E3S Web of Conferences 415, 01012 (2023)
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https://doi.org/10.1051/e3sconf/202341501012

Triggering-runout modelling of rainfall-triggered debris flows: acase study in the Campania region, Italy
Giulia La Porta1 *, Francesco Cafaro1, Alessandro Leonardi2 and Marina Pirulli1
1Politecnico di Torino, Department of Structural, Geotechnical and Building Engineering, Corso Duca Degli Abruzzi 24, Torino,

Italy
2University of Sheffield, Department of Civil and Structural Engineering, Sheffield S10 2TN, United Kingdom

Abstract. Debris flows are unpredictable phenomena, listed among the hugest natural hazards, since they
can cause important damages to humans and structures. Rainfall can trigger this type of movements, as itprovokes the pore water pressure increasing, and so the soil strength reduction. The phenomenon modellingis a key aspect to predict and prevent damages. This article shows an approach for triggering and runout
analysis: triggering is studied through an infinite slope stability model of rainfall-triggered shallow
landslides, while runout is modelled using a depth-averaged numerical method, which replace the real
heterogeneous flow with an equivalent homogeneous fluid. The work focuses the attention to events
characterized by multiple triggering zones and releases converging on the same area, whose complexity isrepresented by the time- and space-distribution of the different flows. The proposed approach is applied toan event that hit part of the Campania region, Italy, in 1998, causing several damages. Two rheological laws
are considered and compared for the analysis. The back-analysis allows the calibration of the rheologicalparameters and validation of the method. Results are discussed to identify the most suitable rheology for thebenchmark event.

1 Introduction
Debris flows [1] are high-speed soil movements,
constituted by water and debris, which can cause bigdamages to human lives and structures. One of the main
triggering causes is rainfall. It increases the pore waterpressure in the susceptible soil, and reduces its shear
strength, till possibly provoking the instability andtriggering of the mass flow [2]. These phenomena areanalysed in two main aspects: triggering and runout, thislast including propagation and deposition. The event
modelling can help in predicting the behaviour in termsof path and damages and designing effective mitigation
structures.
In this paper, the authors face both triggering andrunout modelling. Triggering is analysed through a gridbased slope stability model (TRIGRS [3]), while runout
is simulated with a continuum mechanics-based depthaveraged model (RASH3D [4]), following the approachof La Porta et al [5].
The method is applied to a huge event which hit theCampania region, Southern Italy, in 1998. The
phenomenon involved many zones of the Sarno area,with multiple triggers on each single slope.
Consequently, causalities and damages to structures
were registered [6].
Two rheological laws are considered for the study
case, and the suitability is discussed: the Voellmy law,consisting of a frictional and a turbulent term, and theBingham law, considering a yield stress and a viscous

dissipation term. The rheology parameters are calibrated
through back-analysis.
In the paper, after a brief introduction of usedmethods and of the benchmark event, a comparison of
the runout simulations obtained with the two rheologies
is shown and discussed, to highlight strong and weak
points of the proposed approach.

2 Methods
2.1 Triggering
The triggering is analysed through TRIGRS (TransientRainfall Infiltration and Grid-based Regional SlopeStability model) [3], a Fortran program for modelling
the trigger of rainfall-induced shallow landslides.
Starting from Digital Terrain Model (DTM), rainfall
data, and lithological and morphological characteristicsof the site, the software allows the calculation of porewater pressure changes provoked by rainfall infiltration,and consequent factor of safety variation of the slope.
As output, the distribution of the unstable mass is given.
2.2 Runout
The runout is modelled with RASH3D [4], a continuum
mechanics-based
depth-averagedmodel.
Theheterogeneous mass, made of debris and water, is* Corresponding author: giulia.laporta@polito.it© The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0(https://creativecommons.org/licenses/by/4.0/).

E3S Web of Conferences 415, 01012 (2023)
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For instance, Sorbino et al. [10] proposed a comparisonof TRIGRS and another common triggering model for
the Sarno event of 1998. Table 1 contains the soil
characteristics from Sorbino et al. [10].

modelled as an equivalent fluid, whose rheologicalcharacteristics simulate the behavior of the real mixture.
The aim of the study is to compare two rheologies
for the benchmark event and identify the most suitableone. Voellmy and Bingham rheologies are considered.
The Voellmy rheology consists of two terms, in thedefinition of the basal shear resistance τz: a Coulomb
frictional term, and a turbulent one. The rheology
equation is the following:𝜏𝑧 = 𝛾ℎ tan 𝜑 +𝛾𝑣 2
𝜉,Table 1. Mechanical characteristics of Sarno soil, adopted forthe triggering analysis [10]. Here, ’ is the friction angle, c’the cohesion, s the soil unit weight, Ks the hydraulicconductivity, D0 the diffusivity,  a triggering numericalfitting parameter, r the residual water content and s thesaturated water content.

(1)

in which γ is the bulk specific weight, h is the flowheight, φ is the bulk friction angle, v is the depthaveraged velocity and ξ is the turbulence coefficient [7].
The Bingham rheology defines the basal shear
resistance τz as a combination of a viscous dissipation
term and a constant yield stress τ0:𝜏𝑧 = 𝜏0 + 𝜈𝐵

𝜕𝑣
𝜕𝑡,

(2)

’
[°]

c’
[Pa]

s
[N/m3]

Ks
[m/s]

38

5000

15000

1∙10-5D0[m2/s][m-1]

r[-]

s
[-]

5.910-5

6.3

0.20

0.66

These values are adopted for the triggering analysis,
except for the hydraulic permeability, which iscalibrated within the range of typical values
characterizing the area [8]. The goal is an overall
calibration of the triggering model with reference to theestimated triggering and runout volumes [11]. The best
fit is obtained with a Ks of 3∙10-5 m/s.
The collected rainfall data during the event, at theSan Pietro pluviometric station, registered a cumulative
rainfall of around 120 mm in thirty hours (Fig. 2).
Although the rainfall event was not particularly intense,
it appears that the area was particularly susceptible tosoil movements due to natural and anthropic
predisposing factors [12].

with νB the post-yield dynamic viscosity [7].

3 Description of the study caseSarno is a small town in the Campania region (SouthItaly). The area is characterized by shallow pyroclasticdeposits, coming from the Vesuvius and Somma
volcanoes activity. The zone of Sarno, Siano, Quindici
and Bracigliano, was hit by many huge rainfall-triggered
debris flows in May 1998, causing around 160 casualties
and important structure damages [6]. Fig. 1 shows theaforementioned debris flows in the focusing area of thispaper. At the deposition area, the observed maximumflow heights during the event were around 4 m [8].

a.

Fig. 1. Debris flow event of May 1998 in the focusing area ofthe article (modified from [9]).

4 Triggering-runout modellingb.

4.1 Triggering modelFig. 2. Rainfall event of Sarno, of the 4th and 5th of May 1998.
a) Positioning of the closest pluviometric station to the interestarea, San Pietro; b) cumulative rainfall data.

Previous research provided the morphological andmechanical parameters of the site. Additionally, the area
was already modelled in the literature through TRIGRS.

2E3S Web of Conferences 415, 01012 (2023)
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2000 m/s2, while using the Bingham rheology, 𝜏0 iscalibrated between 700 and 2000 Pa, and 𝜈B between
300 and 500 Pa*s.
Fig. 4 contains two representative results at different
runout instants: a comparison of the simulated
propagation model while using the two rheologies isshown. In the picture, the Voellmy rheology ischaracterized by 𝜑 = 7°, and 𝜉 = 1000 m/s2, while thecalibrated Bingham rheology is defined by 𝜏0 =1000 Pa and 𝜈𝐵 = 500 Pa ∗ s.
The sequence contained in the picture shows that theflow characterized by the Voellmy rheology stops whenreaching gentler slopes. In order to follow the real flow
path, an almost null friction should be considered. This
aspect motivates the use of the Bingham rheology.
In terms of flow heights, the flux characterized by theVoellmy rheology takes excessive simulated values,
with respect to the observed ones [8], because of thefrictional contribution, which forces the stop of the flow;
contrarily, the Bingham rheology proves to be moresuitable, since the simulated flow heights are closer tomeasured values from the field.
Unfortunately, with respect to the deposit, the Bingham
flow better follows the real covered branches and thedeposition shape, but still showing important
discrepancies.

Fig. 3 shows the triggering areas, an output of theanalysis with TRIGRS. Additionally, the surveyed real
path is reported.

Fig. 3. TRIGRS analysis of the Sarno event: instability areas,
provoked by the rainfall event considered.

The previous instances of back-analysis available in theliterature provide a quick validation of the proposedmodel. However, some input parameters are not easily
accessible or indeed measurable (e.g., the susceptible
soil distribution), thus requiring further calibration.
Therefore, the discrepancies that can be observed whencomparing with the results of Sorbino et al. [10] areexpected due to the multiple simplifications.
4.2 Runout model
For the runout model, the aforementioned rheologies aretested on the study case. Parameters are calibrated
referring to typical ranges of the literature [13, 14]. With
the Voellmy rheology, 𝜑 is calibrated between 3 and10°, and the turbulence coefficient 𝜉 between 300 and5 Conclusions
In this paper, an approach for modelling triggering andrunout of rainfall-triggered debris flows is presented.
Triggering is analysed with TRIGRS, a program forFig. 4. RASH3D model of the Sarno event. Comparison of Voellmy and Bingham rheologies, at multiple runout instants.

3

E3S Web of Conferences 415, 01012 (2023)
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https://doi.org/10.1051/e3sconf/202341501012

the grid-based slope stability definition, through thecalculation of the pore water pressure and consequent
factor of safety variation, during a rainfall event. The
runout is studied with the aid of RASH3D, a depthaveraged model, based on the continuum mechanics
approach. The real flow is modelled as a homogenous
flux, whose behaviour is governed by the adopted
rheological law.
Two rheological equations are considered: theVoellmy and the Bingham. Voellmy rheology consistsof two terms: a frictional and a turbulent one. Binghamrheology is defined by a yield stress and a viscous
dissipation term. The suitability of the analysedrheologies is discussed through a benchmark case,represented by the huge event of Sarno, Campania
region, Italy, of 1998. The phenomenon wascharacterized by multiple triggering areas on each slope.
The flow with Voellmy rheology cannot properly
follow the real path since the frictional term causes its
halt when gentler slopes are encountered. On the other
hand, the Bingham reology allows a spreader flow path.
Even in terms of flow heights, the Bingham rheology
shows to be more suitable for the study case.
Unfortunately, the deposit shape still shows to be far
from the real path from field observations.
The complexity of multiple triggering debris flows,i.e. events characterized by many triggers on the same
slope, stays in the time- and space-distribution andinteraction of the flows. It seems realistic, and evenconfirmed by real observations, that not all unstableareas detached at the same instant. Further research will
focus on studying a reliable time- and spacecombination and distribution approach for modellingthese particular events.

8.

P. Revellino, O. Hungr, F.M. Guadagno, S.G.
Evans, Environ. Geol. 45, 3 (2004)
9. P. Versace, G. Capparelli, L. Picarelli, Landslide
investigations and risk mitigation. The Sarno case,
In Proceedings of 2007 International Forum on
Landslide Disaster Management 1, (2007)
10. G. Sorbino, C. Sica, L. Cascini, Nat hazards 53, 2(2010)
11. L. Cascini, D. Guida, G. Sorbino, Il presidio
territoriale: un’esperienza sul campo, Rubbettino
ISBN: 884980962X (2005)
12. G. Chiavazzo, L. Colombo, A. Minutolo, P.
Ruggiero, G. Zampetti, FANGO Il modello Sarno
vent’anni dopo (2018)
13. M. Pastor, M. Quecedo, E. González, M.I.
Herreros, J.F. Merodo, P. Mira, J. Hydraul.
Eng. 130, 2 (2004)
14. M. Pirulli, M. Barbero, M. Marchelli, C. Scavia,
Geoenvironmental Disasters 4, 1 (2017)

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