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Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
933
DOI: 10.4408/IJEGE.2011-03.B-101
REGIONAL-SCALE DEBRIS-FLOW RISK ASSESSMENT
FOR AN ALPINE VALLEY
s. LARI
(*)
, G. b. CROSTA
(*)
, P. FRATTINI
(*)
, P. HORTON
(**)
& m. JABOYEDOFF
(**)
(*)
Università degli Studi di Milano Bicocca - Dep. Geologic Sciences and Geotechnologies - Italy
(**)
Institut de géomatique et d'analyse du risque (IGAR), Unil, Lausanne - Switzerland
K
ey
words
: economic risk, societal risk, regional scale risk
assessment, debris flow modelling
INTRODUCTION
Debris flow in Alpine areas are widespread phe-
nomena threatening people and goods (C
anCelli
&
n
ova
, 1985; a
leotti
& P
olloni
, 1998c; C
Rosta
et alii,
2003; C
aRRaRa
et alii, 2008). The considerable hazard
potential of debris flows is related to the abundance of
susceptible areas, the high areal density and the high
velocity of the movements (C
Rosta
et alii,2003). In the
last 30 years, lower Valtellina (1,050 km
2
, Central Alps,
Northern Italy, about 90,000 residents) was frequently
affected by debris-flow triggering rainstorms (1983,
1987, 1997, 2000, 2002, 2004, 2008) causing extensive
damages to private buildings and public facilities, and
31 casualties (G
ovi
& t
uRitto
, 1994; t
RoPeano
et alii,
1999; P
RoGetto
IFFI, 2007; AVI, 2007). These data
highlight the importance of a regional scale debris-flow
risk assessment for land planning and management.
Triggering and propagation of debris flows are
strongly controlled by local topography, mechanical
and hydraulic soil properties (C
osta
, 1984). Due to
the fact that they are difficult to fully understand, the
occurrence of debris flows hardly can be precisely
forecast (H
e
et alii, 2003). At present, there are few
methods allowing a strict assessment to determine an
exact probability of debris-flow occurrence, based ei-
ther on physically measured characteristics of a catch-
ment or on a statistical analysis. Information available
ABSTRACT
In this paper, we perform a societal and eco-
nomic risk assessment for debris flows at the re-
gional scale, for lower Valtellina, Northern Italy.
We apply a simple empirical debris-flow model,
FLOW-R, which couples a probabilistic flow rout-
ing algorithm with an energy line approach, provid-
ing the relative probability of transit, and the maxi-
mum kinetic energy, for each cell.
By assessing a vulnerability to people and to
other exposed elements (buildings, public facili-
ties, crops, woods, communication lines), and their
economic value, we calculated the expected annual
losses both in terms of lives (societal risk) and goods
(direct economic risk). For societal risk assessment,
we distinguish for the day and night scenarios. The
distribution of people at different moments of the
day was considered, accounting for the occupational
and recreational activities, to provide a more real-
istic assessment of risk. Market studies were per-
formed in order to assess a realistic economic value
to goods, structures, and lifelines.
As terrain unit, a 20 m x 20 m cell was used, in
accordance with data availability and the spatial reso-
lution requested for a risk assessment at this scale.
Societal risk the whole area amounts to 1.98 and 4.22
deaths/year for the day and the night scenarios, re-
spectively, with a maximum of 0.013 deaths/year/cell.
Economic risk for goods amounts to 1,760,291 €/year,
with a maximum of 13,814 €/year/cell.
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Italian national mean (197,6 p/km
2
) and regional mean
(404,1 p/km
2
), since it includes a wide mountainous
territory with a very low density. Considering only the
valley bottom, the density grows up to 790 p/km
2
.
The road network, due to territory morphology, is
not very developed, but the whole area is crossed by
the Stelvio state street SS 38, which is very busy, be-
ing the main road along the valley.
The orientation of the valley strongly controls the
sun exposure, so that slopes facing South and North
have different vegetation and land use. The first ones
have been used extensively since centuries to develop
an agricultural activity (vineyards) up to 600-700 m
a.s.l., the second has a prevalent forestal vocation.
Agricultural activities are widely diffused, also in the
valley bottom, with permanent grasses and corn cultures.
RISK ASSESSMENT METHODOLOGY
The adopted methodology leads to the quantifica-
tion of risk in terms of:
• societal risk (annual casualties): R
s
= f * e * v * n
• economic risk (direct economic annual losses):
R
e
= f * e * v * w
where:
f = expected annual frequency of occurrence of the event;
e = probability of an exposed element present in the
area to be effectively impacted, not accounting
for implemented mitigation works (i.e., exposure
factor);
v = degree of damage;
n = exposed people effectively present in the impac-
ted area.
w = economic value of goods in the impacted area.
on past debris flow events is often the most reliable
data (R
iCkenmann
, 1999).
Physically-based models are widely used to assess
debris-flow susceptibility (m
ontGomeRy
& d
ietRiCH
,
1994; w
u
& s
idle
, 1995; b
uRton
& b
atHuRst
, 1998;
C
Rosta
& f
Rattini
, 2003). Although these models may
be suitable for modelling the predisposing hydrologi-
cal conditions, they have several limitations if applied
to predict the spatial distribution of debris flows, at
the regional scale (C
aRRaRa
et alii, 2008). With the
exception of slope morphology, in fact, the physical
variables that control the spatial distribution of debris
flows (i.e., physical and mechanical parameters of the
slope and the failed material) cannot be acquired over
large areas at reasonable cost (C
aRRaRa
et alii, 2008).
In order to perform a debris flow risk assessment
and to provide sound basis for the design protective
measures, it is necessary to estimate important pa-
rameters describing the phenomena, such as potential
debris volume, mean flow velocity, peak discharge,
and runout distance (R
iCkenmann
, 1999): empirical
studies demonstrated to be useful to achieve this tasks
(C
osta
, 1984; H
unGR
et alii, 1984; J
oHnson
,1984; J
an
& s
Hen
, 1997; PwRi, 1988; R
iCkenmann
, 1999).
Due to the diffuse nature of the phenomena, a
spatially distributed modelling tool which is capable
to simulate the propagation over complex terrain is
needed (i
veRson
, 1987). The complexity of physical
processes governing debris-flow propagation and the
uncertainty in modelling parameters (H
e
& x
ie
), re-
quires a simplified model, which is still more suitable
for regional scale study (i
veRson
et alii, 1998).
In this paper, we perform a societal and economic
risk assessment for debris flows at the regional scale,
for lower Valtellina, Northern Italy. We apply a simple
empirical debris-flow model, FLOW-R, which couples
a probabilistic flow routing algorithm with an energy
line approach, providing the relative probability of
transit, and the maximum kinetic energy, for each cell.
STUDY AREA
The study area encompasses 40 municipalities
of lower Valtellina, including Sondrio and Morbegno
(Fig. 1), which are the two most populated munici-
palities (almost 22,000 and 12,000 inhabitants, respec-
tively). In total, 90,278 people live in the study area
(ISTAT, 2007), with a mean density of population of 76
people/km
2
. This is a low value if compared with the
Fig. 1 - Study area and main recent historical events
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REGIONAL-SCALE DEBRIS-FLOW RISK ASSESSMENT FOR AN ALPINE VALLEY
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
935
In particular,
if x = 1, f
si
= multiple flow direction method
if x→∞, single flow direction (D8)
To take into account the inertia, in terms of di-
rection, which is the tendency of the flow to maintain
its direction, a further weighting of the flow direction
is included in the code. Based on G
amma
(2000), the
persistence weight for each cell is a function of the
change α in angle from the last flow direction.
f
pi
= w
0
if α=0°
f
pi
= w
45
if α=45°
f
pi
= w
90
if α=90°
f
pi
= w
135
if α=135°
f
pi
= 0
if α=180°
where i = flow directions, f
pi
= persistence term of
flow proportion in direction i, α
i
=angle between the
previous flow direction and the new flow direction
from the central cell i, w = weights for the corre-
sponding change in direction.
The slope-related algorithm and the persistence are
combined to obtain the resulting probabilities (Fig. 2).
The energy line approach calculates the run-out
distance based on a reach angle and an upper limit
for flow velocity. Runout distance algorithms are
energy-based calculations that define, for each cell,
if the debris flow can potentially reach another cell.
Thus, they control the distance reached by the debris
flow. Moreover, they influence the flow direction: in
fact, some of the cells that could receive a flow from
the direction algorithm, are not reached by the flow
because of energy, and their debris flow probability
is set to zero. The source mass, is unknown, thus,
runout distance calculation is based on unit energy
balance, a constant loss function and a maximum
velocity threshold. This approach does not aim to ex-
actly represent the physical processes, but to provide
a realistic figure of the phenomena.
Potential energy is in part transformed in kinetic
energy, and in part lost as friction. Energy loss is mod-
FREQUENCY OF OCCURRENCE
The expected frequency of occurrence, f, of the
debris flows was considered as composed of a trigger-
ing frequency, f
d
, and a transit frequency, f
t
.
Triggering frequency, f
d
, was assumed to be con-
stant in the study area, and calculated from the frequen-
cy of past events, divided by the number of source are-
as. Source areas were detected by means of a simplified
simulation of slope instability due to shallow landslides
using a model, which couples steady state hydrology
and a limit equilibrium infinite slope stability model
(SHALSTAB, m
ontGomeRy
& d
ietRiCH
, 1994). The
majority of debris flow occurring in the areas, in fact,
are triggered as shallow landslides, and the number of
debris flows triggered in different circumstances (de-
bris erosion in riverbed, fire-hose effect) is assumed
to be balanced by the number of shallow landslides
not evolving into debris flow. Triggering frequency in
lower Valtellina results to be 9.4 10
-4
events/year/cell.
To calculate the transit frequency, we used the
semi-empirical model FLOW-R proposed by H
oRton
et alii (2008), which couples a probabilistic flow rout-
ing algorithm with an energy line approach.
The routing algorithm spreads flow downstream
by calculating the probability that flow passes through
a cell based on slope gradient and inertia. The slope
gradient has a strong effect on the debris flow direc-
tion. Many different algorithms have been proposed in
the literature. In the simple single-flow D8 approach,
the flow is entirely transferred from each cell to the
neighbouring cell along the steepest direction. The
multiple flow direction method (Q
uinn
et alii 1991)
considers the spreading over every downward cell in a
continuous, and not random way:
where:
i, j = flow direction;
f
si
= flow proportion in direction i;
tan β
i
= slope gradient between the central cell and cell
in one down slope direction
H
olmGRen
(1994) introduced an exponent, x, in the
algorithm, to allow a control on the spreading of the flow.
The higher the exponent x, the more convergent the flow:
(1)
(2)
Fig. 2 - Example of flow apportion with persistence effect.
Provenience of flow is indicated by the arrow, and
it is divided into the lower cells. The probability
deriving from the product of slope algorithm and
persistence is rescaled to 0-1
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S. LARI, G.B. CROSTA, P. FRATTINI, P. HORTON & M. JABOYEDOFF
936
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
related to larger water content (Tab. 1). Holmgren al-
gorithm (H
olmGRen
, 1994) with exponent 10 and 9
results the best in order to simulate the flow direction
for open slope and channelled debris flows, respec-
tively. In both cases, a limiting kinetic energy of 30
m/s results to be reasonable (Tab. 1).
DEGREE OF DAMAGE, v
The degree of damage, v, related to debris flows
depends on both the intensity, in terms of depth and
velocity of the flow, and the vulnerability of exposed
elements. The model provides velocity, but not the
depth of the flow. For this reason, a constant flow
depth of 2 m was assumed, which is a conservative
value based on observations of historical events. Vul-
nerability of buildings and infrastructures was calcu-
lated starting from the simulated kinetic energy using
empirical vulnerability curves available in the litera-
ture for debris flows (b
ovolin
& t
aGliatatela
, 2002).
In general, the flow proceeds with high velocities and
has a great destructive power. For this reason, people
impacted by debris flow are supposed to have a high
probability of death. By means of expert evaluations,
a value of v = 0.75 was assumed.
elled with a pre-determined friction angle. Kinetic en-
ergy is limited by a upper velocity threshold to avoid
excessive or unrealistic energies.
At the beginning, a debris flow source has a cer-
tain unit potential energy (without considering the
volume) (Fig. 3) (a).
During propagation, part of the energy is lost in
friction (b). The kinetic energy increases and may reach
the maximum threshold value, leading to an energy line
having the same profile as the terrain. In fact, while the
threshold is reached, energy loss is equal to the differ-
ence in potential energy. The debris flow stops when
the energy becomes null (H
oRton
et alii, 2008).
Outputs of each simulation provide the maximum
kinetic energy of the debris flow in each cell, and the
propagation probability for each cell. The model re-
quires a DTM for terrain description, and a few cali-
brated parameters that controls the routing (i.e., flow
direction algorithm, inertial scheme, reach angle, up-
per limit velocity). We used a 20 x 20 m DTM.
Outputs of the model are the relative probabil-
ity of transit, and the maximum kinetic energy, for
each cell. Probability of transit in the model is to be
considered mainly in a qualitative way rather than as
real probabilities values (H
oRton
et alii, 2008). These
outputs were used to calculate risk for people and for
private and public goods for the study area (Fig. 4).
To calibrate the model, it was necessary to make
a number of simulations modifying each time the
control parameters. After several attempts, we iden-
tified the two different parameterizations, for open-
slope and channelled debris flows, best fitting the
distribution and the extension of the historical events
in the area. For open-slope debris flows we used more
dispersive flow direction algorithms to account for
small-scale topographic variability which is not fully
represented in the DTM, and a reach angle of 15°.
For channelled-debris flows, we decreased the reach
angle to 5° to account for higher mobility basically
Fig. 3 - Iillustration of the runout distance calculation
principles, from h
ortoN
et alii, 2008
Tab. 1 - Parameters for debris flow model calibration
Fig. 4 - Expected frequency of occurrence, f, for the day
scenario, obtained combining triggering frequen-
cy f
d
, and transit frequency, f
t
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REGIONAL-SCALE DEBRIS-FLOW RISK ASSESSMENT FOR AN ALPINE VALLEY
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
937
RISk ASSESSMENT
A map of economic risk, in terms of €/year, and
a map of societal risk, in terms of casualties/year, for
the day and the night scenario, was produced (Fig. 7).
DISCUSSION AND CONCLUDING REMARKS
As resulting from the modelling, debris flow on the
slopes cover a wide surface, especially in the south fac-
EXPOSURE FACTOR, e
Once a debris flow reaches a certain grid cell,
where an element at risk is located, the probability
of this element to be effectively impacted by a debris
flow, e, is quite high, being debris flows sudden, fast
and in general unpredictable phenomena. The value
of e depends on 1) the time of permanence of the
elements in the grid cell (1 for buildings and infra-
structures, <1 for people); 2) debris flow extent with
respect to cell size; 3) the proportion of people and
goods located either at the first floor or in the base-
ment of buildings. The exposure factor e was then
calculated as 0.125 for people and 0.25 for the other
exposed elements.
For each activity (such as staying at home,
working, moving, frequenting schools or other pub-
lic facilities), a different spatial and temporal expo-
sure was considered for day (from 8 a.m. to 6 p.m.)
and night scenarios (from 6 p.m. to 8 a.m.) (Fig.5
and 6).
VALUE
The value of the damaged elements at risks, w,
was calculated for each cell using different data
sources. For societal risk, the value corresponds to the
number of injured people, considering both residents,
workers and people in transit.
For economic risk, the value was calculated
considering different categories of elements at risk,
mapped from aerial photographs and economically
evaluated using local market prices (Tab.2).
Fig. 5 - Equivalent population for day scenario, Valtellina
Fig. 6 - Equivalent population for night scenario, Valtellina
Tab. 2 - Economic value of exposed elements. For sources:
1 market researches; 2 provincial administration;
3 regional administration; 4 Centre for Environ-
ment and Sustainable Development of Lombardy
(CRASL), personal communication; 5 Italian
Railways; 6 ERSAF (2007)
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S. LARI, G.B. CROSTA, P. FRATTINI, P. HORTON & M. JABOYEDOFF
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5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
(Tab.3). In part, this is due to the different duration
of the two temporal intervals, but in some measure it
shows that houses and roads, which are busy during
the evening ad the night, are in general more threat-
ened than working plants or recreational facilities.
In the last 30 years, debris flows in the study area
caused 31 deaths. Societal risk calculated in this study is
consistent with this data, since we consider the number
of expected casualties as comprehensive of injuries,
adequately weighted by means of the vulnerability, v.
Economic losses are distributed on large surfaces
on the open slopes, but risk values do not reach high
levels per cell (max 13,814 €/year) (Tab. 4). Most of
the cells do not reach 50 €/year of damage. Impacted
elements, in fact, are nearly always woods, pastures,
ing slope: here the presence of old agricultural terraces
with scarce maintenance increases the triggering of the
events (C
Rosta
et alii, 2003). Impacted areas on the al-
luvial fans are quite limited in space, but they show con-
siderable values of societal and economic risk. Clearly,
the villages located at the outlet of the secondary valleys,
built on the fans, are the most impacted by debris flows.
Societal risk connected with debris flow is con-
centrated at the foot of the slopes, where settlements
and communication lines are located. The impacted
areas are quite narrow both for the day and the night
scenario, but showing high level of risk.
The number of expected casualties for the night
scenario on the whole study area (4.22) is about the
double of the one expected for the day scenario (1.98)
Fig. 7 - Debris flow frequency of occurrence, societal and economic risk values
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REGIONAL-SCALE DEBRIS-FLOW RISK ASSESSMENT FOR AN ALPINE VALLEY
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
939
was estimated without the use of models, just accord-
ing to the type of activity, and to the opening hours.
Probabilistic studies of debris flow risk at the re-
gional scale are generally difficult, due to the impossi-
bility of calculating a correct return time for the events.
FLOW-R allows a good modelling of both open slope
and channelled debris flows. The availability of photo-
interpreted data was extremely important to calibrate the
models, and to guarantee realistic previsions. The adopt-
ed methodology, then, rescaled the results of the mod-
elling with the historical events registered on the area,
allowing a more realistic representation of the process.
ACKNOWLEDGEMENTS
The authors would like to thank Marco Buldrini
(Nier Ingegneria), Stefano Oliveri and Paolo Seminati
(CRASL Brescia) for the collaboration in the project,
and for the estimate of economic value of the exposed
elements.
and cultivations, which have a limited economic value
if compared with equivalent surfaces of built areas.
Some settled areas are involved, mainly at the toe of
the northern slope and on alluvial fans.
The annual expenditure of the province of Sondrio
for the mitigation of hydrogeological risk, amounts
for the period 2007-2010 to 65 M€. Considering that
a large number of other hydrogeological processes
threaten the area of the province (rockfalls, floods),
the result of risk assessment can be considered largely
in accordance with this data.
Some approximations were necessarily intro-
duced in the analysis while assessing value and expo-
sure of the exposed elements. For the economic risk,
values/m
2
were assumed to be homogeneous on the
study area, while some differences can be found be-
tween cities and villages, between town centres and
agricultural areas.
The time of permanence of people in structures
Tab. 3 - Societal risk values for day and night scenario
Tab. 4 - Economic risk values for day and night scenario
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DATA SOURCES
AVI - Aree Vulnerate Italiane da frane ed inondazioni, http://avi.gndci.cnr.it, visited on April 2007.
DUSAF - Uso del Suolo Agricolo Forestale. http://www.cartografia.regione.lombardia.it/geoportale/ptk?command=openchann
el&channel=157, visited on April 2007.
ISTAT i
stituto
nazionale
di
statistiCa
, http://www.istat.it/, visited on April 2007.
PAI - Piano stralcio di Assetto Idrogeologico http://www.adbpo.it/online/ADBPO/Home/Pianificazione/Pianistralcioapprovati/
PianostralcioperlAssettoIdrogeologicoPAI/Pianovigente.h ml, visited on April 2007.
P
RoGetto
iffi - Inventario dei Fenomeni Franosi in Lombardia, http://www.cartografia.regione.lombardia.it/geoportale/ptk?co
mmand=openchannel&channel=152, visited on April 2007.
R
eGione
l
ombaRdia
(1990) - Carta inventario delle frane e dei dissesti della provincia di Sondrio.
R
eGione
l
ombaRdia
(2005) - Archivio storico della Regione Lombardia, 1988-2005.
R
eGione
l
ombaRdia
(2009) - Catalogo degli eventi di frana e di inondazione della Regione Lombardia.
Statistics