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Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
661
DOI: 10.4408/IJEGE.2011-03.B-072
AN INTEGRATED APPROACH TO SIMULATE CHANNALIZED DEBRIS
FLOWS FROM TRIGGERING TO DEPOSITION
C. DEANGELI
(*)
, C. GREGORETTI
(**)
, E. PALTRINIERI
(*)
, D. RABUFFETTI
(***)
& TIRANTI D.
(***)
*)
Department of Land, Environmental and Geoengineering , Politecnico di Torino, Turin, Italy
(**)
Department of Land and Agro-Forest Environment, University of Padova, Padua, Italy
(***)
Hydrology and Natural Hazards, Department of Forecasting Systems, Environmental Protection Agency of Piemonte,
Turin, Italy
Several methodologies to predict and modeling
their behavior have been proposed in the literature.
However models capable to analyze all the involved
processes from the critical rainfall, through the trig-
gering, to the debris flow propagation and deposition
arequite scarce.
This study is devoted to the development of an
integrated method capable to characterize debris flows
from the source rock mass generating the loose ma-
terial through triggering, propagation and deposition
modeling. The proposed method is based on the merg-
er of three different approaches: a geological model
for basins and sedimentary processes classification,
a triggering hydrological model and a routing model
The geological model identifies three basin
Groups in the Alpine environment. Each class is char-
acterized by different catchment lithology, basin area/
fan area ratio, alluvial fan architecture, debris flow
rheology, depositional style and triggering rainfall-
characteristics (t
iRanti
et alii, 2008). This method
permits to capture the essential features of the flow
phenomenon and to address the choice of proper mod-
els for the initiation and propagation phases..
The triggering model descends from the method
proposed by G
ReGoRetti
& d
alla
f
ontana
(2008) to
determine the critical runoff that triggers debris flow
by channel-bed failure. In particular G
ReGoRetti
&
d
alla
f
ontana
(2008) compared the runoff simulated
by a distributed kinematic hydrological model with
the critical discharge value computed by an empirical
ABSTRACT
The purpose of this study, which is currently un-
derway, is the analysis of debris flows from the lithol-
ogy of the bedrocks (source rocks) that gives rise to
the loose material, through the triggering process, to
the routing and deposition phases. In particular three
methods of analysis have been linked: a geological
model, a triggering model that couples the results of
a distributed kinematic hydrological model with a
critical discharge relationship and a numerical model
based on Cellular Automata for the simulation of de-
bris flow routing and deposition. The geological mod-
el concerns the catchment lithology and outlines some
links between the main lithology forming a basin bed-
rock and the characteristics of debris flow triggering
process. The triggering model, computes debris flow
hydrogram which is the input of the routing model.
The methodology outlined above was successfully
applied to debris flows occurred in a basin located in
North-western Alps.
K
ey
w
ords
: catchment lithology, sedimentary processes,
Cellular Automata routing model, hydrological modelling,
triggering discharge, North-western Alps
INTRODUCTION
Debris flows are among the most destructive natu-
ral phenomena. The Alpine regions are frequently af-
fected by such a type of mass movements that can cause
serious damages to structures and infrastructures.
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DEANGELI C. , GREGORETTI C. , PALTRINIERI E., RABUFFETTI D .& TIRANTI D.
662
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
BASIN CLASSIFICATION METHOD
According to a recent study conducted on several
alluvial fans in the alpine region (m
osCaRiello
et alii,
2002), the Northwestern Alps basins have been clas-
sified by t
iRanti
et alii (2008) into three main typolo-
gies of catchment lithology: (1) massive and/or crude-
ly stratified/foliated carbonate rocks (e.g., dolostones,
limestones, marbles); (2) fine-grained sheared finely-
foliated metamorphic rocks (e.g., calc-schists, shales,
phyllades); (3) massive or coarse-grained crystalline
rocks or massive quarzite rocks (e.g., granitoids,
gneiss, ultrabasites, meta-Qz-conglomerates).
On the basis of these lithological characteristics,
the dominant alluvial fan aggradational processes are
related to a cohesive debris flow (CDF) and to a non-
cohesive debris flow (N-CDF) based on the amount of
clay or clay-like minerals and clayey silt produced by
different bedrocks. Matrix clay content greater than
5% characterizes the CDF with viscous-plastic rheol-
ogy; matrix clay amount lower than 5% characterizes
N-CDF with collisionalfrictional rheology. In the ba-
sins of Group 1 and 2 the CDF are predominant, how-
relationship. If runoff exceeds the value computed by
the empirical relationship debris flow starts. The cou-
pling of runoff production at the onset of debris flow
and a reliable concentration value for the debris flow
routing allows the determination of the water-sediment
hydrograph needed as input by the routing model. The
input water-sediment hydrograph is estimated through
a mass balance involving input runoff and sediment
volumes, interstitial water, debris flow sediment con-
centration and dry bed sediment concentration.
Debris flow propagation is simulated by a Cellular
Automata model (s
eGRe
& d
eanGeli
, 1995 d
eanGeli
,
2008). The model allows the 3D simulation of solid
liquid mixture flows on slopes or channels by taking
into account the local properties of the debris material
in the computational domain. The site is subdivided
into a series of cells. Each cell is characterized by the
values of some representative quantities. The system
evolution is governed by local rules and depends on
the state of the cell and the neighboring cells. The
system is synchronously updated at the end of each
discrete time step. The Cellular Automata model has
been used to back analyze granular flows occurred in
northern (d
eanGeli
& G
Rasso
, 1996) and southern Ita-
ly (d’a
mbRosio
et alii, 2003), and to forecast possible
scenarios in tailing slopes (d
eanGeli
& G
iani
, 1998).
In the paper are reported the preliminary results
obtained by the application of the proposed method-
ology to a basin located in NorthWestern Alps. The
basin is periodically subjected to “viscous” debris
flows, being characterised by a debris material with a
relatively high clay content.
T
ab. 1 - The three catchment lithology Groups in western
Alps (modified after t
irANti
et alii, 2008)
Fig. 1 - View of the Rio Fosse basin with the watershed
contributing to the triggering area
Fig. 2 - The Rio Fosse basin view from alluvial fan apex to
the upper part
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AN INTEGRATED APPROACH TO SIMULATE CHANNALIZED DEBRIS FLOWS FROM TRIGGERING TO DEPOSITION
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
663
The cohesive-debris flows are the dominant proc-
esses along the R. Fosse main incised-channel and they
are the main processes forming the large alluvial fan.
The general basin settings are shown in Table 2.
The triggering area has been identified in a second-
ary gully where debris deposit is relevant (red outline
in fig. 1). This main source area is characterized by a
high production of loose material and very steep slopes
constituted by dolomitic limestones and by secondary
outcrops of gypsum and carbonate breccias.
Generally, the debris flows occurring at Rio Fosse,
are triggered if the runoff is able to mobilize the coarser
sediments deposited on the surface bed-sediment layer.
The surface layer is somehow armoured through
the presence of winnowed partially open-work deposit
that cover a clast-supported deposit formed by blocks
and boulders in a matrix formed by gravel, sand and
clayey-silt. The mobilization of coarse sediments of
surficial layer triggers the debris flow and the entrain-
ment of underlying deposits is responsible of the cohe-
sive behaviour of debris flows.
The historical records of this basin showed 20
debris flow events characterized by a low-moderate
magnitude since 1868. However, only the data be-
tween 1947 and 1973 are forming a continuous histori-
cal dataset, because just before this time-interval there
was the Second World War, and, many risk mitigation
works were made after 1973. Moreover, the main tar-
get-object (the "Camping mari e monti") was removed
in 1985 (a
RPa
P
iemonte
G
eoloGiCal
d
atabase
, 2010
- http://marcopolo.arpa.piemonte.it /bdge/index.php).
Rainfall data have been provided until 2000 by
a rain gauge station, located about 3 km far from
the basin. The analysis of these data have shown a
relatively high variability in rainfall values (from 55
mm to 0 mm), due to the location of the gauge with
respect to the to the Rio Fosse basin. Since 2000 the
set up of a meteorological radar system allowed de-
tailed data related to the triggering of debris flows
in Alpine environment. The analysis of post event
depositions of debris flows are generally qualita-
tive, although for a few events are well documented
in terms of area and thickness. For this reason the
numerical simulations reported in the following are
based on the average value of rainfall data that trig-
gered debris flows. The debris deposition obtained
by the numerical analysis are compared with two
documented events.
ever in Group 3 the N-CDF are the main processes.
The bedrock nature influences all basin behaviours,
such as the sedimentary processes an depositional
styles, the frequency of debris flow occurrence and the
seasonality, and the alluvial fan architectures.
In Table 1 the main features of the three basin
types are summarized.
SELECTED BASIN FOR PRELIMINARY
TEST
The Rio Fosse is a northwestern Alpine basin, lo-
cated near to Bardonecchia locality, in upper Susa Val-
ley (Fig. 1 and 2) The Rio Fosse is a small G1 basin
extending over about an area of 1.40 km
2
characterized
by a catchment lithology mainly formed by dolostones
and limestones, and, subordinate calc-schists (Fig. 3).
Fig.3 - Geological sketch map of Rio Fosse basin: 1)
colluvial cover; 2) talus deposit; 3) alluvial fan
deposit; 4) landslide deposit; 5) glacial deposit;
6) karst carbonate breccia; 7) limestone; 8) do-
lostone; 9) gypsum; 10) calcschist; 11) carbonate
schist. In the pai chart the percentages of outcrops
are represented: a) 50% are surficial deposits ; b)
37% are carbonate rocks; c) 7% are calc-schists;
d) 6% are gypsum
Tab. 2 - A synthesis of Rio Fosse basin characteristics
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DEANGELI C. , GREGORETTI C. , PALTRINIERI E., RABUFFETTI D .& TIRANTI D.
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5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
larger than 4 %, the simulation is repeated us-
ing the computed average cross-section velocity as
network velocity. The procedure is repeated until the
relative difference between the velocities becomes
smaller than 4%.
The hydrograph at the outlet is obtained adding the
single cell runoff productions (discharge pulses) that
reach the outlet in the same computation time interval.
The critical discharge relationship is that obtained
by G
ReGoRetti
& d
alla
f
ontana
(2008) using flume-
laboratory data for debris flow initiation (G
ReGoRetti
,
2000) following the approach of t
oGnaCCa
et alii
(2000) and depends on the mean grain size of sedi-
ments d
M
and bed slope angle θ:
where q is the unit width discharge.
Debris flow is triggered if the runoff discharge
Qr is larger than Q
CRIT
= q
CRIT
B
, being B the channel
width in the triggering section. The runoff contributing
to debris flow is then all runoff for t > t
CRIT
, time cor-
responding to QCRIT (Figure 4).
The debris flow hydrogram is then computed by a
mass balance after assigning the sediment volumetric
concentration, C, for debris routing. By definition:
where V
S
is the sediment volume of debris flow; V
r
the
contributing runoff volume to debris flow; and Vw the
interstitial water volume of entrained sediments. The
quantity V
w
is equal to (1- C*) V
S
and then V
S
can be
computed by equation (2). The value of debris flow
discharge Qt is then:
TRIGGERING MODEL
The triggering model is based on the capability of
surface runoff descending from cliff and rock walls to
mobilize sediments laying on channels incised on the
scree at their foot. A number of studies (G
RiffitHs
et
alii 1997; t
oGnaCCa
et alii, 2000; G
ReGoRetti
, 2000;
b
eRti
& s
imoni
, 2005; Griffiths et al. 2004; G
odt
&
C
oe
, 2007; C
oe
et alii, 2008a, 2008b; G
ReGoRetti
&
d
alla
f
ontana
, 2008; t
eCCa
& G
enevois
, 2009), re-
late, in fact, the triggering of debris flow oneither in-
cised channels or on a hillslope, to the erosion power
of thewater stream flowing over the sediment bed.
The triggering model is given by the coupling of
an hydrological model for runoff simulation and a crit-
ical discharge relationship for debris flow initiation.
The hydrological model is that used by G
ReGoRetti
& d
alla
f
ontana
(2008) for the simulation of runoff
triggering debris flow by channel-bed failure.
The model is physically based and distributed
and is derived from the KLEM model (Kinematic Lo-
cal Excess Model) proposed by C
azoRzi
(2002) and
used for computing flash flood hydrograph discharges
(Borga et al., 2007; n
oRbiato
et alii 2009; s
anGati
&
b
oRGa
, 2009; s
anGati
et alii, 2009). The runoff simu-
lation is given by the coupling of SCS method for the
determination of excess rainfall or direct runoff with
a kinematic method to route it to the outlet. The ba-
sin is divided in square cells and for each of these the
effective rainfall or runoff production is computed by
the Curve Number (CN) method of the Soil Conserva-
tion Service. The runoff is then propagated to the ba-
sin outlet (the triggering site) along the flow path and
the channel network derived from the digital elevation
model (DEM) on the basis of the topographic gradi-
ent. The channel network is composed by cells with
contributing area larger than a threshold value. Differ-
ent propagation velocities are assigned to the channel
network and to the flow paths along slopes. The veloci-
ties along the flow paths are varied, depending on the
soil characteristics (e.g., runoff velocity on rocky soil
is larger than that on a scree). The network velocity
is the average velocity in the outlet cross section cor-
responding to the maximum value of simulated runoff
and is assigned by an iterative method: surface runoff
is computed using a trial value of the network velocity
and using the Gauckler- Strikcler uniform law relation-
ship the average cross section velocity is computed;
if the relative difference between the two velocities is
Fig .4 - The runoff contributing to debris flow (shaded
area)
(1)
(2)
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AN INTEGRATED APPROACH TO SIMULATE CHANNALIZED DEBRIS FLOWS FROM TRIGGERING TO DEPOSITION
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
665
where C is the solid volume concentration, ρs is the
solid density and ρ
w
the water density.
The lattice geometry implemented in the model is
the Cartesian square lattice (b=4) (Figure 5).
Volume and consequently mass conservation are
separately imposed for solid and water. Energy and
momentum conservation are not enforced here. This is
consistent with modeling a process which is dissipative.
The assumption that the debris previously in motion can
suddenly be stopped within the space of a single cell,
depending only on the instantaneous local conditions, is
equivalent to the assumption that kinetic energy is read-
ily dissipated, gravity being the main energy source.
Initial conditions for the model are imposed speci-
fying the site topography and the debris distribution at
the initial time.
Boundary conditions are easily implemented on
any set cells: to realize an open boundary it is just suf-
ficient to force the content of these cells to be always
null, while to achieve closed boundaries any resulting
out flux is set to zero.
Each cell is connected to a number of its near-
est neighboring cells in order to transfer material at
each time step. In a 3D field the whole lattice could
be considered as a network of elementary slopes (with
dips related to the different local topography and de-
bris layers). A two neighbours partition rule for the
transfer of debris has been implemented, in order to
achieve lattice isotropy. A local slope angle θ (i, v) is
defined in the cell (i) for each pair of adjacent neigh-
bours (j
v,
j
v+1
) (v=1,..b modulo b) (Fig. 6).
for t>t
CRIT.
This methodology is currently imple-
mented by the GIS tools AdBToolBox (2010).
ROUTING MODEL
The propagation phase of the debris flow at Rio
Fosse basin has been simulated by a 3D numerical
code based on Cellular Automata (s
eGRe
& d
eanGeli
1995; d
eanGeli
2008).
Cellular Automata are mathematical idealizations
of physical systems in which space and time are dis-
crete, and physical quantities take on a finite set of
discrete values. A cellular automaton consists of a reg-
ular uniform lattice (or array), that is usually infinite,
with a discrete variable at each site (cell). The state of
a cellular automaton is specified by the values of the
variables at each site. A cellular automaton evolves
in discrete time steps, with the value of the variable
at one site being affected by the values of variables
at sites in its neighborhood at the previous time step.
The variables at each site are updated simultaneously,
based on the values of the variables in their neighbor-
hoods at the preceding time step, and according to a
definite set of local rules (w
olfRam
, 1987).
The numerical code was set up to analyze debris
flows over a rigid substratum. The debris flow is as-
sumed to be completely mixed. The model does not
take into account variations in vertical direction of
the debris properties, by adopting a vertically aver-
aged description.
The landslide site is discretized in elementary
cells of finite size. In each one the state of the sys-
tem is specified by the values of some representative
quantities.
These include: the height of the impermeable
rigid bed r; the amounts of water w and gas g and
of granular solids s in the cell. All the contents are
given as partial heights (volumes/ base area of the
cell), so that the top height in the cell (i) is given by:
The density of the mixture in each cell is given
by:
(3)
(4)
(5)
Fig. 5 - Cartesian square lattice.
Fig. 7 - Two neighbours partition rule
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DEANGELI C. , GREGORETTI C. , PALTRINIERI E., RABUFFETTI D .& TIRANTI D.
666
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
Evolution rules for the automaton considered the
mixture to behave as a Bingham fluid, according to
the geological classification of the Rio Fosse basin.
The results of the triggering model constitute the input
data of the CA model. In particular source cells has
been generated in the upper part of the basin. These
cells supply a rate of solid water mixture during the
first steps of the numerical simulations, according to
the total volume predicted by the triggering model.
The propagation of elementary flows in each lattice
sector (i,v) occurs if:
where τ
y
(i) is the yielding stress of the mixture in
cell (i) and h(i) is height of the flow at the previous
timestep. The cross sectional mean velocity U is :
Let quantities q of material flow out of the cell
i toward its critical neighbours and evaluate q by
putting [z(i)-r(i)]-[z(j
v
)-r(j
v
)] as h and θ (i, v) as θ in
Equation 7. In the model it has been assumed that q(C,
Δz)
are constant during the time step and rely on the
first order approximation for small values of the time
step Δt. The simplified elementary rate is thus:
where
All the computed elementary rates are stored be-
fore the simultaneous updating of the lattice. Instan-
taneous flow rates q(i) are evaluated in each cell by
vector summing all the incoming flows. The determi-
nation of the stoppage travel of a debris flow is still an
open problem. A simple local rule that accounts a dy-
namically corrected slope direction vector p(i,v) can
be implemented in the model
where q(i,t-Δt) is the volume inflow in cell (i) at the
preceding time step, and β is a parameter of the model
that must be properly calibrated.
THE SIMULATION OF DEBRIS FLOWS
IN RIO FOSSE BASIN
At this preliminary stage of the work, it has been
assumed the triggering area of debris flows is the out-
let of the watershed basin whose boundary are report-
ed in Figure 1. In that area, debris deposits are laying
on the channel bottom while the upper part is char-
acterized by larger slope values and the quantity of
sediments constituting the bed is not enough for debris
flow formation. The channel width is b = 4 m, and the
bed slope is tanθ = 0.4. The sediments showed the fol-
lowing a grain-size features: d
90
= 50 mm, d
60
=18 mm,
and (d
84
/d
16
)
0.5
= 26.7. The average diameter, based on
the average value of each soil class is dM = 0.015 m.
On the basis of G
ReGoRetti
& d
alla
f
ontana
(2008) analysis of critical runoff in which 19 of 20 peak
times of simulated runoff corresponding to the occurred
and documented debris flows were close to the triggered
times, the triggering rainfall is assumed to be the daily
non-stop rainfall producing the highest runoff value.
The runoff simulation was carried out using the CN
values shown in Table 3 and a roughness coefficient K
s
= 9 m
1/3
/s according to G
ReGoRetti
& d
alla
f
ontana
(2008). The critical unit width discharge computed by
eq. (1) is 0.005 m
2
/s that is 0.02 m3/s. The saturation
discharge computed according to the methodology pro-
posed by G
ReGoRetti
& d
alla
f
ontana
(2008) is 0.08
m
3
/s and then the triggering discharge is 0.1 m3/s. The
largest value of simulated runoff is Q = 0.4425 m
3
/s and
then the triggering discharge is Q = 0.3425 m
3
/s.
The runoff volume contributing to debris flow
(Fig. 4) is 10100 m
3
and the corresponding debris flow
volume is 21400 m
3
(sediment volume = 7490 m
3
) has
been computed by adopting a sediment volumetric con-
centration C = 0.35.
The basin has been discretized in elementary cells.
The volume of the solid water mixture, calculated on
the basis of the watersediment hydrograph has been
subdivided between the source cells.
The consequent rates of moving material from
these cells to the neighbouring cells of the model last
until the complete depletion of the calculated volume.
The transfer of material between the cells occurs ac-
(6)
(7)
(8)
(9)
Tab. 3 - The entire list of recorded debris flow events oc-
curred in the basin
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AN INTEGRATED APPROACH TO SIMULATE CHANNALIZED DEBRIS FLOWS FROM TRIGGERING TO DEPOSITION
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
667
cal model and a routing model, has been applied to a
basin located in the North-western Alps. The basin is
periodically subjected to “viscous” debris flows, be-
ing characterised by a debris material with a relatively
high clayey silt content. The results of this first ap-
plication show a relatively good agreement with the
available data of debris flows occurred in the basin.
Because of the promising results in the future the
methodology will be improved and extended to the
other two lithological Groups of material by imple-
menting appropriate constitutive laws.
ACKNOWLEDGEMENTS
This research was financially supported by: PAR-
Amount project of Alpin Space Programme of Euro-
pean Union (2-2-2-AT) and by MIUR, in the frame-
work PRIN 2007, “Assessment of debris flow hazard
in different geological and climatic conditions”, Re-
search Partner: Politecnico di Torino. The authors
wish to thank M. Degetto for the collaboration.
cording to equations 7 and 8. The input parameters have
been estimated on the basis of literature data, for similar
types of rocks.
Figure 7 reports the final results of the numerical
simulation. By a general point of view these results
seem to be consistent with the characteristics of debris
flows in the Rio Fosse basin.
Figures 8 and 9 show the deposition features of
the two debris flow events occurred on July 1994 and
September 2006 respectively. Although the rainfall data
(both recorded by the rain gauge stations of Bardonec-
chia) were not so different deposition volumes of these
two events were definitely different. Probably the main
reason of this behaviour can be attributed to the avail-
ability of debris material and the serviceability of the
small dams located in the upper part of the channel.
The comparison between Figure 7 and Figures 8
and 9 show that the debris flow simulated on the basis
of the characteristics of several debris flows occurred in
the Rio Fosse basin, by considering the triggering area
reported in Fig. 1 and by assuming, on the basis of the
geological model, a viscous behaviour of the mixture,
exhibits depositional features in agreement with the re-
ported real cases.
CONCLUDING REMARKS
The paper has reported the first results of the applica-
tion of a comprehensive methodology for the analysis of
debris flows from the lithology of the bedrocks (source
rocks) that gives rise to the loose material, through the
triggering process, to the routing and deposition phases.
The proposed methodology, based on the link
between a geological model for basins and sedimen-
tary processes classification, a triggering hydrologi-
Fig.7 - Results of the numerical analysis for the phase
of propagation of debris flows in the Rio Fosse
basin
Fig.8 - Deposition of the debris flows occurred on July
1994
Fig. 9 - Deposition of the debris flows occurred on Sep-
tember 2006
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DEANGELI C. , GREGORETTI C. , PALTRINIERI E., RABUFFETTI D .& TIRANTI D.
668
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
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imoni
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anti
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