E3S Web of Conferences 415, 02007 (2023)
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https://doi.org/10.1051/e3sconf/202341502007

faDebrisFOAM validation using field data surveyed in Crucecita(Chile) alluvial fan for the event of 13th May 2017
Alex Garcés1*, Álvaro González2, Aldo Tamburrino1,2, and Santiago Montserrat1
1Advanced Mining Technology Center (AMTC), Universidad de Chile, Av Tupper 2007, Santiago, Chile
2Departamento de Ingeniería Civil, Universidad de Chile, Av Blanco encalada 2002, Santiago, Chile

Abstract. The openFOAM solver faDebrisFOAM was recently developed to simulate debris flows withthe finite area method. This new solver includes, among other capabilities, a variable density for the solidliquid mixture, erosion and deposition processes, and a terrain modification algorithm. To test theperformance of this new solver, we simulate the debris flow event that occurred in the Crucecita alluvial fan
on the 13th May 2017 in the Atacama Desert, Chile. Thanks to pre- and post-event topographies, we havean accurate measure of the morphological changes that took place. Comparing the field data and ournumerical model results shows that faDebrisFOAM can reproduce the main flooded, eroded, and depositedareas. Once the model is calibrated, we study the behavior of the terrain modification algorithm. Finally, wediscuss the advantages of using this model to reproduce erosion and deposition processes together withchanging rheologies for a debris flow event.

1 Introduction
Due to climate change, increases in temperatures,droughts, and extreme precipitation events, anincrement of debris flow triggering has taken place. A
significant part of the Chilean territory is exposed todebris flows due to the presence of the Andes Cordillerathat runs along all of Chile. In 2015, a catastrophic
debris flow event impacted the Atacama Desert innorthern Chile. In the following years, smaller eventsoccurred in more specific parts of Atacama.
Garces et al. [1] characterized the behavior of Crucecita
creek for the debris flow event that occurred in 2015
using the FLO-2D commercial software. The authors
concluded that, despite the correct representation of theevent in general terms, this numerical model should
improve how it resolves the erosion and deposition
processes and changes in rheology, to achieve betterrepresentations of the sediment transport processes inalluvial fans.
This work presents the use of a recently developedmodel called faDebrisFOAM [2]. This solver isvalidated by employing accurate field measurements ofthe topographic changes observed in Crucecita for the
13th May 2017 event. Furthermore, a comparison of the
field data and our numerical model results is presented
here. Finally, it is concluded about the advantages that
this solver has in representing erosion and deposition
processes, added to the fact that it can consider changes
in the rheology simultaneously.

2 Study site
Crucecita basin has an area of 13 km2, being a lateraltributary to the El Carmen River in the southern limit of
the Atacama Desert. This creek has been previously
studied due to the debris flows that occurred in 2015
[1,3]. As a result of the previous studies, high-resolution
topography was surveyed in the confluence zone withthe river, including Crucecita’s alluvial fan.

2016

2017
Fig. 1. Pre-event (up) and post-event (down) satellite imagesof the Crucecita alluvial fan. Map data: Google Earth Pro(CNES/Airbus).

* Corresponding author: agarces@uchile.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/).

E3S Web of Conferences 415, 02007 (2023)
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𝜕(ℎ𝑒 𝑆𝐵 )= −𝑢𝑏 𝑆𝐵
𝜕𝑡

In May 2017, another precipitation event occurred at
Crucecita creek. While El Carmen Basin receives 60mm per year on average, this rainfall event accumulated
188 mm, with maximum intensities of ~6.7 mm/h. As aresult of the 2015 event, a gully incision developed in
the Crucecita alluvial fan. In 2017, this incision, whichconnects the apex with the river, conveyed flows fromthe creek to the main river. After the 2017 event, a new
high-resolution topography was surveyed tocharacterize the main topographic changes that occurredin the creek.

(5)

where 𝜌 is the density of the solid-liquid mixture, ℎ is
̅ the flow rate. Despite being a model
the height and 𝒖
whose equations have been vertically averaged, thevelocity vector continues to be a three-dimensional
vector because the flow moves along a threedimensional surface. 𝐶𝑤 corresponds to the volumetricconcentration of water. These variables are defined at
the centroid of each element and vary in time 𝑡.
The area S = ∂V corresponds to the area of the control
volume V, while SB corresponds to the lower boundaryof this control volume. This border conforms to theterrain.

Figure 1 shows satellite images of the pre- and postevent conditions. The incision that connects the apex
and the river widened during the 2017 event. As a resultof the sediment coming from the creek, a deposit wasgenerated in the river confluence, blocking the originalriver path. Consequently, the river was forced to find a
new course around this lobe (avulsion).

3.1 Governing equations

In equations (3) and (4), 𝑔𝑆 and 𝑔𝑛 correspond to thetangential and normal components of the acceleration ofgravity 𝑔, 𝜏𝑏 is the basal shear stress and 𝑝𝑏 the basalpressure. 𝒏𝒃 corresponds to the normal vector to thesurface 𝑆𝐵 . With 𝑛𝑏 , ∇𝑠 = (𝐼 − 𝑛𝑏 𝑛𝑏 ) ⋅ ∇ and 𝛻𝑛 =(𝑛𝑏 𝑛𝑏 ) ⋅ 𝛻 are defined, which correspond to differential
operators tangential and normal to the surface,respectively.

González [2] implemented the faDebrisFOAM solver inopenFOAM to represent the movement of shallow
debris flows over slightly curved surfaces. This model
was based on [4,5], uses the method of finite areas, andinherits functions from its predecessor model
faSavageHutterFOAM [5]. Gonzalez [2] madeimportant improvements such as (1) variable density, (2)terrain modification algorithm (TMA), (3) hydrographfor the inlet boundary condition, (4) incorporation oferosion, deposition, and friction equations for debrisflows.

faDebrisFOAM incorporates the ability to modify theterrain using the Terrain Modification Algorithm(TMA). To consider ground modifications, it isnecessary to know the density of the substrate 𝜌𝑏 and thevolumetric concentration of water in the substrate 𝐶𝑊𝑏 .
When this algorithm is activated, the boundary SB
moves with a speed 𝒖𝒃 , defined as positive pointing outof the control volume. This velocity is calculated fromthe entrainment of sediments rates into the flow 𝑢𝑏𝐸 andthe rate of deposition 𝑢𝑏𝐷 , such that 𝑢𝑏 = 𝑢𝑏𝐸 − 𝑢𝑏𝐷 .

3 Methodology

For the friction models, faDebrisFOAM includes theManning, Quadratic-rheology, and Voellmy-Salmmodels. This solver also includes seven entrainment
models and four deposition models. They can bereviewed in [2].

To include these improvements, González [2] developed
the system of equations (1) to (5) presented below.
Equations (1) and (2) correspond to the continuity
equations for the solid-liquid mixture and water,respectively. Equations (3) and (4) conform tomomentum equations in their tangential and normalcomponents, respectively. Equation (5) considers theprocesses of erosion and deposition for the modificationof the terrain.
𝜕(𝜌ℎ𝑆𝐵 )̅ )𝑑𝑆 = 𝜌𝑏 𝑢𝑏 𝑆𝐵+ ∫ ∇ ∙ (𝜌ℎ𝒖𝜕𝑡𝑆𝑏
𝜕(𝐶𝑤 ℎ𝑆𝐵 )̅ )𝑑𝑆 = 𝐶𝑤 𝑏 𝑢𝑏 𝑆𝐵+ ∫ ∇ ∙ (𝐶𝑤 ℎ𝒖𝜕𝑡𝑆𝑏𝜕(𝜌ℎ𝒖̅ 𝑆𝐵 ) + ∫ 𝜒∇s ∙ (𝜌ℎ𝒖̅𝒖̅ )𝑑𝑆𝜕𝑡𝑆𝑏= 𝜌ℎ𝒈𝒔 𝑆𝐵 − 𝝉𝒃 𝑆𝐵
1− ∫ ∇s (𝑝𝑏 ℎ)𝑑𝑆
2 𝑆𝑏𝑝𝑏 = 𝐧𝒃 (𝜌ℎ𝒈𝒏 −1̅𝒖̅ )𝑑𝑆∫ 𝜒∇ ∙ (𝜌ℎ𝒖𝑆𝐵 𝑆𝑏 n−

3.2 Field data characteristics
We characterized the morphological alterations during
the May 2017 event at the confluence of the Crucecita
stream with the El Carmen River. The characterization
was made by high-resolution sequential topographies.
Through the difference of these sequential topographies,
we obtained the so-called DEM of Difference (DoD)[6]. DoDs are helpful in measuring the eroded anddeposited volumes and their distribution.

(1)
(2)
(3)

The pre-event topography is a LiDAR topography witha resolution of 1m/pixel and has an associated error of
σ1 = 0.07m. On the other hand, the post-event
topography results from a photogrammetric UAV
survey and has an associated error of σ1 = 0.16m.
Consequently, the generated DoD has an associatederror propagation of 𝜎𝐷𝑂𝐷=0.17 m. A coregistration
procedure is necessary to remove the possible offsets ofour topographies prior to differentiating the DEMs [7].

(4)1∫ ∇ (𝑝 ℎ)𝑑𝑆 )2𝑆𝐵 𝑆𝑏 n 𝑏

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E3S Web of Conferences 415, 02007 (2023)
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We used demcoreg for the DEM coregistration.
Demcoreg reduces the random error from 0.23 m to 0.15
m. This reduction in the random error highlights theimportance of the coregistration procedure to keep theminimum detection threshold as small as possible. Since
the error propagation and the random error are similar,
the minimum detection threshold is defined as 0.2 m.
3.3 Simulation and validation of the May 2017event
For the numerical simulation, on the other hand, wedecided to use the Voellmy-Salm equation for theresistance law, the RAMMS model [8] for the sedimententrainment, and the Fagents & Baloga [9] model for thedeposition rate of the sediment. These models containcalibration parameters found by trial and error,
comparing the field and simulated variables such as thefinal flooded areas and the estimated flow heights.

4 Results
During the 2017 event, the Crucecita alluvial fan
suffered an erosion of the channel slopes but depositionin the channel bed. In the original channel of the El
Carmen River, a deposit up to 6 meters high pushed theriver path towards the opposite side of the valley,
generating an adjacent erosion of up to 6 meters. At thealluvial fan toe, the original channel of the El Carmen
River was blocked, so the river sought a new path, which
is identified in Figure 2.a as a red area due to the erosion
generated.

Fig. 2. Field data (up) and simulated debris flow (down)

5 Conclusions

The debris flow simulation using faDebrisFOAM ispresented in Figure 2.b. Here, the volumetric sedimentconcentration of the river and the debris flow are shown.
The debris flow coming from Crucecita creek has a
CV=0.4, whereas the river starts at its inlet with CV=0.
At the confluence, the mixture of these two flows is notinstantaneous. Here, the debris flow remains in a welldefined lobe of high sediment concentration.
Conversely, the river is forced to flow over the opposite
side of the valley without increasing its sedimentconcentration. The mixing of both flows starts
downstream from the confluence point, where thevolumetric sediment concentration is around 0.1.

Having sound field evidence of a debris flow event isdifficult, especially in areas such as the Atacama Desert,
where debris flow events are not frequent. The DoD
presented here gives us a unique possibility to validate
numerical models and study the processes that takeplace in the confluence of a debris flow with a trunkriver.
Since faDebrisFOAM is a recently developed model, its
validation is still a work in progress. Here, erosion anddeposition processes simulated by the model arecompared against the field data showing a goodcorrelation.
Interestingly, the model shows an inefficient mixing
process where most of the sediment remains at thealluvial fan toe, while the rest continues downstream,changing the sediment concentration of the river. This
was also observed on the field but needs furtherinvestigation to validate the mixing process.
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 Garcésand Alvaro González were financially supported by the ANID
doctoral grant 2019-21191593 and the ANID master grant2019-22191193, respectively.

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E3S Web of Conferences 415, 02007 (2023)
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https://doi.org/10.1051/e3sconf/202341502007

Code availability: The openFOAM solver may be requested atalvaro.gonzalez.b@ug.uchile.cl or agarces@uchile.cl

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