Document Actions

IJEGE-11_BS-Gregoretti-et-alii

background image
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
425
DOI: 10.4408/IJEGE.2011-03.B-048
GIS-BASED CELL MODEL FOR SIMULATING DEBRIS FLOW
ROUTING AND DEPOSITION PHASES ON A FAN
C. GREGORETTI
(*)
, m. FURLAN
(*)
& m. DEGETTO
(*)
(*)
University of Padova - Dipartimento Territorio e Sistemi Agro-Forestali - Italy
of channels incising debris fan after the impact with
runoff descending from the upstream cliffs. The routing
path of debris flows is usually obliged and coincides
with the channel in the upper part of the fan but in the
medium part it can deviates (t
akanasHi
et alii, 2007)
and in the lower part, where terrain slope diminishes,
can spread (i
veRson
et alii, 1998; R
iCkenman
, 2005;
b
eRti
& s
imoni
, 2007). Hazard mapping concerns the
identification of the threatened area, historical or poten-
tial, by debris flows. Therefore hazard maps are built
both using data from surveys of areas flooded by de-
bris flows and through the simulation of potential sce-
narios. The models (methods) used for the simulation
of a potential scenario are empirical (a
ulitzky
, 1973),
empirical-statistical (b
eRti
& s
imoni
, 2007; G
Riswold
& i
veRson
, 2008; s
CHeidl
& R
iCkenman
, 2010), topo-
graphic gradient based (G
RubeR
, 2007), numerically
based by integration of shallow water equations (b
Ru
-
fau
et alii, 2000; a
Rmanini
et alii, 2009), SPH (P
astoR
et alii, 2008) and automata cellular (d
eanGeli
& s
eGRe
,
1995; d’a
mbRosio
, 2003, d
eanGeli
, 2008). In this
work a GIS-based cell model is proposed. Cell model
was proposed by z
anobetti
et alii, (1970) for simulate
flood inundation of rural area of large extension and
was successively adapted to simulate flood and runoff
routing in urban areas (R
iCCaRdi
, 1997; m
asCaRenHas
& m
iGuez
, 2002; m
iGuez
et alii, 2009; C
Hen
et alii,
2009). In these models cells are linked on the base of
flow characteristics (channel flow, weir flow, floodplain
flow). Moreover, a cell model was also used to simulate
ABSTRACT
A GIS-based cell model is proposed for the simula-
tion of the routing and deposition phases of debris flow
on a fan. Flow pattern is discretized by square cells,
2m size, which coincide with the DEM cells and the
mixture is assumed a monophasic continuum. Flow ex-
change between adjacent cells is ruled by uniform flow
or broad-crested weir laws and by continuity equation.
Flow occurs from cells with higher surface to those
with lower surface and is simulated by uniform flow
law if the elevation of the formers is higher than the
latter and by broad-crested weir law otherwise. Erosion
and deposition are simulated using the empirical law of
Egashira, adjusted for monophasic continuum. The cell
model is used to simulate debris flow occurred on Rio
Lazer (Dolomites, Eastern Italian Alps) the 4
th
of No-
vember 1966. The same event was also simulated us-
ing Flo-2D model for a comparison with a widely used
model for debris flow simulation. Results of the two
simulations were compared with extension of deposi-
tion area and the map of measured depths of deposited
sediments. Both the model simulate quite well the ex-
tent of deposition area, whereas the deposited debris
depths are better simulated by the cell model.
K
ey
words
: GIS, cell model,fan spreading, hazard map
INTRODUCTION
Debris flows in the Dolomites usually occur for
the mobilization of sediment accumulated on the bed
background image
C. GREGORETTI, M. FURLAN & M. DEGETTO
426
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
only one flow direction, that conveys flow towards the
more depressed cell is inadequate to simulate debris
flow spreading in the deposition areas. Objective of this
paper is a robust model based on strong simplification
of hydraulics (i.e. flow cell) that allows a reliable simu-
lation of routed areas and sediment deposits of debris
flow. In this work the flow cell is used to simulate the
debris flow routing and deposition phases on a fan and
the flow cell scheme of z
anobetti
et alii (1970) is there-
fore adapted to debris flow spreading on a fan using two
hydraulic links to simulate flow exchange of a cell with
the neighbours. Flow occurs from cell with higher flow
surface elevation towards cell with lower surface eleva-
tion and is simulated by the uniform flow equation in
the case of flow from higher elevation cell to lower el-
evation cell and by the weir equation otherwise.
Flow patterns is discretized using pixel of the
DEM and flow exchange between cells is computed
by uniform flow and weir equation laws, requiring the
respect of continuity equation. The governing equa-
tions, then, are those of continuity for each cell and
discharge relationships between linked cells. Eight
possible flow directions are assumed (Figure 1) as in
the FLO-2D model and a possible lattice geometry in
automata cellular models (s
eGRe
& d
eanGeli
, 1995).
Basic assumptions of the model are summarized
as follows:
1. The solid-liquid mixture is assumed continuum
and monophasic;
2. Exchange flow relationship between adjacent cells
are uniform flow and broad-crested weir equations;
3. The cell flow surface is considered horizontal;
4. There are eight possible flow directions;
5. Flow section between cells are considered rectan-
gular;
6. Flow volume inside cell is function of the flow depth;
7. Exchange flow of a cell with the neighbouring
ones is simultaneous;
8. The discharge exchanged between neighbouring
cells depends on the flow levels of the cells.
9. The computation method is explicit and the time
step is computed using the CFL condition.
soil erosion and sediment outflow from a catchment
where flow paths to the outlet are, a priori, determined
using topographic gradient and the routing is ruled by
De Saint Venant equation without inertia terms (J
ain
et
alii, 2005). The proposed model does not distinguish
the cells but the hydraulic links that depend on both the
bottom and flow surface elevation between neighbour-
ing cells and is not limited by the topographic gradient.
The mathematical structure of the model is analogous
to that used by cellular automata models and that of
FLO-2D model even if the latter does not simulate the
sediment entrainment and deposition.
THE CELL MODEL
OVERVIEw
The flow cell concept, as introduced by z
anobetti
et alii, (1970), proposes to represent a basin through
homogeneous compartments, channels, floodplain gal-
leries, weirs which are in turn represented by cells. Each
cells interacts with the neighbouring cell by hydraulic
links (Saint Venant equations, with or without inertia
terms, broad-crested weirs, orifices, gates laws) that are
chosen on the base of the cell type: two “channel” cells
interact using the De Saint Venant equation, a “chan-
nel” cell interacts with a “floodplain” cell by the weir
equation, and so on. The cell model is able to reproduce
multiple flow patterns as those of urban areas and over-
comes the difficulty of implementing the usual numeri-
cal 2D models based on the shallow water equations in
a complex environment of streets, buildings, elevated
terrains and so on. On the other hand J
ain
et alii (2005)
used a cell model to route runoff and sediment to the
outlet considering only a flow path departing from each
cell along the steepest slope, that is, towards the sur-
rounding cell of lowest altitude. The model proposed by
J
ain
et alii (2005) is therefore an hybrid between one
and two-dimensional models, because for each cell the
inflow could come from more than one of the neighbour-
ing cells but the outflow is only to the lowest altitude
cell. Moreover, this technique needs the pre-processing
of DEM at the purpose to eliminate holes that can inter-
rupt the flow path between a cell and the outlet.
In the case of debris flows, as the case of urban
areas, the usual dam-break two-dimensional models
which integrate the shallow water equations, meet
some difficulties that are due to the irregular and slop-
ing flow pattern and the presence of civil structures. On
the other hand the distributed cell model considering
Fig. 1 - Scheme of the possible
flow directions
background image
GIS-BASED CELL MODEL FOR SIMULATING DEBRIS FLOW ROUTING AND DEPOSITION PHASES ON A FAN
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
427
where n and m are the number of surrounding cells for
which sin q
i,k
and h
i
- h
k
are positive. The broad-crested
equation has been modified considering the difference
between flow surface elevations of the two cells in-
stead of the difference h
i
- z
k
. This modification holds
the larger energy loss due to the presence of sediments
and should avoid the use of a diminution discharge co-
efficient in the case of drowned “weir”. The weighting
functions depend on the topographic and flow surface
drops respectively and are used to narrow the flow
width because of the flow is not one-dimensional.
EROSION AND DEPOSITION
Erosion and deposition are modelled through
the empirical equation of e
GasHiRa
& a
sHida
(1987)
which is converted for a continuum mono-phase:
where K is an empirical constant between 0 and 1; U
i,k
is the mean velocity corresponding to the discharge Q
i,k
;
θ
i,k
is the angle respect to the horizontal between the
line joining the centres of the cells i and k in the case of
uniform flow and the angle between the line joining the
centres of flow surfaces of cell i and k diminished of the
adverse topographic slope between the two cells in the
case of weir flow; θ
LIM
is the limit angle for both erosion
and deposition (it assume different values for erosion and
deposition respectively: θ
LIM-E
and θ
LIM-D
). Erosion occurs
for θ
i,k
> θ
LIM-E
and U
i,k
> U
LIM-E
, being U
LIM-E
the limit
inferior value of mean velocity for erosion. Deposition
occurs for θ
i,k
< U
LIM-D
and U
i,k
< U
LIM-D
, being U
LIM-D
the
limit superior value of mean velocity for deposition.
ALGORITHM STRUCTURE
Dem cells are divided into two classes: boundary
cells where the input hydrograph is inserted (input
CONTINUITY EQUATION
Two basic assumptions of continuity equation are:
a) the flow volume V
i
t
in the cell i at time t is obtained
multiplying the corresponding flow depth at time t, h
i
t
, by the cell area; b) the exchanged discharge at time
step n∆t (t = (n-1) ∆t) depends on the flow depths of
cells. In differential form, the continuity equations is:
where A = cell area; i
b,i
is the bed erosion/deposition
velocity; Q
i,k
is the discharge exchanged between cell
i and k and is assumed positive if directed towards
cell k, negative otherwise.
DISCHARGE EXCHANGE RELATIONSHIP
BETwEEN CELLS
There are two types of exchange relationships be-
tween a cell and those surroundings with lower flow
elevation: uniform flow equation if cell elevation is
higher than that of the surrounding one (Figure 2a);
modified broad-crested equations if cell elevation is
lower than that of the surrounding one (Figure 2b). The
discharge equations in the two case are respectively:
where C is the conductance coefficient (t
subaki
,
1972); ∆x is cell size; q
i,k
is the angle respect to the
horizontal between the line joining the centres of cell
i and k (atan(z
i
- z
k
)/∆x); z
i
is the bottom elevation of
cell; w
i,k
e s
i,k
are two weighting functions:
Fig. 2 - Scheme of the possible flow between two adjacent cells
(1)
(3)
(2)
(5)
(4)
(6)
background image
C. GREGORETTI, M. FURLAN & M. DEGETTO
428
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
between these volumes. After computing the outflow
volumes of all the cells and the corresponding bed
erosion/deposition velocities, flow surface elevations
of all the cells are simultaneously updated summing,
for each cell, the outflow, inflow, deposited and eroded
volumes just computed. The output boundary cells ex-
change flow discharge both with the surrounding cells
and with the extern. The flow exchange with the extern
is simulated without weighting functions by equations
(2) and (3) along flow directions by which the bound-
ary cell receives flow discharges according to uniform
flow and broad-crested weir equations respectively. In
other words, the flow directions from the boundary cell
toward the extern coincide with those from inner cells
to the boundary cell. Moreover there are other two pa-
rameters hROUT and hER. The first, hROUT, is the
minimum flow depth for routing to avoid the routing
of very small flow depth (inferior to 0.01 m) that is a
physical non sense. This parameter is somehow com-
parable to the roughness height. The second, hER, is
analogous to the previous one and is a lower bound for
the flow erosion capacity. At the end of the simulation
flow depths inferior to hROUT are assumed deposited.
The simultaneous updating of flow surface el-
evation for all the cells approaches the parallelization
technique used in the cellular automata models. On
the base of that written above there is a strong simi-
larity between this cell model and cellular automata
models. In fact this model corresponds to a cellular
automata model without substates with local rules
given by equations (1), (2) and (3) and mobilisation
condition given by flow level larger than that in the
surrounding cells and a flow depth larger than h
ROUT
.
RIO LAZER BASIN AND DEBRIS FLOW
OCCURRED THE 4
TH
OF NOVEMBER 1966
Rio Lazer basin is located in the Trento province
(Dolomites, Nort Eastern Italy) with the largest altitude
equal to 1608 m a.s.l.. Its extension is 1.57 km
2
and the
average slope 30.8 %. Rio Lazer torrent origins at 1200
m a.s.l. and joins Cismon torrent at 742 m a.s.l. between
the built-up areas of Siror and Tonadico (figure 3). The
4th of November 1966 a debris flow initiated at 850 m
a.s.l. after high intensity rainfall and routed along the
main channel. Just downstream the wooded area (figure
3), it spilled out the channel and flooded the entire fan
depositing sediments of about 80800 m
3
volume (com-
puted associating a deposition depth d to the four deposi-
boundary cells) or there is outflow (output boundary
cells) and routing cells. At the first time step, only the
input boundary cells are activated by filling it with
the volume of the input hydrograph corresponding
to the first time step. At the second time step, flow
routing from input boundary cells towards those sur-
roundings occurs. At the third time step, flow routing
occurs from input boundary cells and those surround-
ings and from the cells routed at the previous time
step towards those surrounding the last ones. The
coordinates of cells routed for the first time during a
same time step are stored in a vector. So at each time
step corresponds a vector containing the coordinate of
activated cells, that is those routed for the first time.
Flow routing is computed sequentially from the input
boundary cells followed from the first order routed
cells (cells routed at the second time step) and so on.
Input boundary cells cannot be routed by other cells
but receive flow only by the input hydrograph and are
not subjected to erosion and deposition. The time step
is computed according to the CFL condition with the
Courant number equal to 0.95. This last constraint
does not origin from numerical instabilities problems
but is used at the purpose of respecting the physics of
routing. The numerical scheme is explicit, that is the
quantity at the time t + ∆t is computed by the values
of the quantities at time t. Therefore, equation (1) after
the integration in time, for the generic cell i, becomes:
The computation procedure is as it follows: for
each cell the possible flow discharges versus the sur-
roundings cells are computed according to equations
(2) and (3); once all the flow discharges are computed
the cell outflow volume is checked and in the case it
results lower than the cell flow volume at the begin-
ning of the time step, all the flow discharges are pro-
portionally diminished to obtain the equality between
outflow volume and flow volume of the cell at the be-
ginning of time step. For each cell, then, the erosion
bed velocities corresponding to the flow discharges are
computed and summed according to equation (6). Pos-
itive value of i
b,i
means erosion and a negative value,
deposition. If the product A i
b,i
∆t in the case i
b,i
< 0
(deposition), results larger than the difference between
flow cell volume at the beginning of time step and the
outflow volume computed for the present time step, it
is assumed a deposited volume equal to the difference
(7)
background image
GIS-BASED CELL MODEL FOR SIMULATING DEBRIS FLOW ROUTING AND DEPOSITION PHASES ON A FAN
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
429
tion depth intervals of figure 3 that is equal to 0.05, 0.3,
0.75 and 1.5 m respectively). Most of deposited sediment
(70686 m
3
) are in the area where d is larger than 0.5 m.
Figure 3 shows the aerial photo of the lower part
of the basin with superimposed the contour of DEM
that was built (pixel size 2 m) and the deposit map.
The digital elevation model was built on the base of
3000 topographic measurements covering an area of
0.2 km2. The input hydrograph was built combining
the measured volume of deposited sediments with the
runoff computed by an hydrological model. The total
volume is 93900 m
3
that corresponds to a sediment
concentration equal to 0.86. The inlet cells where the
hydrograph is entered are ten and located in the upper
part of the watershed (the input hydrograph is distrib-
uted over a 20 m length). Therefore the total volume
is equally divided for 10 and assigned to each of the
hydrograph of the ten cells and is showed in figure 4.
FLO-2D SIMULATIONS
The scenario of debris flow occurred on Rio Lazer
was simulated as a mudflow because FLO-2D cannot
simulate erosion or deposition for the grain-inertial be-
haviour of mixture. Simulations were carried out using
the values of parameters of the rheological quadratic
law given by O’ Brien and Julien (1985) correspond-
ing to Aspen Natural Soil (Flo-2D user manual) which
allowed the best reconstruction of the occurred event.
In this case the sediment concentration was assumed
equal to 0.45 instead of 0.86 that causes the deposition
of most of sediments in the upper part of the watershed.
The discrepancy is resolved considering a mud-
flow with a 0.86 solid concentration value whose rhe-
ology corresponds to the Natural Aspen Soli with a
0.45 solid concentration value. Using roughness coef-
ficient values K
S
= 3, 13, 30 and 40 m
1/3
/s for buildings,
wooded area, grass and roads respectively, mudflow
mass after, 4 hour, has velocities lower than 0.001 m/s
(Figure 5) and is assumed deposited. Figure 6 shows
the comparison between the measured deposition
depths and the simulated flow depths (as FLO-2D does
not simulate the deposition, flow depth is considered
deposition depth if velocity is less than 0.001 m/s).
Fig. 3 - Arial photo of Rio Lazer flooded area with su-
perimposed the sediment deposits maps and the
DEM contour
Fig. 4 - Reconstructed hydrograph for each
of the ten inlet cells
Fig. 5 - Flow depth (0<h<4 m) simulated by FLO-2D af-
ter 0.25, 1, 2 and 4 hours
Fig. 6 - Comparison between the measured (left) and sim-
ulated (righjt) deposition depths
background image
C. GREGORETTI, M. FURLAN & M. DEGETTO
430
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
osition in the lower right corner of the basin where the
debris deposits are absent. This fact could be due to the
initial assumption of monophasic flow. Considering a
bi-phase flow after sediments deposition, flow is largely
constituted of fluid that spills out from the border of the
considered basin. The monophasic assumption causes
the continuous deposition until the basin border.
DISCUSSION OF THE SIMULATIONS
RESULTS
The comparison of the extension of deposition
area simulated by the two models with that measured
is shown in Table 1.
Table 1 also shows the comparison in percentage of
the value of the measured deposition depths with those
simulated by the two models. The first comparison is
direct and the second one is carried out verifying that
the simulated value is included in a fixed interval. The
measured depths have been divided in four intervals: d
< 0.1 m, 0.1 < d < 0.5 m, 0.5 < d < 1 m and d > 1.0 m.
Figure 9 also shows this second comparison. In-
undated areas are well simulated by both the models
(91% of inundated area in the case of Flo-2D and
95.9% in the case of the cell model) even if they
The extension of the simulated area satisfactory
coincides with the deposition area while the simulat-
ed sediment depth distribution is somehow reversed
respect to that measured. The measured sediment
depths are larger upstream and decrease downstream
while the simulated sediment depths are lower up-
stream and increase downstream. This fact is due to
the missing of a direct deposition mechanism in the
FLO-2D model for which flow depths, when veloci-
ties are lower than 0.001 m/s, become larger when
slope decreases, in the present case downstream.
CELL MODEL SIMULATIONS
Cell model simulations were carried out using the
same input hydrograph and same inlet cells of Flo-2D
simulations. The value of the conductance coefficient
C was assumed constant and equal to 3 according to
G
ReGoRetti
(2000), that is about 10 m
1/3
/s. Considering
that coefficient C contains the rheological law the flow
resistance is equivalent in the two cases. The values of
parameters of the best simulation, that is, with the best
agreement with measured deposits, are K = 0.1, θ
LIM
=
20° for erosion and θ
LIM
= 6° for deposition, U
LIM-E
= 3
m/s, U
LIM-D
.= 1 m/s, h
ER
= 0.1 m and h
ROUT
= 0.01 m. The
parameters relative to the erosion are irrelevant. The val-
ue θ
LIM
= 6° corresponds to bed slope angles for which
solid phase of sediment debris flow begins deposition.
The value of parameter K is slightly inferior to the minus
value of those used for 1D simulation by Brufau et alii
(2000): 0.2 ≤ K ≤ 1. A change of hROUT in the range
0.01-0.05 m does not imply substantial modification of
results. The simulation time is about 0.39 h (about 24
minutes). Figure 7 is analogous to figure 5 and shows the
inundated areas and flow depth values at different times.
The routing times of Flo-2D and cell model simula-
tion are different. This difference depends on the rheo-
logical law. Flo-2D uses a viscous flow law while cell
model uses a grain-inertial flow law. The routing time of
cell model simulation is more physically plausible than
the routing time of Flo-2D simulation that is too large.
Figure 8 shows the comparison between the measured
deposit depths and those simulated by the cell model.
The extension of the simulated area satisfactory coin-
cides with the deposition area, as in the case of Flo-2D,
and the simulated sediment depth distribution somehow
agrees with that measured. The measured and simulated
sediment depths are both larger upstream and decrease
downstream. The cell model, as Flo-2D, simulates dep-
Fig. 7 - Flow depth (0<h<4 m) simulated by cell model
after 0.065, 0.13, 0.26 and 0.39 hours
Fig. 8 - Comparison between the measured (left) and sim-
ulated (righjt) deposition depths
background image
GIS-BASED CELL MODEL FOR SIMULATING DEBRIS FLOW ROUTING AND DEPOSITION PHASES ON A FAN
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
431
simulated deposition area, the 36% of it is correctly
simulated in the case of the cell model and the 14.5
% in the case of Flo-2D model. Considering only the
area with deposit depths larger than 0.5 m, that corre-
sponds to the 87 % of measured sediment volume, the
cell model provides 47 % of deposition area correctly
simulated while Flo-2D provides 27.1 % of it.
Comparing the measured deposition depths with
those simulated of figure 9, it can be observed that
the cell model is able to simulate right deposition
depth in all the inundated area while Flo-2D model
predicts the deposits only in a intermediate position.
This is the reason why Flo-2D simulates correctly
only the 27.4% of the area with deposits larger than
0.5 m that are located in the upper part.
This aspect can be better seen in Figure 10
where the zones with correct simulated deposit
depths are shown along with zones with uncorrect-
ed simulated deposit depths, zones with measured
deposit but not simulated and zones with simulated
deposit but no measured. It can be observed that
the blue areas corresponding to correctly simulated
deposit depths are distributed on all the inundated
areas in the case of the cell model while this does
not occurs in the case of Flo-2D.
both predicts a larger inundated area (124 % and
139% of inundated areas respectively). Neverthe-
less cell model simulates more correctly the deposit
depths than the Flo-2D (50.5 % against 18% of the
measured area: the half of the simulated deposition
depths by the cell model in the measured deposition
area are correct whereas it occurs only for more than
a fourth of the simulated deposition depths by Flo-2D
in the measured area. Moreover as regard the total
Tab. 1 - Comparison of the extension of measured deposi-
tion area and deposition depths with those simu-
lated by the two models
Fig. 9 - Comparison between the measured deposit depths (middle) and those simulated by Flo-2D (left) and cell model (right)
Fig. 10 - Comparison between measured and simulated deposition depths (left Flo-2D simulation, middle measured depths and
right cell model simulation): gray deposition depths measured but not simulated; green deposition depths simulated but
not measured; red deposition depths with simulated uncorrected values; blue deposition depths correctly simulated
background image
C. GREGORETTI, M. FURLAN & M. DEGETTO
432
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
In this last case the blue areas are located in a
intermediate position. These differences in the results
of the two model are due to the different rheologi-
cal laws implemented by the models. Flo-2D models
debris flow as viscous continuous and this implies
larger deposition depths in the downstream part of
deposition area as it occurs in many real cases but
not in the present one. Cell model that includes the
rheological law in the conductance coefficient C is
not subjected to any chain under this point of view.
The fact that Flo-2D cannot directly simulate the
deposition phase forbids the correct simulation of de-
posit depths in the upstream part (most of sediment
of debris flow deposited just after the spilling out of
the channel during the event). On this point of view,
cell model appears more suitable to simulate debris
flow deposition phase on a fan. Moreover the rout-
ing times of cell model are more physically realistic
than those of Flo-2D when simulating the deposition
phase of the debris flow occurred on Rio Lazer.
It should be added that the use of a same hy-
drograph can introduce some bias when comparing the
results of the simulations of the two models. The cor-
rect hydrograph to be used with Flo-2D should be little
lower than that of Figure 4 because the debris flow vol-
ume and the deposition volume must coincide. As the
difference between the hydrograph volume and deposit
volume is little it means that the use of an hydrograph
with a little smaller volume does not change signifi-
catively the results of the Flo-2D simulation. The
percentage of deposition area correctly simulated and
the percentage of measured area with deposit depths
correctly simulated should change just a bit while the
simulated deposition area should decreases.
Finally some words about the influence of cell
size on the simulation in the case of flow cell mod-
el. Table 2 is analogous to table 1 and compares the
performance of flow cell model for three different
cell size ∆x: 1, 2 and 4 m.
The performance of cell model slightly increas-
es with the decrease of cell size in the case of per-
centage of measured area with deposit depth larger
than 0.5 m correctly simulated and percentage of
deposition simulated but not measured. In the other
case the differences in the performances are negligi-
ble. This leads to affirm a very slightly influence of
cell size in the simulation results.
CONCLUSIONS
A cell model is proposed for simulating debris
flow routing and deposition phases on a fan and de-
sign hazards maps. The simplifications at the base of
the model do not strictly respect the physics of routing
when considering the routing times but allow a simula-
tion of deposition depth quite realistic. Debris flow oc-
curred the 4th of November 1966 on Rio Lazer torrent
has been simulated with satisfactory results. The same
event has been simulated by the commercial model
Flo-2D for comparison with a largely used model for
debris flow simulation. The two simulations provide
both nearly equal and different results. Both the mod-
els simulate a deposition area larger than that meas-
ured which cover the 91% of the measured area for
Flo-2D and 95.9 % for the cell model. However, cell
model provides a better simulation of the deposit depth
about more than two times respect to Flo-2D (50.5 %
against 18% of measured area). Moreover, the correct-
ly simulated deposition depths are distributed all over
the deposition area while in the case of Flo-2D simu-
lation, they are grouped in a unique zone of it. This
fact is due to the missing of direct deposit mechanism
in the Flo-2D model that indirectly simulates it when
velocity reduces to the order of 0.001 m/s. This obliges
the use of viscous flow, a prori excluding the granular
inertial flow, with large routing times. On this point of
view, cell model appears more suitable than Flo-2D for
simulating debris flow. It must be added that Flo-2D,
due to the viscous flow rheological law should better
simulate the extension of inundated areas. For a bet-
ter comparison the two models should be both tested
in cases where the deposition depths are larger on the
downstream part of deposits of occurred debris flows.
Tab. 2 - Comparison of the extension of measured deposi-
tion area and deposition depths simulated by cell
model using different cell sizes
background image
GIS-BASED CELL MODEL FOR SIMULATING DEBRIS FLOW ROUTING AND DEPOSITION PHASES ON A FAN
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
433
K
S
= roughness coefficient;
i
b,i
= bed erosion/deposition velocity of cell i;
Q
i,k
= discharge exchanged between cell i and k;
s
i,k
= weighting function;
U
i,k
= flow velocity from cell i to cell k;
U
LIM-D
= upper limit velocity for deposition;
U
LIM-E
= inferior limit velocity for erosion;
V
i
= flow volume in cell i;
w
i,k
= weighting function;
z
i
= bottom elevation of cell i;
∆t = time step;
∆x = cell size;
q
i,k
= the angle respect to the horizontal between the
line joining the centres of cell i and k;
θ
i,k
= adopted angle for computing erosion and deposition;
θ
LIM-D
= upper limit angle for deposition;
θ
LIM-E
= inferior limit angle for erosion.
ACKNOWLEDGEMENTS
This research was financially supported by the
University of Padova grant ex60%, the Italian Ministry
of Education and Research grant PRIN 2007 and Euro-
pean grant PARAmount (imProved Accessibility: Reli-
ability and security of Alpine transport infrastructure
related to mountainous hazards in a changing climate),
within the Alpine Space Programme 2007-2013.
The writers wishes to thank the reviewers for they
useful comments.
NOTATIONS
C = conductance coefficient;
A = cell area;
h
i
= flow depth of cell i;
h
ER
= minimum flow depth for erosion;
h
ROUT
= minimum flow depth for routing;
K = empirical constant;
REFERENCES
a
Rmanini
a., f
RaCCaRollo
l. & R
osatti
G. (2009)- Two-dimensional simulation of debris flows in erodible channels, Computers
& Geosciences, 35(5): 993-1006).
b
eRti
m & s
imoni
a. (2007) - Prediction of debris flow inundation areas using empirical mobility relationships. Geomorphology,
90: 144-161.
b
Rufau
P., G
aRCia
-n
avaRRo
P., G
HilaRdi
P., n
atale
l. & s
avi
f. (2000) - 1-D mathematical modelling of debris flow. Journal of
Hydraulic Research, 38(6): 435-446.
C
Hen
J., a
Rleen
a.H. & u
Rbano
l.d. (2009) - A GIS-based model for urban flood inundation. Journal of hydrology, 373: 184-192.
d’a
mbRosio
d., d
i
G
ReGoRio
s., i
ovine
G., l
uPiano
v., R
onGo
R. & s
PataRo
w. (2003) - First simulation of the Sarno debris
flows through Cellular Automata modelling. Geomorphology, 54: 91-117.
d
eanGeli
C. (2008) - Laboratory granular flows generated by slope failures. Rock Mechanics and Rock Engineering, 41(1): 199-217.
e
GasHiRa
s. & a
sHida
k. (1987) - Sediment transport in steep slope flumes. Proc. of Roc Japan Joint Seminar on Water Resources.
G
ReGoRetti
C. (2000) - Estimation of the maximum velocity of a surge of debris flow propagating along an open channel.
Interpraevent2000 - Villach 26-30 June, 99-108.
G
Riswold
J.P. & i
veRson
R.m. (2008) - Mobility Statistics and Automated Hazard Mapping for Debris-flows and Rock
Avalanches, US Geological Survey Scientific Investigation Report 5276, US Geological Survey: Reston, VA; 59.
G
RubeR
S. (2007) - A mass-conserving fast algorithm to parametrize gravitational transport and deposition using digital
elevation models. Water Resources Research, 43.
i
veRson
R.m., s
CHillinG
s.P. & v
allanCe
J.w. (1998) - Objective delineation of lahar-inundation hazard zones. GSA Bulletin
110(8): 972-984.
J
ain
m.k., k
otHyaRi
u.C. & R
anGa
R
aJu
k.G. (2005) - GIS based distributed model for soil erosion and rate of sediment outflow
from catchments. Journal of Hydraulic Engineering, ASCE, 131, 9: 755-769.
m
asCaRenHas
f.C.b. & m
iGuez
m.G. (2002) - Urban flood control through a mathematical cell model. Water International,
IWRA, 2002, 27(2): 208-218.
m
iGuez
m.G., m
asCaRenHas
f.C.b., C
anedo
de
m
aGalHaes
l.P. & v
ellozo
d’a
lteRio
C.f. (2009) - Plannig and design of
urban flood control measures: assessing effect combination. Journal of Urban Planning and Development, ASCE, 135(3):
100-109.
o’b
Rien
J.s. & J
ulien
P.y. (1985) - Physical processes of hyperconcentrated sediment flows. Proc. of the ASCE Conference
on the Delineation on Landslides, Floods and Debris Flow hazards in Utah. Utah Water Research Laboratory, Series
background image
C. GREGORETTI, M. FURLAN & M. DEGETTO
434
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
UWRL/g85/03: 260-279.
P
astoR
m., H
addad
b., s
oRbino
G. & C
uomo
s. & d
emPtRiC
v. a. (2008) - A depth integrated-coupled SPH model for flow like
landslides and related phenomena. International Journal for Numerical and Analytical Methods in Geomechanics.
R
iCkenmann
D. (2005) - Runout prediction methods. In Debris-Flow Hazards and Related Phenomena, J
akob
m. & H
unGR
O.
(
eds
). Praxis Springer: Berlin Heidelberg: 305-324.
R
iCCaRdi
G.A. (1997) - The mathematical modeling of flood propagation for the delineation of flood risk zones. IAHS publication,
240: 355-363.
s
CHeidl
C. & R
iCkenmann
d. (2010) - Empirical prediction of debris-flow mobility and deposition on fans. Earth and Surface
Process Landform, 35: 157-173.
R
osatti
G.a. & f
RaCCaRollo
l. (2007) - Simulation of debris flow in erodible channels. Proceedings of the 32rd Congress of
IAHR, Venice, Italy.
s
eGRe
e. & d
eanGeli
C. (1995) - Cellular automaton for realistic modeling of landslides. Nonlinear Processes in Geophysics,. 2: 1-15
s
eminaRa
G. & t
ubino
m. (1993) - Debris flows: meccanica, controllo e previsione. Monografia G.N.D.C.I., 1993.
t
akanasHi
k., m
izuyama
t. & n
akano
y. (2007) - A method for delineating restricted hazard areas due to debris flows.
Proceedings of the 4th International Congress on Debris-Flow Hazards Mitigation, Chengdu 10-13 September: 471-478.
t
subaki
(1972) - keikoku taiseki dosha no ryndo. XXVII Japenese National Congress on Civil Engineering (in Japanese).
z
anobetti
d.H., P
Reissman
a., & C
unGe
J.a. (1970) - Mekong Delta mathematical program construction. Journal of Waterways
and Harbour Division, ASCE, 96(2): 181-199.
Statistics