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Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
183
DOI: 10.4408/IJEGE.2011-03.B-022
SIMPLE GEOMORPHOLOGIC APPROACH TO ESTIMATE DEBRIS-FLOW
ENTRAINMENT. APPLICATIONS TO THE PYRENEES AND THE ALPS
C
laudia
abanCó (*) & m
aRCel
HÜRLIMANN (*)
(*) Dept. of Geotechnical Engineering and Geosciences, Technical University of Catalonia, Spain
material along the travel path. The entrainment has a
great influence on both the final volume of the event
and the flow behaviour, since it causes variations in
the bulk density.
A basic step towards debris flow hazard assess-
ment is the prediction of the magnitude (volume). In
order to predict the volume of a possible event, the en-
trainment has to be considered, however there are very
few quantitative approaches proposed (e.g., H
unGR
et
alii, 1984; s
PReafiCo
et alii, 1999)
On the other side, some authors have suggested
that entrainment varies the mobility of the debris flows;
therefore it is also relevant to delineate the possible ru-
nout lengths (H
unGR
et alii, 2005; C
Rosta
et alii, 2008).
The “channel yield rate” or “erosion rate” is a pa-
rameter used to describe the amount of material en-
trained along a travel path. It is described as the volume
of debris entrained along the travel path, proportioned
to the length of the path (H
unGR
et alii, 1984).
Several authors have shown that the amount of
material involved in a debris-flow event can consid-
erably increase compared to the volume of the initial
landslide (in landslide triggered debris flows), due to
the erosion of material produced along the travel path
(e.g., H
unGR
et alii, 2005; G
utHRie
et alii, 2009) The
Glyssibach case study, located in Switzerland, is a per-
fect example of the significance of the entrainment.
The total volume of the event obtained by LIDAR data
was of about 80000 m
3
, while approximately 50000
m3 correspond to entrainment occurred along the de-
ABSTRACT
The basal incorporation of material, also called
entrainment, is a common characteristic of debris
flow dynamics. The volume of a debris flow can con-
siderably increase when compared to the initial vol-
ume, due to the erosion of material produced along
the travel path. This study is a preliminary attempt to
establish a simple geomorphologic approach for the
calculation of volume to be entrained in a torrent, if
a granular debrisflow event would occur. The meth-
odology presented has been developed using data ob-
tained by comprehensive field surveys, carried out in
six torrents affected by granular debris-flow events.
The torrents, divided into 43 reaches, are located in
the Pyrenees and the Alps. The application of the
methodology requires data to be measured along the
flow path (geologic and geomorphologic factors). As a
result, a predicted erosion rate for determined reaches
can be estimated in function of these factors, properly
weighted. Although the results indicate a high scatter,
the total predicted erosion volume calculated for each
test site using the proposed approach coincides rather
well with the volumes observed in the field.
K
ey
words
: entrainment, granular debris flow, erosion rate,
Pyrenees, Alps
INTRODUCTION
The entrainment is a common characteristic of de-
bris flows and can be described as the incorporation of
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5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
in the initiation reach than the landslide triggered de-
bris flows in the Pyrenees. Detailed information on the
Schipfenbach event can be found in H
üRlimann
et alii
(2003), while only unpublished reports are available
on the Gesäuse event.
The events of the Alps are in-channel triggered
debris flows. However, they show higher bed slopes
in the initiation reach than the landslide triggered de-
bris flows in the Pyrenees. Detailed information on the
Schipfenbach event can be found in H
üRlimann
et alii
(2003), while only unpublished reports are available
on the Gesäuse event.
There are two approaches to describe the mecha-
nism of the entrainment:
1) The “sliding mechanism” approach based on
Mohr- Coulomb failure criterion.
2) The hydrodynamic approach based on bedload
transport formulas of fluvial hydraulics.
The first one, the “sliding mechanism”, is a static ap-
proach supported by some authors (e.g.t
akaHasHi
1978;
t
akaHasHi
1991; H
unGR
et alii, 2005) where the entrain-
ment can be easily explained by the infinite stability slope
theory (Fig. 2). Based on this model, the erosion depth
bris-flow path (s
CHeidl
et alii, 2008).
Some attempts to quantify the entrainment pro-
duced by debris flows are found in the literature. H
un
-
GR
et alii (1984) established a classification of stream
channels in British Columbia, based on geologic and
geomorphologic parameters, which is linked to a chan-
nel debris yield rate. Meanwhile, others have looked
for correlations between geomorphologic factors and
entrainment produced in specific events (b
Reien
et alii,
2008). However, no clear empirical relationships have
been established because in many cases there is a wide
scatter in the available data sets (C
Hen
et alii, 2005;
H
unGR
et alii, 2005). Thus, only general rules have
been derived up to now.
The main purpose of the present study is to pro-
pose a general and simple methodology to estimate the
entrainment that can occur in a torrent.
DESCRIPTION OF EVENTS OCCURRED
IN THE TEST SITES
The data used in this study was gathered in 6 tor-
rents subdivided in 43 reaches, located in two different
mountainous regions: the Pyrenees and the Alps. In all
these torrents a granular debris flow occurred and field
surveys were carried out after the events, in order to
collect data about erosion patterns (Table 1).
The events of the Pyrenees (Figure 1) can be divid-
ed in: landslide triggered debris flows (Sant Nicolau),
and in-channel debris flows (Ensija, Riu Runer and
Port Ainé). The in-channel events are generally char-
acterized by large catchment areas above the initiation
point and lower bed slopes in the initiation reach, while
the landslide triggered one presents a smaller catch-
ment area and higher bed slope at the initiation zone
(P
oRtilla
et alii, 2010).
The events of the Alps are in-channel triggered
debris flows. However, they show higher bed slopes
Tab 1 - Description of the events occurred in the sur-
veyed torrents
Fig 1 - Location of the surveyed torrents in the Pyr-
enees
Fig 2 - S
cheme of a channel bed with a layer of loose de-
posits that is being overflowed by a debris- flow
mass. This approach supports that the entrain-
ment occurs when the shear motion stress (τmov)
overcomes the resistant one (τres)
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SIMPLE GEOMORPHOLOGIC APPROACH TO ESTIMATE DEBRIS-FLOW ENTRAINMENT. APPLICATIONS TO THE PYRENEES AND
THE ALPS
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
185
DEFINITION OF GOVERNING FACTORS
The entrainment estimation in the present work is
based on geologic and geomorphologic features that
can be reported in the field and by GIS analysis, while
hydrometeorological conditions in the catchments
have not been considered. The main goal is to obtain
a volume estimation of material that can be entrained,
from observations of static features of the torrent.
Five main factors were selected according to their
relevance in the process, but also to the simplicity to
obtain all of them directly from field surveys or GIS
analysis: the available sediment, the bed slope of the
analysed reach, the shape of the torrent in this particu-
lar reach, the normalised upstream contributing area
of the reach and the catchment area of the torrent.
The five governing factors are divided into differ-
ent classes (Tab. 2), which will be described in the
following. The ratings of the classes vary from 0 to 1
depending on their relevance in entrainment process.
SEDIMENT AVAILABILITY
One of the factors most influencing the entrain-
ment during a debris-flow event is the sediment avail-
ability. In one torrent, some reaches may have un-
limited sediment (here called “not limited” reaches).
Then, the erosion produced is totally conditioned by
other factors. But, in some other reaches, the lack of
sediment limits the entrainment (here, classified in
different classes, depending on the level of limitation)
The purpose of this work has been to classify the
reaches regarding the sediment availability. Five main
classes have been described depending on how much
material is available to be entrained. Some authors have
done similar work in other regions, like in British Co-
lumbia (H
unGR
et alii, 1984), or the Swiss Alps (s
PRe
-
afiCo
et alii, 1999), but the description of the classes
depends on the characteristics of each study area.
The definition and description of the five classes
(maximum depth of material entrained) can be estimated.
Other authors assume that, as in bedload trans-
port formulas of fluvial hydraulics, the flow can
entrain material until the equilibrium condition is
reached (R
iCkenmann
et alii, 2003, f
RaCCaRolo
&
C
aPaRt
, 2002). This approach is dynamic, since it
depends on the velocity and other parameters associ-
ated to the movement.
Another aspect that must be taken into account
for estimating total debris-flow volume is the effect of
secondary failures. The mechanism of this sediment
supply is not related to a sliding mechanism caused by
the passage of the flux over the erodible sediment, but
rather to the erosion at the foot of the slope (H
unGR
et alii, 2005). In our approach this type of sediment
incorporation has only been considered when estimat-
ing the total event volume in the field, but has not been
taken into account for the erosion rate.
Tab 2 - Five governing factors selected for the calcu-
lation of the entrainment (NUCA: normalised
upstream contributing area)
Tab 3 / Sediment availability classes defined for granular debris flow. The limits have been described according to the char-
acteristics of the surveyed areas, specially the Eastern Pyrenees, but it should be adapted to the regional features
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5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
been divided into classes of intervals of 10º, consider-
ing the upper limit of 40º, according to the characteris-
tics of the Pyrenean events (P
oRtilla
et alii, 2010). In
the present study, the mean slope was calculated from
a Digital Elevation Model (DEM) with 5 m resolution.
Alternatively, the mean slope can also be obtained from
a topographic map or from measurements in the field.
SHAPE
The shape of the reach is a factor that has been con-
sidered in order to explain how the incision of the reach
can be important in the entrainment process of the de-
bris flow. Although no relationships between the shape
of the torrent and the erosion rate were established in
previous works, our field observations were an evi-
dence of this fact. G
abet
& b
ookteR
(2008) described
the shape of the studied gullies in southwest Montana
(USA) using the “mean width to depth ratio”, and the
relation between the width at different heights from the
bed. A similar concept is proposed in our work.
Here we suggest the width at 3 m height as the rel-
evant dimension to describe the reach incision. Accord-
ing to the morphologic properties of the torrents in the
Pyrenees, if the width (at 3 m height) is over 15 m, the
reach can be considered wide (Fig. 3). If it is between
15 and 5 m, we called it medium, and if it is less than 5
m it can be considered as incised reach. These are limits
absolutely depending on the characteristics of the tor-
rents in the area, and should be verified for other areas.
NORMALISED UPSTREAM CONTRIBUTING
AREA
The upstream contributing area, UCA, of a reach
represents the drainage basin at the lowest point of the
reach. The UCA-value of each reach i, UCA
i
, can be
normalized by the total catchment area CA:
where NUCAi is the normalised upstream contribut-
ing area of reach i (Fig. 4). This factor ranges from 0
to 1 and it has been divided into 5 classes according
to Table 2.
The normalisation of UCA should be a way to iden-
tify the hydraulic load of the reach, that is clearly in-
fluencing the mean erosion (R
iCkenmann
et alii, 2003).
A better way would be to calculate the concentration
of the flow, however this information needs detailed
is based on the amount or percentage of the cross sec-
tion that is covered by sediment (Table 3). In addition
the reach is considered as a unique global part, with-
out considering local exceptions.
The class ”no limitation of sediment” means that
the bedrock is almost not visible in the cross sections
along the reach analysed. The class “low limitation of
sediment” is related to reaches, when sediment is cover-
ing more than 75%of the cross section but the bedrock
is still visible. “Medium limitation of sediment” means
that bedrock and sediment appear in the cross section
at equal proportion, while “high limitation of available
sediment” indicates reaches where bedrock appears at
both sides of the channel, but some sediment is cover-
ing the channel bed. Finally, the class “complete limita-
tion of sediment” means that bedrock is visible at both
sides of the channel. Even though, little sediment can
be available in the channel bed.
SLOPE
Some authors studied the relation between the ero-
sion rate and the slope of the reach or the local cross
section. In some cases the relation clearly shows that
as the slope increases, the entrainment rate also gets
higher (R
iCkenmann
& z
immeRmann
1993; Guthrie et
al. 2009). In other circumstances it can be seen that
there is a feedback effect, which means that the entrain-
ment is higher at low slopes. It can be justified with the
increasing flow concentration or peak discharge as the
travelled distance increases (and the slope decreases,
normally) (b
Reien
et alii, 2008). Other studies contra-
dict these two situations indicating that, there is not a
clear tendency, as it is completely related to the avail-
ability of sediment in the reach (H
unG
r et alii, 1984;
m
aRCHi
et alii, 2009).
In our work the average slope of the reaches has
Fig. 3 - wide reach in a debris flow torrent (Pyrenees)
(1)
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SIMPLE GEOMORPHOLOGIC APPROACH TO ESTIMATE DEBRIS-FLOW ENTRAINMENT. APPLICATIONS TO THE PYRENEES AND
THE ALPS
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
187
charge increases, the capability of the flow to entrain
material grows. Therefore, in conclusion, the capacity
to entrain volume is higher for larger catchment areas
In our approach, the catchment area is a global
factor and thus equal for all the reaches. The factor
was divided into three classes: <0.1 km
2
, 0.1 - 1 km
2
,
and >1km
2
(Table 2). The catchment area as the afore
mentioned UCA
i
can be obtained directly by hydro-
logical GIS tools and a DEM, or manually from topo-
graphic maps..
SIMPLE APPROACH TO ESTIMATE THE
EROSION RATE
The purpose of this methodology is to estimate
the volume of material that we can expect to be eroded
in a certain torrent due to a debris-flow event
An overview of the different phases related to the
approach is shown in Figure 5. The first phase consists
in the division of the debris-flow torrent into reaches,
with similar characteristics regarding the governing
factors. Using the values of classes in Table 2, the
Erosion Index, EI, can be calculated. This value is
used to obtain the Predicted Erosion Rate, PER, that
expresses the volume of material that might be eroded
in a reach (cubic meter per running meter). The total
volume to be eroded in the torrent can be obtained eas-
ily from the Predicted Erosion Rate and the length of
each reach, L
i
..
Pyrenees and the Alps that we collected in the
field surveys. Nevertheless, this approach may also
be applied in an adapted form to other mountainous
areas, where granular debris flows occur. In the fol-
lowing, the two most important steps of the approach,
the calculation of EI and PER, are explained in detail
EROSION INDEX
The erosion index is a dimensionless parameter
and is calculated for every reach using the selected
class rating of each governing factor (Table 2). In ad-
dition, the weight of each governing factor is intro-
duced, which leads to the final expression:.
where W
X
is the weight of governing factor X and
R
Xi
is the value of the governing factor in reach i. The
index X stands for SA: sediment availability; S: bed
calculations, and therefore it’s not adequate for a sim-
ple approach. Hence we propose to use the normalised
upstream contributing area to give semi-quantitative
information on thehydraulic load of the flow.
CATCHMENT AREA
The relationship between debris-flow volume and
catchment area is characterised by a large scatter, but
there is a general positive trend (R
iCkenmann
& z
im
-
meRmann
1993; d'a
Gostino
& m
aRCHi
2001).
At the same time, a larger volume produces a
higher peak discharge (H
unGR
et alii, 1984; R
iCken
-
mann
1999). Finally, we assume that as the peak dis-
Fig 4 / Left:Scheme of the upstream contributing area of
various reaches in a catchment. Right:Example in
Sant Nicolau torrent (Pyrenees)
Fig. 5 - Flow-chart of approach
(2)
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C. ABANCÓ & M. HÜRLIMANN
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5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
slope; SH: cross section shape; NUCA: Normalised
Upstream Contributing Area and CA: Catchment Area
While the class rating can be determined using
field observations and Table 2, the weights of each
governing factor are determined in a second phase
applying statistical analysis. This statistical analysis
calibrates the weights by the comparison of the erosion
rates observed in the field with the EI calculated.
The EI-values range from 0 to 1, as the terms of
the summation are normalized. High values of Erosion
Index indicate more erosion than values close to 0.
.
PREDICTED EROSION RATE
In order to quantify the entrainment, the dimen-
sionless erosion index is transformed into the Predict-
ed Erosion Rate, PER. PER expresses the amount of
material per running meter that may be entrained by a
debris-flow event along a defined reach. Thus, the Pre-
dicted Erosion Rate, in contrast to the Erosion Index,
has a physical meaning, and is expressed in m
3
/m.
The transformation of EI into PER can be done us-
ing the best-fit function obtained during the statistical
analysis. This function can be expressed in a simple
form by
where α represents the pair of parameters (α1 and α2)
that define the linear regression (see below for detailed
explanation).
RESULTS
FIELD DATA ON GOVERNING FACTORS
The field data collected in the Pyrenees and the
Alps has been plotted in order to study the relation be-
tween the five governing factors and the erosion rate
observed in the reaches. Additionally, the class ranges
of values of the governing factors established in Table
1 have been checked.
As observed in other studies (C
Hen
et alii, 2005;
H
unGR
et alii, 2005), the data show a large scatter.
Nevertheless, some genera patterns of particular inter-
est can be detected. On one hand, it can be seen that
there is an increase of scouring in the steepest reaches
(Fig. 6), as was also revealed by G
utHRie
et alii (2009).
The importance of the sediment availability for the en-
trainment process is also relevant.
On the other hand, it can be noted that there is a
rough trend between the upstream contributing area
and the erosion produced in the reaches (Fig. 7). It can
be related to the amount of water-solid volume enter-
ing to the reach (H
unGR
et alii, 2005).
EROSION INDEX
As described previously, the weights of the differ-
ent governing factors must be defined by a statistical
analysis comparing the estimated EI-value with the
observed erosion rate (OER). The OER is the channel
yield rate estimated after occurring an event, along a
certain reach (H
unGR
et alii, 1984).
In a first attempt (Tab. 4), we assumed the same
weights for each governing factors, which means Wx–
values of 0.2 in (2). The results of the calculated EI-
values are compared with the erosion rates observed
in the field, OER. A qualitative analysis of this plot
shows an overestimation of the EI-values, since all
EI-values are higher than 0.4, even for very low or
no OER. The quantitative check of the results was
performed by a statistical analysis and the coefficient
(3)
Fig 6: Slope vs. Erosion rate of the reaches in the surveyed
catchments, depending on the sediment availabil-
ity class. Each point corresponds to a reach
F
ig 7: Normalised upstream contributing area vs. Erosion
rate of the reaches in the surveyed torrents, de-
pending on the sediment availability class. Each
point corresponds to a reach
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SIMPLE GEOMORPHOLOGIC APPROACH TO ESTIMATE DEBRIS-FLOW ENTRAINMENT. APPLICATIONS TO THE PYRENEES AND
THE ALPS
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
189
PREDICTED EROSION RATE
The transformation from the dimensionless EI
into the quantitative PER was performed by using the
best-fit linear function obtained in the previous sec-
tion. Then, the ER
i
is called PER
i
, and the final equa-
tion can be given by:
This expression was applied to all reaches and the
results were compared with the OER
i
(Figure 10). The
plot shows that the PERvalues are generally overes-
timated when low erosion rates were observed in the
field and underestimated when high erosion rates were
detected. This means that extreme values may not be
represented correctly by our approach, since most of
the PER-values are in the range from 1 to 3 m
3
/m. This
fact should be taken into account in the application of
the approach and may be corrected incorporating ad-
ditional field data.
Finally, the total predicted erosion volume, PEV,
for a torrent could be calculated by:
where L
i
is the topographic length of the torrent reach
i. This task was carried out and two examples will be
presented in the following section.
EXAMPLES OF TOTAL EROSION VOLUME
PREDICTED
Regarding debris-flow hazard assessment, the
most interesting information is generally the total
of determination, R
2
. In our case we applied a very
simple linear regression given by:
where ER
i
is the erosion rate we want to approxi-
mate to the one observed in a torrent reach i, and
α1 and α
2
are two coefficients. The low R2-value
of 0.045 is not surprising due to the high scatter of
the data. Other statistical regressions may provide
a better fit, but only a slight improvement could be
observed in our field data applying polynomial or
other functions
In the next attempts, the weights of the governing
factors were adjusted. The results were checked again
by linear regression and the coefficient of determina-
tion R2 was compared. Finally, the bestfit weights
were obtained in attempt 4, when the weights of the
sediment availability and slope were increased and the
other onesreduced. The results of this best-fit attempt
are shown in Figure 9..
(4)
Fig. 9 EIi vs OERi, fourth attempt (Table 4): Regression
line is calculated with best-fit weights for the gov-
erning factors
Tab. 4 - Results of the linear regression analysis ap-
plied to calibrate the weights of the governing
factors in order to calculate EI
(5)
(6)
Fig 10 - OERi vs PERi
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C. ABANCÓ & M. HÜRLIMANN
190
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
factors. The factors have been weighted according to
their relevance in the entrainment process. Each fac-
tor has been divided in several classes, with ratings
from 0 (less prone to entrainment) to 1 (more prone
to entrainment).
The ratings of the factor classes have been defined
using the observations obtained from six debris flows
within our test areas. The weights of the governing
factors have been adjusted according to a linear re-
gression. In future works, when more data is going to
be available, this simple regression may be replaced
with another statistical function
The results of the field observations showed that
the relations between observed erosion rate and the
governing factors indicate high scatter, even though
some general trends can be observed. In spite of the
uncertainties related to this simple approach, realis-
tic total volumes could be estimated for the six debris
flows in the test sites, and show that this methodology
could be very helpful in hazard assessments.
The application of the presented methodology to
other areas should include a verification of the class
limits and weights of the five governing factors. Fi-
nally, similar approaches may be incorporated into
numerical models in order to improve the entrainment
processes in granular debris flow.
ACKNOWLEDGEMENTS
The authors wish to thank the Institute of Natu-
ral Hazards in Universität für Bodenkultur Wien
(BOKU), in particular to Christian Scheidl, for dis-
cussions and the field trip to Gesäuse. Special thanks
to the administration of the Gesäuse National Park
for the cartographical data and the DEM. The authors
are also grateful to Christoph Graf, Swiss Federal Re-
search Institute (WSL), for his collaboration in the
Schipfenbach event.
This research was supported by the Spanish Min-
istry of Science and Innovation, contract CGL2008-
00299/BTE.
volume mobilized by a future event. With the purpose
of making a first test of the approach proposed, the
evolution of the volume along the flow path has been
calculated for the five debris-flow events in the test
sites. The cumulative eroded volume has been com-
pared to the predicted one.
Figure 11 shows the two examples of Sant Nico-
lau (landslide triggered, with an initial volume of 800
m3) and Schipfenbach (inchannel debris flow).
From the comparison of the total predicted eroded
volume and the total observed volume of the events,
it can be seen that the methodology proposed shows
rather coherent results
Although local differences in some reaches can
be detected, the final volume is comparable between
observations and calculations
CONCLUDING REMARKS
A simple methodology to approximate the en-
trainment that can occur in a torrent has been pre-
sented. The methodology estimates an erosion rate
in a selected channel reach based on five governing
Fig 11. - PERi calculated in every reach and com-
parison between evolution of predicted and
observed volume along the flow path. a) Sant
Nicolau torrent (Pyrenees), b) Schipfenbach
torrent (Alps)
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SIMPLE GEOMORPHOLOGIC APPROACH TO ESTIMATE DEBRIS-FLOW ENTRAINMENT. APPLICATIONS TO THE PYRENEES AND
THE ALPS
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
191
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