Field and laboratory investigations of runout distances of debris flows

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Field and laboratory investigations of runout distances of debris ows in theDolomites (Eastern Italian Alps)

Vincenzo D'Agostino a,, Matteo Cesca a,1, Lorenzo Marchi b,2

a Department of Land and Agro-Forest Environments, University of Padova, Agripolis, Viale dell'Universit 16, 35020 Legnaro (Padova), Italyb CNR-IRPI, Corso Stati Uniti 4, 35127 Padova, Italy

a b s t r a c ta r t i c l e i n f o

Article history:

Received 22 December 2007Received in revised form 30 April 2008

Accepted 15 June 2009

Available online xxxx

Keywords:

Alluvial fan

Debris ow

Runout distance

Laboratoryume

Alps

The estimation of runout distances on fans has a major role in assessing debris-ow hazards. Different methods

have been devised for this purpose: volume balance, limiting topographic methods, empirical equations, and

physical approaches. Data collected from eld observations are the basis for d eveloping, testing, and improving

predictive methods, while laboratory tests on small-scale models are another suitable approach for studying

debris-ow runout undercontrolled conditions and for developing predictive equations. Thispaper analysesthe

problemof assessing runout distance, focusingon sixdebrisowsthat were triggered on July5th, 2006 by intense

rainfall near Cortina d'Ampezzo (Dolomites, north-eastern Italy). Detailed eld surveys were carried out

immediately after the e vent in the triggering zone, along the channels, and in the deposition areas. A ne-scale

digital terrain model of the study area was established by aerial LiDAR measurements. Total travel and runout

distances on fans measured in the eld were compared with the results of formulae from the literature

(empirical/statistical and physically oriented), and samples of sediment collected from deposition lobes were

used for laboratory tests. The experimental device employed in the tests consists of a tilting ume with an

inclinationfrom 0 to 38,on which a steel tank with a removable gatewas installed at variable distances from the

outlet. A nal horizontal plane works as the deposition area. Samples of different volumes and variable sediment

concentrations were tested.Multipleregressionanalysis wasused toassessthe length ofthe deposits as a function

of boththe potential energy of themass andthe sedimentconcentrationof theow. Ourcomparison of theresults

of laboratory tests with eld data suggests that an energy-based runout formula might predict the runoutdistances of debris ows in the Dolomites.

2009 Elsevier B.V. All rights reserved.

1. Introduction

Debrisows are one of the most important formative processes of

alluvial fans under various climatic conditions. They can transport and

deposit large amounts of water and solid material in short time

intervals, creating a major hazard for people and structures.

The assessment of runout distance, i.e. the length travelled on an

alluvial fan by a debris ow from the initiation of the deposits until

their lowest point, is of utmost importance for delineating the areas at

risk from debris ows. Another key parameter in debris-ow studies is

the total travel distance (the distance from the initiation of the debris

ow to the lowest point of deposition). Methods for determining

debris-ow runout distance and total travel distance can be based on

eld data as well as on data generated by physical models. By

combining these two sources of data, a promising approach emerges

for rening the methods for assessingrunout distance on alluvial fans.

This paper contributes to the assessment of debris-ow runout

distance on fans and total travel distance by integrating eld

measurements and laboratory tests on a tilting plane rheometer. The

study methods were applied to six debris ows of the Dolomites

(eastern Italian Alps). Field surveys and a hydrological analysis made

it possible to assess the principal parameters relevant for the analysis

of runout distance. Samples taken from the debris-ow deposits were

used to analyse the depositional processes on the tilting plane

rheometer; both quasi-static tests of fan formation and dynamic tests

using a umewere carried out. Field data on runout distance and total

travel distance were compared with both empiricalstatistical and

dynamic methods for runout assessment, and with predictive

equations developed from the laboratory test.

This paper is divided into seven sections. Section 2 describes the

principal methods available for assessing runout distance and total

travel distance.Section 3presents the study area, theeld surveys, and

the hydrological analysis implemented for assessing the main variables

Geomorphology xxx (2009) xxxxxx

Corresponding author. University of Padova, Department of Land and Agro-Forest

Environments, Agripolis, Viale dell'Universit 16, 35020 Legnaro (PD), Italy. Tel.: +39

0498272682; fax: +39 0498272686.

E-mail addresses:[email protected](V. D'Agostino),

[email protected](M. Cesca),l [email protected](L. Marchi).1 Tel.: +39 0498272700; fax: +39 0498272686.2 Tel.: +39 0498295825; fax: +39 0498295827.

GEOMOR-03031; No of Pages 11

0169-555X/$ see front matter 2009 Elsevier B.V. All rights reserved.

doi:10.1016/j.geomorph.2009.06.032

Contents lists available at ScienceDirect

Geomorphology

j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / g e o m o r p h

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Please cite this article as: D'Agostino, V., et al., Field and laboratory investigations of runout distances of debris ows in the Dolomites(Eastern Italian Alps), Geomorphology (2009), doi:10.1016/j.geomorph.2009.06.032
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of the debris ows studied.Section 4reports the results of applying

methods from previously published literature.Section 5describes the

laboratorytests. Finally,Sections 6and7 discuss theresults and summa-

rise the conclusions of the study, respectively.

2. Methods for assessing debris-ow runout

Several authors have proposed methods for assessing runout

distances (e.g.,Hungr et al., 1984; Cannon, 1989; Bathurst et al., 1997;Fannin and Wise, 2001; McDougall and Hungr, 2003). Rickenmann

(2005)classies the methods for predicting the runout distance into

empiricalstatistical and dynamic methods. A more detailed classi-

cation of the approaches in the literature includes volume balance

approaches, limiting topographic methods, other empirical equations,

physically-oriented methods, and laboratory studies.

a) Volume balance approach

Volume balance methods predict ooded area (A) as a function of

total volume (V):

A= kVd

1

wherek andd are empirical coefcients.Iverson et al. (1998) proposed a method that has received

signicant attention; it predicts the valley cross-sectional area and

planimetric area inundated bylahars from lahar volumeon thebasisof

two semi-empirical equations. Iverson et al. (1998) developed the

equationA = 200 V2/3 using data from 27 laharsat nine volcanoes with

volumes from 8104 to 4 109m3. A similar equation (A = 6.2V2/3)

was calculated by Crostaet al. (2003) for 116 debris ows in theItalian

Alps. These authors observed that the empirical coefcient k is

predominantly dependent on the characteristics of the debris-ow

material.Berti and Simoni (2007) studied forty debris-ow basins

withmetamorphic and sedimentary lithologies in the Italian Alps,with

debris-ow volumes up to 50,000 m3. Theyconrmed that therewas a

signicant correlation betweenooded area and volume.

b) Limiting topographic methods

Limiting topographicmethodsare primarily related to the fan slope Sdor to parameters related to the energy dissipated along the depositional

path (Vandre,1985; Ikeya,1989; Burton and Bathurst,1998).

Ikeya (1989) proposed a limiting topographic method based on fan

slope. The angle after deposition ranged from 2 to 12 with a modal

value between 4 and 6; the spread channel width ratio (the ratio

between deposition width to channel width upstream of the fan) is,

on average, equal to 5 and generally assumes a value lower than 10.

Vandre (1985)proposed an empirical approach to estimate the

runout distance of a debris ow:

R= H 2

where R is the runout distance,is the elevation difference between

the initiation point and the point where deposition starts and is an

empirical constant. According to Vandre's data, the value ofis 0.4

(i.e. the runout distance is 40% of the elevation difference H).

A runout criterion based empirically on Eq. (2) was proposed by

Burton and Bathurst (1998). A debris ow stops when the following

condition is met:

Distance travelled on slopesbetween 4 and 10

N0:4

Elevation loston slopes N 10

3

where travel distances are measured along the slope. The potential

trajectoryof the debrisow startsat theinitiation point and progresses in

the channel networkuntil possible deposition occurs. Therules applied to

govern debrisow transport and sediment deposition are as follows:

for slopes greater than10, the debrisow continues unconditionally; for slopes between 4 and 10, the debrisow comes to a halt either if

the condition expressed by Eq. (2) is satised or upon reaching the 4

slope; and

for slopes less than 4, the debris ow halts unconditionally and

deposits all remaining material.

c) Empirical equations

Empirical equations use variables, such as debrisow volume (V),

potential mass energy (H), fan slope (Sd), upstream gradient (u),

mean slope angle of the whole path (), and catchment area (AC), to

predict the runout distance on the fan and the total travel distance.

The mobility ratio (H/L; see notation for symbols), termed the

effective friction angle (Heim, 1882), has been recently applied by a

number of authors (e.g., Corominas, 1996; Toyos et al., 2007) as a

measure of mobility. According to a personal communication of

Takahashi, Bathurst et al. (1997) assumed that H/L =tan =0.20,

very close to the minimum value (tan = 0.19) obtained by

Rickenmann and Zimmermann (1993). The mobility index roughly

correlates with the volume of theow (Iverson,1997) and can beused

to approximate the maximum potential runout of debris ows.

Table 1summarizes some well-known empirical equations used toassess runout distance and total travel distance. The relationships, Eqs.

(4)(8), are mainly based on eld data and often include the debris-

ow volume (V) as an independent variable coupled to morphometric

information (H,Sd=tand,u,, AC, Fig. 1).

d) Physically-oriented methods

Dynamic methods consider mass, momentum and energy conserva-

tion to simulate the propagation of debris ows using 1D or 2D models

(O'Brien et al., 1993; Hungr, 1995; Iverson and Denlinger, 2001; Laigle

et al., 2003). Numerical models may adopt a variety of hypotheses for

solving the motion equations,and takeintoaccount different rheological

models of the material involved. Based on a momentum consideration

Table 1

Empirical equations used to compute runout distance R and total travel distance L of

debris ows.

Variable Empirical equation Authors Eq.

Runout (R) R= 8:6Vtan u0:42 Ikeya (1989)a (4)

R= 25V0:3 Rickenmann (1994)b (5)

R= 15V1 =3 Rickenmann (1999) (6)

Travel distance

(L)

H=Lmin = tanmin = 0:20AC0:26 Zimmermann et al.

(1997)

(7)

L= 1:9V0:16

H0:83

Rickenmann (1999) (8)a Mathematical rearrangement from the original form (in Bathurst et al., 1997).b Personal communication inBathurst et al. (1997).

Fig. 1. Idealized debris ow labelled with the parameters involved in the empirical

relationships.

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fora ow travelling over a surfacewithconstantslope, therunoutlengthRcan be described by the following theoretical equation developed by

Hungr et al. (1984) and Takahashi (1991):

R= fuucosud1 + g hucosu=2u

2ug

2

gSfcosd sind 9

where d=the terrain slope angle along the area of deposition, u=

the entry channel slope angle, uu=entry velocity, hu=entry

owdepth, and Sf=the friction slope, which is assumed to be constant

along therunout path andaccountsonly forsliding friction.The model

assumes a constant discharge from upstream and no change in ow

width after the break in slope.

Hungr et al. (1984) assumed the friction slope angle of 10 and

reported a good agreement between observed values ofR and those

predicted by Eq. (9) for ve debris ows in western Canada. However,

when Eq. (9) is applied to 14 debris ows in Japan using measuredow

quantities (Okuda and Suwa,1984), better predictions ofR are obtained

for Sf=f tan d (with f=1.12) rather than arctan (Sf ) =10. The

application of Eq. (9) to Swiss debris ows from 1987 (Rickenmann,

2005) also predicts reasonable runout lengths using Sf=1.08 tan d,

when observed ow depths are used to estimate the entry velocity uu.

Forthe back analysisof theJapaneseand Swiss data, it wasassumed that

the main surge travelled in the existing channel on the fan to the lowest

point of deposition with essentially no change in ow width.

e) Laboratory studies

Post-event surveys allow researchers to detect only debris-ow

features visible after the end of the processes, such as erosional scars,

ow marks, and deposits. Field monitoring in instrumented areas is an

invaluablewayto gatherdata on debris-ow dynamics(Okuda etal.,1980;

Genevois et al.,2000; Arattano andMarchi, 2008; Hrlimannet al.,2003).

However, eld monitoring of debris ows is expensive and time-

consuming, and is only convenient for sites that show both a high

frequency of events and favourable logistical conditions. To overcome

these issues, several authors have used laboratory umes (small-scale

model experiments) in order to simulate debris-ow deposition

(Mizuyama and Uehara, 1983; Van Steijn and Coutard, 1989; Liu, 1996;Deganutti et al., 2003; Ghilardi et al., 2003). Quantities such as ow

velocity, the shape of deposits, deposited volume, and grain-size

distribution can be measured and controlled in the laboratory tests.

Problems of scale arerelevantforphysically simulatingthesephenomena:

with only a few exceptions (for example the USGS experimental debris-

owume,95 m longand2 m wide; Major, 1997), channels are typically

narrower than 0.5 m and up to a few meters long; the volume of source

material isgenerallylower than 0.1 m3, anddebris mixturesarecommonly

restrictedto clay,sand,or muddy sand slurries.This notwithstanding,tests

in laboratory umes make it possible to analyse the relations between

physicalvariables of debrisows under controlled conditions, andprovide

useful data for developing and testing predictive methods.

3. Case study: Fiames debris ows of July 5th, 2006

3.1. Study area

The debrisow studied in this paper occurred in Fiames, a locality

of the Dolomites (eastern Italian Alps), near the town of Cortina

Fig. 2.Location of the study area with rock basins and debris-ow deposits highlighted.

3V. D'Agostino et al. / Geomorphology xxx (2009) xxxxxx

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d'Ampezzo. An intense rainstorm triggered six debris ows in the

afternoon of July 5th, 2006.

Three main morphological units can be identied in the study area

(shown in Fig. 2). Rock basins, composed of dolomite, are present in the

upper part. A thick talus, consisting of particles from silt to boulders (up

to 12 m in size), is situated below the rock cliffs (Figs. 3, 4). The lower

part of the slope is occupied by coalescing fans built by debris ows,

whose initiation points are located at the contact between the rock cliffs

and the scree slope (Fig. 4).The areas of the rock basins range from 0.024 to 0.182 km2, the

maximum elevations are between 1984 and 2400 ma.s.l., and the mini-

mum elevations, which correspond to the initiation areas of the debrisows, are between 1521 and 1624 ma.s.l. The channel lengths vary

between 110 and 540 m and the mean channel slope between 22 and

28. The climatic conditions are typical of an alpine environment: the

annual precipitation at Cortina d'Ampezzo ranges between 900 and

1500 mm, with an average of 1100 mm. Snowfall occurs normally from

October to May, and intense summer thunderstorms are common and

constitute a maximum in the seasonal precipitation regime.

3.2. Field surveys

Immediately after the debris ows of July 2006, eld surveys were

carried out in the study area. These eld surveys made it possible to

measure several features of debris-ow deposits: mean and max-

imum depth, depths and slopes of depositionlobes, and cross-sections

of the deposits(Fig. 3). Moreover, cross-sections were measured along

the main channel and detailed descriptions of debris-ow initiation

areas were made (Fig. 4). The grain size distribution was assessed:

i) by means of transect-line measurements on thesurfacesof terminal

deposition lobes (84% ner than 0.09 m for the nest sample and

0.17 m for the coarsest); ii) by direct measurements of the largest

deposited boulders (1.0 to 1.4 m; intermediate axis); and iii) by

processing photographs of vertical trenches and assessing the

proportion of sediments with diameters ner than 2 cm (estimated

range from 25 to 40% by weight). The boundaries of the debris-ow

deposits were mapped using a hand-held GPS; the other geometriccharacteristics were measured using a laser range nder and a tape.

LiDAR and photographic data were acquired from a helicopterying at an average altitude of 1000 m above ground level during

snow free conditions in October 2006. The ying speed was 80kn, thescan angle was 20, and the scan rate was 71KHz. The survey design

Fig. 3.Debris-ow deposition area (basin 5).

Fig. 4.Debris-ow channel close to the triggering area (basin 3).


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point density was specied to be greater than 5 points per m2. LiDAR

point measurements were ltered into returns from vegetation and

bare ground using TerrascanTM software classication routines and

algorithms. A comparison between LiDAR and ground GPS elevation

points carried out in a neighbouring basin showed a vertical accuracy

of 0.1 m.

3.3. Event reconstruction

The debris ows of July 5th, 2006 were triggered by an intense

thunderstorm and hailstorm from 6 p.m. to 7 p.m. (Central European

Summer Time). The highest values of rainfall intensity during the

event were 12.5 mm/5 min and 64 mm/h. These values were

measured at a meteorological station located about 1 km from the

study area and are the highest values ever measured at this station

since it began operating in 1984. After the event, many hailstones

covered the slopesfor about 2h. The debrisows blocked the National

Road and a bicycle trail (located on a former railway track) (Fig. 2).

Local low slopes next to the bicycle trail and the National Road helped

slow down and deposit the debris ows.

The debris ows initiated at the outlet of the rock basins by the

mobilization of loose debris into a ow with progressive entrainment

of debris from channel bank erosion and bed scour (Fig. 4). The main

channel stopped (between 1441 and 1553 ma.s.l.) where the slope

angle decreases and the depositional zone starts.

The deposited volume was assessed by subtractingthe 5meter grid

digital terrain model of the deposits (LiDAR data) from the pre-event

topographic surface, tted from a topographic map at a scale of

1:5000. The results were checked at sample areas in the eld and a

vertical accuracy of 0.10 m was inferred.

Water runoff from the rock basins was simulated by means of a

kinematic hydrological model that integrates the US Soil Conservation

Service-Curve Number (SCS-CN) method (Soil Conservation Service,

1956, 1964, 1969, 1971, 1972, 1985, 1993) with a geomorphologic unit

hydrograph (Chow et al., 1988). The SCS-CNmethod is one of the most

popular methods for assessing direct surface runoff from rainfall data

through a weighted value of the CN parameter of the basin. The

adopted unit hydrograph is extracted from the hypsographic curve byassuming equivalence between the contour lines and lines with the

same concentration time (Viparelli, 1963). We calculated the

corresponding CN values on the basis of the geological setting and

land use of the six basins upstream of the triggering point (Soil

Conservation Service, 1993). Under normal antecedent moisture

conditions, the obtained CN values are around CN=85. The second

SCS parametric variable to compute surface runoff involves initial

abstraction, accounting for depression storage, interception, and

inltration before runoff begins. Its value was set to 10% of potential

maximum retention (directly expressed by the CN) following the

suggestion ofAron et al. (1977)and the assumption ofGregoretti and

Dalla Fontana (2008) in the hydrologic modelling of headwater basins

of the Dolomites. The concentration time was evaluated as the ratio

between the main channel length and the ow velocity along theslopes (assumed to be equal to 2 m/s).

Subsequently, the following relation was adopted for assessing

debris-ow dischargefrom thewaterood discharge (Takahashi,1978):

Qd = Qw

1cec

10

where Qd is the debris-ow discharge associated with the liquid

discharge Qw, and c and ce are the in situ volumetricconcentrations of

bed sediments before the ood and the debris-ow sediment

concentration at equilibrium conditions, respectively. Eq. (10) refers to

a debrisow generated by sudden release ofQw from the upstream end

of an erodible and saturated grain bed. The assumption in Eq. (10) of a

constant ratio ce/c* for the entire duration of the ood would be too

severe a hypothesis in relation to the type of debris-ow surges observed

in the streams of theDolomites (D'Agostino andMarchi, 2003). Therefore,

the debris-ow graph was computed from the hydrograph plotted,

assuming a linear variation ofce/c*in Eq. (10) from a minimum (ce min=

0.2) to a maximum value (cemax in correspondence to Qwat thepeak). The

concentration cemax was calibrated to match the sediment volumes of the

debris-ow deposits estimated by means of the LiDAR data and it resulted

in a range of 0.630.72 (mean of 0.69).Table 2 also reports, for each

catchment, the basin areaAC, the deposited volume V, the ooded areaA,

the mean thicknessh, the debris-ow sediment concentration at the peak

(ce max) and the corresponding debris-ow dischargeQd max. The mean

thickness of the debris-ow deposits is the ratio between the deposited

volume and the ooded area.

Table 3presents the main geometric features related to the runout

and the channel reach bounded by the debris-ow triggering point

and the cross-section where deposition starts.

4. Application of runout and travel distance prediction methods

Themethods forassessingrunout lengthandtraveldistance described

inSection2 of this paper were applied to the eld data of the Fiames

debris ows. The results are discussed in the following paragraphs.

a) Volume balance approach

Using the scheme of Eq. (1), we computed an empirical mobility

relationship for the Fiames debris ows (Fig. 5); the relationship

displays high coefcient of determination (R2=0.92) and has a value

ofk equal to to 14.2 for d =2/3. According toCrosta et al. (2003)and

Berti and Simoni (2007), k is almost constant in each lithological

context and reects yield stress and mobility of the owing mass.

b) Limiting topographic methods

The debris ows of Fiames decelerate and stop at slopes higher

(Table3) than thoseassumed by the methods proposed by Ikeya (1989)

andBurton and Bathurst (1998). Neither method is applicable to theFiamescase study. Such behaviour canbe ascribed to a highlydissipative

Table 2

Basin areaAC, deposited volumeV, planimetricooded areaA, meanthicknessh (volume V

divided by the area of deposition), maximum debris-ow sediment concentration

at equilibrium conditions ce max and hydrologic estimation of the debris-ow peak

discharge Qd max for each basin; [Qd max] is computed with theMizuyama et al. (1992)

equation: [Qd max]=0.0188V0.79.

Basin Ac (km2) V(m3) A (m2) h(m) ce max () Qd max

(m3s1)

[Qd max]

(m3s1)

1 0.182 15,000 10,116 1.39 0.665 32 37

2 0.087 10,600 8543 1.19 0.700 21 283 0.147 46,800 16,934 2.57 0.710 100 92

4 0.092 11,000 6785 1.50 0.700 22 29

5 0.091 5200 4609 1.00 0.630 12 16

6 0.024 2100 3751 0.50 0.725 16 8

Table 3

Main topographic characteristics of the Fiames case study: channel length LCand mean

widthBc, upstream channel slopeu, slope of depositional zoned, average slope angle

of the whole path , sloped runout lengthR, horizontal travel distanceLand associated

total dropH, and estimated peak velocity uuof the surge in the channel.

Basin LC(m)

BC(m)

u()

d()

()

R

(m)

L

(m)

H

(m)

H

(m)

uu(m/s)

1 109 15.5 23.3 19.3 20.1 394 472 43 173 4.17

2 241 11.7 21.9 16.2 18.2 427 634 90 209 3.89

3 539 9.9 21.9 16.0 19.7 312 800 201 287 6.93

4 189 12.2 23.0 21.2 21.9 329 481 74 193 3.96

5 144 12.5 21.6 21.4 21.5 129 254 53 100 3.15

6 238 6.04 27.9 25.9 27.0 183 375 111 191 4.78


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debrisowand large roughnessof theterrain.ApplyingEq. (2)produces

nonphysicalRvalues (1/4 to 1/20 of observations), because the partial

drop measured in the eld is very limited (Table 3).

c) Empirical equations

Eq. (5)tends to overestimate therunout distance, so it can be deemed

conservative in the dolomitic environment (Fig. 6). The recalibrated

Rickenmann (1999) formula (Eq. 6) gives fairly satisfactory results, but it

underpredicts thedistances in twocases.The Ikeya (1989) relation (Eq.4)

shows a similar pattern (Fig. 6), but it has a more marked tendency to

underestimate R. These ndings are not surprising, because even though

Eq. (4)is usuallyapplied in different topographicconditions, Ikeya (1989)

suggested its use when the top portion of the fan is less than 8, whereas

the Fiames alluvial fans are much steeper (Table 3).

The empirical equations for assessing total travel distance agree

well with observed values (Fig. 7). Eq. (7) in particular provides a

correct estimate of the measured values in the study area. Considering

the high fan slope and the L observed values, it is likely that the

rheology expresses high basal shear stresses. Eq. (8) also gives values

that agree fairly well, but it is implicit and theresults aretoo positivelyaffected by the use of observed Hvalues.

d) Physically-oriented methods

The application of Eq. (9) requires that there be no signicant

change in ow width moving from the entry channel to the fan area.

The observed depositional forms make this conditionpossible (Fig.2);

it is also supported by the fact that deposits areelongatewith a spread

width to runout length ratio close to 0.15.

In order to calibrate Eq. (9) with the data in Tables 2 and 3, we

must rst make a preliminary computation of the entering velocityuuand the assessment ofSfor the parameterfif we set Sf=ftan d. Weevaluateduufor the peak discharges (Table 2) using the Chzy equation

(uu=C g1/2 hu

1/2 sinu1/2; C=dimensionless Chzy's roughness) adapted

tothesurgemotionof debrisows(Rickenmann,1999). Gregoretti(2000)

analyzed theneighbouringbasin of Acquabona(Genevois et al., 2000)and

came up with a C value close to 3 when the ratio of ow depth to

intermediate diameter of the front sediments is less than 3 and the

channel bed is not congested with loose debris before the surge transit

(both conditions agree with the Fiames event). After computinguuwithC=3 (Table 3), the iterative solution of Eq. (9) for the unknown Sf, where

Ris the measured runout distance, gives sixfvalues in the range 1.016

1.072, with a mean value f=1.030. The relationship can be adequately

calibrated, but is too sensitive tofvariations to the third decimal place

when, as in our case study, the upstream slope u and the fan slope d are

very close.

5. Laboratory tests

Twenty-nine tests were carried out using a tilting-plane rheometer

(Fig. 8a): twenty tests simulated the quasi-static formation of a fan, and

the remaining nine examined dynamic fan formation by the means of a

ume.

5.1. Experimental device

The physical model consists of a 2 m 1 m tilting plane with an

inclination() between 0and 38,on which a steel tankwitha removablegate wasinstalled. Axed horizontalplane (1.5 m 1 m), with anarticial

roughness (Fig. 8b) to simulate the natural basal friction, served as the

deposition area.

The quasi-static tests of fan formation were performed by installing

thetank at the lower end of the tilting plane, i.e. without a ume (Fig. 8a).

The steel tank, with a removable gate facing the deposition plane, is a

parallelepiped with a squarebase(15 cm15 cm; 33 cm high) and with a

maximum usable volume of 7 dm3.

Dynamic fan formation was simulated using an articial ume

installed on the tilting plane (Fig. 9).

The width of the ume is 0.15 m, and it is between 0 and 180 cm

long, depending on the tank position. The articial channel bottom is

composed of a steel plate with an articial roughness (Fig. 10a); four

datum lines were painted on the bottom (Fig. 10b).

Fig. 6. Comparison of runout distances observed in the eld with those calculated using

the relationships shown inTable 1for the six studied debris ows.

Fig. 7.Comparison of travel distances observed in the eld with those calculated using

the relationships shown inTable 1for the six studied debris ows.

Fig. 5.Relationship between debris-ow volume and ooded area.


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5.2. Tests

The laboratory tests were carried out using debris-ow matrix

collected from lobes in the Fiames fan area. This matrix corresponds,

on average, to 30% by weight of the eld deposits. In the laboratory

tests, samples of debris-ow matrix with maximum diameters up to

19 mm were used (Fig. 11); ne material (b0.04 mm) amounts to

28.6%. The tested material has a density of 2.55 g/cm3, a porosity of

25%, an angle of friction of 40 and a mean diameter of 2.14 mm.

Eight quasi-static simulations were performed using a constant

total volume of 3 dm3 to simulate solid concentrations by volume of

45% and 50%; in the remaining twelve quasi-static tests, a constant

solid volume of 3 dm3 was used, and varying amounts of water were

added to obtain solid concentrations by volume of 55%, 60%, and 67%.

The gradients of the tilting plane were 0, 5, 10, and 15. In the nine

dynamic runs, a constant total volume of 5.5 dm3 was used and the

solid concentrations by volume were 45%, 50%, 55%, 60%, and 65%; the

ume length was 1.8 m with a constant slope of 15.

Each of the tests followed the same procedure: the material was

placed in the steel tank, the plane was tilted to the chosen slope and the

gate wasquickly removed from the tank. Themaximum runout distance

(R) and maximum lateral width of deposit (Bmax) were directly

measured during the tests; the area of deposit (A) was measured from

orthophotos of the deposition area. Data measured during the labo-

ratory tests are reported in Table 4.

5.3. Data analysis and application

Fig.12shows the geometric parameters involved in the laboratory

data analysis: total drop (H), runout distance (R), total travel distance

(L), distance travelled in the ume by the debris-ow mixture (LF),

upstreampoint of themass (t), inclination of thetilting-plane (), and

the angle of the frictional energy line (). The total dropH, related to

, was found to be more signicant if computed with respect to the

upstream point of mass (t). It is useful to dene the correspondence

between eld characteristics of debris ows and laboratory tests. The

initiation area corresponds to the point where the steel tank isinstalled, the channel length (LC) corresponds to the distance travelled

in the ume by the debris-ow mixture (LF), and the upstream

channel slope (u) is the inclination of the tilting-plane ().

Analysing the variation ofas a function ofCV, different trends

result for quasi-static and dynamic tests (Fig. 13). Highervalues in

the dynamic tests explain the larger expenditure of available potential

energy (H) due to ow in the channel. Fitting the data ofversusCV,

an approximate linear relationship can be drawn for the quasi-static

runs (=50 CV14; R2=0.90) and the following power function

result for the dynamic tests (Fig. 13;R2=0.99):

= 12 + 1600 C11:3V 11

Bathurst et al. (1997) assumed H/L =tan =0.20 (=11.3).

Similarly in Eq. (11), for CV=0.50, the H/L ratio is equal to 0.22

(=12.6), but increasing the volumetric concentration causes theH/Lratio to rise quickly (i.e. with CV=0.60, is 17) and highlights

a strong dependence ofL onHandCVand a weak dependence on the

released sediment volume (Table 4).

Eq. (11) was applied to predict travel distances surveyed in the

eld (Table 3). We assumed thatCV=0.60 and 0.65, corresponding to

the highest sediment concentrations tested in the dynamic runs and

near the back-calculated eld values (ce max, Table 2). The best

prediction (Fig. 14) comes from using CV=0.65; the errors are

comparable to those gotten by applying Eq. (7) (Zimmermann et al.,

1997), which proved to be the more accurate empirical equation.

Fig. 8.(a) Tilting-plane rheometer: set-up for quasi-static tests. (b) Detail of the horizontal plane with articial roughness (thickness 2 mm).

Fig. 9.Rheometer with ume: set-up for dynamic tests.


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6. Discussion

Werst comment about the magnitude of the Fiames debris ows,

i.e. the volumes deposited during the event. The unit magnitudes of

the debris ows that occurred in Fiames on July 5th, 2006, computed

as the ratio of total discharged volume to the drainage area upstream

of the fan apex (Table 2), range from 60,000 to 300,000 m3/km2.

These values, compared to the extensive analysis carried out in the

Eastern Italian Alps byMarchi and D'Agostino (2004)on historical data

of debris-ow volumes (upper envelope: V/Ac=70,000 m3/km2), shed

light on the low frequencies (b1/100 year1) of the events in the six

basins of Fiames (Italy).

It is difcult to reconstruct ood hydrographs in ungauged basins,

especially for oods caused by intense and spatially limited rainstorms.

Thus, possible uncertainties in the hydrological analysis, which was

carried out as a preliminary step in assessing debris-ow graphs, deserve

some attention.

The homogeneous characteristics of the basins, dominated by

dolomite outcrops, make it possible for us to state that only minorerrors affect the choice of CN and time of concentration. Larger

uncertainties could be associated with rainfall amounts: convective

rainstorms have strong spatial gradients, and in mountainous areas,

wind may also have a non-negligible inuence on rainfall amounts.

The large magnitude of the debris ows under study, stressed at the

beginning of this section, could indicate that they were caused by

rainfall higher than that recorded at the rain gauge used in rainfall-

runoff modelling. However, the assessment of debris-ow graphs by

means of Eq. (10) produced a realistic balance of water and sediment

volumes, with sediment concentration at the peak (0.630.72;

Table 2), which agrees with the topographic conditions of deposition

surveyed in the fans and replicated by means of the tilting plane

(Cv=0.650.67). Finally, the resulting back-calculated peak dis-

charges match those from the equation of Mizuyama et al. (1992)

for muddy debris ows (Table 2), which are comparable to debris

ows from dolomite rocks (Moscariello et al., 2002). These circum-

stances all corroborate the robustness of our hydrological approach for

back-calculating the debris-ows ood evolution, when sediment

availability is unlimited (Fig. 4) and the triggering rainfalls have large

return periods, as in the Fiames case study. Our analysis of deposition

areas and runout distances overlapped various approaches, ranging

from empirical methods to those requiring kinematic characteristics

of the ow.

The powerrelationship betweenooded area and deposited volume

(Eq.1) has two constants, oneof which (the d exponent) is proved to be

scale-invariant when is setequal to 2/3(Iverson et al.,1998; Crostaet al.,

2003). Following this assumption, the remaining coefcient (k)

becomes a surrogate for debris-ow mobility. The Fiames debris-ows

derive from carbonatecolluviumwith an abundant presence of granularmaterial (mainly smallbouldersand coarsegravel) in a silty-sandmatrix

(Fig. 11). The best-t k value of 14.2 for the Fiames debrisowsis higher

than the value obtained for the debris ows of Valtellina (Lombardy,

northern Italy), studied byCrosta et al. (2003)(k =6.2), but it is much

lower than the value calibrated byBerti and Simoni (2007)for debris

ows in various parts of the Italian Alps (k=33). A high value of this

coefcient (k=32.5) was also obtained for rapid debris-earthows in

the volcaniclastic cover near Sarno (southern Italy) (Crosta et al., 2003).

The Valtellina data have a dominant lithology comprised of

dolostone (Val Alpisella), phyllites and paragneiss (Campo Nappe, Val

Zebr). If we rearrange the best-t equation obtained byCrosta et al.

(2003)for the two subsamples (forcing the exponent d to 2/3), we

obtain k=5.3 for phyllites andk=8.8 fordolomites. Wecould therefore

conclude that an average value ofkof about 10 would be applicable fordebris ows fed by dolomite rocks. This value ofk is low and quite close

to that obtained for debris ows rich in ne material derived from

metamorphic rocks in Valtellina: the calibration of k supports the

cohesive behaviour of debris ows from dolomite colluvium. This

nding agrees with the classication of dolomite debris ows as

cohesive sediment gravityows proposed byMoscariello et al. (2002)

on the basis of sedimentological observations.

Thefailure of limiting topographic methods (Ikeya,1989; Burton and

Bathurst, 1998) and the occurrence of deposition on fan slopes greater

than 16 conrm that high basal shear stresses developed during the

Fiames event. Debris-ow deceleration was likely enhanced by water

draining from the mixture during its movement. As it is typical in the

Dolomites, the Fiames alluvial fans are arid and dominated by loose,

coarse debris. Actually, ne material is abundant in fresh deposits, but is

Fig. 10.(a) Detail of the ume bottom with articial roughness (thickness 2 mm). (b) Upstream view of the articialume.

Fig. 11.Grain size distribution of debris-ow material used in the laboratory tests.


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soon winnowed away from the surface layer by overland ow. As a

consequence, subsequent debris-ow runout occurs on very permeable

surfaces that favour water inltration.

The assessment of Eq. (9) based on the momentum conservation

conrms the ndings of Okuda and Suwa (1984) and Rickenmann

(2005) that the frictional energy slope Sf is very close to the slope Sd of

alluvial fans generated from debris ows. The maximum calibrated

ratio between the two slopes (coefcient f=1.072) is close to thatproposed byRickenmann (2005)(f=1.08) and is lower than the value

(f=1.12) obtained byOkuda and Suwa (1984). The case study would

therefore suggest that, in alpine debris ows, an assumption off=1.07

to 1.08 is reasonable for a cautionary assessment of travel distances.

The applications of empirical formulas for runout and travel distance

indicate that they remain a useful tool for creating a preliminary hazard

map. Eq. (8) implicitly contains the distance under prediction as an

independent variable (H, on the right side of the equation, is a function

ofL). The performance of Eq. (8) for the Fiames debrisows isinuenced

by knownHvalues, but a non-convergent topographic solution can be

reached for steep alluvial fans. Considering the remaining empirical

formulas, Eq. (5) generally overpredicts R, whereas Eqs. (4) and (6) give

less conservative results, but the underestimates ofRdo not exceed 33%

and 23%, respectively (Fig. 6). The acceptable performance of theIkeya

(1989)equation (Table 1; Eq. 4) is noteworthy, considering that it was

developed for Japan, i.e. under different geomorphological, geological and

climatic condition (Fig. 6). Eq. (7) was proposed byZimmermann et al.

(1997) as a lower envelope of the H/L ratio. In this research, the equation

best predicts the observed traveldistances (Figs. 7 and 14) and isa further

conrmation of the previous remarks on the highly dissipative behaviour

of debris ow originating in drainage basins with dolomite lithology.

The H/L ratio, which corresponds to a resistance coefcient, was one

of the earliest dimensionlessvariablesused (Heim,1882) when studying

the potential travel distance of gravitational phenomena(rockand snowavalanche, earthow, landslides). The inverse of the H/L ratio (L/H=1/

tan) is the net travel efciency and expressesenergy dissipationsboth

inside (frictional, turbulent and viscous) and outsidethe ow. The latter

arecaused by thetopography and theroughnessof the surface on which

debrisows propagate, as well as by the presence of obstacles (houses,

levees, woods, etc.). Several researchers (Corominas, 1996; Iverson,

1997) suggest a range ofL/Hfrom 2 to 20 and a decreasing trend with

the logarithm of deposited volume. According to Japanese eld

Table 4

Data from the laboratory tests (L=H/tan). Debris ow of run No.1 stopped in the channel ( Hreported for this run is the difference in elevation between point tof Fig. 12 and the

end of the deposit in the channel).

Test N R(m) Bmax(m) A(m2) LF(m) MT(kg) H(m) () () C V eq(g cm

3)

Dynamic runs 1 1.23 11.080 0.580 15 24.49 0.65 2.015

2 0.580 0.350 0.176 1.80 10.615 0.728 15 16.85 0.60 1.930

3 1.140 0.425 0.405 1.80 10.150 0.728 15 13.80 0.55 1.845

4 1.180 0.610 0.596 1.80 9.763 0.728 15 13.62 0.50 1.775

5 1.350 0.880 0.800 1.80 9.375 0.728 15 12.92 0.45 1.705

6 1.150 0.435 0.416 1.35 10.150 0.611 15 13.54 0.55 1.8457 1.060 0.615 0.515 0.90 10.150 0.495 15 13.80 0.55 1.845

8 1.410 0.670 0.769 1.35 9.375 0.611 15 12.32 0.45 1.705

9 1.300 0.950 0.831 0.90 9.375 0.495 15 12.38 0.45 1.705

Quasi-static runs 10 0.450 0.525 0.207 0.00 9.153 0.211 0 19.38 0.67 2.034

11 0.760 0.770 0.531 0.00 9.623 0.235 0 14.45 0.60 1.925

12 0.890 0.955 0.685 0.00 10.136 0.258 0 13.93 0.55 1.843

13 0.750 0.710 0.423 0.00 5.325 0.141 0 8.89 0.50 1.775

14 0.810 0.830 0.524 0.00 5.093 0.141 0 8.34 0.45 1.698

15 0.490 0.475 0.197 0.00 8.684 0.213 5 18.93 0.67 1.930

16 0.745 0.745 0.475 0.00 9.660 0.232 5 14.86 0.60 1.932

17 0.960 0.980 0.680 0.00 10.135 0.257 5 13.30 0.55 1.843

18 0.680 0.770 0.456 0.00 5.325 0.147 5 10.16 0.50 1.775

19 0.780 0.840 0.541 0.00 5.093 0.147 5 9.07 0.45 1.698

20 0.490 0.560 0.234 0.00 9.170 0.220 10 20.03 0.67 2.038

21 0.760 0.795 0.466 0.00 9.667 0.238 10 15.28 0.60 1.933

22 0.935 1.005 0.705 0.00 10.138 0.262 10 14.15 0.55 1.843

23 0.700 0.770 0.462 0.00 5.325 0.151 10 10.38 0.50 1.775

24 0.800 0.840 0.567 0.00 5.093 0.151 10 9.28 0.45 1.698

25 0.500 0.610 0.269 0.00 9.139 0.224 15 20.65 0.67 2.031

26 0.710 0.825 0.436 0.00 9.664 0.242 15 16.80 0.60 1.933

27 0.960 0.950 0.686 0.00 10.112 0.262 15 14.07 0.55 1.839

28 0.750 0.780 0.464 0.00 5.325 0.155 15 10.16 0.50 1.775

29 0.780 0.870 0.591 0.00 5.093 0.155 15 9.83 0.45 1.698

Fig. 12.Schematic diagram of tilting-plane rheometer with the geometric parameters

involved in the laboratory data analysis.

Fig.13.Relationship betweenthe angle of thefrictional energy line() andthe volumetric

concentration (CV).


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observations,Bathurst et al. (1997)suggests a value ofL/H=5 for debris

ows. Inthe 71casesreported byCorominas (1996), L/Hvariesfrom 1.3 to

15. The studies byToyos et al. (2007)on the Sarno event, dealing with

volumes of 104105m3, report a range ofL/Hfrom 2.4to 4.2,(mean=3.1).

Iverson (1997),for10m3ofpoorlysortedsand graveldebris-ow mixture,

obtained values close to 2.

Our eld data (Table 3) range between 2 and 3 (mean=2.6) and

show increasing values in the volume range 21031104m3, while

for the largest magnitude (4.7 104m3),L/Hremains close to 3. The

laboratory experiments on a sub-sample of the Fiames debris ow

(static and dynamic tests; CVvaries between 0.45 and 0.67) stress a

higher travel efciency (Fig. 13), between 2.2 and 6.8 (mean=4.3).

The efciency decreases (L/H=2.24.2; mean of 3.5) when consider-

ing the volumetric concentration CVN0.5, but still tends to be larger

than eld data (mean laboratory value 3.5 against 2.6).

Iverson (1997)showed that: a) scale is of paramount importance in

experimental studies of debris ows, and b) small-scale models do notsatisfactorilyreplicatethe naturalprocess. Inparticular,two scaling factors

mustbe taken into consideration (Iverson and Denlinger,2001;Denlinger

and Iverson 2001): a non-Newtonian Reynolds number and a number

expressing theinuence on theow motionof thepore pressure diffusion

normal to the ow direction.Therigorous study by Iverson and Denlinger

(2001) shows that viscous effects are less important and pore pressure is

preserved much longer inows at larger scales. The rapid dissipation of

pore pressure could then increase the resistance to motion in small-scale

models.

In our laboratory tests,the measured higher mobility with respect to

the eld scale seems to depict a different behaviour from that expected

on the basis of the aforementioned physical conditions. The lower

energydissipation in themodel is likely to be ascribed to theincomplete

range of debris sizes, and to thelow roughness of the channel (Fig.10a)and deposition plane (Fig. 8b), which does not represent the

topographic irregularities of the alluvial fan and the presence of

vegetation.

Model experiments make it possible to analyse the inuence of the

volumetric concentration on R . In fact, CVstrongly controls R, almost

regardless of the mass of the sediment (Fig. 13;Table 4). The dynamic

tests also reect the fraction of the initial potential energy dissipated

along the channel due to the distance travelled in theume (Lf; Table 4).

A quasi-static formation of the fan caused by a dam-break at its apex

corresponds to lower angle compared to the alluvial fan formation

controlled by an entering channel (Fig. 13). The application of Eq. (11)

with themore competentCVvalue (0.65) in theeldts theFiames data

well(Fig.14) andgives an accuracy(meanunderestimation around13%)

comparable to Eq. (7), which wasderived from Swiss eld data. The use

in Eq. (11) of a lowerCV(0.6) overestimatesL on average by 30% and

gives a large response ofLto a small variation inCv, whenCvis close to

maximum values for debrisows. The tight dependence ofL on Cv could

be surrogated by the link ofL with the catchment area (Ac) (Eq.7),asAc,

from a morpho-hydrological point of view,is directly proportionalto the

runoff volume and inversely proportional to Cv. In this context, further

research is necessary to better dene whether and under which

conditions laboratory results on fan formation and runout distance are

comparable to corresponding

eld features.

7. Conclusions

The runout distance and total travel distance were investigated for

six debris ows triggered by the same rainstorm in contiguous

catchments of the Dolomites. Basin areas (from 0.02 to 0.1 km2) and

debris-ow volumes (from 2 103 from 5 104m3) vary byoneorder of

magnitude and offered the possibility of comparing several methodsfor

assessing the terminal displacement of the debris-ow sediments. The

approach adopted in this study coupled eld observations with

laboratory tests on material collected from debris-ow deposits.

The applicationofelddata to therelationshipbetweenoodedarea

on the alluvial fan and debris-ow volume made it possible for us to

calculate a value of the coef

cient k in Eq. (1) fordebris

ows generatedfrom basinswith dolomite lithology,in topography typicalof thestudied

area.

The application of empirical methods for predicting the runout

distance on fans and total travel distance of eld data enabled us to

identifyequations suitable forassessingthesevariables fordebrisows on

scree slopes and alluvial fans of the studied region. Both thecalibrationof

the volume balance relationship and the application of empirical

equations outline low mobility of viscous silt-rich debris ows of the

Dolomites.

Experiments carried out on sediment samples collected from

debris-ow deposits allowed us to analyse the relationships between

variables that control the distances attained by debris-ow mixtures.

Although scale issues cause major problems in small-scale laboratory

studies of debris ows, integrating laboratory tests with eld

documentation of debris ows proved promising for studying these

hazardous phenomena.

Acknowledgments

We thank Marco Cavalli for collaborating in the eld surveys. LiDAR

data have been arranged by C.I.R.GEO (Interdepartmental Research

Center for Cartography, Photogrammetry, Remote Sensing and G.I.S.),

University of Padova. The research was supported by: MURST ex 60%

Italian Government funds, years 20072008, Prof. Vincenzo D'Agostino;

PRIN-2007 project: Rete nazionale di bacini sperimentali per la difesa

idrogeologica dell'ambiente collinare e montano, Prof. Sergio Fattorelli.

The comments of Paul Santi and an anonymous reviewer helped

improve the manuscript.

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GlossaryA ooded area (m2) (eld and laboratory)AC catchment area (km

2)B maximum lateral width of deposit (m)Bc mean width of the channel upstream of deposition initiationBmax maximum lateral dispersion of deposit in the laboratoryc in situvolumetric concentration of bed sediments before the oodce debris-ow sediment concentration at equilibrium conditionsC dimensionless Chzy coefcientCV solid concentration by volume, CV= VS/ (VS+ VL), where VS is the solid

volume andVL is the water volume)d empirical coefcient in Eq. (1)

f empirical coefcientg gravitational acceleration (9.81 m s2)h mean thickness of the deposit (m)hu entry ow depth (m)H potential mass energy and total drop (m) (eld and laboratory)H elevation difference between the initiation point and the point where

deposition starts (m)k empirical coefcient in Eq. (1)L total travel distance (m)LC channel length (m)LF distance travelled in the ume by the debris-ow mixture (m)MT total mass of sediment in laboratory tests (kg)N number of the testQd debris ow discharge (m

3s1)Qw liquid discharge (m

3s1)R runout distance (m) (eld and laboratory)Sf friction slope (m/m)Sd fan slope (m/m);Sd=tan dt upstream point of the massuu entry velocity (m s

1)V debris-ow volume (m3) inclination of the tilting-plane () mean angle of the frictional energy line () (eld and laboratory)d terrain slope angle along the deposition, angle of the fan slope ()u angle of the channel upstream of deposition initiation ()eq bulk density of the debris ow in laboratory tests (g cm3) empirical coefcient in Eq. (2)


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Please cite this article as: D'Agostino, V., et al., Field and laboratory investigations of runout distances of debris ows in the Dolomites

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Field and laboratory investigations of runout distances of debris flows