# ijege-15_02-moraci-et-alii.pdf

*Italian Journal of Engineering Geology and Environment, 2 (2015)*

*© Sapienza Università Editrice*

*www.ijege.uniroma1.it*

*DOI: 10.4408/IJEGE.2015-02.O-03*

*Mediterranea University of Reggio Calabria - Dep. DICEAM - via Graziella Loc. Feo di Vito - 89060 Reggio Calabria, Italy. nicola.moraci@unirc.it*

*ETS de Ingenieros de Caminos - Universidad Politécnica de Madrid - Ciudad Universitaria, s/n - 28040 Madrid, Spain*

*University of Padua - Dep. ICEA - via Ognissanti, 39 - 35129 Padova, Italy*

**ANALYSES AND DESIGN PROCEDURE OF A NEW PHYSICAL MODEL FOR DEBRIS**

**FLOWS: RESULTS OF NUMERICAL SIMULATIONS BY MEANS OF LABORATORY TESTS**

**ExTENDED ABSTRACT**

nel territorio.

della colata detritica.

dimensioni in grado di studiare il fenomeno della propagazione dei debris flow.

rettangolare adibito al contenimento e al rilascio, con un meccanismo di tipo “dam-break”, di miscele acqua-terreno; iii) una struttura per il

sollevamento del serbatoio alle varie altezze di prova; iv) un sistema di misura, trasmissione, registrazione ed elaborazione dei dati di prova

mediante l’impiego di sensori a ultrasuoni, trasduttori di pressione e videocamere ad alta definizione.

calcolo SPH (P

*et alii*, 2009) che lavora su un modello non lineare e accoppiato, permettendo la soluzione delle equazioni della

• il “modello matematico” basato sulle equazioni di conservazione della massa e della quantità di moto è semplificato effettuando

rispetto alla loro lunghezza o larghezza;

interpolando in ogni punto del continuo i valori relativi ai singoli punti mobili attraverso l’uso di opportune funzioni di interpolazione.

Il modello, combinato alle adeguate relazioni costitutive, restituisce le velocità secondo il piano perpendicolare alla direzione di

quale sono stati aggiunti volumi d’acqua tali da ottenere diverse concentrazioni solide in volume. La scelta delle concentrazioni solide in

volume è stata opportunamente operata prendendo in considerazione i valori tipici dei debris flow.

attritivo che governa tale legge reologica (coefficiente di attrito cinematico) ha consentito di definire una correlazione tra le concentrazioni

solide in volume delle miscele e gli angoli di attrito ad esse corrispondenti.

variare i volumi (in termini di altezza di rilascio) e gli angoli di attrito delle miscele (considerando i casi estremi di solo fluido e materiale

secco e le concentrazioni solide in volume tipiche dei debris flow); la lunghezza e l’inclinazione della canaletta rispetto all’orizzontale.

**N. MORACI, M. PISANO, M.C. MANDAGLIO, D. GIOFFRE’, M. PASTOR, G. LEONARDI & S. COLA**

*Italian Journal of Engineering Geology and Environment, 2 (2015)*

*© Sapienza Università Editrice*

*www.ijege.uniroma1.it*

**ABSTRACT**

potentially dangerous for human lives and lifelines.

a parametric analysis has been performed in order to reproduce,

with the flume tests, the debris flow velocities observed during

real events.

have also been carried out, with the aim to find the rheological

behaviour of the debris flow material.

**K**

**eywords***debris flow, flume test, rheological law, numerical*

**:****INTRODUCTION**

the characteristics of the flow material may change, modifying

the flow mobility. The high velocity that the flow mass can reach

during propagation, due to the characteristics of both the moving

material (i.e. debris) and the type of material in basal surface,

allows that long distances can be rapidly covered. Moreover,

the consequences of debris flow impact are pronounced when

it occurs near infrastructures or other main lifelines, because it

can produce the interruption of traffic or other activity or even

the loss of human lives.

clay.

and onto the front. Moreover, spatial gradational sorting of

debris flows, due to the development of inverse grading or

coarse surge fronts, is common and may be important for the

flow behaviour (e.g., P

*et alii*, 2001, etc.). According to H

*et alii*

to extremely rapid surging flows of saturated debris in a steep

channel with strong entrapment of material and water from the

flow path. It occurs periodically on established paths, usually

gullies and first- or second order drainage channels. Thus,

debris flow hazard is specific to a given path and deposition

area (“debris fan”). This, with the periodicity of occurrence

at the same location, influences the methodology of hazard

avalanches, whose occurrence is not bound to an established

path. Once debris begins to move in a steep channel, the bed

is subjected to rapid undrained loading, often so sudden that it

could be characterized as impact loading (S

suffer a significant increase in pore-pressure. The bed material

will become dragged in a growing surge. As the surge moves

downstream, erosion undermines the steep banks and further

soil material, as well as organic debris, is added to the flow. The

surges travel down the channel on slopes steeper than 10-20°. In

many cases, it is found that the final mass is much larger to the

initial, because of the entrainment along the path of propagation.

Therefore, the magnitude of debris flows depends primarily on

the characteristics of the channel and it can be estimated by

empirical means (H

*et alii*, 2005).

dragged into the flow (H

*et alii*, 2005). Debris surges

debris (colluvial) fan, at typical slopes of 5° to 10°. The frontal

boulder accumulation rapidly deposits in the form of levees

or abandoned boulder fronts, while the finer and more dilute

material continues further downslope.

can be used. In both cases, it is important to predict the possible

scenarios in order to propose effective protection works and

safety measures.

decreasing the destabilizing forces that can trigger landslide;

whereas the second approach (passive approach) is to carry out

containment measures of the movement of the debris.

geometry by excavation or toe fill and the drainage of surface

and ground water. In particular, drainage is the most widely

used method for slope stabilization. These remedial measures

are excellent site-specific management tools for landslides if

correctly designed and constructed, for example with regard to

proper design of the filtering transitions (M

*et alii*, 2012a,

*et alii*, 2014a; M

*et alii*, 2014b; c

*et*

*alii*, 2014; M

*et alii*, 2015).

debris so as to reduce the spatial impact of landslides on

elements sensitive at risk. Mitigation measures consist in the

passive structural barriers usually made with earth reinforced

**ANALYSES AND DESIGN PROCEDURE OF A NEW PHYSICAL MODEL FOR DEBRIS FLOWS:**

**RESULTS OF NUMERICAL SIMULATIONS BY MEANS OF LABORATORY TESTS**

*Italian Journal of Engineering Geology and Environment, 2 (2015)*

*© Sapienza Università Editrice*

*www.ijege.uniroma1.it*

along the channel.

material, the evolutionary characteristics of viscous water / soil

mass movement, speed profile, thickness) are required to design

protection embankments. The state of knowledge for the design

passive structures for the protection from rapid debris flows,

especially for the design of earth reinforced embankments, is

not yet supported by a comprehensive scientific literature.

models have been developed for simulating landslide propagation

and runout (e.g. S

*et alii*, 1999;

*et alii*, 2004; P

*et alii*, 2009;

*et alii*, 2012). Whatever code

parameter values is fundamental. Due to the large dimensions of

real phenomena, back analyses of debris flows already occurred

are the only way to obtain data for runout prediction analyses

(e.g. H

back analyses, to wrong interpretations of the mechanics of the

event and inaccurate calibration of numerical models.

the theoretical aspects of the problem (determination of the

rheological behaviour, calibration of numerical models) and

in terms of practical aspects (passive barrier or prevention of

phenomenon, definition of alarm systems, etc.). The main

variables that can be measured or calculated are: physical and

mechanical properties, height, velocity, image or video and

mobility of debris flow (S

*et alii*, 1997; G

*et alii*, 2000a, b; B

*et alii*, 2000;

*et alii*, 2012). Many studies aim at the analysis of

*et alii*, 2004)

flows (i

*et alii*, 2015).

debris flow propagation.

during real events.

law has been found carrying out several experimental tests.

characteristics of the physical model, necessary to reproduce the

typical velocities of debris flows.

**MODEL USED TO SIMULATE THE PROPAGATION**

**(DEPTH-INTEGRATED COUPLED SPH MODEL)**

of the involved materials, which are responsible for their

long travel distances (up to tens of kilometres) and the high

velocities (in the order of meters/second) they may attain.

The prediction of both run out distances and velocity through

mathematical modelling of the propagation stage can notably

reduce losses inferred by these phenomena, as it provides a

mean for defining the hazardous areas, estimating the intensity

of the hazard (which serves as input in risk studies), and for

working out the information for the identification and design of

appropriate protective measures. In the past decades, modelling

of the propagation stage has been largely carried out in the

framework of the continuum mechanics, and a number of new

and sophisticated numerical models have been developed.

framework of the continuum and discrete element mechanics,

the depth-integrated SPH method proposed by P

*et alii*

*et alii*(2009) is based on v-pw Zienkiewicz–Biot model,

(i) The balance of mass, combined with the balance of linear

soils reads

*k*

*w*

*v*

*s*

*D*

*(s)*

*Q*

*n*and volumetric stiffnesses of

pore water

*K*

*w*

*and soil grains*

*K*

*s*

*b*the body forces and s

the Cauchy stress tensor.

**N. MORACI, M. PISANO, M.C. MANDAGLIO, D. GIOFFRE’, M. PASTOR, G. LEONARDI & S. COLA**

*Italian Journal of Engineering Geology and Environment, 2 (2015)*

*© Sapienza Università Editrice*

*www.ijege.uniroma1.it*

to simplify the 3D propagation model described above by

integrating its equations along the vertical axis.

constitutive models (Bingham, Voellmy, Mohr-Coulomb, etc.),

obtaining a 2D depth-integrated model, which presents an

excellent combination of accuracy and simplicity and provides

information about propagation, such as average velocity or depth

of the flow along the path.

(SPH). The SPH model is a mesh-free method that provides an

interesting and powerful alternative to more classical numerical

methods such as the finite elements method.

The method has been introduced independently by l

over other methods. The SPH method introduces the concept of

‘particles’, to which information concerning field variables and

their derivatives is linked.

*(x)*

and its spatial derivatives by integral approximations defined in

terms of a kernel. In a second step these integral representations

are numerically approximated by a class of numerical integration

based on a set of discrete point or nodes, without having to define

any “element”.

**PHYSICAL MODEL**

the study of geosynthetic reinforced earth structures’ behaviour

subjected to debris flow impact, currently in progress at the

“Mediterranea” University of Reggio Calabria. The aim of

the research has been to design a large-size flume in order to

simulate debris flows propagation.

main parts (Fig. 1).

ranging between 20° and 45° evaluated according to the slope

inclinations of real debris flows on granular and weathered

cohesive soils (G

*et alii*, 2004, 2006), occurred in Calabria.

simulate, at the bottom of the flume, flow velocities comparable

to those ones reported for debris flows in the scientific literature

(r

top of the flume.

various heights of test, 8.86 m high, and a reticular structure for

the lifting of the walkway necessary for tank’s inspection.

definition video cameras. The phenomenon of propagation will

be monitored by pressure transducers, located on the base of

the flume, and by ultrasonic level sensors supported by joists

or aluminium profiles, orthogonally positioned to the bottom of

*Fig. 1 -*

*Schemes of the physical model*

**ANALYSES AND DESIGN PROCEDURE OF A NEW PHYSICAL MODEL FOR DEBRIS FLOWS:**

**RESULTS OF NUMERICAL SIMULATIONS BY MEANS OF LABORATORY TESTS**

*Italian Journal of Engineering Geology and Environment, 2 (2015)*

*© Sapienza Università Editrice*

*www.ijege.uniroma1.it*

instantly released, through the rapid opening of a gate, in order

to reproduce the “dam break” trigger mechanism.

has the grain size distribution shown in Fig. 2. The soil is a

well-graded sand with medium-fine gravel, classified as SW,

according to USCS classification system, and as A1-b, according

to CNR-UNI 10006 classification system, with grain shape from

sub-rounded to rounded, uniformity coefficient

*U*=7.48 and

average grain size

*D*

*50*

**CALIBRATION OF THE RHEOLOGICAL LAW**

**FOR SELECTED MIxTURES**

(Italy).

*L*=2.10 m long (including the tank),

*B*=0.25

*i*=30°, and it has a rigid bottom. The

triggering of the mixture propagation occurs by means of a

removal gate (Fig. 3).

in the large-size physical model) with different water volumes.

From a constant solid volume of dry material corresponding to

*W*

*s*

*Fig. 3 -*

*Flume test apparatus used to evaluate the rheological law of*

*water-soil mixtures*

*Fig. 2 -*

*Grain size distribution of soil*

**N. MORACI, M. PISANO, M.C. MANDAGLIO, D. GIOFFRE’, M. PASTOR, G. LEONARDI & S. COLA**

*Italian Journal of Engineering Geology and Environment, 2 (2015)*

*© Sapienza Università Editrice*

*www.ijege.uniroma1.it*

*C*

*v*

*C*

*v*

*C*

*v*

*C*

*v*

*C*

*v*

*C*

*v*

are those typical of debris flows, according to P

analyses using the SPH code (Fig. 6). As it can be seen from the

figure, for example for the volumetric solid concentrations 74%

(Fig. 6a), 65% (Fig. 6b) and 62% (Fig. 6 c), the trend of the flow

velocity over the time is quite reproduced.

(H

*gh*(cos

*i*+

*a*

*c*

*/g*) tan f

*h*= flow depth;

*i*= slope

angle;

*a*

*c*

*= (v*

*2*

*/R)*= centrifugal acceleration (resulting from the

*R*of the flow path);

*tan*f

*=(1-r*

*u*

*) tan*f

*’*

*r*

*u*

angle.

*=tan*f) , which

controls the frictional rheological law (equation 4) (Tab. 1), and

it was thus possible to find a correlation between friction angles

and solid concentrations by volume of the mixture (Fig. 7). The

figure shows that the friction angle of mixture sharply increases

for

*C*

*v*

*C*

*v*

**NUMERICAL ANALYSIS PERFORMED TO**

**DESIGN THE PHYSICAL MODEL**

mentioned frictional rheological law for the mixtures.

typical flow velocity of real events.

*L*; the inclination of flume,

*i*; the released height of

mixture,

*H*and the friction angles of mixture, f.

*Fig. 5 -*

*Rheological classification of flows (P*

*ierson*

*& C*

*osta*

*, 1987)*

*Fig. 4 -*

*Different mixtures used in the research, varying the solid con-*

*centrations by volume*

**ANALYSES AND DESIGN PROCEDURE OF A NEW PHYSICAL MODEL FOR DEBRIS FLOWS:**

**RESULTS OF NUMERICAL SIMULATIONS BY MEANS OF LABORATORY TESTS**

*Italian Journal of Engineering Geology and Environment, 2 (2015)*

*© Sapienza Università Editrice*

*www.ijege.uniroma1.it*

concentrations by volume typical of debris flows (f=20°, 30°),

the friction angle corresponding to the pure fluid (f=0°) and the

friction angle corresponding to the dry material tested in the

current research (f=36°) (Tab. 2).

bottom. The tank’s length is 1.5 m and the parametric analyses

have been carried out for different values of released height of

the mixture (i.e.

*H=1 m*and

*H=2 m*) corresponding to different

mixture volumes,

*V=0.25 m*

*3*

*V=0.94 m*

*3*

*L=8 m*.

*Fig. 6 -*

*Flow front velocities: comparisons between experimental and*

*numerical results for the different mixtures, C*

*v*

*=74 % (a),*

*C*

*v*

*=65 % (b), C*

*v*

*=62% (c)*

*Tab. 1 -*

*Friction angles of the mixture according to the different solid*

*concentrations by volume*

*Fig. 7 -*

*Friction angle values obtained by numerical analyses for the*

*different mixtures*

*Tab. 2 -*

*Parameters considered in the numerical analysis*

**N. MORACI, M. PISANO, M.C. MANDAGLIO, D. GIOFFRE’, M. PASTOR, G. LEONARDI & S. COLA**

*Italian Journal of Engineering Geology and Environment, 2 (2015)*

*© Sapienza Università Editrice*

*www.ijege.uniroma1.it*

for different values of mixture’s friction angle, in case of released

heights

*H=1 m*and

*H=2 m*, considering three different lengths of

flume equal to

*L=6, 8 and 10 m*.

the flow velocity decreases with increasing mixture friction angle.

and flume inclination.

values of mixture’s friction angle, in case of released heights

*H=1*

mand

m

*H=2 m*, considering three different lengths of flume equal

to

*L=6, 8 and 10 m*.

with increasing the mixture friction angle.

*i≥35°*) and solid concentrations by volume (friction

angles), in the case of lower released height of mixture (

*H=1 m*),

the characteristic velocities of real debris flows (

*v>5 m/s*) can be

obtained with a flume having length equal to

*L=8 m*. Therefore, it

has been chosen to design a 8 meters long physical model.

**CONCLUSIONS**

have shown that the model which best fits the behaviour of the

selected mixtures is the frictional law.

correlation between friction angles and solid concentrations by

volume of the mixtures.

*Fig. 9 -*

*1-D numerical analysis of mixture’s propagation in the large-size physical model at different times in the case of length L = 8 m*

*Fig. 8 -*

*Scheme of large-size physical model used in numerical analysis*

**ANALYSES AND DESIGN PROCEDURE OF A NEW PHYSICAL MODEL FOR DEBRIS FLOWS:**

**RESULTS OF NUMERICAL SIMULATIONS BY MEANS OF LABORATORY TESTS**

*Italian Journal of Engineering Geology and Environment, 2 (2015)*

*© Sapienza Università Editrice*

*www.ijege.uniroma1.it*

*Fig. 10 -*

*Flow velocities versus physical model inclination, for length L=6 m, in the case of released height: (a) H=1 m and (b) H=2 m respectively*

*Fig. 11 -*

*Flow velocities versus physical model inclination, for length L=8 m, in the case of released height: (a) H=1 m and (b) H=2 m respectively*

*Fig. 12 -*

*Flow velocities versus physical model inclination, for length L=10 m, in the case of released height: (a) H=1 m and (b) H=2 m respectively*

**N. MORACI, M. PISANO, M.C. MANDAGLIO, D. GIOFFRE’, M. PASTOR, G. LEONARDI & S. COLA**

*Italian Journal of Engineering Geology and Environment, 2 (2015)*

*© Sapienza Università Editrice*

*www.ijege.uniroma1.it*

*Fig. 13 -*

*Height of flow versus physical model inclination, for length L=6 m, in the case of released height: (a) H=1 m and (b) H=2 m respectively*

*Fig. 14 -*

*Height of flow versus physical model inclination, for length L=8 m, in the case of released height: (a) H=1 m and (b) H=2 m respectively*

*Fig. 15 -*

*Height of flow versus physical model inclination, for length L=10 m, in the case of released height: (a) H=1 m and (b) H=2 m respectively*

**ANALYSES AND DESIGN PROCEDURE OF A NEW PHYSICAL MODEL FOR DEBRIS FLOWS:**

**RESULTS OF NUMERICAL SIMULATIONS BY MEANS OF LABORATORY TESTS**

*Italian Journal of Engineering Geology and Environment, 2 (2015)*

*© Sapienza Università Editrice*

*www.ijege.uniroma1.it*

inclinations typical of real debris flows, the velocities reach the

debris flows values in the case of flume length equal to

*L=8 m*.

Thus, the numerical analysis has allowed to design the length of

the large-size physical model.

**REFERENCES**

*Rock slopes: from the analysis to the definition of the*

*risk mitigation works. The “Scilla Rupe” case (RC, Italy).*Rend. Online Soc. Geol. It.,

**21**: 377-378.

*Debris flow monitoring activities in an instrumented watershed on the italian Alps.*Proceedings of the 1

*An approach to the sediment transport problem from general physics: physiographic and hydraulic studies.*Professional Paper 422-I.

*Debris flow monitoring in the Acquabona watershed (Dolomites, Italian Alps).*Physics

**25**(9): 707-715.

*Suscettibilità alle frane superficiali e veloci in terreni di alterazione: un possibile contributo della*

*modellazione della propagazione.*Rend. Online Soc. Geol. It.,

**2**: 534-536.

*The contribution of soil suction measurements to the analysis of flowslide triggering.*In P

*The influence of vertical effective stress and geogrid length on*

*interface behavior under pullout conditions*. Geosynthetics,

**32**(2): 40-50. ISSN: 1931-8189.

*Numerical simulation of debris flows.*Can. Geotech. J.,

**37**(1): 146-160.

*Landslide types and processes.*In: t

*Landslides investigation and mitigation*.

*Granular avalanches across irregular three-dimensional terrain: 1. Theory and computation.*J. Geophys. Res.

**109**(F1): 1-16.

*Pore pressure distribution in the initiation area of a granular debris flow.*In: B

*Debris flows in Dolomites: experimental data from a monitoring system*. In. w

*Smoothed particles hydrodynamics: Theory and application to non-spherical stars.*Monthly Notices of the Royal

**181**: 375-389.

*Gravity-driven free surface flow of granular avalanches over complex basal topography.*Proc. R. Soc.

*Effect of weathering on the compressibility and shear strength of a natural clay.*Canadian Geotechnical

**43**: 618-625.

*Definizione degli elementi generali dei modelli geotecnici per l’analisi delle instabilità*

*superficiali per scorrimento-colata in Calabria Jonica.*Atti XXII Convegno Nazionale di Geotecnica, Palermo, 22-24 Settembre 2004:127-134.

*andslides and human lives (Bergsturz and Menschenleben)*. In: S

*A model for the runout analysis of rapid flow slides, debris flows and avalanches.*Canadian Geotechnical Journal,

**32**(4): 610-623.

*Rock avalanche run-out prediction using a dynamic model.*Proceeding 7

*Review of the classification of landslides of the flow type.*Environ Eng. Geosci.

**VII**: 221-238.

*The Varnes classification of landslide types, an update.*Landslides DOI 10.1007/s10346-013-0436-y. ©

*Entrainment of material by Debris Flows.*In: J

*Debris flow hazards and related*

*phenomena.*Chapter 7: 135–158. Springer, Heidelberg (in association with Praxis Publishing Ltd)

*Mass movement.*In: f

*Encyclopedia of geomorphology.*Reinhold Publishers, New York, 688-695.

*General report: morphological and geotechnical parameters of landslides in relation to geology and hydrogeology*. In: Proceedings

**ACkNOWLEDGMENT**

**N. MORACI, M. PISANO, M.C. MANDAGLIO, D. GIOFFRE’, M. PASTOR, G. LEONARDI & S. COLA**

*Italian Journal of Engineering Geology and Environment, 2 (2015)*

*© Sapienza Università Editrice*

*www.ijege.uniroma1.it*

*The physics of debris flows.*Reviews of Geophysics,

**35**: 245-296.

*Earthflows: morphology, mobilization and movement.*USGS Professional Paper 1264.

*Detecting debris flows using ground vibrations*. U.S. Geological Survey Fact Sheet 236-96.

*A numerical approach to the testing of fusion process*. Astronomical Journal,

**82**: 1013-1024.

*A model for the analysis of rapid landslide runout motion across three-dimensional terrain*. Can. Geotech. J.,

**41**(6):

*Susceptibility analysis of rapid flowslides in southern Italy*. International Symposium on

*A new theoretical method to evaluate the internal stability of granular soils.*Canadian Geotechnical

**49**(1): 45-58.

*Reply to the discussion by Dallo and Wang on “A new theoretical method to evaluate the internal stability*

*of granular soils*”. Canadian Geotechnical Journal,

**49**(7): 866-868.

*A new theoretical method to evaluate the upper limit of the retention ratio for the design of geotextile filters*

*in contact with broadly granular soils.*Geotextiles and Geomembranes,

**35**: 50-60.

*Analysis of the internal stability of granular soils using different methods.*Canadian Geotechnical Journal.

*The influence of soil type on interface behavior under pullout*

*conditions.*Geosynthetics,

**32**(3): 42-50. ISSN: 1931-8189.

*Reply to the discussion by Ni et alii, on “Analysis of the internal stability of granular soils using different*

*methods”.*Canadian Geotechnical Journal,

**52**: 1-7. DOI.org/10.139/cgj-2014-0495.

*Flowslides in pyroclastic soils: transition from “static liquefaction” to “fluidization”*. In: P

*A mechanism of pore pressure accumulation in rapidly sliding submerged porous blocks*. Computers and

**31**(3): 209-226.

*Shallow flowslides triggered by intense rainfalls on natural slopes covered by loose unsaturated pyroclastic soils*.

**53**(2): 283-288.

*A depth-integrated, coupled SPH model for flow-like landslides and related*

*phenomena.*Int. J. Numer. Anal. Meth. Geomech.,

**33**: 143-172.

*Flow behavior of channelized debris flows, Mount St. Helens, Washington.*In: a

*Hillslope processes*. Allen &

*Hyperconcentrated flow-transitional process between water flow and debris flow.*In: J

*Debris flows and*

*related phenomena*. Vol. 8: 159-196. Springer, Heidelberg.

*A rheological classification of subaerial sediment-water flows.*In: c

*Debris flow/*

*avalanches: process, recognition and mitigation reviews in engineering geology.*Volume VII: 1-12. Boulder, CO. Geological Society of America.

*Numerical study on the entrainment of bed material into rapid landslides*. Geotechnique,

**62**(11): 959-972.

*Earthquake-induced ground failures in Italy.*Engineering Geology,

**58**(3-4): 387-397.

*Numerical modelling of the propagation of fast landslides using the finite*

*element method.*Int. J. Numer. Methods Engng,

**59**(6): 755-794.

*Empirical relationships for debris flows.*Natural Hazards,

**19**(1): 47-77.

*The mechanism of debris flows*. In: Proceedings 11

*The motion of a finite mass of granular material down a rough incline*. J. Fluid Mech.,

**199**: 177-215.

*Field observation of debris flow.*Proc. Japan-China (Taipei) Joint Seminar on Natural Hazard Mitigation, Kyoto: 343-352.

*Volcanic debris flows.*In: J

*Debris flows and related phenomena*. Vol 10. Springer, Heidelberg: 247-271.

*Landslide types and processes.*In: e

*Landslides and engineering practice*, special report 28. Highway research board.

*Slope movement types and processes.*In S

*Landslides, analysis and control*. Special report 176:

*Received July 2015 - Accepted November 2015*