Vol.2, No.1, 9-15 (2011) Agricultural Sciences
Copyright © 2011 SciRes. Openly accessible at http:// www.scirp.org/journal/AS/
Assessment of debris flow magnitude in small
catchments of the lombardy alps: the val gola case
Daniele de Wrachien1, Stefano Mambretti2*
1Department of Agricultural Hydraulics, State University of Milan, Milano, Italy;
2 DIIAR, Politecnico di Milano, Piazza Leonardo da Vinci, Milano, I taly; *Corresponding Author: stefano.mambretti@polimi.it
Received 12 December 2010; revised 30 December 2010; accepted 6 January 2011
Debris flows are among the most destructive of
all water-related disasters. They mainly affect
mountain areas in a wide range of morpho-
climatic environments. Therefore, accurate pre-
diction of their run out distances, magnitudes
and velocities plays a role of paramount impor-
tance, in order to plan and design appropriate
structural and non-structural defence measures.
In this context, a number of Authors have de-
veloped methods feasible to evaluate the ten-
dency of a catchment to generate debris flow,
without giving an estimation of the magnitude.
Other empirical procedures are based on the
analysis of historical series of debris flow, oc-
curred in similar environments, to assess the
relationship between the catchment character-
istics and the maximum movable debris vol-
umes. In this paper, and with reference to Val
Gola—a small catchment in the North-East Lom-
bardy where debris flows frequently occur—a
number of methods, belonging to each of the
above mentioned categories, have been briefly
reviewed and applied in order to evaluate their
effectiveness a nd c ons istency.
Keywords: Val Gola Catchment; Debris Flow;
Magnitude Assessment; Frequency Analysis
Sediment transport in steep, small (<10 km2) catch-
ments of the Alps is often characterised by both newto-
nian (flood waves of clear water) and non newtonian
(debris and mud flows) behaviour. The availability of
long-term series of data (e.g. volumes, magnitude, ve-
locity and frequency) is crucial in order to provide sta-
tistically significant analyses and predictions, thus
making experimental measuring stations highly valu-
able for the scientific community as well as for the lo-
cal agencies dealing with structural protection meas-
ures and land use planning.
In Italy, like the other European countries, there is a
lack of such experimental data, with a few exceptions
In this context, a number of authors developed me-
thods feasible to evaluate the tendency of a catchment
to generate debris flow, without giving an estimation of
the magnitude [4,5]. Other empirical (statistical and
semi-quantitative) procedures are based on the analysis
of historical series of debris flow, occurred in similar
environments, to assess the relationship between the
catchment characteristics and the maximum movable
debris volume.
In this paper, and with reference to Val Gola—a
small catchment in the North-East Lombardy where
debris flow frequently occur—a number of procedures,
belonging to each of the above mentioned categories,
have been briefly reviewed and applied in order to
evaluate their effectiveness and consistency.
At present, there are no rigorous methods feasible to
assess the exact probability of debris flow occurrence.
Semi-quantitative methods which allow to estimate the
likelihood of debris flow occurrence in a particular tor-
rent basin have been proposed by different authors [6].
As an alternative, numerical simulation models can be
used to assess the flow properties and the deposition
process [7].
2.1. Debris Flow Characteristics
From the point of view of the evaluation of a potential
hazard, the volume
and the peak discharge
Q of
a debris flow represent the most important parameters.
In general, a spectrum of possible debris flow volumes
D. de Wrachien et al. / Agricultural Sci ences 2 (2011) 9-15
Copyright © 2011 SciRes. Openly accessible at http:// www.scirp.org/journal/AS/
and peak discharges can be expected to occur with dif-
ferent probabilities.
a) Many attempts have been made to estimate a
maximum debris flow volume for a given torrent catch-
ment. These empirical equations are usually based on the
most important morphometric characteristics of a catch-
ment [8,9]. It was found that these equations may over-
estimate the actual debris flow volume by up to a factor
of 100 [2]. To overcome these uncertainties, D’Agostino
[10-12] introduced a Geologic Index, which takes into
account the different lithologic units of the catchment.
Others followed the same path [13]. On the other hand,
simplest method relies on fewer parameters, as the area
b) Knowledge of the peak discharge and the associ-
ated flow velocity play a role of paramount importance
when evaluating the conveyance capacity of a stream
channel reaches or critical cross sections, as, for example,
under bridges. It has been shown that empirical rela-
tionships can be established between the peak discharge,
Qp, of a debris flow and the debris flow volume [15].
c) Other parameters like mean flow velocity, flow
cross-section, travel distance and runout distance on fan
play important roles in the assessment of a debris flow
potential hazard [2].
Further characteristics, observed in the field, may also
be used to estimate the probability of debris flow occu r-
rence and feature the triggering, mobilisation and stop-
ping processes [4 ,5 ,1 6,17].
2.2. Probabilistic Analysis of Historical Data
Most empirical and statistical procedures for the esti-
mation of debris flow magnitude compute “maximum”
or “extreme” possible volumes. Less information is usu-
ally available about magnitude-frequency relations,
which can usefully contribute to the definition of de-
fence measures [18].
On the whole, empirical and probabilistic predictive
relationships provide an approximate assessment of de-
bris flow characteristics and their use should be re-
stricted to the environmental context (geological, geo-
morphological, climatic) where they have been devel-
oped. It has been pointed out [19] that these procedures
produce very different results where employed in other
geographical areas, without a previous check of their
applicability in a given region.
3.1. Geological and Geographical
The Val Gola catchment (3.5 km2), located in the
eastern Italian Alps (Val Camonica, Lombardy Region),
belongs to the Olio river basin. The catchment shows an
elliptical form, with the main axes oriented in NW-SE
direction (Figure 1).
Geologically, the catchment, of great importance from
both economic and turistic points of view, is character-
ised by different lithologies, essentially represented by
Figure 1. Location map of the study area.
D. de Wrachien et al. / Agricultural Sci ences 2 (2011) 9-15
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evaporite and carbonate sedimentary units (Angolo,
Camorelli, and Esimo limestones) chronologically dated
between low and medium Triassic. Quaternary fans are,
mostly, present in the lower part of th e valley. According
to their genesis, these deposits can be classified as
gravitative fans or screes, deposits due to the fluvial
processes and glacial deposits (moraines). Upper Qua-
ternary fans, outcropping in different areas and having
different stratigraphical positions are present, mainly, in
the southern part of the catchment (Fermata Castello).
3.2. Field Surveys
Field surveys have been carried out to directly collect
data and to verify those indirectly collected by air-photo
interpretation and historical sources (flood frequencies,
date and magnitude of past events, damages, landsliding
and areal extension of flooded areas). Based on these
observations an estimatio n of the main debris flow char-
acteristics (magnitude, mixture and water discharges etc.)
has been carrie d out .
From the morphology of the fans, the knowledge of the
occurred past events, the characteristics of the drainage
basin and the prevalent transport mechanism associated
with individual fans were determined. The main outcomes
of these investigations are summarized in the following
The analysis of morphometric and hydrologic pa-
rameters used to describe the catchment characteristics
and behaviour was based on the most frequently adopted
approaches for the assessment of the type and magnitude
of dominant alluvial fan activity.
The main aims of the analysis performed in this study
can be summarized as follow:
to put in evidence any significant statistical rela-
tionship among the parameters;
to analyse the relationships between the group of
morphometric parameters and the type of activity;
to analyse the relationships between the mor-
phometric parameters and the feasible maximum inten-
sity of the different events.
4.1. Empirical Methods
Figure 2 shows the catchment’s tendency to debris
flow generation according to Melton and Aulitzky’s in-
dexes, modified by Ceriani et al. [20]. The Aulitzky’s
index was evaluated equal to 15, featuring the bent of
the basin for debris flow triggering as medium-high.
Table 1 summarizes the results of the first nine em-
pirical relationships. It is quite evident that this formulae
give only approximate estimations of the possible maxi-
mum intensity of debris flow events. Such relationships
00.1 0.2 0.3 0.4 0.5 0.6 0.70.8 0.91
Melton Fan Index
Slope Fan
Bed load fan
Debris flood fan
Debris flow fan
Figure 2. Catchment’s tendency to the debris flow genera-
tion according to Melton index.
Table 1. Comparison of debris flow magnitude assessed by
empirical relationships based on morphometric parameters
Applied method Magnitude [m3]
Marchi and Tecca [9] 20440
Bottino, Crivellari and Mandrone [14] 28674
Rickenmann [2] 150000
Kronfellner—Kraus [16] 186150
Hampel [8] 296150
M1 = 51257
D'Agostino et al. [10,11] M2 = 58250
D'Agostino et al. [12] 64482
Bianco and Franzi [13] 37547
h = 1 m 42395
h = 1.5 m 63592
Tropeano and Turconi [17]
h = 2 m 84790
can probably be improved if factors controlling sediment
supply are also taken into account.
At present it appears that a geomorphologic assess-
ment in the field of material likely to be mobilized may
be the best approach to arrive at a more precise estimate
of a possible debris flo w v ol u m e .
It seems, therefore, necessary to test the reliability of
these relationships by means of physically based meth-
Beside the above mentioned empirical formulae, the
following relationship can be used, suitable to assess the
rate between the debris flow T
Q and water W
Q dis-
charges of the catchment [15]:
*b b*
QcS Scc
 
where *
c is the packing concentration of the solid
phase (usually equal to 0.65), c is the debris flow con-
centration and b
S the degree of saturation of the river
bed before the debris flow passage. Assuming b
S = 1
[21] the expected debris flow discharge is equal to 2-3
times the liquid discharge. The trend of the function (1)
is shown in Figure 3.
The simplicity of this procedure does not prevent the
assessment of the debris flow magnitude as function of
D. de Wrachien et al. / Agricultural Sci ences 2 (2011) 9-15
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Sb = 0
Sb = 1
Figure 3. Ratio between the debris flow and liquid dis-
charges Vs the debris flow concentration, with a variation of
the ground saturation.
the return period, which plays a role of great importance
in the design of defensive measures.
In the case of the Val Gola catchment, in order to per-
form these computations, the estimation of the flood
wave for different return times has been carried out. To
do that, starting from Depth Duration Frequency (DDF)
curves of different return times, a Chicago hyetograph
has been built, which is critical for any duration shorter
than its base time. On the basis of these hyetographs two
infiltration methods have been used: Soil Conservation
Service, with CN = 72; and Horton’s, considering a soil
of type C [22]. Depression storages have been consid-
ered equal to zero, being this assumption on the safe side,
but without be exaggerated because of the very high
slope of the catchment.
The rainfall/runoff relationship is of the usual convo-
lution type, where the instantaneous unit hydrograph is
the derivative of the time-area curve, normalized with
respect of the total area.
The travel times have been computed considering the
flow over a plane [23]:
where L is the catchment length,
k its roughness, s the
slope and i the rainfall intensity. The catchment rough-
ness is a model parameter, tabled in [24], and assumed,
in this work, equa l to 10.
Generally speaking, not all the discharges produce
solid transport, but with the simple application of the
Schoklitsch’s relationship [25] it was easy to verify that,
due to the very high slope, the hydrograph tails, which
do not produce solid transport, are very limited.
With the described methodology, the following results
have been obtained:
5075900 3
T years,Wm,W
150000230000 3
10088038 3
T years,Wm,W
170000 270000m;
200 100807
T years,Wm,W
200000 300000m.
4.2. Physically Based Methods
Physically based approaches for assessing debris flow
volumes are founded on the recognition of sediment
sources, located along the channel network and feasible
to be moved, in order to evaluate the probability of col-
lapse. Some of these methods, known as geomor-
phological methods [26], assume that all eroded material
reaches the alluvial fan, whereas others consider the
possibility of a partial redeposition within the basin.
Generally speaking, differences in density amongst
debris in source areas, flowing water-sediment mixture
and debris flow deposits are usually neglected.
In this work with the term “mass of sediment” is in-
tended a debris volume made up of a single typology of
prevalent material with homogeneous dimensions and
materials, which represents an approximate hypothesis.
The probability of collapse of a mass of sediment has
been assessed on the basis of the typology of the mate-
rial and the topographical and morphological character-
istics of the catchment.
For each single mass, the following parameters have
been measured: area m
, length m
L, average slope
average thickness H, porosity n, permeability k, internal
friction angle
and the upstream subcatchment char-
acteristics, in particular the area b
, the runoff coeffi-
and the slope S. The porosity and permeability
values have been evaluated in a detailed study performed
by Ghilardi et al. [27], assigning literature values checked
with maps drawn up by the competent Authority (the
Lombardy Region).
On the basis of field surveys, the thickness of the
sediments have been assessed within the range 1-3 m.
Table 2 shows the debris volumes and the upstream
catchment characteristics, while Ta b l e 3 gives the mov-
able volumes, as function of the mean thickness.
Different p roc edur es a re av ailab le , fe asib le to ev alu ate
the probability of movement of a sediment mass [28].
According to Chen and Jan [28], the water depth that can
move the mass is given by:
ss s
tantanGG nsn
mtantans n ntan
 (3)
G specific weight of the solid divided by the
specific weight of the liquid (Gs = γs/γw);
specific weight of the solid;
specific weight of the liquid (water);
n porosity;
D. de Wrachien et al. / Agricultural Sci ences 2 (2011) 9-15
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Table 2. Debris volumes and upstream catchment characteristics.
Area Am [km2] 0.266 0.237 0.132
Maximum elevation Hmax [m asl] 1400 1300 1150
Minimum elevation Hmin [m asl] 900 890 944.74
Length Lm [km] 0.861 0.666 0.519
Mean slope θ [° ] 30.14 31.4 21.55
Mean thickness H [m] 1-3
Porosity n [-] 0.5
Permeability k [m/s] 0.1
Int. friction angle Φ [°] 33
Area Ab [km2] 0.158 0.113 0.976
Maximum elevation hmax [m asl] 1600 1400 1718.32
Minimum elevation hmin [m asl] 1400 1300 1150
Length Lb [km] 0.252 0.156 0.903
Mean slope S [°] 38.31 32.62 32.61
Runoff coefficient φ [-] 0.7 0.7 0.7
Table 3. Debris movable volumes vs mean thickness.
Potentially movable volume [m3]
H = 1.0 m H = 1.5 m H = 2.0 m H = 2.5 m H = 3.0 m
AM1 266000 399000 532000 665000 798000
AM2 237000 355500 474000 592500 711000
AM3 132000 198000 264000 330000 396000
saturation of the solid;
stratification angle of the solid.
Known m and H, the critical water depth h to generate
a slide is given by:
hmH (4)
while the discharge Q through a vertical section of a
sediment mass with height H can be assessed as follows:
Qkhnl (5)
where m
l is the mean width of the debris mass, defined
as the ratio between its area and length along the direc-
tion of the maximum slope:
The critical intensity of the rainfall to generate Q is
given by:
 (7)
with b
the area of the subcatchment upstream the
debris mass.
For the Val Gola catchment 07.
has been se-
lected on the basis of accurate hydrologic investigations
On the basis of these parameters, further characteris-
tics have been evaluated. Ta bl e 4 gives the return peri-
ods needed to move masses of debris flows of different
For masses so large, the hypothesis that they can col-
lapse entirely at the same time cannot be accepted. So,
these debris masses have been divided in “sub-masses”,
generated by different subcatchments.
Table 5 gives the return periods of the rainfalls that
triggered the collapse of the debris flow sub-masses.
To achieve a more reliable assessment of the catch-
ment instability, the well-known Shalstab code [29] was
applied. To this end, the basin area has been divided with
DEM cells of 20 m × 20 m (Figure 4). The Figure 4
shows that about 65% of the area results to be uncondi-
tionally unstable (indep endently of the rainfall intensity)
and for about 30% the stability depends on the rate be-
tween the rainfall intensity and the soil p ermeability. The
remaining 5% of the catchment results unconditionally
With respect to the hazard assessment of a small tor-
rent catchment of the Alps (Val Gola) different empirical
methods have been applied with the aim of determining
whether debris flow are likely to occur or not.
Each of the considered methods shows both advan-
tages and shortcomings. The wise application and a
D. de Wrachien et al. / Agricultural Sci ences 2 (2011) 9-15
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Table 4. Return period of the rainfall necessary to move the debris flow volume (function of the
average depth).
H [m] 1.0 1.5 2.0 2.5 3.0
AM1 <5 5-10 10-20 20-50 100-200
AM2 <5 <5 5-10 10-20 20-50
AM3 <5 <5 10 20-50 50-100
Table 5. Return period T of the rainfall necessary to move the sub-masses of the volume AM1.
1.0 T < 5
V = 15000 m3
T < 5
V = 50000 m3
T < 5
V = 123000 m3
T < 5
V = 219000 m3
T < 5
V = 266000 m3
1.5 T < 5
V = 22500 m3
T < 5
V = 75000 m3
T < 5
V = 184500 m3
T = 10-20
V = 328500 m3
T = 5-10
V = 399000 m3
2.0 T < 5
V = 30000 m3
T < 5
V = 100000 m3
T = 5
V = 246000 m3
T = 50
V = 438000 m3
T = 10-20
V = 532000 m3
2.5 T < 5
V = 37500 m3
T < 5
V = 125000 m310-20
V = 307500 m3
T = 100-200
V = 547500 m3
T = 20-50
V = 665000 m3
3.0 T < 5
V = 45000 m3
T < 5
V = 150000 m320 – 50
V = 369000 m3
T > 200
V = 657000 m3
T = 100-200
V = 798000 m3
Figure 4. Evaluation of the stability of the catchment performed with the Shalstab program.
Cells characterised by chronic instability, complete stability and those which are unstable
from the hydrologic point of view are reported in the legend. Practically the whole catchment
has to be considered unstable.
cross-check of different estimation approaches can help
attenuate the intrinsic limitations of each single method,
offering a more reliable assessment of the bent of a
catchment to generate debris flows.
Such relationships can be improved if hydrologic and
hydraulic parameters and factors controlling sediment
supply are also taken into accoun t. At present it is agreed
that a better knowledge of the hydrologic characteristics
of the catchment and a more detailed assessment in the
field of the material likely to be mobilized may be the
best approach to achieve a more precise estimate of a
possible debris flow volume. Once a design debris flow
volume has been determined, a number of other impor-
tant parameters characterizing debris flow behaviour can
be estimated, as shown in this work.
Further studies are in progress, with the uses of physi-
cally based mathematical models, suitable to describe in a
more realistic way the triggering, propagation and deposi-
tion processes of debris flows, in order to design more effi-
cient structural and non-structural defence measures.
D. de Wrachien et al. / Agricultural Sci ences 2 (2011) 9-15
Copyright © 2011 SciRes. Openly accessible at http:// www.scirp.org/journal/AS/
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