# IJEGE-11_BS-Sosio-&-Crosta

*Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza*

*DOI: 10.4408/IJEGE.2011-03.B-026*

**DATA UNCERTAINTY AND VARIABILITY IN MODELING**

**DEBRIS FLOW PROPAGATION**

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**

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**

a 90,000 m

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.

*R. SOSIO & G.B. CROSTA*

*5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011*

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.

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**

triggered on the right-hand side of the Rossiga Valley

(Valsassina, Lombardy, s

*et alii*., 2007) between

nated from the failure of the main and uppermost land-

slide (C

*et alii*., 2006). The landslide ran up on

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

total volume detached by the landslides were about

200,000 m

discharge at the channel bends (J

*et alii*., 1984) suggest flow velocities of

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.

evaluation of the uncertainties generally lacks.

of determining the rheological parameters (i.e. direct

measurements, back analyses) have been deserved

large attention (i

ment discharge) to be routed in the model can be equal-

ly critical, particularly with respect to the highest sedi-

ment concentration adopted (b

*et alii.*, in press).

curred on November 2002 along the Rossiga valley,

Valsassina, Central Italian Alps (Fig. 1, s

*et alii*.,

a Bingham plastic rheological behaviour (o’b

*et alii*., 1993). The event was both described by eye-

witness and documented by field surveys.

(C

*et alii*., 2006). Other failure events had oc-

rial in the Rossiga channel.

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*

**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*

ing into account the exponential dependence of the

rheological parameters on sediment concentration

(o’b

*MODELING SCENARIOS*

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

*et alii*, 2007;

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.

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).

slide (source 4 in fig. 1) before the transformation

into debris flow. They are: (A) rigid block model, (B)

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

respectively (Sosio et al., 2007).

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**

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*

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*

coefficient, which depends on an equivalent Manning

*n*-value. The model neglects any frictional effect due

to direct contacts among the coarse clasts.

*R. SOSIO & G.B. CROSTA*

*5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011*

centration is aimed at obtaining a total inflow volume

of approximately 90,000-95,000 m

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*

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*

motion (m

basal rheologies as frictional (eq 4) and Voellmy (eq.

5), alternatively:

*σ*is described through

empirical coefficients to be

gle,

*φ*, in the frictional model, and the friction co-

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**

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

flow initiation, and the suggested base time is about

7.5 min (s

*et alii.*, 2007). The maximum estima-

about 80,000-90,000 m

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*

**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*

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

tenuation during its propagation downstream (P

**DEFINING THE RHEOLOGICAL PARA-**

**METERS**

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).

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

*et alii.*, 2007), which

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

Voellmy model.

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*

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*

*R. SOSIO & G.B. CROSTA*

*5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011*

*et alii*,

*et alii*, 2007) and a Vane (a

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*

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).

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)*

**DATA UNCERTAINTY AND VARIABILITY IN MODELING DEBRIS FLOW PROPAGATION**

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*

drograph, varying the water peak discharge from 350

m3s-1 (Scenario A) to 450-500 m3s

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*

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

value necessary for permanent deformation to occur.

*RHEOMETRY: VANE*

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.

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

**DISCUSSION**

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.

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*

*R. SOSIO & G.B. CROSTA*

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.

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 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).

of about 8–10 m s

mated velocity values (i

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).

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*

tion, shear rate, and grain size distribution (o’b

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.

only observed at shear rates higher than 10–20 s

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

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*

**DATA UNCERTAINTY AND VARIABILITY IN MODELING DEBRIS FLOW PROPAGATION**

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.

*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

*et alii*., 1993; b

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

are in agreement with the field estimations and pro-

duces good results when adopted for replicating the

Rossiga debris flow event (figure 5).

**ACKNOWLEDGEMENTS**

sions about the rheological analyses and the numerical

modelling.

**CONCLUDING REMARKS**

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.

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.

*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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