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Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
219
DOI: 10.4408/IJEGE.2011-03.B-026
DATA UNCERTAINTY AND VARIABILITY IN MODELING
DEBRIS FLOW PROPAGATION
R. SOSIO & G.B. CROSTA
(*)
(*)
University of Milano-Bicocca, Department of Scienze Geologiche e Geotecnologie, Italy
Among the condition tested, the largest uncertain-
ty is related to the initial hydrograph, which the model
is very sensitive to (particularly with respect to peak
discharge). Moreover, the hydrograph input data are
unknown in most of the cases and a-priori derivable
only with large approximation. The alternative inflow
hydrographs require a variation larger than one order
of magnitude in the values of the rheological param-
eters obtained by the back analyses. The rheological
properties measured directly on samples of varying
composition (e.g. origin and grain size included) fall
in most of the cases within the range of uncertainty
defined by the alternative inflows considered. Over-
all, the vane geometry is preferable against the Ball
Measuring System. The latter suffers for more narrow
testable conditions, more marked experimental limits,
and produces results which are more scattered than the
vane geometry.
K
ey
words
: numerical modelling, rheometry, viscosity, yield
strength
INTRODUCTION
Modeling debris-flow propagation requires as-
sumptions and simplifications because of (i) the lack
of data which are either not measurable or not avail-
able, (ii) the variability of the involved material, (iii)
the difficulty at characterizing the flow behavior, and
(iv) the limitations of the adopted rheological kernels.
Although all the necessary assumptions cause the
ABSTRACT
We replicate the propagation of the Val Rossiga
debris flow (November 2002, Central Italian Alps),
a 90,000 m
3
event triggered by a rapid retrogressive
landslide with high water content. The rheologi-
cal model combines in a linear sum the viscoplastic
terms of the Bingham model and a quadratic inertial
term. The model requires as input data the bulked
hydrograph and the empirical coefficients which de-
scribe the exponential dependence of the rheological
parameters (i.e. Bingham viscosity and yield stress)
on sediment concentration. We provided these data
through different methods. Alternative hydrographs
were produced by simulating the propagation of the
triggering landslide according to different rheologies
(i.e. rigid block model, frictional material, and Voe-
llmy material). The rheological parameters are either
determined by back analyses and directly through
laboratory measurements and field investigation. Lab-
oratory measurements were performed using a Ball
Measuring System and a vane apparatus connected to
a rotational rheometer on three samples from different
sectors of flow path (i.e. source, channel and fan de-
posit). The samples were analyzed at varying the solid
concentration and the grain size included in the tested
suspensions (maximum grain size of 0.425 mm). The
alterative conditions assumed for the input data were
modeled on topographies of 5 m and 10 m cell-size.
The seven scenarios we obtained were optimized by
back analyses of the rheological parameters.
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5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
ments. The complexity of the event evolution and the
different origin of the debris material, pose an high
degree of uncertainty at reconstructing the proper con-
ditions for the modelling, which is only partly com-
pensated by the large amount of available data.
We propose different alternative choices for una-
vailable or uncertain data (i.e. total inflow hydrograph,
rheological parameters), and we compare models
at different topographical resolution. As a result we
evaluate: (i) which assumptions better approximate
the debris flow evolution; (ii) which aspect of the
modeling (i.e. initial inflow, rheological description)
is more critical by comparing the range of variability
the alternative conditions tested and the final results
produced thereof; (iii) the capability of different meth-
ods of determining the rheological parameters; (iv) the
grain size composition which better approximates the
flow behavior; (v) which level of detail in the input
data is relevant for modeling purposes.
THE ROSSIGA DEBRIS FLOW EVENT
At the end of an exceptional rainy period which
affected the Central Italian Alps, four landslides were
triggered on the right-hand side of the Rossiga Valley
(Valsassina, Lombardy, s
osio
et alii., 2007) between
27 and 29 November (Fig. 1). The debris flow origi-
nated from the failure of the main and uppermost land-
slide (C
Rosta
et alii., 2006). The landslide ran up on
the opposite valley flank for about 15 m, slightly dam-
ming the Rossiga creek. Field evidence and eyewit-
ness accounts indicate that the transformation of the
sliding mass into a fluid-like, rapidly moving debris
flow was instantaneous, as predicted for ‘high-porosi-
ty’ soils (i
veRson
, 2000). This excludes the hypothesis
of a debris flow resulting from the breach of a dam.
The debris flow travelled along a channel partially
filled by the accumulations of previous landslides (the
total volume detached by the landslides were about
200,000 m
3
). The event magnitude was evaluated as
80,000–90,000 m
3
. Measurements of super-elevation
of the flow surface by the mudlines left during the peak
discharge at the channel bends (J
oHnson
& R
odine
,
1984; H
unGR
et alii., 1984) suggest flow velocities of
8–10 m s−1. The debris flow evolved into a main surge,
eventually followed by a smaller, secondary one, and it
took between 4 and 8 minutes to travel 800 m from the
initiation point to the confluence of the Rossiga chan-
nel into the Pioverna river, in the main valley.
model results to diverge more or less from reality, an
evaluation of the uncertainties generally lacks.
Among these criticalities, the rheological assump-
tion (i.e. one, two- phase; resistance law) and the mode
of determining the rheological parameters (i.e. direct
measurements, back analyses) have been deserved
large attention (i
veRson
, 2003). The choice of the total
hydrograph (i.e. water discharge and associated sedi-
ment discharge) to be routed in the model can be equal-
ly critical, particularly with respect to the highest sedi-
ment concentration adopted (b
eRGeR
et alii., in press).
In this paper we present the results of the analy-
ses conducted on a well documented event which oc-
curred on November 2002 along the Rossiga valley,
Valsassina, Central Italian Alps (Fig. 1, s
osio
et alii.,
2007), adopting a one-phase model, which assumes
a Bingham plastic rheological behaviour (o’b
Rien
et alii., 1993). The event was both described by eye-
witness and documented by field surveys.
The debris flow originated from the failure of a
rapid, retrogressive landslide with high water content
(C
Rosta
et alii., 2006). Other failure events had oc-
curred in the previous days, delivering the failed mate-
rial in the Rossiga channel.
The debris flow material is poorly sorted with
medium–low clay to silt content. As a consequence,
both the viscous and the frictional–collisional effects
can be relevant, thus posing the event in an interme-
diate condition between the one-phase and two-phase
conditions, and makes difficult a rheometrical charac-
terization of the material by means of direct measure-
Fig.1 - The Rossiga debris flow event (80 000–90 000
m3) initiated from landslide 4. The debris flow
deposition (grey area) largely took place at the
fan apex and at the confluence with the Pioverna
river. Points of measurement of the maximum flow
thickness, used for comparison of the modelling
results (Figure 6 b) and sampling points for the
laboratory analyses are shown
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DATA UNCERTAINTY AND VARIABILITY IN MODELING DEBRIS FLOW PROPAGATION
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
221
scaled on user-defined empirical coefficients tak-
ing into account the exponential dependence of the
rheological parameters on sediment concentration
(o’b
Rien
& J
ulien
, 1988; m
aJoR
& P
ieRson
, 1992;
C
oussot
& P
iau
, 1994):
where C
v
represents the sediment concentration
by volume.
MODELING SCENARIOS
We applied the Flo-2D routing model to the Ros-
siga event, assuming that the overall flow behaviour
can be approximated by one-phase assumption and
the viscoplastic behaviour assumed into the numerical
model is consistent with the results of the rheologi-
cal analyses performed on the debris-flow samples for
shear rates exceeding 5–10 s−1 (s
osio
et alii, 2007;
s
osio
& C
Rosta
, 2009).
We reconstruct the topography by resampling a 1
m resolution LIDAR DEM, taken after the event into
a 5*5 and 10*10 m cell-size grids. We defined the
channel geometry by interpolating 24 surveyed cross-
sections spaced to represent about 30 m river reaches.
Scour or aggradation processes along the channel
have been neglected. Both these effects have been
relevant as indicated by the distribution of the debris
along the channel cross section, and by the roughness
of the channel bottom after the event. In particular,
the delivered sediment at the confluence of the main
landslides (Fig. 1) probably affected the flow dynam-
ics, both supplying material and constraining the flow
path on the opposite valley flank.
Different modelling scenarios are performed at
changing the total inflow hydrograph originated from
the transformation of the landslide into debris flow
and for the rheological coefficients that empirically
accounts for the exponential dependency of the mate-
rial properties on the sediment concentration (α and β
in eq. 2 and 3).
The alternative total inflow hydrographs consider
different modes of propagation for the initial land-
slide (source 4 in fig. 1) before the transformation
into debris flow. They are: (A) rigid block model, (B)
Field measurements revealed a maximum flow
thickness along the channel of 10 m and a deposit
depth of 3-5 m in the fan area. Mudline observations
along the path revealed a nearly constant maximum
flow cross-sectional area. A tabular and lobate depos-
it about 60 m wide and 80 m long, with an average
thickness of 2-5 m, formed on the 6° sloping surface
of the fan. Based on field evidence, we empirically
estimated yield strength (J
oHnson
, 1970; J
oHnson
&
R
odine
, 1984) and viscosity (J
oHnson
& R
odine
,1984)
ranging between 4000 ± 200 Pa, and 108–134 Pa s,
respectively (Sosio et al., 2007).
The debris-flow material is mono-lithologic, con-
sisting of Verrucano Lombardo (Permian conglom-
erate and sandstone), derived both from the original
landslide and from the sediments available along the
channel. The material is poorly sorted, varying from
clay to boulders up to 5 m in diameter. The deposit is
massive and matrix supported.
THE NUMERICAL MODELING
We performed a series of numerical simulations
using the physically based Flo-2D model for the
forecast of debris flow runout and inundation area
(O’Brien et al., 1993). The model describes the rout-
ing behaviour of a bulked inflow hydrograph as a ho-
mogeneous, one-phase material over a rigid bed. The
flow behaviour is provided by matrix properties and
follows the Bingham model.
MODEL DESCRIPTION
Flo-2D is a flood-routing model, which uses a dy-
namic-wave momentum equation and a finite-differ-
ence routing scheme on an Eulerian framework. The
model routes a user-defined water discharge and the
associated solid discharge on a square elevation grid
according to a quadratic rheological model. The shear
stress, τ, results by a linear sum of the viscoplastic
terms of the Bingham model and a quadratic, inertial
term, referring to the turbulent and dispersive stresses:
t = t
y
+ h g + C g
2
where is the shear rate, C is the inertial shear stress
coefficient, which depends on an equivalent Manning
n-value. The model neglects any frictional effect due
to direct contacts among the coarse clasts.
The yield strength, τ
y
, and viscosity, η, terms are
(1)
(2)
(3)
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5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
precedes the water peak discharge (o’b
Rien
2003).
Bulking the water discharge with variable solid con-
centration is aimed at obtaining a total inflow volume
of approximately 90,000-95,000 m
3
. This range of
values exceed the estimation of the volume detached
from the landslide which initiated the debris flow, as
to include erosion of the material detached by the
previous landslide events which was available along
the channel. The alternative inflow hydrographs
consider different mode for the propagation of the
initial landslide, and are: (A) rigid block model, (B)
Voellmy rheology, and (C) frictional rheology. The
debris flow hydrographs produced by the alternative
mode of propagation of the initial landslide change
by their peak discharges and time durations.
RIGID BLOCk MODEL
The total inflow (water and sediment) hy-
drograph is derived from the pre- and post-failure
longitudinal profiles of the failed slope, assuming a
shape equal to the landslide depth at the source area
(Fig. 2a). From the depth–longitudinal profile we
derived a discharge-time hydrograph (fig 2b), con-
sidering a constant source area width and assuming
that the sliding material has been moved as a single,
rigid, mass from the scarp to the valley. We scaled
the bulked, depth profile as to obtain a total (water
and solid) hydrograph with a 350 m3 s−1 peak dis-
charge and a 7.5 minutes base time.
FRICTIONAL AND VOELLMY MODELS
We modelled the initial landslide (#4 in figure 1)
using a quasi-3D model for simulation of landslide
motion (m
C
d
ouGall
& H
unGR
, 2004). The model
assumes the internal rheology as frictional and the
basal rheologies as frictional (eq 4) and Voellmy (eq.
5), alternatively:
The relationship between the shear force, τ, and
the effective normal stress, σ is described through
empirical coefficients to be
find by trial and error calibration. They are: the
pore-pressure ratio, ru, and the dynamic friction an-
gle, φ, in the frictional model, and the friction co-
Voellmy, and (C) frictional rheology. The alternative
mode for determining the empirical coefficient de-
scribing the rheological flow behaviour (eq. 2 and 3)
are (A) back analyses of the documented event, direct
measurement by (B) ball measuring system (BMS)
and (C) vane rheometrical apparatus, at changing the
sample and the investigated grain size.
DEFINING THE INITIAL DISCHARGE
Field observations and eyewitness accounts re-
vealed the development of the debris flow as a main
surge followed by a low-discharge tail. Following
this observation we derived an inflow hydrograph
with a single peak discharge. A peak discharge of
350 m
3
s
−1
has been estimated from the flow velocity
and cross sectional area in the vicinity of the debris
flow initiation, and the suggested base time is about
7.5 min (s
osio
et alii., 2007). The maximum estima-
tion of the debris removed from the source area is
about 80,000-90,000 m
3
. This value does not include
erosion along the channel.
According to the landslide triggering mecha-
nism, we loaded the water discharge with sediment
at large mean (40–45 per cent in volume) and maxi-
mum (55-60 per cent in volume) solid concentra-
tions. The maximum solid concentration slightly
Fig. 2 - (a) Pre- and post-failure longitudinal profiles
for landslide 4, (Figure 1). The thickness of the
removed material in the source area was used
to derive the inflow hydrograph required in the
numerical model. (b) Inflow hydrographs routed
by the numerical model. At varying bulking con-
centrations the total discharge was kept constant.
Refer to table 1 for scenario’s names
(4)
(5)
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DATA UNCERTAINTY AND VARIABILITY IN MODELING DEBRIS FLOW PROPAGATION
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
223
We reconstructed the total hydrograph accord-
ing to the debris volumes passing through an imagi-
nary cross section at the head of the Rossiga channel
through time (fig 3a). Time intervals of 6 minutes
(assuming a frictional model), and 7 minutes (assum-
ing a Voellmy model) are required for the detached
debris to arrive entirely into the valley. The peak
discharges resulting from the numerical modelling
of the landslide propagation are approximately 500
m3s-1 for both the models (Fig 3b), thus resulting
slightly higher than the discharge estimation in the
field (350 m
3
s
-1
), for the rigid block assessment. This
difference can be explained considering the wave at-
tenuation during its propagation downstream (P
ieR
-
son
1986;a
Rattano
& m
oia
, 1999). The obtained
base time (table 1), is comparable to observations
DEFINING THE RHEOLOGICAL PARA-
METERS
The empirical coefficients which describe the
exponential relationship of the yield strength and
viscosity with solid concentration are alternatively
defined by (A) back analyses and (B) direct meas-
urement of the rheological properties of the material
for three samples at varying solid concentration. The
samples were collected along the flow path, from the
landslide scarps (source areas 1 and 4) and from the
deposit (Fig. 1).
More than providing the empirical coefficient
required for the modelling, the rheometrical charac-
terization allows to verify the rheological behaviour
assumed in the model. The material has a relevant
and variable content of fines (5-15% of the frac-
tion finer than 20 mm, s
osio
et alii., 2007), which
pose the event at the boundary to be considered
as one-phase. For the diverse samples tested, the
flow curves are best approximated by the Herschel-
Bulkley model, shear thinning or shear thickening
depending on the grain size considered for the anal-
yses (s
osio
&C
Rosta
, 2009).
The measurements have been performed with the
efficient, µ, and the turbulence coefficient, ξ, in the
Voellmy model.
We modelled the motion of a shallow landslide
of about 91,000 m
3
of material. The model geom-
etry and the local depths of the detached material
have been derived by the pre and post –event topog-
raphies. The landslide front takes about 20-25 sec-
onds from the initial detachment to reach the head of
Rossiga valley. At the confluence into the valley, the
debris has a velocity of 18 ms-1 (assuming the fric-
tional rheology,
φ=32°, u
r
=0.25) and 14 ms
-1
(assuming the Voellmy, µ,=0.21 ξ=50 ms
-2
). In
both the models, part of the material runs up on to
the opposite valley at the height indicated by the ob-
served mudlines (i.e. about 15 m, Fig. 3), and then
continues its motion downstream, channelled along
the valley. This behaviour is confirmed by the field
observations which suggest an immediate transfor-
mation of the landslide into debris flow and exclude
the debris-flow initiation by breaching of a landslide
dam constituted by the landslide material accumu-
lated in the valley.
Fig. 3 - (a) Time evolution of the propagation of landslide
4, (Figure 1) assuming the Voellmy rheologi-
cal model. The thickness of the material passing
through a cross section at the head of the valley
(indicated in the figure) was used to derive the in-
flow hydrograph required in the numerical model.
(b) Inflow hydrographs routed by the numerical
model assuming a Voellmy and frictional rheol-
ogy for the landslide propagation. At varying the
rheological model, the shape of the total and wa-
ter hydrographs changes. The peak discharge for
the rigid block models is indicated by
the line
Tab. 1 - Modelling conditions for each scenario
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Ball Measuring System (BMS, s
CHatzmann
et alii,
2003, s
osio
et alii, 2007) and a Vane (a
nCey
& J
oR
-
Rot
, 2001; a
nCey
, 2001) installed in the rheometer
Paar Physica MCR 300. The standard experiments
consisted of measuring the torque required by the ma-
terial to flow at fixed rotational velocities during time
(i.e., stress growth curves), by the material when sub-
jected to a constant shear stress (creep curves) From
the stress growth curves we derived the flow curves
(Fig. 4) and the deformation undergone.
BACk ANALYSES
The coefficients (α, β, γ and δ in Equations 2
and 3) that define the rheological properties of the
material have been back-calculated by a trial and
error calibration on the (maximum) flow and (final)
deposit thickness, travel time, flow velocities, and
depositional areas. The back analysis has been per-
formed at varying modelling conditions (i.e. initial
hydrograph, grid cell size; see table 1 for a descrip-
tion of the scenarios).
Figure 5 and 6 show the results of the back analy-
ses for the diverse scenarios considered, whereas fig-
ure 7 compares the trend of the rheological parameters
obtained by the different methods adopted.
Fig. 4 - Flow curves for a sample collected at the source
area on fraction finer than 0.425 mm (source 1,
figure 1). The data refers to the results obtained
performing the analyses with (a) the vane geo-
metry, (b) the ball measuring system (BMS). The
different tools have different range of applicabi-
lity with reference to the shear rate to be applied
and the solid concentration of the suspension to
be tested. In the graphs, the vertical lines indi-
cate the shear rate interval where the material
viscosity has been determined as a mean value
Fig. 5 - Deposit distribution of the Rossiga debris-flow
event: (a) field reconstruction of the flow thickness
and (from b to h) computed flow thicknesses for
different modelling conditions compared to ob-
served limits (dashed lines) for the different sce-
narios
Fig. 6 - (a) Flow velocity along the channel compared
for the modelled scenarios. Dots define peak flow
velocities computed at the channel bends based
on the mudline left during the peak discharge
(Johnson and Rodine, 1984; Hungr et al., 1984).
(b) Comparison between measured and computed
values for the deposit thickness. The location of
the measuring sites is shown in Figure 1 (crosses)
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DATA UNCERTAINTY AND VARIABILITY IN MODELING DEBRIS FLOW PROPAGATION
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
225
large variations into the values assumed by the rheo-
logical parameters which results from the back analy-
ses more than to changes in event replication (i.e.
flow evolution, final deposition, etc). As an example,
reducing the grid cell size from 10 m to 5 m (Scenario
A and B) induces an increase of the viscosity by one
order of magnitude for the whole range of sediment
concentration (see the values of the rheological co-
efficient in table 2). Smaller cells require larger vis-
cosities to assure the maintenance of subcritical flow
through the rough and steep slope topography of the
area and the replication of the flow velocity estimated
in the field. On the other hand, no relevant variations
in the replication of the event were observed.
MODELLING CONDITIONS
The input hydrographs differ among the scenarios
(see Fig. 2, 3) by 30% with respect to the total hy-
drograph, varying the water peak discharge from 350
m3s-1 (Scenario A) to 450-500 m3s
-1
(Scenario D-V,
D-F), and by 10% with respect to bulking, varying the
solid concentration by volume from 55% (Scenarios
A, D-F, D-V) to 60% (Scenario C). The results for all
the scenarios capture the gross features of the debris
flow which are either measured (i.e. flow thicknesses,
propagation area) or estimated (i.e. flow velocity,
yield strength, viscosity) in the field (Fig. 5 and 6, ta-
ble 3). Among them, Scenario Dan-F and Scenario B
best capture the observed thickness both for the de-
posit (final values) and for the flow mudlines along the
channel (maximum values), as suggested by the low-
est values of standard deviation (figure 6, b), whereas
Scenarios C and Dan-V best recognize the area of
propagation (table 4). The field estimation for the ve-
RHEOMETRY: BALL MEASURING SYSTEM
The rheological analyses were performed on two
samples, one from the distal portion of the fan, and one
from the source area 1 (Fig. 1), considering the fraction
finer than 0.425 mm (25–30 per cent of the sieved mate-
rial) at different solid contents (from 45 to 63 per cent, by
volume). We derive the viscosity as the mean slope in the
Bingham region of the flow curves (o’b
Rien
& J
ulien
,
1988; m
aJoR
& P
ieRson
, 1992). Creep curves provide the
direct measurements of the yield strength, as the stress
value necessary for permanent deformation to occur.
RHEOMETRY: VANE
We investigated the rheological behavior of three
samples taken from the debris flow deposit and source
area at varying solid concentration (from 38.0 to 54.2%
by volume) and grain size distribution. Experiments
were performed first on the fraction finer than 0.075
mm. Additional experiments evaluate the effects on the
rheological behaviour at varying the grain size distribu-
tion of the suspension. These where conducted includ-
ing sand with different grain sizes (from 0.106 mm to
0.425 mm in size) and percentages (from 10 to 50%) to a
suspension constituted of particles finer than 0.075 mm.
The flow curves, obtained in a control rate mode
and regularized by the Tikhonov’s method (a
nCey
,
2005), were fitted with the Bingham and Herschel-
Bulkley models to derive the rheological parameters
The viscosity has been evaluated as the mean slope in
the region of the flow curve where there is a linear in-
crease of the shear stress with the shear rate (between 1
and 10 s
-1
, see fig Fig. 4). We assumed the yield strength
as the value obtained by the regularization procedure.
DISCUSSION
Applying any numerical model to natural events
has uncertainties related both to unknown input data
and numerical computation, particularly when an
optimization procedure is not performed. Some data
can only be hypothetically postulated (i.e. sediment
content and discharges, Manning n-values etc.), oth-
ers depend on modeller requirements (i.e. cell-size
dimension). These parameters can change largely and
their choice requires assumptions and simplification
which are only seldom supported.
In some cases, perturbing unknown conditions
among different scenarios largely affects the results of
the back-analysis. The changes eventually determine
Tab. 2 - Values of coefficients for eq. 2 and 3 obtained
through back analyses from numerical modelling
of varying scenarios and rheometrical measure-
ment on different samples
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5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
or shear thinning behaviour, respectively. The type of
shear rate behaviour depends on the material
composition, being thinning for fine grained, cohesive
material (i.e. mudflows) and thickening for coarse –
grained, frictional and collisional material (i.e. gran-
ular flows). The condition of constant viscosity (i.e.
n=1) assumed in the Bingham model is only a restrict-
ed, transitory condition in between the more frequent
shear thinning and shear thickening behaviours.
The rheological parameters varies largely among
the tested samples (figure 7), confirming that the flow
behaviour may change during the same event from
the source area to the deposition zone according to
any variation in the material constituents. The yield
strength, in particular, varies markedly with the mate-
rial composition. The largest values are observed for
the samples composed by material finer than 0.075
mm alone. In this case the yield strength is provided
by cohesion and its magnitude (at the solid concentra-
tions considered in the analyses) is compatible with
the value observed in the field. Adding larger sized
particles first reduces and then increases the yield
strength (table 3; Sosio and Crosta, 2009).
The variations resulting from changing the mate-
rial composition and origin are marked and are out of
the range of variability of the back calculated param-
eters (figure 7 a). The viscosity values resulting from
direct measurements, on the other hand, vary within
the range of uncertainty of the back calculated param-
eters (figure 7 b).
locity with the super- elevation method suggest values
of about 8–10 m s
-1
, but these data are sparse and the
method can overestimate by up to 30 per cent the esti-
mated velocity values (i
veRson
1997; w
HiPPle
, 1997).
On the other hand, the flow velocity resulting from
the modelling is very sensitive to local morphology
(figure 6 a). Large differences are otherwise observed
with respect to the values assumed by the rheological
coefficients adjusted by back analyses (table 2).
The viscosity change by one-two orders of mag-
nitude among the scenarios, and larger values are re-
quired by larger peak discharges. The yield strength
is otherwise less sensitive to variation in modelling
conditions. Assuming the frictional and Voellmy mod-
el for the propagation of the initial landslide allows
obtaining values which are comparable to field esti-
mation both for the viscosities and the yield strength.
RHEOLOGICAL BEHAVIOR
The mixture behavior is viscoplastic and it varies
markedly with small variations in solid volume frac-
tion, shear rate, and grain size distribution (o’b
Rien
a
& J
ulien
, 1988; P
HilliPs
& d
avies
, 1991; m
aJoR
&
P
ieRson
, 1992). At shear rates lower than 3–5 s
-1
, shear
stress is rate-independent suggesting a frictional be-
haviour. At higher shear rates, the shear stress increas-
es depending on the grain particle size included within
the suspension. We used the Herschel- Bulkley and
Bingham models to describe the monotonous increase
of the shear stress with the shear rate in this region.
At changing the grain size distribution, the behaviour
varies from shear thinning to shear thickening, and the
n values in the Herschel-Bulkley model increase with
the maximum grain diameter.
A linear increase of the shear stress with the shear
rate (i.e. n=1) as assumed in the Bingham model, is
only observed at shear rates higher than 10–20 s
-1
,
which are larger than the shear rates more typical for
debris flows. For the Rossiga event, shear rates of 1–2
s−1 were estimated as the ratio between the maximum
velocity and flow depth measured in the field (P
HilliPs
& d
avies
, 1991; i
veRson
, 1997), whereas values of
1-5 s-1 result from the numerical model. This discrep-
ancy affects the relevance of the values assumed by
the coefficient relative to the viscosity. These values
are very sensitive to the shear rate interval considered
for their calculation and they can be either underes-
timated or overestimated in case of shear thickening
Tab. 3 - Field estimated viscosity and yield strength pa-
rameters compared against the values of the
same parameters resulting from back analyses
(evaluated at the maximum Cv adopted in each
scenario) and rheometrical measurement (evalu-
ated at Cv=55%). The confidence interval in the
field estimation data refers to the uncertainty of
the measurement
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DATA UNCERTAINTY AND VARIABILITY IN MODELING DEBRIS FLOW PROPAGATION
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
227
the modelling results. To replicate the event evidenc-
es, the viscosity values have to be adjusted by more
than one order of magnitude among the scenarios.
The back-analysed yield strength, which controls the
deposit thickness, accomplishes more narrow varia-
tions. On the other hand, the values of the rheologi-
cal parameters determined by direct measurements
fall within the range of possible values defined by the
back analyses, so that the uncertainty related to the
inflow hydrograph remain the most critical.
The use of the vane geometry is suggested against
those of the Ball Measuring System (s
CHatzmann
et
alii., 2003). The vane cell geometry reduces some ex-
perimental problems (e.g., slip at the wall, evapora-
tion, and extrusion of the sample), which commonly
occur when testing concentrated suspensions (C
ous
-
sot
et alii., 1993; b
aRnes
& n
Guyen
, 2001) and en-
sures an higher homogeneity of the sample. This re-
sults in an higher reproducibility of the measurements
(±12%) in a wider range of shear rates and testing
conditions. Adopting the vane geometry (minimum
gap between the vane blades and the shear cell of
3.5 mm), a maximum grain size dimension of 0.300
is suggested for avoiding perturbing effects (i.e. end
effects, lack of homogeneity within the suspension)
during measurements (s
osio
& C
Rosta
, 2009). The
measures obtained on the suspensions with 0.300 mm
are in agreement with the field estimations and pro-
duces good results when adopted for replicating the
Rossiga debris flow event (figure 5).
ACKNOWLEDGEMENTS
The authors wish to thank G. Mojoli, C. Ancey,
& J. O’Brien for their suggestions and useful discus-
sions about the rheological analyses and the numerical
modelling.
CONCLUDING REMARKS
We propose different alternative choices for as-
sessing unavailable or uncertain data (i.e. inflow hy-
drographs, rheological parameters), and we compare
models at different topographical resolution to evalu-
ate which assumptions better approximate the debris
flow event and which input data are more critical for
the modelling within the alternative consider.
The Rossiga event is best replicated assuming the
initial motion of the landslide as frictional and Voe-
llmy (Scenarios Dan-F and Dan-V) with slight varia-
tion among each other, either considering the flow and
deposit thicknesses and the values resulting from the
back analyses of the rheological parameters.
Changing the initial conditions (i.e. initial inflow,
rheological description) determines large variations in
Fig. 7 - Trends of the viscosity and yield strength with
sediment concentration determined by each anal-
ysis, for the different scenarios. Estimation of the
rheological parameters assessed in the field are
reported. The viscosity values obtained by the
rheological analysis (a) fall into the range of un-
certainties of the model while the yield strength
values (b) are up to one order of magnitude lower
than the back-calculated ones
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