# IJEGE-11_BS-Abanco-&-Hurlimann

*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-022*

**SIMPLE GEOMORPHOLOGIC APPROACH TO ESTIMATE DEBRIS-FLOW**

**ENTRAINMENT. APPLICATIONS TO THE PYRENEES AND THE ALPS**

great influence on both the final volume of the event

and the flow behaviour, since it causes variations in

the bulk density.

order to predict the volume of a possible event, the en-

trainment has to be considered, however there are very

few quantitative approaches proposed (e.g., H

*et*

*alii,*1984; s

*et alii*, 1999)

therefore it is also relevant to delineate the possible ru-

nout lengths (H

*et alii*, 2005; C

*et alii,*2008).

trained along a travel path. It is described as the volume

of debris entrained along the travel path, proportioned

to the length of the path (H

*et alii*, 1984).

erably increase compared to the volume of the initial

landslide (in landslide triggered debris flows), due to

the erosion of material produced along the travel path

(e.g., H

*et alii*, 2005; G

*et alii*, 2009) The

fect example of the significance of the entrainment.

The total volume of the event obtained by LIDAR data

was of about 80000 m

**ABSTRACT**

flow dynamics. The volume of a debris flow can con-

siderably increase when compared to the initial vol-

ume, due to the erosion of material produced along

the travel path. This study is a preliminary attempt to

establish a simple geomorphologic approach for the

calculation of volume to be entrained in a torrent, if

a granular debrisflow event would occur. The meth-

odology presented has been developed using data ob-

tained by comprehensive field surveys, carried out in

six torrents affected by granular debris-flow events.

The torrents, divided into 43 reaches, are located in

the Pyrenees and the Alps. The application of the

methodology requires data to be measured along the

flow path (geologic and geomorphologic factors). As a

result, a predicted erosion rate for determined reaches

can be estimated in function of these factors, properly

weighted. Although the results indicate a high scatter,

the total predicted erosion volume calculated for each

test site using the proposed approach coincides rather

well with the volumes observed in the field.

**K**

**ey**

**words**

**:**entrainment, granular debris flow, erosion rate,*Pyrenees, Alps*

**INTRODUCTION**

*C. ABANCÓ & M. HÜRLIMANN*

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

bris flows in the Pyrenees. Detailed information on the

Schipfenbach event can be found in H

*et alii*

on the Gesäuse event.

in the initiation reach than the landslide triggered de-

bris flows in the Pyrenees. Detailed information on the

Schipfenbach event can be found in H

*et alii*

on the Gesäuse event.

*et alii*, 2005) where the entrain-

theory (Fig. 2). Based on this model, the erosion depth

*et alii*, 2008).

*et alii*(1984) established a classification of stream

geomorphologic parameters, which is linked to a chan-

nel debris yield rate. Meanwhile, others have looked

for correlations between geomorphologic factors and

entrainment produced in specific events (b

*et alii,*

been established because in many cases there is a wide

scatter in the available data sets (C

*et alii*, 2005;

*et alii*, 2005). Thus, only general rules have

entrainment that can occur in a torrent.

**DESCRIPTION OF EVENTS OCCURRED**

**IN THE TEST SITES**

mountainous regions: the Pyrenees and the Alps. In all

these torrents a granular debris flow occurred and field

surveys were carried out after the events, in order to

collect data about erosion patterns (Table 1).

and in-channel debris flows (Ensija, Riu Runer and

Port Ainé). The in-channel events are generally char-

acterized by large catchment areas above the initiation

point and lower bed slopes in the initiation reach, while

the landslide triggered one presents a smaller catch-

ment area and higher bed slope at the initiation zone

(P

*et alii*, 2010).

*Tab 1 - Description of the events occurred in the sur-*

*veyed torrents*

*Fig 1 - Location of the surveyed torrents in the Pyr-*

*enees*

*Fig 2 - S*

*cheme of a channel bed with a layer of loose de-*

*posits that is being overflowed by a debris- flow*

*mass. This approach supports that the entrain-*

*ment occurs when the shear motion stress (τmov)*

*overcomes the resistant one (τres)*

**SIMPLE GEOMORPHOLOGIC APPROACH TO ESTIMATE DEBRIS-FLOW ENTRAINMENT. APPLICATIONS TO THE PYRENEES AND**

**THE ALPS**

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

**DEFINITION OF GOVERNING FACTORS**

can be reported in the field and by GIS analysis, while

hydrometeorological conditions in the catchments

have not been considered. The main goal is to obtain

a volume estimation of material that can be entrained,

from observations of static features of the torrent.

obtain all of them directly from field surveys or GIS

analysis: the available sediment, the bed slope of the

analysed reach, the shape of the torrent in this particu-

lar reach, the normalised upstream contributing area

of the reach and the catchment area of the torrent.

following. The ratings of the classes vary from 0 to 1

depending on their relevance in entrainment process.

*SEDIMENT AVAILABILITY*

ability. In one torrent, some reaches may have un-

limited sediment (here called “not limited” reaches).

Then, the erosion produced is totally conditioned by

other factors. But, in some other reaches, the lack of

sediment limits the entrainment (here, classified in

different classes, depending on the level of limitation)

classes have been described depending on how much

material is available to be entrained. Some authors have

done similar work in other regions, like in British Co-

lumbia (H

*et alii*, 1984), or the Swiss Alps (s

*et alii,*1999), but the description of the classes

entrain material until the equilibrium condition is

reached (R

*et alii*, 2003, f

ated to the movement.

secondary failures. The mechanism of this sediment

supply is not related to a sliding mechanism caused by

the passage of the flux over the erodible sediment, but

rather to the erosion at the foot of the slope (H

*et alii*, 2005). In our approach this type of sediment

incorporation has only been considered when estimat-

ing the total event volume in the field, but has not been

taken into account for the erosion rate.

*Tab 2 - Five governing factors selected for the calcu-*

*lation of the entrainment (NUCA: normalised*

*upstream contributing area)*

*Tab 3 / Sediment availability classes defined for granular debris flow. The limits have been described according to the char-*

*acteristics of the surveyed areas, specially the Eastern Pyrenees, but it should be adapted to the regional features*

*C. ABANCÓ & M. HÜRLIMANN*

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

ing the upper limit of 40º, according to the characteris-

tics of the Pyrenean events (P

*et alii*, 2010). In

a Digital Elevation Model (DEM) with 5 m resolution.

Alternatively, the mean slope can also be obtained from

a topographic map or from measurements in the field.

*SHAPE*

can be important in the entrainment process of the de-

bris flow. Although no relationships between the shape

of the torrent and the erosion rate were established in

previous works, our field observations were an evi-

dence of this fact. G

(USA) using the “mean width to depth ratio”, and the

relation between the width at different heights from the

bed. A similar concept is proposed in our work.

ing to the morphologic properties of the torrents in the

Pyrenees, if the width (at 3 m height) is over 15 m, the

reach can be considered wide (Fig. 3). If it is between

15 and 5 m, we called it medium, and if it is less than 5

m it can be considered as incised reach. These are limits

absolutely depending on the characteristics of the tor-

rents in the area, and should be verified for other areas.

*NORMALISED UPSTREAM CONTRIBUTING*

AREA

AREA

reach. The UCA-value of each reach i, UCA

ing area of reach i (Fig. 4). This factor ranges from 0

to 1 and it has been divided into 5 classes according

to Table 2.

fluencing the mean erosion (R

*et alii,*2003).

of the flow, however this information needs detailed

tion that is covered by sediment (Table 3). In addition

the reach is considered as a unique global part, with-

out considering local exceptions.

along the reach analysed. The class “low limitation of

sediment” is related to reaches, when sediment is cover-

ing more than 75%of the cross section but the bedrock

is still visible. “Medium limitation of sediment” means

that bedrock and sediment appear in the cross section

at equal proportion, while “high limitation of available

sediment” indicates reaches where bedrock appears at

both sides of the channel, but some sediment is cover-

ing the channel bed. Finally, the class “complete limita-

tion of sediment” means that bedrock is visible at both

sides of the channel. Even though, little sediment can

be available in the channel bed.

*SLOPE*

section. In some cases the relation clearly shows that

as the slope increases, the entrainment rate also gets

higher (R

there is a feedback effect, which means that the entrain-

ment is higher at low slopes. It can be justified with the

increasing flow concentration or peak discharge as the

travelled distance increases (and the slope decreases,

normally) (b

*et alii*, 2008). Other studies contra-

clear tendency, as it is completely related to the avail-

ability of sediment in the reach (H

*et alii*, 1984;

*et alii,*2009).

*Fig. 3 - wide reach in a debris flow torrent (Pyrenees)*

**SIMPLE GEOMORPHOLOGIC APPROACH TO ESTIMATE DEBRIS-FLOW ENTRAINMENT. APPLICATIONS TO THE PYRENEES AND**

**THE ALPS**

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

material grows. Therefore, in conclusion, the capacity

to entrain volume is higher for larger catchment areas

was divided into three classes: <0.1 km

graphic maps..

**SIMPLE APPROACH TO ESTIMATE THE**

**EROSION RATE**

in a certain torrent due to a debris-flow event

in the division of the debris-flow torrent into reaches,

with similar characteristics regarding the governing

factors. Using the values of classes in Table 2, the

Erosion Index, EI, can be calculated. This value is

used to obtain the Predicted Erosion Rate, PER, that

expresses the volume of material that might be eroded

in a reach (cubic meter per running meter). The total

volume to be eroded in the torrent can be obtained eas-

ily from the Predicted Erosion Rate and the length of

each reach, L

be applied in an adapted form to other mountainous

areas, where granular debris flows occur. In the fol-

lowing, the two most important steps of the approach,

the calculation of EI and PER, are explained in detail

*EROSION INDEX*

class rating of each governing factor (Table 2). In ad-

dition, the weight of each governing factor is intro-

duced, which leads to the final expression:.

ple approach. Hence we propose to use the normalised

upstream contributing area to give semi-quantitative

information on thehydraulic load of the flow.

*CATCHMENT AREA*

there is a general positive trend (R

*et alii,*1984; R

*Fig 4 / Left:Scheme of the upstream contributing area of*

*various reaches in a catchment. Right:Example in*

*Sant Nicolau torrent (Pyrenees)*

*Fig. 5 - Flow-chart of approach*

*C. ABANCÓ & M. HÜRLIMANN*

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

Upstream Contributing Area and CA: Catchment Area

governing factor are determined in a second phase

applying statistical analysis. This statistical analysis

calibrates the weights by the comparison of the erosion

rates observed in the field with the EI calculated.

Index indicate more erosion than values close to 0.

*PREDICTED EROSION RATE*

ed Erosion Rate, PER. PER expresses the amount of

material per running meter that may be entrained by a

debris-flow event along a defined reach. Thus, the Pre-

dicted Erosion Rate, in contrast to the Erosion Index,

has a physical meaning, and is expressed in m

analysis. This function can be expressed in a simple

form by

that define the linear regression (see below for detailed

explanation).

**RESULTS**

*FIELD DATA ON GOVERNING FACTORS*

tween the five governing factors and the erosion rate

observed in the reaches. Additionally, the class ranges

of values of the governing factors established in Table

1 have been checked.

*et alii*, 2005;

*et alii*, 2005), the data show a large scatter.

est can be detected. On one hand, it can be seen that

there is an increase of scouring in the steepest reaches

(Fig. 6), as was also revealed by G

*et alii*(2009).

trainment process is also relevant.

and the erosion produced in the reaches (Fig. 7). It can

be related to the amount of water-solid volume enter-

ing to the reach (H

*et alii,*2005).

*EROSION INDEX*

analysis comparing the estimated EI-value with the

observed erosion rate (OER). The OER is the channel

yield rate estimated after occurring an event, along a

certain reach (H

*et alii,*1984).

values of 0.2 in (2). The results of the calculated EI-

values are compared with the erosion rates observed

in the field, OER. A qualitative analysis of this plot

shows an overestimation of the EI-values, since all

EI-values are higher than 0.4, even for very low or

no OER. The quantitative check of the results was

performed by a statistical analysis and the coefficient

*Fig 6: Slope vs. Erosion rate of the reaches in the surveyed*

*catchments, depending on the sediment availabil-*

*ity class. Each point corresponds to a reach*

*F*

*ig 7: Normalised upstream contributing area vs. Erosion*

*rate of the reaches in the surveyed torrents, de-*

*pending on the sediment availability class. Each*

*point corresponds to a reach*

**SIMPLE GEOMORPHOLOGIC APPROACH TO ESTIMATE DEBRIS-FLOW ENTRAINMENT. APPLICATIONS TO THE PYRENEES AND**

**THE ALPS**

*PREDICTED EROSION RATE*

best-fit linear function obtained in the previous sec-

tion. Then, the ER

timated when low erosion rates were observed in the

field and underestimated when high erosion rates were

detected. This means that extreme values may not be

represented correctly by our approach, since most of

the PER-values are in the range from 1 to 3 m

the approach and may be corrected incorporating ad-

ditional field data.

presented in the following section.

*EXAMPLES OF TOTAL EROSION VOLUME*

PREDICTED

PREDICTED

α1 and α

the data. Other statistical regressions may provide

a better fit, but only a slight improvement could be

observed in our field data applying polynomial or

other functions

by linear regression and the coefficient of determina-

tion R2 was compared. Finally, the bestfit weights

were obtained in attempt 4, when the weights of the

sediment availability and slope were increased and the

other onesreduced. The results of this best-fit attempt

are shown in Figure 9..

*Fig. 9 EIi vs OERi, fourth attempt (Table 4): Regression*

*line is calculated with best-fit weights for the gov-*

*erning factors*

*Tab. 4 - Results of the linear regression analysis ap-*

*plied to calibrate the weights of the governing*

*factors in order to calculate EI*

*Fig 10 - OERi vs PERi*

*C. ABANCÓ & M. HÜRLIMANN*

their relevance in the entrainment process. Each fac-

tor has been divided in several classes, with ratings

from 0 (less prone to entrainment) to 1 (more prone

to entrainment).

within our test areas. The weights of the governing

factors have been adjusted according to a linear re-

gression. In future works, when more data is going to

be available, this simple regression may be replaced

with another statistical function

governing factors indicate high scatter, even though

some general trends can be observed. In spite of the

uncertainties related to this simple approach, realis-

tic total volumes could be estimated for the six debris

flows in the test sites, and show that this methodology

could be very helpful in hazard assessments.

limits and weights of the five governing factors. Fi-

nally, similar approaches may be incorporated into

numerical models in order to improve the entrainment

processes in granular debris flow.

**ACKNOWLEDGEMENTS**

(BOKU), in particular to Christian Scheidl, for dis-

cussions and the field trip to Gesäuse. Special thanks

to the administration of the Gesäuse National Park

for the cartographical data and the DEM. The authors

are also grateful to Christoph Graf, Swiss Federal Re-

search Institute (WSL), for his collaboration in the

Schipfenbach event.

00299/BTE.

of making a first test of the approach proposed, the

evolution of the volume along the flow path has been

calculated for the five debris-flow events in the test

sites. The cumulative eroded volume has been com-

pared to the predicted one.

m3) and Schipfenbach (inchannel debris flow).

it can be seen that the methodology proposed shows

rather coherent results

observations and calculations

**CONCLUDING REMARKS**

sented. The methodology estimates an erosion rate

in a selected channel reach based on five governing

*Fig 11. - PERi calculated in every reach and com-*

*parison between evolution of predicted and*

*observed volume along the flow path. a) Sant*

*Nicolau torrent (Pyrenees), b) Schipfenbach*

*torrent (Alps)*

**SIMPLE GEOMORPHOLOGIC APPROACH TO ESTIMATE DEBRIS-FLOW ENTRAINMENT. APPLICATIONS TO THE PYRENEES AND**

**THE ALPS**

**REFERENCES**

*(2008) -*

*Erosion and morphology of a debris flow caused by a glacial lake*

*outburst flood, western Norway.*Landslides.

**5**: 271-280.

*(2008) -*

*Numerical modelling of entrainment/deposition in rock and debris-avalan-*

*ches.*Engineering Geology,

**109**: 135-145.

*.*(2005) -

*Debris flow erosion and deposition in Jiangjia Gully, Yunnan, China.*Environ Geol,

**48**:

*(2001) -*

*Debris flow magnitude in the Eastern Italian Alps: data collection and analysis.*Physics

**26**: 657-663.

*Riemann wave description of erosional dam-break flows.*J. Fluid Mechanics,

**461**: 183–228.

*.*(2008) -

*A morphometric analysis of gullies scoured by post-fire progressively bulked debris flows in*

*southwest Montana, USA.*Geomorphology,

**96**: 298-309.

*An examination of controls on debris flow*

*mobility: Evidence from coastal British Columbia.*Geomorphology,

**114**: 601-613.

*(2005) -*

*Entrainment of material by debris flow.*In Debris-flow Hazards and Related

*.*(1984) -

*Quantitative analysis of debris torrent hazards for design of remedial mea-*

*sures.*Canadian Geotechnical Journal,

**21**: 663-677.

*(2003) -*

*Field and monitoring data of debris-flow events in the Swiss Alps.*Can. Geot.

**40**: 161-175.

*Hydrometeorological controls and erosive response of an extreme*

*alpine debris flow.*Hydrological Processes,

**23**: 2714-2727.

*.*(2010) -

*Description and analysis of major mass movements occurred during 2008*

*in the Eastern Pyrenees.*Nat. Hazards Earth Syst. Sci.,

**10**: 1635-1645.

*Empirical relationships for debris flows.*Natural hazards,

**19**: 47-77.

*.*(2003) -

*Erosion by flow in field and laboratory experiments.*3

*(1993) -*

*The 1987 debris flows in Switzerland: documentation and analysis.*Geomorphology,

**8**: 175-189.

*(2008)*

*- The use of airbone LIDAR data for the analysis of debris flow events in Swit-*

*zerland.*Nat. Hazards Earth Syst. Sci.

**8**:

*1113-1127.*

*(1999)*

*- Recommandations concernant l'estimation de la charge sédimentaire dans les*

*torrents.*Communication No. 4, Groupe de travail pour l'hydrologie opérationnelle (GHO) Berne.

*(1978)*

*- Mechanical characteristics of debris flow.*Journal of Hydraulic Division ASCE,

**104**:

*1153-1169.*

*- Debris Flow.*Balkema, Rotterdam. 165 pp.