E3S Web of Conferences 415, 04011 (2023)
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https://doi.org/10.1051/e3sconf/202341504011

Rheology of hail-debris flow and implications in flow mobility
Santiago Montserrat1*, Alex Carcés1, Jorge Romero3, Germán Aguilar1 and Aldo Tamburrino1,2
1Advanced Mining Technology Center, AMTC, Universidad de Chile, Av. Tupper 2007, Santiago.
2 Departamento de Ingeniería Civil, Universidad de Chile, Av. Blanco Encalada 2002, Santiago.
3 Department of Earth and Environmental Sciences, University of Manchester, Manchester, UKAbstract. During 29-31 January 2021 (austral summer), an extreme storm event triggered catastrophic
debris flows in central Chile (33-36°S). At small and precarious rural settlements in the commune of Malloa
in central Chile, debris flows where triggered by a hailstorm. Hail-debris flows, with hail volumeconcentration near 10%-20%, caused 200 injured individuals and 73 damaged houses. In this study, haildebris flows where modelled using the FLO2D. software, calibrated against flow velocities and flooded
areas obtained from audio-visual records taken by local inhabitants (using cell phones) and a high-accuracy
post-event topography obtained with a drone. Results suggest that hail content significantly reduces flow
resistance compared to typical debris flows, thus increasing flow velocity, and run out. On the other hand,damage to infrastructure was more related to the materiality of the houses (precarious settlements) than to
debris flow severity.

1 Introduction
Debris flows are water sediment mixtures, in roughly
similar proportions, flowing downs slopes due to gravity[1]. In debris flows, friction is dominated by fluid stress(viscous stress, the same as water flows), and fluidparticle (drag) and particle-particle interactions(Coulombic friction and collisions) [1, 2]. Apparent
flow friction angles are significantly lower than typicalrepose angles, resulting in larger run-out distances than
expected [3,4]. Friction reductions are attributed todifferent mechanisms, as particles interacting withbottom roughness or particle-fluid interactions causing
fluidization [1,4]. Single phase numerical models
introduce friction mechanisms in as part of the use
resistance law by ad-hoc rheological formulation.
An extreme storm event during 29-31 January 2021(austral summer) triggered several catastrophic debris
flows in central Chile (33-36°S) [5]. In the ruralcommune of Malloa (34°S), several hail-debris flows
caused 200 injured individuals and 73 damaged houses
in small and precarious settlements located at thealluvial fan of steep small catchments (<0.4 km²). Hailtriggered and hail bearing debris flows areunderreported in the literature [3]. Coppus and Imeson[7] give a qualitative description of hail erosion
capacity. However, to our knowledge, there no literature
regarding the effects of hail in debris flows rheology.
In this work, Using the FLO2D model, we study theeffects of hail in the mixture rheology and its
consequences reducing frictional stress.

2 Study area
characteristics

andstormevent

The study area corresponds to four small catchments(<1.4 km², Table 1) at the north face of the Cerro Negro
hill (CR1 to CR4, Table 1 and Fig. 1), located in the rural
settlement of Cantarrana. They are characterized bysteep-slope hillsides covered by herbaceous shrubby
undergrowth, historically degraded by livestock [6].
Settlements are mainly in the alluvial fans, since lower
lands are used for agriculture, increasing its commercialvalue.
Table 1. Catchments characteristic and hydrology
Catchment

Areakm²

Conc. timemin

CR1CR2
CR3
CR4

0.18
0.12
0.16
0.36

6.2
6.1
7.0
6.7

Max. waterflow rate
m³/s
2.49
1.32
1.25
3.79

Precipitation was recorded by four meteorologicalstations surrounding the study area: San Vicente (4.5 kmSW), El Tambo (8.6 km SE), Quinta de Tilcoco (7.7 kmNE), and El Arenal (6.3 km NE). The event developed
in four main rain pulses, accumulating near 40 to 65
mm. Antecedent wet conditions were dry because of thesummer period and the unprecedented long-lived
drought affecting central Chile from 2010, with annual
rainfall deficits of 20%-40% [8].

* Corresponding author: santiago.montserrat@amtc.cl© 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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https://doi.org/10.1051/e3sconf/202341504011According to grain size analysis in the deposits, clays tomedium sand matrix represented 16-20% by weight.
Original deposits contained near ~15% of hailstones
mostly concentrated on top of the deposits, apparently
because of segregation process during flow motion.

3 Methods
3.1 Hydrology
As hail-debris flows occurs during the third rainfall
pulse, and because of small catchments, we estimate theflow hydrograph using the synthetic unit hydrographmethod, SCS, assuming soil saturated conditions due tothe antecedent precipitation pulses. The catchments
concentration times were estimated in near 6-7 min,obtaining peak water flows ranging from 1.25 to 3.79
m³/s (Table 1).

Fig. 1. Study area. Coloured polygons define eachcatchments limits.

The rainfall event started with a first intense pulse ofnear 10 h precipitation, accumulating 23-35 mm, withmaximum intensities about 6 mm/h. After 22-24 h, asecond rainfall pulse of ~4 h duration, accumulatingnear 0.6-3 mm, occurred. Few hours later, a short pulse(~2 h) of intense precipitation (~4 mm/h) accumulated~1.4-5.8 mm. This third pulse was accompanied by 5 to
9 min of intense hail precipitation, with hailstones
diameter ~2-3 cm, rapidly generating a 5-10 cm white
deposits over land [6]. At the same time, hail-debris
flows where triggered in northern slopes, affecting rural
settlements in alluvial fans (Figure 2). A final fourth
intense rainfall pulse, accumulating between 7 and 24
mm occurred. However, no debris flows where triggeredat this time.

3.2 Post-event topography
After the event, a 1.65 km² high resolution topography
was obtained covering the four studied catchments.
Topography
wasperformed,bythe
aerophotogrammetry technique using a drone. The
drone flight was made at fixed 150 m height from theground, obtaining a digital elevation model (DEM) with
13.5 cm/pixel resolution. Topographical data was used
for configuring channel and alluvial fan geometry in thenumerical model, and to compute flooded areas formodel calibration.

3.3 Debris flow modelling
We use the two-dimensional FLO-2D model to solve theflood wave progression for water and debris flows incomplex topographical terrains [9]. FLO-2D solves twodimensional depth-averaged continuity and momentum
equations, known as Saint-Venant equations, for waterand debris flows. Frictional stress (Sf) are calculatedusing the so-called quadratic rheology model, Eq. (1),which combines different terms accounting for yield andcoulomb, viscous, and turbulent and dispersive
stresses [9].
𝜏𝑦𝐾𝜂𝑉𝑛2 𝑉 2𝑚𝑚ℎ3

𝑆𝑓 = 𝛾 ℎ + 8𝛾 ℎ2 + 𝑡 4(1)Where, τy is the yield stress, γm, the specific weight ofthe solid–liquid mixture, h the element (cell) flow
depth, K a resistance parameter for laminar flow, η thedynamic viscosity of the fluid phase, V the element(cell) flow velocity, and ntd a pseudo-Manningcoefficientcorrectedbythesedimentconcentration. O'Brien and García (2009) suggest thefollowing empiric relationships, Eq. (2 -4), forestimating the parameters η, τy, and ntd as functions ofsediment volume concentration, CV (O'Brien andGarcía, 20).

Fig. 2. A) Hail-debris flows deposits around houses. B) Freshhail-debris flows mixture near the top of the deposit.

2E3S Web of Conferences 415, 04011 (2023)
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https://doi.org/10.1051/e3sconf/202341504011

Fig. 3. A) maximum flow depth and B) maximum flow velocities resulting from the calibrated FLO2D model.

𝜂 = 𝛼1 𝑒𝛽1𝐶𝑣
𝜏𝑦 = 𝛼2 𝑒 𝛽2𝐶𝑣

𝑛𝑡𝑑 = 𝑛𝑏𝑒 𝑚𝐶𝑣

Table 2. Calibrated Rheology and comparison between
modelled and observed velocities (video records)

(2)
(3)
(4)

where α1,2 and β1,2 are empirical coefficients that must
be calibrated, n is the conventional Manningcoefficient, b=0.0538, and m=6.0896.

Catchment

ViscosityPa s

CR1
CR2
CR3
CR4

4.7
3.0
3.7
4.5

Yieldstress
Pa
54.8
33.6
42.1
52.4

Max.
velocity
m/s
3.5
5.5
4.6
2.4

Obs.
Velocitym/s
3
4
2

After calibration, we obtained values for viscosity andyield stress in the order of ~4 Pa s and ~50 Pa,
respectively, and maximum flow velocities in the sameorder than estimated from video records. Viscosities arein the lower limit compared to the debris flow literature,and probably near one order magnitude below expectedvalues for similar debris mixtures [12]. Calibrated yieldstress values are in the range of 30-50 Pa, that is one or
two order magnitude lower than reported in theliterature.

4 Results
FLO2D models were configured for the four catchments
using obtained topographical data and waterhydrographs. Detrital flow rates were computed
assuming 45% to 47% of sediment volumeconcentrations.
As starting point, we used typical rheologicalparameters obtained by different authors for debris
flows mixtures in laboratory tests (see references in[10]), and by calibrating debris flows models using fieldpost-event data [2,11,12]. However, this set ofrheological parameters overestimate frictional stress,
resulting in lower flow velocities and flooded areas
compared to observation.

5 Discuss and Conclusions
During a rainfall event accompanied by 5-10 min
intense hailstorm, catastrophic hail-debris flows
occurred in the commune of Malloa, central Chile,affecting precarious rural settlement located at alluvial
fans. The presence of hails as part of the granular
mixture, 2-3 cm diameter and ~15% volumeconcentration, significantly increases flow mobility byreducing frictional stress. We conclude thar hailinteracting with sediment-water mixture appears as new
friction reduction mechanisms for debris flows.

Thus, rheological model parameters were calibrated
against observed flooded areas following Zegers et al.
[2] and Garces et al. [12] and validated against flow
velocities estimations obtained from videos recorded byinhabitants. Results are shown in Figure 3 and Table 2.

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E3S Web of Conferences 415, 04011 (2023)
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https://doi.org/10.1051/e3sconf/202341504011

This research was supported by the Advanced Mining
Technology Center (AMTC) and the Department of Civil
Engineering from Universidad de Chile. This research has
been supported by the National Agency of Research andDevelopment ANID/PIA project AFB180004. Alex Garcés
was financially supported by the ANID doctoral grant 201921191593.

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