E3S Web of Conferences 415, 05022 (2023)
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https://doi.org/10.1051/e3sconf/202341505022

The debris flow event of 29 October 2018 in the Rio Rotiano(Italy) and its challenges for the mathematical and numericalmodelling
Giorgio Rosatti1*, Daniel Zugliani1, and Luigi Fraccarollo1
1Dipartimento di Ingegneria Civile, Ambientale e Meccanica, via Mesiano, 77 38123 Trento, Italy

Abstract. The debris flow that interested the Rio Rotiano, a creek located in the Province of Trento (Italy)
on 29 October 2018, is an event that, because of its peculiar features, presents formidable challenges interms of mathematical and numerical modelling. Here we present some results of our research, which
required both physical and mathematical modelling, aimed at developing a numerical tool necessary to face
the back analysis of the event and the validation of the planned protection works. Exploiting some results of
the laboratory tests and coupling an advanced description of the debris flow dynamics (TRENT2D model)
over fixed and mobile bed with a sub-surface flow model, we obtained a model that can be defined as amobile-bed rainfall-runoff model, where the runoff is composed by both water and sediments and represents
a new paradigm in the field of debris flow simulations. First applications give promising results but somefurther developments are required before completing the back analysis of the Rio Rotiano event.

1 The Vaia storm and its effect on theRio Rotiano
From 26 to 30 October 2018, the northeast part of Italy
was hit by an Atlantic extreme storm, called Vaia, withintense rainfalls and very strong winds. In addition tothe felling of about 42 million trees, one of the mostsevere damages caused by the storm occurred along theRio Rotiano (Provence of Trento, Italy) on 29 October,because of a debris flow.

dams and 16 closed check dams of different shape andconstructive characteristics collapsed or was heavily
damaged, releasing the sediments present in the relevant
upstream storage areas. This phenomenon led to large
erosions in the upper part of the creek and deposition in
the alluvial fan, where the debris flow overtopped thebanks and hit the village (Fig. 2).

Fig. 2. Aerial view of the consequences of the debris flow
developed in the Rio Rotiano on the village of Dimaro.
Fig 1. Remnants of two destroyed check dams along the Rio
Rotiano.

What characterized this debris flow was the fact that
it affected almost the whole length of the creek but,above all, that most of the protection works present
along the river shaft were damaged (Fig. 1): 2 slit check

2 Back analysis and design ofprotection works: two sides of thesame coin
Besides emergency restoration works, soon after theevent the Servizio Bacini Montani, the public service* Corresponding author: giorgio.rosatti@unitn.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/).

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that oversees the management of the mountainous
territory of the province of Trento, had to face theproblem of understanding, on the one hand, what
happened along the creek and, on the other hand, ofverifying the capabilities of the planned protection
works to reduce the hazard to an acceptable level. To
face this difficult task, a team, composed of threedifferent research institutions (TESAF, University ofPadua; CNNR IRPI and our institution), has started
working on it. Our role has been to develop amathematical and numerical tool capable of tackling theproblems and performing the relevant simulations. In
this contribution, we want to present the efforts we have
made, and are still making in this direction.
The back-analysis of this event presents formidable
difficulties because of the complexity of the phenomenainvolved and because we know very little of what
happened along the creek, in particular, when and whyeach dam collapsed. Available data regard somealtimetric features (the DTM and the DSM surveyed
after the event and a DTM surveyed some years before
the events), the estimated volume of sediments involvedin this event (about 170000 m3), an orthophoto of thewhole basin, taken the days after the event (useful for
mapping the extension of the involved area), data froma rain gauge located 5 km from to the upper part of theRotiano basin (showing a peak of rain of 36.5 mm/hour
lasting for 40 minutes around 19:00) and, finally,
testimonials indicating the occurrence of three distinct
pulses of debris flow (indicatively occurring at 19:00,19:50 and 23:30).
As for the protection works, a complex system ofopen check dams in the upper part of the stream and achannel, running through the village, paved with tiedboulders immersed in concrete was planned.

bends occurred. Similar flow and deposition conditions
were expected along the designed paved-bed channel.
For this reason, a model was needed that could only
erode the bed to a certain level and, under certain otherconditions (to be determined), deposit on it. In otherwords, the model should have been able to switch frommobile to non-erodible bed conditions and vice versa.
Though a numerical algorithm has already beendeveloped for the 1D case [2], a 2D extension and somelaboratory data to validate the model were required.
Therefore, since no data were available in the literature
concerning the limit conditions beyond which there is aswitch between the fixed and mobile-bed conditions, we
performed some experiments in a flume and derived anempirical relation (see Section 4). Moreover, we built aphysical model of the Rio Rotiano comprising a part of
the rocky, sinuous gorge, the waterfall and the channel
designed to protect the village, which we used, among
other things, to validate the numerical model (Section5).
3.2 A rainfall-runoff model comprising thedebris flow formation
Since in the Rio Rotiano basin the debris flow
affected almost the entire length of the creek, the debris
flow model should have considered the distributed
increase of the liquid phase due to the rainfall
contribution connected to the superficial flow.
Moreover, because of the geological characteristics ofthe basin, the model should have also considered thesub-surface flow as a source of water. However, during
the event, due to the large erosions that occurred, thesub-surface flow must have undergone large changes
compared to the initial condition of the bed. Therefore,
unlike common modelling where runoff can beevaluated by considering the bed as fixed, the model
should have coupled the debris flow dynamics with thesub-surface model. The resulting model was to becomea mobile-bed rainfall-runoff model, in which the runoff
would be both solid and liquid. The characteristics ofthis model are briefly presented in Section 5.

3 The challenges for the mathematicaland numerical modelling
When we started to analyse this event, it
immediately appeared that the numerical tool we had atour disposal to model this debris flow, i.e., theTRENT2D model [1], despite its advanced features(two-dimensional, two-phase description of the mixture
flow over a mobile bed), was insufficient to describesuch a complex situation, even in its main features.
Therefore, a significant improvement was needed toaddress what we considered to be the most importantphenomena to be simulated, present in both the backanalysis and the validation of the protection works.
These phenomena, and the relevant modelling, aredescribed in the following two sections.

4 The limit values of the solid discharge
on a fixed bed
To obtain the empirical relation expressing the limit
conditions beyond which there is a switch between thefixed and mobile-bed conditions we carried out someexperiments in a tilting flume in which the bed wasmade of sand particles glued on the bottom, to form arigid bed. As for the solid particles, we used PVC
cylinders about three times bigger than the sand. Eachrun was performed considering a given value of the bed
slope of the flume and a uniform flow condition.
Feeding was done with a constant value of water while
the solid discharge was increased, step by step, passing
from fixed bed to mobile bed transport. At each step, theShields stress was calculated by measuring the mixture
depth.
The results of some of these runs are shown, withcoloured symbols joined with lines, in Fig. 3, where the3.1 Debris flow over a non-erodible bed.
In the Rotiano creek, while for almost the entire
stretch the flow runs on a mobile bed, where both
erosions and depositions may occur, just before reaching
the alluvial fan, the flow passes through a rocky, sinuous
gorge, about 500 m long. During the event, in this reach,
erosion of a thin layer of about 0.5m of soil present
before the event and deposition of material in some2E3S Web of Conferences 415, 05022 (2023)
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dimensionless sediment discharge 𝑞̂𝑠 = 𝑞𝑠 /(𝑑√𝑔∆𝑑) is
plotted versus the Shields stress 𝜏̂ = 𝜏0 /(𝜌𝑤 𝑔∆𝑑),where 𝑞𝑠 is the solid discharge, 𝑑 is the diameter of thesediments, 𝑔 is the gravity acceleration, ∆= (𝜌𝑠 −𝜌𝑤 )/𝜌𝑤 is the solid relative submerged density, 𝜌𝑠 and𝜌𝑤 are the densities ofsediments and water
respectively and finally 𝜏0 is the bed shear stress. Eachcolour refers to a different bed slope.

Fig. 4. Overview of the physical model.

Considering all the uncertainties present in themeasurements and in the model, the results, shown in
Fig. 5, show a satisfactory agreement.

Fig. 3. Nondimensional discharge vs Shield stress. The
meaning of the symbols is given in the text.

As the solid discharge increases, also the Shield stressincreases. Hence, the solid lines with a given colour
move bottom-up and left-right in the plot. They develop
till the maximum solid discharge is reached, and thencollapse to the mobile bed conditions. The maxima areapproximated by a Meyer-Peter Müller relation (dashedline in the figure) whose numerical constant is about
twice the value (solid line) employed to approximate themobile-bed values (black stars). In other words, themaximum solid discharge over rigid bed reaches values
about 50% higher than the transport capacity relevant tothe same Shields value.
On the contrary, the results of other simulations
show that when the roughness of the rigid bed tends tobe about the same or bigger than the size of thetransported particles, then the maximum discharge over
the rigid bed and the capacity transport coincide.

Fig. 5. Comparison between the DoD of the physical modeland the simulation obtained with the numerical model. Flowis from left to right upwards.

6 The mobile-bed rainfall-runoff model
The model addressed to simulate the mixture discharge
formation starting from the rainfall input is composed ofa set of partial differential equations describing, in acoupled way, the sub-surface flow and the superficial
flow that can consist of water (in the upper parts of thebasin) and in a mixture of water and sediments from thepoints in which the debris flow initiates to the end of thebasin. Due to lack of space, the relevant partial
differential equations, the algebraic closure relations,and the numerical schemes employed are not reported.
For sake of simplicity, the complete model can bedivided into two submodels that are briefly described in
the following sections.

5 Physical modelling and comparison
with numerical modelling
The physical model (Fig.4) was obtained by imposing
the Froude similarity, (which intrinsically induces therespect of the Shields stress, 𝜏̂ ). The geometric scale,applied to both the domain geometry and the grain-size
distribution, was assumed equal to 1:30 (model:real).
In the physical model, we worked out several runs,
with controlled and measured liquid and solid
discharges at the upstream end, measurements of thesurface velocities and flow depth in a cross-section, andtopographical DEM over the entire model at the end of
any run. They were used mainly to study thecharacteristics of the waterfall while one of these runs
was used to validate the TRENT2D numerical model inwhich, the empirical relation described in the previous
section was introduced.

6.1 The surface flow (sub)modelThis model is none other than the TRENT2D model withthe features presented in the Section 3.1, in which asource term is considered, expressing the directcontribution of rain, a possible source term resulting
from the water upwelling from the sub-surface modeland a sink term expressing the infiltration by using theGreen-Ampt expression. In the upper part of the basin,3

E3S Web of Conferences 415, 05022 (2023)
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the flow takes place over a non-erodible bed without
sediment. This feature can be faced by the TRENT2D
model by imposing a non-erodible condition and nosediments coming from upstream. When the bed shear
exceeds a certain threshold, the model automaticallyswitches to movable bed conditions, except in areas
explicitly designated by the user as non-erodible (with apossible initial erodible layer).

dynamics in the formation of the response of a basin to
an extreme rainfall event and, on the contrary, the effectof the coupled hydrology on the debris flow
development.

6.2 The sub-surface (sub)model
The model describes the flow by using the 2D watermass balance equation where the velocity is expressedwith the Darcy law. Referring to Fig. 6, where for thesake of simplicity a 1D vertical section is reported, it canbe seen that the model considers a source term given by
the superficial models (the Green-Ampt infiltration f)while a sink term allows transferring some water
towards deep runoff (𝑓𝑑𝑒𝑒𝑝 ). When the depth of the subsurface water equals the depth of the soil, a sink termtransfers water from the sub-surface to the superficialmodel (upwelling term 𝑓𝑢𝑝𝑤 ). The position of the bed isdynamic, in compliance with the result of the mobilebed surface flow model.

Fig. 7. Comparison between the discharges obtained with afixed-bed (light blue) and a mobile-bed (blue) rainfall-runoff
model.

7 Conclusions
Although the results of the model we have developed so
far are promising, there is still much work to be done
before completing a back analysis of the Rio Rotiano
event. In addition to a demanding calibration of theparameters, a modelling approach needs some further
developments to describe the release of debris and water
due to the collapse of a dam. The work is undergoing,
and we are confident to find a simple, but reliable, way
to do that.
In conclusion, we think that even if the challenges
connected to the study of the Rio Rotiano debris flow
are not completely won yet, the development of themobile-bed rainfall-runoff model introduces a newparadigm in the field of debris flow simulations to beused, after suitable validation, both in back analysis andin hazard assessment.

Fig. 6. Sketch of a 1D vertical section of the sub-surface flow
model with the indication of the relevant variables.

6.3 Coupling the models

This research has been developed within the research project“GPR - Approfondimento delle strategie di Governo della
Pericolosità alluvionale a seguito dell’evento del 29 ottobre
2018 sul rio Rotiano”, funded by the Autonomous Province ofTrento, Italy and partially within the research project “Progetto
WEEZARD: un sistema integrato di modellazione matematica
a servizio della sicurezza nei confronti di pericoli
idrogeologici in ambiente montano” funded by Fondazione
CARITRO - Cassa di Risparmio di Trento e Rovereto.

Because of the different spatial scales characterizing thetwo submodels, two different grid resolutions are
employed: the sub-surface flow is evaluated on a coarser
grid while the surface mobile-bed model is evaluated ona finer grid, necessary to describe the details of the bed
surface geometry. Equations are integrated by using anexplicit finite volume method with Godunov fluxes
while the spatial coupling is obtained by using anextension of the overlapping grids methods.

References

6.4 A preliminary application

1.

To evaluate the mobile-bed rainfall-runoff model
capabilities, we performed some preliminary
simulations on a different basin with respect the Rio
Rotiano (namely, Ru d’Alberch, BL (Italy)),
characterized by the absence of protection works.
Fig. 7 shows a comparison of the results obtainedwith a classical fixed-bed and the new mobile-bed
rainfall-runoff model. The difference in the liquid
discharge as a function of time is evident, both in termsof discharge values and in terms of times, highlighting
the importance of considering the effect of debris flow

2.

4

A. Armanini, L. Fraccarollo, G. Rosatti, Comput.
Geosci. 35, 993-1006 (2009)
G. Rosatti, D. Zugliani, J. Comput. Phys. 285,
226-250 (2015)