposition), maximum debris-flow sediment concentration
at equilibrium conditions ce max and ‘hydrologic’ estimation of the debris-flow peak
discharge Q d max for each basin; [Q d max] is computed with the Mizuyama et al. (1992)
equation: [Q d max]= 0.0188V0.79.
Basin
Ac (km2)
V (m3)
A (m2)
h (m)
ce
1
2
3
4
5
6
0.182
0.087
0.147
0.092
0.091
0.024
15,000
10,600
46,800
11,000
5200
2100
10,116
8543
16,934
6785
4609
3751
1.39
1.19
2.57
1.50
1.00
0.50
0.665
0.700
0.710
0.700
0.630
0.725
max
(−)
Q d max
(m3 s− 1)
[Q d max]
(m3 s− 1)
32
21
100
22
12
16
37
28
92
29
16
8
constant ratio ce/c* for the entire duration of the flood would be too
severe a hypothesis in relation to the type of debris-flow surges observed
in the streams of the Dolomites (D'Agostino and Marchi, 2003). Therefore,
the debris-flow graph was computed from the hydrograph plotted,
assuming a linear variation of ce/c* in Eq. (10) from a minimum (ce min =
0.2) to a maximum value (ce max in correspondence to Qw at the peak). The
concentration ce max was calibrated to match the sediment volumes of the
debris-flow deposits estimated by means of the LiDAR data and it resulted
in a range of 0.63–0.72 (mean of 0.69). Table 2 also reports, for each
catchment, the basin area AC, the deposited volume V, the flooded area A,
the mean thickness h, the debris-flow sediment concentration at the peak
(ce max) and the corresponding debris-flow discharge Q d max. The mean
thickness of the debris-flow deposits is the ratio between the deposited
volume and the flooded area.
Table 3 presents the main geometric features related to the runout
and the channel reach bounded by the debris-flow triggering point
and the cross-section where deposition starts.
4. Application of runout and travel distance prediction methods
The methods for assessing runout length and travel distance described
in Section 2 of this paper were applied to the field data of the Fiames
debris flows. The results are discussed in the following paragraphs.
a) Volume balance approach
Using the scheme of Eq. (1), we computed an empirical mobility
relationship for the Fiames debris flows (Fig. 5); the relationship
displays high coefficient of determination (R2 = 0.92) and has a value
of k equal to to 14.2 for d = 2/3. According to Crosta et al. (2003) and
Berti and Simoni (2007), k is almost constant in each lithological
context and reflects yield stress and mobility of the flowing mass.
b) Limiting topographic methods
The debris flows of Fiames decelerate and stop at slopes higher
(Table 3) than those assumed by the methods proposed by Ikeya (1989)
and Burton and Bathurst (1998). Neither method is applicable to the
Fiames case study. Such behaviour can be ascribed to a highly dissipative
Table 3
Main topographic characteristics of the Fiames case study: channel length LC and mean
width Bc, upstream channel slope θu, slope of depositional zone θd, average slope angle
of the whole path β, sloped runout length R, horizontal travel distance L and associated
total drop H, and estimated peak velocity uu of the surge in the channel.
⁎
where Q d is the debris-flow discharge associated with the liquid
discharge Q w, and c⁎ and ce are the “in situ” volumetric concentrations of
bed sediments before the flood and the debris-flow sediment
concentration at equilibrium conditions, respectively. Eq. (10) refers to
a debris flow generated by sudden release of Q w from the upstream end
of an erodible and saturated grain bed. The assumption in Eq. (10) of a
5
Basin
LC
(m)
BC
(m)
θu
(°)
θd
(°)
β
(°)
R
(m)
L
(m)
ΔH
(m)
H
(m)
uu
(m/s)
1
2
3
4
5
6
109
241
539
189
144
238
15.5
11.7
9.9
12.2
12.5
6.04
23.3
21.9
21.9
23.0
21.6
27.9
19.3
16.2
16.0
21.2
21.4
25.9
20.1
18.2
19.7
21.9
21.5
27.0
394
427
312
329
129
183
472
634
800
481
254
375
43
90
201
74
53
111
173
209
287
193
100
191
4.17
3.89
6.93
3.96
3.15
4.78
Please cite this article as: D'Agostino, V., et al., Field and laboratory investigations of runout distances of debris flows in the Dolomites
(Eastern Italian Alps), Geomorphology (2009), doi:10.1016/j.geomorph.2009.06.032
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V. D'Agostino et al. / Geomorphology xxx (2009) xxx–xxx
Fig. 5. Relationship between debris-flow volume and flooded area.
debris flow and large roughness of the terrain. Applying Eq. (2) produces
nonphysical R values (1/4 to 1/20 of observations), because the partial
drop ΔΗ measured in the field is very limited (Table 3).
c) Empirical equations
Eq. (5) tends to overestimate the runout distance, so it can be deemed
conservative in the dolomitic environment (Fig. 6). The recalibrated
Rickenmann (1999) formula (Eq. 6) gives fairly satisfactory results, but it
underpredicts the distances in two cases. The Ikeya (1989) relation (Eq. 4)
shows a similar pattern (Fig. 6), but it has a more marked tendency to
underestimate R. These findings are not surprising, because even though
Eq. (4) is usually applied in different topographic conditions, Ikeya (1989)
suggested its use when the top portion of the fan is less than 8°, whereas
the Fiames alluvial fans are much steeper (Table 3).
The empirical equations for assessing total travel distance agree
well with observed values (Fig. 7). Eq. (7) in particular provides a
correct estimate of the measured values in the study area. Considering
the high fan slope and the L observed values, it is likely that the
rheology expresses high basal shear stresses. Eq. (8) also gives values
that agree fairly well, but it is implicit and the results are too positively
affected by the use of observed H values.
d) Physically-oriented methods
The application of Eq. (9) requires that there be no significant
change in flow width moving from the entry channel to the fan area.
The observed depositional forms make this condition possible (Fig. 2);
it is also supported by the fact that deposits are elongate with a spread
width to runout length ratio close to 0.15.
Fig. 7. Comparison of travel distances observed in the field with those calculated using
the relationships shown in Table 1 for the six studied debris flows.
In order to calibrate Eq. (9) with the data in Tables 2 and 3, we
must first make a preliminary computation of the entering velocity uu
and the assessment of Sf or the parameter f if we set Sf =f tan θd. We
evaluated uu for the peak discharges (Table 2) using the Chézy equation
(uu =C g1/2 hu1/2 sinθu1/2; C=dimensionless Chézy's roughness) adapted
to the surge motion of debris flows (Rickenmann,1999). Gregoretti (2000)
analyzed the neighbouring basin of Acquabona (Genevois et al., 2000) and
came up with a C value close to 3 when the ratio of flow depth to
intermediate diameter of the front sediments is less than 3 and the
channel bed is not congested with loose debris before the surge transit
(both conditions agree with the Fiames event). After computing uu with
C=3 (Table 3), the iterative solution of Eq. (9) for the unknown Sf, where
R is the measured runout distance, gives six f values in the range 1.016–
1.072, with a mean value f =1.030. The relationship can be adequately
calibrated, but is too sensitive to f variations to the third decimal place
when, as in our case study, the upstream slope θu and the fan slope θd are
very close.
5. Laboratory tests
Twenty-nine tests were carried out using a tilting-plane rheometer
(Fig. 8a): twenty tests simulated the quasi-static formation of a fan, and
the remaining nine examined dynamic fan formation by the means of a
flume.
5.1. Experimental device
Fig. 6. Comparison of runout distances observed in the field with those calculated using
the relationships shown in Table 1 for the six studied debris flows.
The physical model consists of a 2 m×1 m tilting plane with an
inclination (α) between 0° and 38°, on which a steel tank with a removable
gate was installed. A fixed horizontal plane (1.5 m×1 m), with an artificial
roughness (Fig. 8b) to simulate the natural basal friction, served as the
deposition area.
The quasi-static tests of fan formation were performed by installing
the tank at the lower end of the tilting plane, i.e. without a flume (Fig. 8a).
The steel tank, with a removable gate facing the deposition plane, is a
parallelepiped with a square base (15 cm×15 cm; 33 cm high) and with a
maximum usable volume of 7 dm3.
Dynamic fan formation was simulated using an artificial flume
installed on the tilting plane (Fig. 9).
The width of the flume is 0.15 m, and it is between 0 and 180 cm
long, depending on the tank position. The artificial channel bottom is
composed of a steel plate with an artificial roughness (Fig. 10a); four
datum lines were painted on the bottom (Fig. 10b).
Please cite this article as: D'Agostino, V., et al., Field and laboratory investigations of runout distances of debris flows in the Dolomites
(Eastern Italian Alps), Geomorphology (2009), doi:10.1016/j.geomorph.2009.06.032
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V. D'Agostino et al. / Geomorphology xxx (2009) xxx–xxx
7
Fig. 8. (a) Tilting-plane rheometer: set-up for quasi-static tests. (b) Detail of the horizontal plane with artificial roughness (thickness 2 mm).
5.2. Tests
The laboratory tests were carried out using debris-flow matrix
collected from lobes in the Fiames fan area. This matrix corresponds,
on average, to 30% by weight of the field deposits. In the laboratory
tests, samples of debris-flow matrix with maximum diameters up to
19 mm were used (Fig. 11); fine material (b0.04 mm) amounts to
28.6%. The tested material has a density of 2.55 g/cm3, a porosity of
25%, an angle of friction of 40° and a mean diameter of 2.14 mm.
Eight quasi-static simulations were performed using a constant
total volume of 3 dm3 to simulate solid concentrations by volume of
45% and 50%; in the remaining twelve quasi-static tests, a constant
solid volume of 3 dm3 was used, and varying amounts of water were
added to obtain solid concentrations by volume of 55%, 60%, and 67%.
The gradients of the tilting plane were 0°, 5°, 10°, and 15°. In the nine
dynamic runs, a constant total volume of 5.5 dm3 was used and the
solid concentrations by volume were 45%, 50%, 55%, 60%, and 65%; the
flume length was 1.8 m with a constant slope of 15°.
Each of the tests followed the same procedure: the material was
placed in the steel tank, the plane was tilted to the chosen slope and the
gate was quickly removed from the tank. The maximum runout distance
(R) and maximum lateral width of deposit (Bmax) were directly
measured during the tests; the area of deposit (A) was measured from
orthophotos of the deposition area. Data measured during the laboratory tests are reported in Table 4.
5.3. Data analysis and application
Fig. 12 shows the geometric parameters involved in the laboratory
data analysis: total drop (H), runout distance (R), total travel distance
(L), distance travelled in the flume by the debris-flow mixture (LF),
upstream point of the mass (t), inclination of the tilting-plane (α), and
the angle of the frictional energy line (β). The total drop H, related to
β, was found to be more significant if computed with respect to the
upstream point of mass (t). It is useful to define the correspondence
between field characteristics of debris flows and laboratory tests. The
initiation area corresponds to the point where the steel tank is
installed, the channel length (LC) corresponds to the distance travelled
in the flume by the debris-flow mixture (LF), and the upstream
channel slope (θu) is the inclination of the tilting-plane (α).
Analysing the variation of β as a function of CV, different trends
result for quasi-static and dynamic tests (Fig. 13). Higher β values in
the dynamic tests explain the larger expenditure of available potential
energy (H) due to flow in the channel. Fitting the data of β versus CV,
an approximate linear relationship can be drawn for the quasi-static
runs (β = 50 CV −14; R2 = 0.90) and the following power function
result for the dynamic tests (Fig. 13; R2 = 0.99):
11:3
β = 12 + 1600 CV
Fig. 9. Rheometer with flume: set-up for dynamic tests.
ð11Þ
Bathurst et al. (1997) assumed H/L = tan β = 0.20 (β = 11.3°).
Similarly in Eq. (11), for CV = 0.50, the H/L ratio is equal to 0.22
(β = 12.6°), but increasing the volumetric concentration causes the
H/L ratio to rise quickly (i.e. with CV = 0.60, β is 17°) and highlights
a strong dependence of L on H and CV and a weak dependence on the
released sediment volume (Table 4).
Eq. (11) was applied to predict travel distances surveyed in the
field (Table 3). We assumed that CV = 0.60 and 0.65, corresponding to
the highest sediment concentrations tested in the dynamic runs and
near the back-calculated field values (ce max, Table 2). The best
prediction (Fig. 14) comes from using CV = 0.65; the errors are
comparable to those gotten by applying Eq. (7) (Zimmermann et al.,
1997), which proved to be the more accurate empirical equation.
Please cite this article as: D'Agostino, V., et al., Field and laboratory investigations of runout distances of debris flows in the Dolomites
(Eastern Italian Alps), Geomorphology (2009), doi:10.1016/j.geomorph.2009.06.032
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V. D'Agostino et al. / Geomorphology xxx (2009) xxx–xxx
Fig. 10. (a) Detail of the flume bottom with artificial roughness (thickness 2 mm). (b) Upstream view of the artificial flume.
6. Discussion
We first comment about the magnitude of the Fiames debris flows,
i.e. the volumes deposited during the event. The unit magnitudes of
the debris flows that occurred in Fiames on July 5th, 2006, computed
as the ratio of total discharged volume to the drainage area upstream
of the fan apex (Table 2), range from 60,000 to 300,000 m3/km2.
These values, compared to the extensive analysis carried out in the
Eastern Italian Alps by Marchi and D'Agostino (2004) on historical data
of debris-flow volumes (upper envelope: V/Ac = 70,000 m3/km2), shed
light on the low frequencies (b1/100 year− 1) of the events in the six
basins of Fiames (Italy).
It is difficult to reconstruct flood hydrographs in ungauged basins,
especially for floods caused by intense and spatially limited rainstorms.
Thus, possible uncertainties in the hydrological analysis, which was
carried out as a preliminary step in assessing debris-flow graphs, deserve
some attention.
The homogeneous characteristics of the basins, dominated by
dolomite outcrops, make it possible for us to state that only minor
errors affect the choice of CN and time of concentration. Larger
uncertainties could be associated with rainfall amounts: convective
rainstorms have strong spatial gradients, and in mountainous areas,
wind may also have a non-negligible influence on rainfall amounts.
The large magnitude of the debris flows under study, stressed at the
beginning of this section, could indicate that they were caused by
rainfall higher than that recorded at the rain gauge used in rainfallrunoff modelling. However, the assessment of debris-flow graphs by
means of Eq. (10) produced a realistic balance of water and sediment
volumes, with sediment concentration at the peak (0.63–0.72;
Fig. 11. Grain size distribution of debris-flow material used in the laboratory tests.
Table 2), which agrees with the topographic conditions of deposition
surveyed in the fans and replicated by means of the tilting plane
(Cv = 0.65–0.67). Finally, the resulting back-calculated peak discharges match those from the equation of Mizuyama et al. (1992)
for muddy debris flows (Table 2), which are comparable to debris
flows from dolomite rocks (Moscariello et al., 2002). These circumstances all corroborate the robustness of our hydrological approach for
back-calculating the debris-flows flood evolution, when sediment
availability is unlimited (Fig. 4) and the triggering rainfalls have large
return periods, as in the Fiames case study. Our analysis of deposition
areas and runout distances overlapped various approaches, ranging
from empirical methods to those requiring kinematic characteristics
of the flow.
The power relationship between flooded area and deposited volume
(Eq. 1) has two constants, one of which (the d exponent) is proved to be
scale-invariant when is set equal to 2/3 (Iverson et al., 1998; Crosta et al.,
2003). Following this assumption, the remaining coefficient (k)
becomes a surrogate for debris-flow mobility. The Fiames debris-flows
derive from carbonate colluvium with an abundant presence of granular
material (mainly small boulders and coarse gravel) in a silty-sand matrix
(Fig. 11). The best-fit k value of 14.2 for the Fiames debris flows is higher
than the value obtained for the debris flows of Valtellina (Lombardy,
northern Italy), studied by Crosta et al. (2003) (k = 6.2), but it is much
lower than the value calibrated by Berti and Simoni (2007) for debris
flows in various parts of the Italian Alps (k = 33). A high value of this
coefficient (k = 32.5) was also obtained for rapid debris-earth flows in
the volcaniclastic cover near Sarno (southern Italy) (Crosta et al., 2003).
The Valtellina data have a dominant lithology comprised of
dolostone (Val Alpisella), phyllites and paragneiss (Campo Nappe, Val
Zebrù). If we rearrange the best-fit equation obtained by Crosta et al.
(2003) for the two subsamples (forcing the exponent d to 2/3), we
obtain k = 5.3 for phyllites and k = 8.8 for dolomites. We could therefore
conclude that an average value of k of about 10 would be applicable for
debris flows fed by dolomite rocks. This value of k is low and quite close
to that obtained for debris flows rich in fine material derived from
metamorphic rocks in Valtellina: the calibration of k supports the
cohesive behaviour of debris flows from dolomite colluvium. This
finding agrees with the classification of dolomite debris flows as
cohesive sediment gravity flows proposed by Moscariello et al. (2002)
on the basis of sedimentological observations.
The failure of limiting topographic methods (Ikeya,1989; Burton and
Bathurst, 1998) and the occurrence of deposition on fan slopes greater
than 16° confirm that high basal shear stresses developed during the
Fiames event. Debris-flow deceleration was likely enhanced by water
draining from the mixture during its movement. As it is typical in the
Dolomites, the Fiames alluvial fans are arid and dominated by loose,
coarse debris. Actually, fine material is abundant in fresh deposits, but is
Please cite this article as: D'Agostino, V., et al., Field and laboratory investigations of runout distances of debris flows in the Dolomites
(Eastern Italian Alps), Geomorphology (2009), doi:10.1016/j.geomorph.2009.06.032
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V. D'Agostino et al. / Geomorphology xxx (2009) xxx–xxx
9
Table 4
Data from the laboratory tests (L = H/tan β). Debris flow of run No.1 stopped in the channel (H reported for this run is the difference in elevation between point t of Fig. 12 and the
end of the deposit in the channel).
Test
N
R (m)
Bmax (m)
A (m2)
LF (m)
MT (kg)
H (m)
α (°)
β (°)
CV
ρeq (g cm− 3)
Dynamic runs
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
–
0.580
1.140
1.180
1.350
1.150
1.060
1.410
1.300
0.450
0.760
0.890
0.750
0.810
0.490
0.745
0.960
0.680
0.780
0.490
0.760
0.935
0.700
0.800
0.500
0.710
0.960
0.750
0.780
–
0.350
0.425
0.610
0.880
0.435
0.615
0.670
0.950
0.525
0.770
0.955
0.710
0.830
0.475
0.745
0.980
0.770
0.840
0.560
0.795
1.005
0.770
0.840
0.610
0.825
0.950
0.780
0.870
–
0.176
0.405
0.596
0.800
0.416
0.515
0.769
0.831
0.207
0.531
0.685
0.423
0.524
0.197
0.475
0.680
0.456
0.541
0.234
0.466
0.705
0.462
0.567
0.269
0.436
0.686
0.464
0.591
1.23
1.80
1.80
1.80
1.80
1.35
0.90
1.35
0.90
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
11.080
10.615
10.150
9.763
9.375
10.150
10.150
9.375
9.375
9.153
9.623
10.136
5.325
5.093
8.684
9.660
10.135
5.325
5.093
9.170
9.667
10.138
5.325
5.093
9.139
9.664
10.112
5.325
5.093
0.580
0.728
0.728
0.728
0.728
0.611
0.495
0.611
0.495
0.211
0.235
0.258
0.141
0.141
0.213
0.232
0.257
0.147
0.147
0.220
0.238
0.262
0.151
0.151
0.224
0.242
0.262
0.155
0.155
15
15
15
15
15
15
15
15
15
0
0
0
0
0
5
5
5
5
5
10
10
10
10
10
15
15
15
15
15
24.49
16.85
13.80
13.62
12.92
13.54
13.80
12.32
12.38
19.38
14.45
13.93
8.89
8.34
18.93
14.86
13.30
10.16
9.07
20.03
15.28
14.15
10.38
9.28
20.65
16.80
14.07
10.16
9.83
0.65
0.60
0.55
0.50
0.45
0.55
0.55
0.45
0.45
0.67
0.60
0.55
0.50
0.45
0.67
0.60
0.55
0.50
0.45
0.67
0.60
0.55
0.50
0.45
0.67
0.60
0.55
0.50
0.45
2.015
1.930
1.845
1.775
1.705
1.845
1.845
1.705
1.705
2.034
1.925
1.843
1.775
1.698
1.930
1.932
1.843
1.775
1.698
2.038
1.933
1.843
1.775
1.698
2.031
1.933
1.839
1.775
1.698
Quasi-static runs
soon winnowed away from the surface layer by overland flow. As a
consequence, subsequent debris-flow runout occurs on very permeable
surfaces that favour water infiltration.
The assessment of Eq. (9) based on the momentum conservation
confirms the findings of Okuda and Suwa (1984) and Rickenmann
(2005) that the frictional energy slope Sf is very close to the slope Sd of
alluvial fans generated from debris flows. The maximum calibrated
ratio between the two slopes (coefficient f = 1.072) is close to that
proposed by Rickenmann (2005) (f = 1.08) and is lower than the value
(f = 1.12) obtained by Okuda and Suwa (1984). The case study would
therefore suggest that, in alpine debris flows, an assumption of f = 1.07
to 1.08 is reasonable for a cautionary assessment of travel distances.
The applications of empirical formulas for runout and travel distance
indicate that they remain a useful tool for creating a preliminary hazard
map. Eq. (8) implicitly contains the distance under prediction as an
independent variable (H, on the right side of the equation, is a function
of L). The performance of Eq. (8) for the Fiames debris flows is influenced
by known H values, but a non-convergent topographic solution can be
reached for steep alluvial fans. Considering the remaining empirical
formulas, Eq. (5) generally overpredicts R, whereas Eqs. (4) and (6) give
less conservative results, but the underestimates of R do not exceed 33%
and 23%, respectively (Fig. 6). The acceptable performance of the Ikeya
(1989) equation (Table 1; Eq. 4) is noteworthy, considering that it was
developed for Japan, i.e. under different geomorphological, geological and
climatic condition (Fig. 6). Eq. (7) was proposed by Zimmermann et al.
(1997) as a lower envelope of the H/L ratio. In this research, the equation
best predicts the observed travel distances (Figs. 7 and 14) and is a further
confirmation of the previous remarks on the highly dissipative behaviour
of debris flow originating in drainage basins with dolomite lithology.
The H/L ratio, which corresponds to a resistance coefficient, was one
of the earliest dimensionless variables used (Heim,1882) when studying
the potential travel distance of gravitational phenomena (rock and snow
avalanche, earthflow, landslides). The inverse of the H/L ratio (L/H = 1/
tan β ) is the net travel efficiency and expresses energy dissipations both
inside (frictional, turbulent and viscous) and outside the flow. The latter
are caused by the topography and the roughness of the surface on which
debris flows propagate, as well as by the presence of obstacles (houses,
levees, woods, etc.). Several researchers (Corominas, 1996; Iverson,
1997) suggest a range of L/H from 2 to 20 and a decreasing trend with
the logarithm of deposited volume. According to Japanese field
Fig. 12. Schematic diagram of tilting-plane rheometer with the geometric parameters
involved in the laboratory data analysis.
Fig. 13. Relationship between the angle of the frictional energy line (β) and the volumetric
concentration (CV).
Please cite this article as: D'Agostino, V., et al., Field and laboratory investigations of runout distances of debris flows in the Dolomites
(Eastern Italian Alps), Geomorphology (2009), doi:10.1016/j.geomorph.2009.06.032
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in Eq. (11) of a lower CV (0.6) overestimates L on average by 30% and
gives a large response of L to a small variation in Cv, when Cv is close to
maximum values for debris flows. The tight dependence of L on Cv could
be surrogated by the link of L with the catchment area (Ac) (Eq. 7), as Ac,
from a morpho-hydrological point of view, is directly proportional to the
runoff volume and inversely proportional to Cv. In this context, further
research is necessary to better define whether and under which
conditions laboratory results on fan formation and runout distance are
comparable to corresponding field features.
7. Conclusions
Fig. 14. Comparison of travel distances observed in the field with those calculated by
means of Eqs. (11) and (7) for the six studied debris flows.
observations, Bathurst et al. (1997) suggests a value of L/H=5 for debris
flows. In the 71 cases reported by Corominas (1996), L/H varies from 1.3 to
15. The studies by Toyos et al. (2007) on the Sarno event, dealing with
volumes of 104–105 m3, report a range of L/H from 2.4 to 4.2, (mean=3.1).
Iverson (1997), for 10 m3 of poorly sorted sand gravel debris-flow mixture,
obtained values close to 2.
Our field data (Table 3) range between 2 and 3 (mean = 2.6) and
show increasing values in the volume range 2 × 103–1 × 104 m3, while
for the largest magnitude (4.7 × 104 m3), L/H remains close to 3. The
laboratory experiments on a sub-sample of the Fiames debris flow
(static and dynamic tests; CV varies between 0.45 and 0.67) stress a
higher travel efficiency (Fig. 13), between 2.2 and 6.8 (mean = 4.3).
The efficiency decreases (L/H = 2.2–4.2; mean of 3.5) when considering the volumetric concentration CV N 0.5, but still tends to be larger
than field data (mean laboratory value 3.5 against 2.6).
Iverson (1997) showed that: a) scale is of paramount importance in
experimental studies of debris flows, and b) small-scale models do not
satisfactorily replicate the natural process. In particular, two scaling factors
must be taken into consideration (Iverson and Denlinger, 2001; Denlinger
and Iverson 2001): a non-Newtonian Reynolds number and a number
expressing the influence on the flow motion of the pore pressure diffusion
normal to the flow direction. The rigorous study by Iverson and Denlinger
(2001) shows that viscous effects are less important and pore pressure is
preserved much longer in flows at larger scales. The rapid dissipation of
pore pressure could then increase the resistance to motion in small-scale
models.
In our laboratory tests, the measured higher mobility with respect to
the field scale seems to depict a different behaviour from that expected
on the basis of the aforementioned physical conditions. The lower
energy dissipation in the model is likely to be ascribed to the incomplete
range of debris sizes, and to the low roughness of the channel (Fig. 10a)
and deposition plane (Fig. 8b), which does not represent the
topographic irregularities of the alluvial fan and the presence of
vegetation.
Model experiments make it possible to analyse the influence of the
volumetric concentration on R. In fact, CV strongly controls R, almost
regardless of the mass of the sediment (Fig. 13; Table 4). The dynamic
tests also reflect the fraction of the initial potential energy dissipated
along the channel due to the distance travelled in the flume (Lf; Table 4).
A quasi-static formation of the fan caused by a dam-break at its apex
corresponds to lower β angle compared to the alluvial fan formation
controlled by an entering channel (Fig. 13). The application of Eq. (11)
with the more competent CV value (0.65) in the field fits the Fiames data
well (Fig.14) and gives an accuracy (mean underestimation around 13%)
comparable to Eq. (7), which was derived from Swiss field data. The use
The runout distance and total travel distance were investigated for
six debris flows triggered by the same rainstorm in contiguous
catchments of the Dolomites. Basin areas (from 0.02 to 0.1 km2) and
debris-flow volumes (from 2 × 103 from 5 × 104 m3) vary by one order of
magnitude and offered the possibility of comparing several methods for
assessing the terminal displacement of the debris-flow sediments. The
approach adopted in this study coupled field observations with
laboratory tests on material collected from debris-flow deposits.
The application of field data to the relationship between flooded area
on the alluvial fan and debris-flow volume made it possible for us to
calculate a value of the coefficient k in Eq. (1) for debris flows generated
from basins with dolomite lithology, in topography typical of the studied
area.
The application of empirical methods for predicting the runout
distance on fans and total travel distance of field data enabled us to
identify equations suitable for assessing these variables for debris flows on
scree slopes and alluvial fans of the studied region. Both the calibration of
the volume balance relationship and the application of empirical
equations outline low mobility of viscous silt-rich debris flows of the
Dolomites.
Experiments carried out on sediment samples collected from
debris-flow deposits allowed us to analyse the relationships between
variables that control the distances attained by debris-flow mixtures.
Although scale issues cause major problems in small-scale laboratory
studies of debris flows, integrating laboratory tests with field
documentation of debris flows proved promising for studying these
hazardous phenomena.
Acknowledgments
We thank Marco Cavalli for collaborating in the field surveys. LiDAR
data have been arranged by C.I.R.GEO (Interdepartmental Research
Center for Cartography, Photogrammetry, Remote Sensing and G.I.S.),
University of Padova. The research was supported by: “MURST ex 60%”
Italian Government funds, years 2007–2008, Prof. Vincenzo D'Agostino;
PRIN-2007 project: “Rete nazionale di bacini sperimentali per la difesa
idrogeologica dell'ambiente collinare e montano”, Prof. Sergio Fattorelli.
The comments of Paul Santi and an anonymous reviewer helped
improve the manuscript.
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Glossary
A
AC
B
Bc
Bmax
c⁎
ce
C
CV
d
f
g
h
hu
H
ΔH
k
L
LC
LF
MT
N
Qd
Qw
R
Sf
Sd
t
uu
V
α
β
θd
θu
ρeq
ω
flooded area (m2) (field and laboratory)
catchment area (km2)
maximum lateral width of deposit (m)
mean width of the channel upstream of deposition initiation
maximum lateral dispersion of deposit in the laboratory
“in situ” volumetric concentration of bed sediments before the flood
debris-flow sediment concentration at equilibrium conditions
dimensionless Chézy coefficient
solid concentration by volume, CV = VS / (VS + VL), where VS is the solid
volume and VL is the water volume)
empirical coefficient in Eq. (1)
empirical coefficient
gravitational acceleration (9.81 m s− 2)
mean thickness of the deposit (m)
entry flow depth (m)
potential mass energy and total drop (m) (field and laboratory)
elevation difference between the initiation point and the point where
deposition starts (m)
empirical coefficient in Eq. (1)
total travel distance (m)
channel length (m)
distance travelled in the flume by the debris-flow mixture (m)
total mass of sediment in laboratory tests (kg)
number of the test
debris flow discharge (m3 s− 1)
liquid discharge (m3 s− 1)
runout distance (m) (field and laboratory)
friction slope (m/m)
fan slope (m/m); Sd = tan θd
upstream point of the mass
entry velocity (m s− 1)
debris-flow volume (m3)
inclination of the tilting-plane (°)
mean angle of the frictional energy line (°) (field and laboratory)
terrain slope angle along the deposition, angle of the fan slope (°)
angle of the channel upstream of deposition initiation (°)
bulk density of the debris flow in laboratory tests (g cm− 3)
empirical coefficient in Eq. (2)
Please cite this article as: D'Agostino, V., et al., Field and laboratory investigations of runout distances of debris flows in the Dolomites
(Eastern Italian Alps), Geomorphology (2009), doi:10.1016/j.geomorph.2009.06.032