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Citation: Kruši´c, J.; Pastor, M.;
Tayyebi, S.M.; Djuri´c, D.; Djuri´c, T.;
Samardži´c-Petrovi´c, M.; Marjanovi´c,
M.; Abolmasov, B. Comparison of
Different Numerical Methods in
Modeling of Debris Flows—Case
Study in Selanac (Serbia). Appl. Sci.
2024,14, 9059. https://doi.org/
10.3390/app14199059
Academic Editor: Haiqing Yang
Received: 9 August 2024
Revised: 17 September 2024
Accepted: 26 September 2024
Published: 8 October 2024
Copyright: © 2024 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
applied
sciences
Article
Comparison of Different Numerical Methods in Modeling of
Debris Flows—Case Study in Selanac (Serbia)
Jelka Kruši´c 1, Manuel Pastor 2, Saeid M. Tayyebi 2, * , Dragana Djuri´c 1, Tina Djuri´c 1,
Mileva Samardži´c-Petrovi´c 3, Miloš Marjanovi´c 1and Biljana Abolmasov 1
1Faculty of Mining and Geology, University of Belgrade, Djušina, 7, 11000 Belgrade, Serbia;
jelka.krusic@rgf.bg.ac.rs (J.K.); dragana.djuric@rgf.bg.ac.rs (D.D.); tina.djuric@rgf.bg.ac.rs (T.D.);
milos.marjanovic@rgf.bg.ac.rs (M.M.); biljana.abolmasov@rgf.bg.ac.rs (B.A.)
2Department of Applied Mathematics, ETS Ingenieros de Caminos, Universidad Politécnica de Madrid,
Calle del Profesor Aranguren, 3, 28040 Madrid, Spain; manuel.pastor@upm.es
3Faculty of Civil Engineering, University of Belgrade, Bulevar Kralja Aleksandra 73, 11000 Belgrade, Serbia;
mimas@grf.bg.ac.rs
*Correspondence: saeid.moussavita@upm.es
Abstract: Flow-type landslides are not typical in this region of the Balkans. However, after the Tamara
cyclone event in 2014, numerous such occurrences have been observed in Serbia. This paper presents
the initial results of a detailed investigation into debris flows in Serbia, comparing findings from
two programs: RAMMS DBF and Geoflow SPH. Located in Western Serbia, the Selanac debris flow is a
complex event characterized by significant depths in the initial block and entrainment zone. Previous
field investigations utilized ERT surveys, supplemented by laboratory tests, to characterize material
behavior. Approximately 450,000 m
3
of material began to flow following an extreme precipitation
period, ultimately traveling 1.2 km to the deposition zone. For validation purposes, ERT profiles from
both the deposition zone and the source area were utilized, with particular attention given to areas
where entrainment was substantial, as this had a significant impact on the final models. The first
objective of this research is to conduct a detailed investigation of debris flow using field investigations:
geophysical (ERT) and aerial photogrammetry. The second objective is to evaluate the capacity of
two debris flow propagation models to simulate the reality of these phenomena. The GeoFlow-SPH
code overestimated the maximum propagation thickness in comparison to the RAMMS model. The
numerical results regarding final depths closely align, especially when considering the estimated
average depth in the deposition zone. The results confirm the necessity of using multiple simulation
codes to more accurately predict specific events.
Keywords: Tamara cyclone; debris flow; entrainment; RAMMS; SPH; ERT
1. Introduction
Debris flows are characterized as one of the most dangerous and least predictable types
of landslides [
1
,
2
]. Following certain natural disasters, flow-type landslides frequently
occur. In Serbia, numerous such events occurred in 2014 due to the Tamara cyclone effect.
Specifically, over 200 flow-type landslides were recorded in the western part of Serbia,
with many others identified indirectly through satellite image analysis [
3
,
4
]. Many of these
incidents were unexpected, even in areas designated as relatively stable according to hazard
maps. Some cases were particularly complex, involving both sliding and flowing processes
and a significant volume of material, rendering them challenging for numerical modeling.
Various runout methods have been developed over time, ranging from empirical
relationships between runout and landslide initial characteristics [
5
], to analytical meth-
ods [
1
,
6
–
8
], and finally to dynamic and complex numerical methods [
9
–
11
]. The complexity
of modeling lies in the consideration of numerous input parameters, including the ap-
propriate rheology law, accurate depth of the source area, entrainment parameters, and
Appl. Sci. 2024,14, 9059. https://doi.org/10.3390/app14199059 https://www.mdpi.com/journal/applsci
Appl. Sci. 2024,14, 9059 2 of 19
the definition of geotechnical parameters such as porosity, friction coefficients, and the
variation in pore water pressure over time and space [12,13].
Some software is designed for ease of use but is also continuously developed and
improved to enhance numerical capabilities in line with the needs and complexity of real-
world scenarios. In cases involving large deformations, large-scale phenomena, and hazard
prediction, propagation models (runout models) have proven to be highly effective. After
identifying unstable areas where mass flows are likely to occur, current programs utilizing
dynamic numerical models are used to predict flow patterns and pinpoint potential impact
zones. Today, numerous numerical models are available for risk assessment and runout
analysis, and selecting the most appropriate simulation code has become a significant
concern due to advances in computational technology.
Running multiple simulations to predict specific events or conducting a detailed back-
analysis can be valuable. This approach enables a comparison of numerical outcomes, helps
identify key differences, and allows for a more precise assessment of potential risks. However,
beyond the capabilities of the chosen simulation code, various other factors—such as the
presence of erosion and the accurate definition of parameters—can greatly influence the results.
RAMMS is widely utilized for back-calculating models of avalanches and debris flows.
Its inclusion of entrainment calculation has been thoroughly tested in study areas [
14
]. The
model operates in 2D, tracking the changing volume over time using Voellmy rheology, a
method commonly employed in debris flow modeling. The initial models for this study
area were developed using RAMMS, facilitating the straightforward determination of
certain input parameters. This involved utilizing terrain data with a resolution of 5
×
5 m
(presented here are the final models based on this resolution DTM) and identifying zones
of potential maximum erosion depth. For accurate interpretation, detailed field charac-
terization of the cases being modeled was essential. These study areas were delineated
through various field research methods: Electrical Resistivity Tomography (ERT), detailed
UAV scanning of the wider area to generate post-event orthophotos, and a DTM with a
5 cm resolution. Additionally, laboratory tests were conducted to analyze granulometry
and consistency across different samples.
SPH (Smoothed Particle Hydrodynamics) is a meshless method utilized across various
fields. Geoflow SPH, proposed by [
10
], has been implemented and tested over the years on
numerous cases [
10
,
15
,
16
], including different scenarios and flume tests. For the first time
in this study, the extraction of the source area from the topographical model was employed
to enhance the accuracy of entrainment calculation. Also, many other researchers have
developed this SPH model [
17
–
20
]. Here, we present a two-phase model that includes
entrainment calculation.
Conducting detailed geotechnical investigations is crucial for acquiring field data.
Given the extensive scale of this study area, traditional geotechnical methods such as
drilling may not be feasible. Electrical Resistivity Tomography (ERT) geophysical research
was therefore employed to effectively delineate key dimensional parameters of the debris
flow, including depth in the source area, potential erosion depths, and depths in the de-
position zone. Since the 2000s, numerous papers have reported the successful application
of geophysical methods in landslide investigations, enabling the determination of vari-
ous parameters such as the thickness of alluvial deposits, depth of bedrock, and shear
surfaces [
21
,
22
]. Among these methods, Electrical Resistivity Tomography (ERT) stands
out as particularly useful for landslide investigations [
23
,
24
]. Additionally, comparing
precise satellite images from different epochs serves as a valuable system for validating
final models.
This paper is structured as follows: the second section is divided into study area
characteristics, geology conditions of the field, investigation methods, and numerical
methods. Finally, in the results section, the final propagation models in both programs are
shown with a validation using the ERT deposition profile.
Appl. Sci. 2024,14, 9059 3 of 19
2. Materials and Methods
2.1. Study Area
The Selanac debris flow was triggered by an extreme precipitation period in May
2014. Following a month of nearly continuous rainfall, floods inundated a vast area of
Serbia, triggering numerous new landslides, some of which were reactivated occurrences.
Consequently, many of these events took place unexpectedly in areas where such incidents
were not anticipated, with most being characterized as flow-type landslides or involving
combined processes [25]. Western Serbia bore the brunt of the impact, with over 200 flow-
type landslides recorded in the field. The Selanac debris flow is situated in the northern
part of the Ljubovija municipality (Figure 1) and garnered significant attention due to
its behavior and magnitude (involving 450,000 m
3
of triggered material). The massive
block of material initially slid in the upper part, and then transitioned into a flow through
two existing gullies. It is noteworthy that a smaller event occurred first in the upper
part, although it was part of a separate landslide. The transported material descended to
an elevation approximately 320 m lower, depositing a heterogeneous mix ranging from
matrix to huge boulders up to 2 m in diameter. Initially, the material formed a dam on the
Selanaˇcka river, which was subsequently breached by the torrential flow of the Selanaˇcka
river, leading to the further transportation of material down the river valley and causing
instabilities. This paper focuses on the model for the initial deposition area, while all other
materials are regarded as outflow material.
Appl. Sci. 2024, 14, x FOR PEER REVIEW 4 of 19
Figure 1. Location of the study area with measured precipitation amounts at the nearest weather
stations.
2.2. Geology Conditions
There are two dominant geological formations in the wider area: the ‘Drina’ for-
mation and the ‘Jadar’ formation. The ‘Drina’ formation comprises a complex of Lower-
(
1
C
1,2
) and Middle-Carboniferous-age (
2
C
1,2
) phyllite, metasandstone, clay and graphitic
schists, limestone, diabase, tuff, and tuffite. The ‘Jadar’ formation (Pz) consists of a com-
plex of sandstone, argillophyllite, and black limestone. These formations overlay trans-
gressively above Permian sediments of shales, sandstones, and limestones, with the lime-
stones transitioning into a block of Upper Permian bituminous limestone. The primary
geological unit involved in the debris flow process is the ophiolitic melange of the Jurassic
period. It is believed that huge boulders of rock were mixed within a matrix mass. In the
upper part, just a few hundred meters from the source area, lies the fault zone with lime-
stones. Other units include Jurassic limestones and Triassic limestones in the middle part.
In the zone of the deposition area, magmatic rocks such as granodiorite, dacite, andesite,
quar-latite, and basalt formed during the Tertiary period (Tc) (Figure 2).
Figure 1. Location of the study area with measured precipitation amounts at the nearest weather stations.
The study area is located in the municipality of Ljubovija, specifically in the Selanac
region. The broader area is characterized by a moderately continental to continental climate.
The Ljubovija region is situated on the right valley side of the Drina River and is marked
by steep slopes prone to instability, including erosion, sliding, flow, and flooding. In
addition to the Drina River, one of the major watercourses in the area is the Ljubovi ¯
da
River, which exhibits a pronounced torrential characteristic. The elevation in the broader
study area ranges from 158 m in the lower parts of the Drina River valley to 1268 m in
the mountainous regions. The terrain is generally mountainous to hilly. Within the flow
Appl. Sci. 2024,14, 9059 4 of 19
activation zone, the initial zone is located at approximately 720 m above sea level, while
the material deposition zone is at an elevation of about 400 m above sea level, extending
down to the Selanaˇcka River.
During this period, there was heavy rainfall for three days. In Western Serbia, the
maximum recorded rainfall was 350 mm, which was measured at Razbojište, one of the
nearest measurement stations to the Selanac debris flow (Figure 1).
2.2. Geology Conditions
There are two dominant geological formations in the wider area: the ‘Drina’ formation
and the ‘Jadar’ formation. The ‘Drina’ formation comprises a complex of Lower- (
1
C
1,2
)
and Middle-Carboniferous-age (
2
C
1,2
) phyllite, metasandstone, clay and graphitic schists,
limestone, diabase, tuff, and tuffite. The ‘Jadar ’ formation (Pz) consists of a complex of
sandstone, argillophyllite, and black limestone. These formations overlay transgressively
above Permian sediments of shales, sandstones, and limestones, with the limestones
transitioning into a block of Upper Permian bituminous limestone. The primary geological
unit involved in the debris flow process is the ophiolitic melange of the Jurassic period. It
is believed that huge boulders of rock were mixed within a matrix mass. In the upper part,
just a few hundred meters from the source area, lies the fault zone with limestones. Other
units include Jurassic limestones and Triassic limestones in the middle part. In the zone of
the deposition area, magmatic rocks such as granodiorite, dacite, andesite, quartz-latite,
and basalt formed during the Tertiary period (Tc) (Figure 2).
Appl. Sci. 2024, 14, x FOR PEER REVIEW 5 of 19
Figure 2. Geological map of the terrain, detailed at 1:10,000 of the general geological map (OGK) at
1:100,000, Ljubovija.
2.3. Investigation
The first field survey was conducted in May 2015 to document the phenomena that
occurred following the impact of cyclone Tamara in 2014, as part of the BEWARE project.
During this survey, the basic geometric characteristics of the debris flow were defined,
including its length, potential depth, the material transport zone with an estimated depth,
rock mapping, and the characterization of displaced blocks.
After mapping the terrain, sampling for laboratory tests was conducted. Samples
were collected from the initiation zone, transportation zone, and deposition zone. The ma-
terial in the debris flow is highly heterogeneous and transported over long distances, with
the majority of the coarse material accumulating in the deposition zone. Since these are
“disturbed” samples, soil samples were taken to be representative for laboratory analysis.
In selecting the samples, care was taken to ensure representation from each element of the
flow. Six samples were selected for laboratory testing: 3 from the initiation zone, 2 from
the deposition zone, and 1 from the transportation zone.
Due to the inaccessibility of the terrain and the significant depth of the debris flow, it
was not possible to apply classical geotechnical methods to define the thickness of the
mobilized and transported material. In November 2015, geophysical investigations using
the Electrical Resistivity Tomography (ERT) method were conducted to precisely charac-
terize the geometry of the debris flow and compare it with subsequent numerical analyses.
Figure 2. Geological map of the terrain, detailed at 1:10,000 of the general geological map (OGK) at
1:100,000, Ljubovija.
Appl. Sci. 2024,14, 9059 5 of 19
2.3. Investigation
The first field survey was conducted in May 2015 to document the phenomena that
occurred following the impact of cyclone Tamara in 2014, as part of the BEWARE project.
During this survey, the basic geometric characteristics of the debris flow were defined,
including its length, potential depth, the material transport zone with an estimated depth,
rock mapping, and the characterization of displaced blocks.
After mapping the terrain, sampling for laboratory tests was conducted. Samples
were collected from the initiation zone, transportation zone, and deposition zone. The
material in the debris flow is highly heterogeneous and transported over long distances,
with the majority of the coarse material accumulating in the deposition zone. Since these are
“disturbed” samples, soil samples were taken to be representative for laboratory analysis.
In selecting the samples, care was taken to ensure representation from each element of the
flow. Six samples were selected for laboratory testing: 3 from the initiation zone, 2 from the
deposition zone, and 1 from the transportation zone.
Due to the inaccessibility of the terrain and the significant depth of the debris flow,
it was not possible to apply classical geotechnical methods to define the thickness of
the mobilized and transported material. In November 2015, geophysical investigations
using the Electrical Resistivity Tomography (ERT) method were conducted to precisely
characterize the geometry of the debris flow and compare it with subsequent numerical
analyses. In March 2017, photogrammetric imaging was performed to compare images
before and after the activation of the flow, and to analyze the resulting Digital Terrain
Model (DTM) and high-resolution orthophoto images (with up to 10 cm accuracy). The
DTM of the terrain prior to the flow activation was obtained by restituting high-resolution
aerial images and was used as input data in flow modeling software.
2.3.1. Remote Detection Methods
Remote sensing methods were employed during the investigation to promptly assess
the aftermath of cyclone Tamara as part of the project. The Pleiades satellite image for
Selanac from June 2014 was scrutinized, taken immediately after the landslide activation
in May 2014. This satellite image served visualization purposes and facilitated the deter-
mination of the location and extent of the broader investigation area [
4
]. Subsequently,
other remote sensing methods were utilized to primarily gather more precise data, such
as generating a high-resolution Digital Terrain Model (DTM). In landslide modeling, we
can consider two epochs crucial for analyzing the distribution of moved material due
to instability:
Epoch I: Referring to the stable terrain before the activation of the landslide;
Epoch II: Referring to the terrain after the activation of the landslide.
In order to obtain high-resolution orthophoto images and the DTM for the second
epoch, after the activation of the flow, a DJI Phantom 4 Pro drone was used.
The procedure for capturing and creating the DTM and orthophoto images was
carried out in the following order: the study areas and the desired pixel resolution of the
orthophoto images were defined; flight parameters (altitude, flight path, and waypoint
locations) were calculated, and the necessary percentages of longitudinal and lateral image
overlap were determined; orientation points on the terrain surface were defined, marked,
and surveyed; control points on the terrain surface were defined, marked, and surveyed;
drone flights were conducted; the collected images were processed photogrammetrically;
point clouds were classified, terrain surfaces were derived, and DTM and orthophoto
images were created.
Comparing the DTMs of these epochs for both landslides served as a validation
method for the final numerical models. The following figure (Figure 3) shows a high-
resolution orthophoto of the large flow area where detailed field investigations and model-
ing were conducted. In addition to the defined elements, images of characteristic parts of
the terrain are presented.
Appl. Sci. 2024,14, 9059 6 of 19
Appl. Sci. 2024, 14, x FOR PEER REVIEW 7 of 19
as the initial block, while the red area in the transport zone was designated as the entrain-
ment zone in both models. As noted, the two programs use different numerical ap-
proaches for calculating the eroded material.
Figure 3. Orthophoto of the Selanac debris flow obtained by UAV photogrammetric survey with
characterization of basic geometric elements.
Figure 4. Map obtained by overlapping two epochs of the Digital Terrain Model (DTM).
Figure 3. Orthophoto of the Selanac debris flow obtained by UAV photogrammetric survey with
characterization of basic geometric elements.
To compare Digital Terrain Models from two epochs, the initial step involved resam-
pling the model with a resolution of 30x30 cm to match the 5 m resolution used in the
final modeling. To achieve a more precise comparison and obtain accurate data on mass
differences before and after the activation of the debris flow, the scans from the two epochs
overlapped (Figure 4). This overlap revealed the differences in terrain elevation within the
debris flow zone.
The image clearly shows that in the initial zone, the maximum depth reaches nearly
29 m, while in the deposition zone, differences of up to 31 m are recorded. Additionally,
in the transportation zone, there is a noticeable area of significant erosion along the right
gully (red zone), as well as material deposition in the left gully (green zone). It should
be noted that, due to the nature of the processes involved, these differences are most
representative in the initial zone, where material transport was the dominant process. In
the deposition zone, the reported values indicate precise differences (with the deepest
values corresponding to the Selanac river bed). However, since both material transport
and deposition occurred in this area, the exact depth of the deposited material cannot be
determined with certainty from these data. This is especially relevant for the transportation
zone, where both significant erosion and continuous material deposition are dominant.
The eroded and initiation zones were directly defined based on the results obtained
from aerial photogrammetry (Figure 4). The red area in the initiation zone was identified as
the initial block, while the red area in the transport zone was designated as the entrainment
zone in both models. As noted, the two programs use different numerical approaches for
calculating the eroded material.
Appl. Sci. 2024,14, 9059 7 of 19
Appl. Sci. 2024, 14, x FOR PEER REVIEW 7 of 19
as the initial block, while the red area in the transport zone was designated as the entrain-
ment zone in both models. As noted, the two programs use different numerical ap-
proaches for calculating the eroded material.
Figure 3. Orthophoto of the Selanac debris flow obtained by UAV photogrammetric survey with
characterization of basic geometric elements.
Figure 4. Map obtained by overlapping two epochs of the Digital Terrain Model (DTM).
Figure 4. Map obtained by overlapping two epochs of the Digital Terrain Model (DTM).
2.3.2. Electrical Resistivity Tomography (ERT)
Electrical Resistivity Tomography (ERT) is a widely utilized method in geophysics,
relying on the transmission of current through electrodes positioned along defined profiles.
It correlates measured resistivity with various geological characteristics of the terrain, such
as lithology, structural arrangement, moisture content, and water presence [21–24].
At the Selanac landslide site, ERT was employed to ascertain its geometric features,
including the depth of the initial block, eroded and deposited material, and accumulated
debris. Given the occurrence’s dimensions, material heterogeneity, and the terrain’s inac-
cessibility, traditional geotechnical investigation methods were impractical, making ERT
the most suitable option. Measurements across all profiles were conducted using a
‘4-point
light HP resistivity meter’ (LGM Lippmann-GERMANY) with 20–60 electrodes. This
system reduces the measurement time. All operational electrodes along the profile were
connected to the resistivity meter via multi-core cables. For each individual measurement,
the resistivity meter selects four electrodes and measures the apparent resistivity [
22
]. This
research was conducted in November 2015 by the expert team from the Faculty of Mining
and Geology, Department of Geophysics.
Validation was conducted by comparing a single cross-section corresponding to the
position of the ERT5 profile in the deposition zone, as well as the difference in DTM heights.
ERT5 (Figure 5) is located in the deposition zone of the transported material. It was not
possible to determine the lateral boundaries, but the thickness of the accumulated material
was estimated. For ERT5, the maximum thickness was estimated at 15–20 m(Figure 6).
Appl. Sci. 2024,14, 9059 8 of 19
Appl. Sci. 2024, 14, x FOR PEER REVIEW 8 of 19
2.3.2. Electrical Resistivity Tomography (ERT)
Electrical Resistivity Tomography (ERT) is a widely utilized method in geophysics,
relying on the transmission of current through electrodes positioned along defined pro-
files. It correlates measured resistivity with various geological characteristics of the ter-
rain, such as lithology, structural arrangement, moisture content, and water presence [21–
24].
At the Selanac landslide site, ERT was employed to ascertain its geometric features,
including the depth of the initial block, eroded and deposited material, and accumulated
debris. Given the occurrence’s dimensions, material heterogeneity, and the terrain’s inac-
cessibility, traditional geotechnical investigation methods were impractical, making ERT
the most suitable option. Measurements across all profiles were conducted using a ‘4-
point light HP resistivity meter’ (LGM Lippmann-GERMANY) with 20–60 electrodes.
This system reduces the measurement time. All operational electrodes along the profile
were connected to the resistivity meter via multi-core cables. For each individual meas-
urement, the resistivity meter selects four electrodes and measures the apparent resistivity
[22]. This research was conducted in November 2015 by the expert team from the Faculty
of Mining and Geology, Department of Geophysics.
Validation was conducted by comparing a single cross-section corresponding to the
position of the ERT5 profile in the deposition zone, as well as the difference in DTM
heights. ERT5 (Figure 5) is located in the deposition zone of the transported material. It
was not possible to determine the lateral boundaries, but the thickness of the accumulated
material was estimated. For ERT5, the maximum thickness was estimated at 15–20 m(Fig-
ure 6).
Figure 5. Position of the ERT profiles on the Digital Terrain Model.
Figure 5. Position of the ERT profiles on the Digital Terrain Model.
Appl. Sci. 2024, 14, x FOR PEER REVIEW 9 of 19
Figure 6. Results of ERT profile 5.
2.3.3. Laboratory Testing
Laboratory testing was conducted to define the basic identification and classification
characteristics of the displaced material. Samples were collected from multiple locations
of the landslide, excluding the deposition zone where the largest material was deposited.
Given the significance of fine-grained material in defining landslide movements, care was
taken in selecting samples to ensure the representation of fine particles, which are integral
to the fluid.
The laboratory tests included sieving of the material, separation of the fine fraction
for hydrometer analysis, selection of a portion of the fine fraction for determining specific
gravity, and tests for plasticity and the falling cone test. To classify the landslide based on
its grain size composition, laboratory tests for determining particle size distribution and
hydrometer analysis were performed. The falling cone test, conducted to determine the
flow limit, followed the standard SRPS EN ISO 17892-12. [26].
A sample prepared by adding water is placed in a vessel with a diameter of 55 mm.
Each subsequent measurement is performed on the same sample with additional water
added. The values of cone penetration are read on the scale, and based on the recorded
values, the flow limit value is obtained. Three measurements are taken on each sample.
For the classification of the mobilized material, the obtained samples are presented
on the USCS diagram (Figure 7). The results show that the matrix has low to medium
plasticity. Two samples, S1 taken from the initial zone and S4 from the deposition zone,
are in the low-plasticity zone CL and on the border with the medium-plasticity state CL,
while the other samples are characterized as clayey material of medium-plasticity CI. The
results are within approximate limits and, considering the heterogeneous nature of the
material and the large dimensions of the flow, they show a very good correlation when
comparing the mobilized material in different elements of the flow.
Figure 7.
USCS
diagram based on soil consistency parameters.
Figure 6. Results of ERT profile 5.
2.3.3. Laboratory Testing
Laboratory testing was conducted to define the basic identification and classification
characteristics of the displaced material. Samples were collected from multiple locations
of the landslide, excluding the deposition zone where the largest material was deposited.
Given the significance of fine-grained material in defining landslide movements, care was
taken in selecting samples to ensure the representation of fine particles, which are integral
to the fluid.
The laboratory tests included sieving of the material, separation of the fine fraction
for hydrometer analysis, selection of a portion of the fine fraction for determining specific
gravity, and tests for plasticity and the falling cone test. To classify the landslide based on
its grain size composition, laboratory tests for determining particle size distribution and
hydrometer analysis were performed. The falling cone test, conducted to determine the
flow limit, followed the standard SRPS EN ISO 17892-12 [26].
A sample prepared by adding water is placed in a vessel with a diameter of 55 mm.
Each subsequent measurement is performed on the same sample with additional water
Appl. Sci. 2024,14, 9059 9 of 19
added. The values of cone penetration are read on the scale, and based on the recorded
values, the flow limit value is obtained. Three measurements are taken on each sample.
For the classification of the mobilized material, the obtained samples are presented
on the USCS diagram (Figure 7). The results show that the matrix has low to medium
plasticity. Two samples, S1 taken from the initial zone and S4 from the deposition zone, are
in the low-plasticity zone CL and on the border with the medium-plasticity state CL, while
the other samples are characterized as clayey material of medium-plasticity CI. The results
are within approximate limits and, considering the heterogeneous nature of the material
and the large dimensions of the flow, they show a very good correlation when comparing
the mobilized material in different elements of the flow.
Appl. Sci. 2024, 14, x FOR PEER REVIEW 9 of 19
Figure 6. Results of ERT profile 5.
2.3.3. Laboratory Testing
Laboratory testing was conducted to define the basic identification and classification
characteristics of the displaced material. Samples were collected from multiple locations
of the landslide, excluding the deposition zone where the largest material was deposited.
Given the significance of fine-grained material in defining landslide movements, care was
taken in selecting samples to ensure the representation of fine particles, which are integral
to the fluid.
The laboratory tests included sieving of the material, separation of the fine fraction
for hydrometer analysis, selection of a portion of the fine fraction for determining specific
gravity, and tests for plasticity and the falling cone test. To classify the landslide based on
its grain size composition, laboratory tests for determining particle size distribution and
hydrometer analysis were performed. The falling cone test, conducted to determine the
flow limit, followed the standard SRPS EN ISO 17892-12. [26].
A sample prepared by adding water is placed in a vessel with a diameter of 55 mm.
Each subsequent measurement is performed on the same sample with additional water
added. The values of cone penetration are read on the scale, and based on the recorded
values, the flow limit value is obtained. Three measurements are taken on each sample.
For the classification of the mobilized material, the obtained samples are presented
on the USCS diagram (Figure 7). The results show that the matrix has low to medium
plasticity. Two samples, S1 taken from the initial zone and S4 from the deposition zone,
are in the low-plasticity zone CL and on the border with the medium-plasticity state CL,
while the other samples are characterized as clayey material of medium-plasticity CI. The
results are within approximate limits and, considering the heterogeneous nature of the
material and the large dimensions of the flow, they show a very good correlation when
comparing the mobilized material in different elements of the flow.
Figure 7.
USCS
diagram based on soil consistency parameters.
Figure 7. USCS diagram based on soil consistency parameters.
The plasticity test was conducted on selected samples by the Casagrande test, while
the cone penetration test was conducted to determine the liquidity index, both according
to the standard SRPS EN ISO 17892-12.
The consistency index (Ic) indicates the consistency (hardness) of the soil. As seen in
Table 1, the Ic values range from
−
0.7 to 0. A negative value of the index indicates that
the soil is in a liquid state. The natural moisture content of all samples was assumed to
be 40%, as it was not possible to measure it in the field (samples were taken 3 years later),
and the material behaved like a fluid. The obtained results for soil consistency and the
determination of Atterberg consistency limits are presented in Table 1.
Table 1. Soil consistency parameters.
Samples S1 S2 S3 S4 S5 S6
w (%) 40.0 40.0 40.0 40.0 40.0 40.0
LL (%) 33 37 40 34 38 37
PL (%) 23 21 23 23 22 22
Ip(%) 10 16 17 11 16 15
Ic(-) −0.700 −0.188 0.000 −0.545 −0.125 −0.200
According to the established experiment, the specific weight of a sample with a mass
of 49.73 g was determined. Based on this value, the density of solid particles was used
as one of the input parameters in the SPH Geoflow modeling program. The results are
presented in Table 2.
Appl. Sci. 2024,14, 9059 10 of 19
Table 2. Measurement results from the experiment determining the specific weight of sample St1.
Determination of Specific Weight of a Sample St1
ms (g) 49.738
mpvm (g) 362.144
mpv (g) 331.554
Gs 2.60
2.4. Numerical Methods
Two different approaches were used for modeling landslide propagation in this re-
search: one based on the Finite Volume Method (FVM) and the other based on the meshless
Smoothed Particle Hydrodynamics (SPH) method. The first approach was implemented
using the RAMMS DBF software, v. 1.5.0 while the second was implemented using code
developed by the research group in Madrid [10].
In propagation modeling, the mathematical formulations used in simulations are
often simplified and reduced to two dimensions through depth-integration approxima-
tions. Many flow-like landslides are relatively long and wide compared to their depth,
allowing the governing equations to be integrated along the vertical axis. This 2D depth-
integrated approach strikes a good balance between accuracy and computational efficiency.
Models like RAMMS DBF and Geoflow SPH rely on integrated solutions of the mass
and momentum balance equations, based on the shallow water flow assumption. While
depth-integrated models provide valuable insights into landslide behavior, they have no-
table limitations due to their simplified representation of 3D dynamics, complex material
properties, and terrain interactions. As a result, they are less effective for irregular ter-
rains, complex flow behaviors, or when small-scale processes are important. However,
these models are particularly useful for large-scale, shallow landslides and long-runout
events, such as the Selanac debris flow. Overall, depth-integrated models offer a practical
balance of simplicity, efficiency, and accuracy, making them highly valuable for landslide
propagation studies.
2.4.1. RAMMS
RAMMS (Rapid Mass Movement Software) was specially developed (2005) from
experts of Avalanche Research SLF and WSL Institute for Snow. The main development
was made by researching a case study of Illgraben debris flow in Switzerland [
14
,
27
,
28
]. It
is one-phase FVM (Finite Volume Method)-based, calculating displacement in a change in
volume, pressure, and depth in time F(V, P, h, t).
As the main input data, the DTM (Digital Terrain Model) was used as information of
terrain using automatic extraction of the source material. The suggested resolution was
from 5 m to 25 m. Here, a pre-event DTM was used on 5 m. The calculation was carried
out in a Cartesian coordinate system.
The mass balance equation incorporates the field variables flow height H(x,y,t) and
flow velocity U (x,y,t) and is given by
Q(x,y,t).=∂tH +∂x(H U x)+∂y(H Uy)(1)
where the earth pressure coefficient ka = p is normally set to 1 when running the standard
Voellmy–Salm friction approach,
cx
and
cy
represent topographical coefficients determined
from the digital elevation model, Sg is the effective gravitational acceleration, and S
f
is the
frictional deceleration in directions x and y[28].
The frictional deceleration S
f
of the flow is determined using the Voellmy friction
relation and specifies the dry-Coulomb term (friction coefficient
µ
) scaling with the normal
stress and the viscous or turbulent friction (coefficient
ξ
depending on the flow velocity
U[11,29]:
Sf=µρg H cos φ+ρgu2/ξ(2)
Appl. Sci. 2024,14, 9059 11 of 19
where
ρ
is the mass density, gis the gravitational acceleration,
φ
is the slope angle, and
Hgcos
φ
is the normal stress on the overflowed surface. The tangent of the effective internal
friction angle of the flow material can be defined for the resistance of the solid phase (the
term containing
µ
which extensively controls the deceleration behavior of a more slowly
moving flow). The resistance of the viscous or turbulent fluid phase (the term including
ξ
)
prevails for a more quickly moving flow [29].
Entrainment Model
The erosion algorithm in the RAMMS model is defined using the maximum potential
erosion depth em and a specific erosion rate. The erosion algorithm predicts the maximum
potential depth of erosion em as a function of the computed basal shear stress in each
grid cell:
em =0f or τ<τc(3)
em =dz/dτ(τ−τc)forτ≥τc(4)
and the shear stress τis approximated using the depth–slope product:
τ=ρghS (5)
The potential erosion depth (per kPa)
dz/dt
controls the rate of vertical erosion (in the
z-direction) as a linear function of channel-bed shear stress.
When the critical shear stress
τ
cis exceeded, sediment can be entrained from the chan-
nel. Entrainment stops when the actual erosion depth et reaches the maximum potential
erosion depth em (Equation (6)). Normally, the specific erosion rate is implemented using
the default value dz/dt =−0.025 m−1.
2.4.2. SPH-Smoothed Particle Hydrodynamics
In this section, we perform the GeoFlow-SPH simulation model which has been
developed in Madrid by an expert research team for almost a decade. It has previously
been applied to theoretical, experimental, and real case histories.
First, we briefly describe a Lagrangian meshless numerical method of Smoothed
Particle Hydrodynamics (SPH) that is used to transform the problems that are basically
in the form of partial differential equations (PDEs) to a form suitable for particle-based
simulation. The SPH method was first invented by [
30
,
31
] to model astrophysical problems.
This technique has been applied in many areas due to its capability to model complicated
cases that involve large-displacement deformations, such as modeling fast landslides in
Solid Mechanics [32–34]. Good reviews can be found in the texts of [35,36].
In this model, these 3D problems are transformed into a 2D form by applying a
depth-integrated model. As a result, the depth-integrated model provides an excellent
combination of accuracy and computational time. This technique has been successfully
applied to landslides by [15,16,37–41].
The two-phase depth-integrated SPH model we follow here is proposed based on
the mathematical model proposed by Zienkiewicz and Shiomi [
42
] and is similar to those
of [42–44].
To discretize the propagating mass in the SPH method, the first step is to present them
as a set of nodes, as depicted in Figure 8, exhibiting individual material properties.
Then, an interpolation process calculates the relevant properties on each node over
neighboring nodes through a kernel function
Wij =Wxi−xj,h
, without having to
define any element. The formulation can be expressed as
f(xi)=ZfxjWxi−xj,hdxj(6)
where the function f(x)is approximated at a position vector xin space.
Appl. Sci. 2024,14, 9059 12 of 19
Appl. Sci. 2024, 14, x FOR PEER REVIEW 12 of 19
First, we briefly describe a Lagrangian meshless numerical method of Smoothed Par-
ticle Hydrodynamics (SPH) that is used to transform the problems that are basically in the
form of partial differential equations (PDEs) to a form suitable for particle-based simula-
tion. The SPH method was first invented by [30,31] to model astrophysical problems. This
technique has been applied in many areas due to its capability to model complicated cases
that involve large-displacement deformations, such as modeling fast landslides in Solid
Mechanics [32–34]. Good reviews can be found in the texts of [35,36].
In this model, these 3D problems are transformed into a 2D form by applying a
depth-integrated model. As a result, the depth-integrated model provides an excellent
combination of accuracy and computational time. This technique has been successfully
applied to landslides by [15,16,37–41].
The two-phase depth-integrated SPH model we follow here is proposed based on the
mathematical model proposed by Zienkiewicz and Shiomi [42] and is similar to those of
[42-44].
To discretize the propagating mass in the SPH method, the first step is to present
them as a set of nodes, as depicted in Figure 8, exhibiting individual material properties.
Figure 8. SPH interactions for two-phase model.
Then, an interpolation process calculates the relevant properties on each node over
neighboring nodes through a kernel function 𝑊 =𝑊𝑥
−𝑥
,ℎ , without having to
define any element. The formulation can be expressed as
𝑓
(𝑥)=
𝑓
𝑥 𝑊𝑥−𝑥
,ℎ𝑑𝑥 (6)
where the function 𝑓(𝑥) is approximated at a position vector 𝑥 in space.
By applying the particle approximation technique and considering that the infinites-
imal volume 𝑑𝑥 is related to the mass and density of the particle 𝑗 , the function at
particle 𝑖 can be wrien as
𝑓
(𝑥)=
∑
𝑓
𝑥
𝑥−𝑥
,ℎ
(7)
Then, in the numerical SPH method, the ordinary differential equations (ODEs) of
the balance of mass and momentum can be produced in discretized form with respect to,
respectively,
+ℎ∑
𝑣 grad𝑊 =𝑛𝑒 (8)
()
=−∑𝑚
+
grad𝑊 −
𝑏ℎ
−∆
∑𝑚
+
grad𝑊
+
𝜏
()+𝑏+
𝑅
−
𝑣
𝑛𝑒 (9)
Figure 8. SPH interactions for two-phase model.
By applying the particle approximation technique and considering that the infinitesi-
mal volume
dxj
is related to the mass and density of the particle
j
, the function at particle
ican be written as
f(xi)∼
=∑N
j=1fxjxi−xj,hmj
ρj
(7)
Then, in the numerical SPH method, the ordinary differential equations (ODEs) of
the balance of mass and momentum can be produced in discretized form with respect to,
respectively,
dhi
dt +hi∑Nh
j=1
mj
ρj
vjgradWij =nieR(8)
d(α)vai
dt =−∑Nh
j=1maj Pai
h2
ai
+Paj
h2
aj !gradWij −1
2
ρw
ρα
b3h2
ai −∆pwhai
ρα∑Nh
j=1maj
nai
h2
ai
+naj
h2
aj !gradWij +1
ραhai
τ(α)
B+bi+1
ρα
Rα−1
hai
vainaieR
(9)
where
α
denotes the phase (
s
or
w
),
nα
are the volume fractions of solid and fluid phases
(
ns=
1
−n
and
nw=n
), and
hα=hnα
.
Pα
is the averaged pressure
Pα
acting on solid or
fluid phases and can be defined as
Ps=1
2b3hhs+∆pwhn
ρsFor Solid (10)
Pw=1
2b3hhw−∆pwhn
ρwFor Fluid (11)
where
∆pw
is the excess pore-water pressure. The interested reader will find in the article
by [40] a detailed description of this two-phase SPH model.
Next, the above mathematical equations are completed by using various rheological
and empirical laws. In this study, the numerical simulations were performed by using
Voellmy’s rheological law, which has the same features as the frictional rheological model,
and the evolution of pore-water pressure can be considered at the basal surface where the
cohesion and all viscous terms are disregarded. The basal shear stress, in the case of a pure
frictional mass, is given by
τB=−((1−n)(ρs−ρw)gh−∆pwb )vi
|v|tan φb+ρg|v|
ξvi(12)
where
τB
is the basal shear stress,
φB
is the basal friction angle,
ξ
is the turbulence coefficient,
and ∆pwb is the excess pore water pressure at the basal surface.
Appl. Sci. 2024,14, 9059 13 of 19
The GeoFlow-SPH code contains various empirical laws governing the landslide
growth rate (
Er
), such as the Hungr erosion law which is based on an algorithm where the
total volume of debris increases by a specified rate, and is given by
eR=Es·h·v(13)
where
Es
can be obtained directly from the initial and final volumes of the material and the
distance traveled as Es≈ln((Vfinal/V0)/(distance)).
In the modeling of consolidation, similar to most depth-integrated models, simple
shape functions were used to fulfill boundary conditions by assuming that the pore pressure
is zero on the free surface and the bottom is impermeable. Consequently, by considering
these assumptions, the vertical distribution of pore water pressure can be approximated as
d∆pw
dt =−cvπ2
4h2∆pw(14)
where cvis the consolidation coefficient and his the mobilized soil depth.
Regarding the time integration scheme, we used the 4th-order Runge–Kutta method,
which provides high accuracy in the calculation of ODE. The time step is adaptive and it is
calculated progressively under the Courant–Friendrichs–Lewy (CFL) condition.
3. Results
3.1. RAMMS Model
For the terrain model, a pre-event DTM with 5
×
5 m resolution was used. The initial
block has an average depth of 15 m, estimated from the analysis of different epoch DTMs.
This method was also useful in defining other parameters such as erosion depth (estimated
to be a maximum of 20 m in some parts), deposition height, and the outline of debris flow.
RAMMS, based on Voellmy rheology, was used to back-calculate parameters of friction and
turbulence. After many iterations, the final best-fitted parameters were determined to be
0.11 for friction and 500 m/s2for turbulence.
For including entrainment, the default value of 1 kPa was used for critical shear stress,
and a rate proportionality factor of dz/dt = 0.1 m/kPa. Greater values of the proportionality
factor tend to overpredict erosion volume. The results of volume and transportation of
material with and without entrainment were compared. In the case of Selanac, an estimated
(on the field) maximum erosion depth of 12 m was used. A comparison of two epochs
of DMT was utilized to define the differences in the transportation zone. Considering
entrainment, the deposition heights were slightly larger, and the total volume was relatively
greater. It can be concluded that entrainment influenced the outflow of material in the
Selanaˇcka river, but generally did not change the model of final heights in the deposition
zone (Figure 9b,c, Table 3). The model shows a height in the deposition zone of almost
25.56 m, while the final depths in the deposition zone are almost 17 m (Figure 9c).
Table 3. Final results of the parameters in RAMMS model.
Debris Flow
Rheology Model
(Voellmy)
µ,ξ(ms−2)
Volume of Initial Block
(m3)
Volume of Entrainment
(m3)
Selanac 0.11; 500 453,061.15 41,023.35
The other model shows changes in velocity (Figure 9d). The maximum velocity was
over 33 m/s, which was also predicted in the Selanaˇcka river zone. However, since we
have torrential flow in that zone, this part of the terrain outside the first deposition zone
cannot be taken as representative, as velocities in this part were probably much greater due
to the river’s influence.
Appl. Sci. 2024,14, 9059 14 of 19
Appl. Sci. 2024, 14, x FOR PEER REVIEW 14 of 19
an estimated (on the eld) maximum erosion depth of 12 m was used. A comparison of
two epochs of DMT was utilized to dene the dierences in the transportation zone. Con-
sidering entrainment, the deposition heights were slightly larger, and the total volume
was relatively greater. It can be concluded that entrainment inuenced the outow of ma-
terial in the Selanačka river, but generally did not change the model of nal heights in the
deposition zone (Figure 9 b,c, Table 3). The model shows a height in the deposition zone
of almost 25.56 m, while the nal depths in the deposition zone are almost 17 m (Figure
9c).
Table 3. Final results of the parameters in RAMMS model.
Debris Flow
Rheology Model
(Voellmy)
µ, ξ(ms−2)
Volume of Initial
Block
(m3)
Volume of Entrainment
(m3)
Selanac
0.11; 500
453,061.15
41,023.35
The other model shows changes in velocity (Figure 9d). The maximum velocity was
over 33 m/s, which was also predicted in the Selanačka river zone. However, since we
have torrential ow in that zone, this part of the terrain outside the rst deposition zone
cannot be taken as representative, as velocities in this part were probably much greater
due to the river’s inuence.
Figure 9. (a) Area of entrainment in the transportation zone; (b) entrainment model of material in
the transportation zone; (c) nal deposition model; (d) maximum ow velocity model of the Selanac
debris ow.
Figure 9. (a) Area of entrainment in the transportation zone; (b) entrainment model of material in
the transportation zone; (c) final deposition model; (d) maximum flow velocity model of the Selanac
debris flow.
3.2. SPH Model
In the SPH code, the same DTM is used as the main topographic file, with representa-
tive points totaling 133,452. This results in a substantial number of inputs, which increases
the calculation time. The definition of the source area was made in the same way, but here,
every point has information about the real depth. The precise definition of the source area
is shown in previous work [
45
]. For the first time, we use the code implementation to
subtract the source area from the terrain model, which influences the movement of material.
The model is two-phase, including interactions between fluid and soil particles, unlike the
previous simplified model.
The selected rheology law is frictional with a Voellmy turbulence coefficient, with
tan
φ
= 0.35 (where
φ
is the frictional angle) and a turbulence coefficient
ξ
= 500 m/s
2
.
Entrainment influence was defined by the law proposed by Hungr (1995) [
1
], with the
erosion coefficient set to 0.0001. Effects of pore water pressure were not included in this
calculation. The final volume of material predicted by this model is 492,300 m
3
, while the
initial block had a volume of 447,400 m
3
, indicating that the amount of material eroded
by the action of the fluid is 44,900 m
3
. Final models of velocity, entrainment, and final
deposition are shown in Figure 10a–d.
Appl. Sci. 2024,14, 9059 15 of 19
Appl. Sci. 2024, 14, x FOR PEER REVIEW 15 of 19
3.2. SPH Model
In the SPH code, the same DTM is used as the main topographic file, with representa-
tive points totaling 133,452. This results in a substantial number of inputs, which increases
the calculation time. The definition of the source area was made in the same way, but here,
every point has information about the real depth. The precise definition of the source area
is shown in previous work [45]. For the first time, we use the code implementation to
subtract the source area from the terrain model, which influences the movement of mate-
rial. The model is two-phase, including interactions between fluid and soil particles, un-
like the previous simplified model.
The selected rheology law is frictional with a Voellmy turbulence coefficient, with
tanφ = 0.35 (where φ is the frictional angle) and a turbulence coefficient ξ = 500 m/s
2
. En-
trainment influence was defined by the law proposed by Hungr (1995), with the erosion
coefficient set to 0.0001. Effects of pore water pressure were not included in this calcula-
tion. The final volume of material predicted by this model is 492,300 m
3
, while the initial
block had a volume of 447,400 m
3
, indicating that the amount of material eroded by the
action of the fluid is 44,900 m
3
. Final models of velocity, entrainment, and final deposition
are shown in Figure 10a–d.
Figure 10. (a,b) Model for calculating achieved maximum flow velocities; (c) model of the material
entrainment rate (er); (d) model for simulating material movement and final deposition depths.
(
a
)
(
b
)
(
c
)
(
d
)
Figure 10. (a,b) Model for calculating achieved maximum flow velocities; (c) model of the material
entrainment rate (er); (d) model for simulating material movement and final deposition depths.
3.3. Validation
The total motion of material from the main deposition zone further into the Selanaˇcka
river valley is also depicted. The final results were compared with deposited material
heights measured using ERT (Electric Resistivity Tomography) profiles. According to
geophysical ERT investigations, the highest depths of the deposits are about 20 m. As the
main profile, we use the same profile position in both the RAMMS and ERT investigations.
Comparison profiles are shown in Figure 11 as well as the final depths in the deposition
zone of the SPH models. In both models of final depths, the eroded mass is about 50,000 m
3
,
which can be concluded from field research, including estimated depths averaging about
10 m. Hence, this amount of material, although not huge in comparison to the total mass,
shows an influence in changing depths in the deposition zone in both models.
The maximum velocity registered is about 45 m/s in SPH, while in RAMMS, it is
about 33 m/s. Since there are no field measurements during the process, these results
are assumed.
The cross-section shows different thicknesses according to the position of the ERT5
profile. For the ERT5 profile, the thickness is shown relative to the lower surface, i.e., the
depth of the channel predicted by geophysical investigations (Figure 11). For the models
obtained using RAMMS and SPH, the thickness is defined based on the input surface
of the DTM. All models predict greater material deposition on the right side of the flow
Appl. Sci. 2024,14, 9059 16 of 19
deposition compared to the ERT5 cross-section. The SPH model predicts greater thicknesses
throughout the area but is more representative in the sense that the majority of the material
is deposited within the deposition zone. In contrast, the RAMMS model predicts a large
amount of overflow material, as seen in the final model (Figure 9c), where the amount of
overflow material is significantly greater than the deposited material.
Appl. Sci. 2024, 14, x FOR PEER REVIEW 16 of 19
3.3. Validation
The total motion of material from the main deposition zone further into the Selanačka
river valley is also depicted. The final results were compared with deposited material
heights measured using ERT (Electric Resistivity Tomography) profiles. According to ge-
ophysical ERT investigations, the highest depths of the deposits are about 20 m. As the
main profile, we use the same profile position in both the RAMMS and ERT investigations.
Comparison profiles are shown in Figure 11 as well as the final depths in the deposi-
tion zone of the SPH models. In both models of final depths, the eroded mass is about
50,000 m
3
, which can be concluded from field research, including estimated depths aver-
aging about 10 m. Hence, this amount of material, although not huge in comparison to the
total mass, shows an influence in changing depths in the deposition zone in both models.
The maximum velocity registered is about 45 m/s in SPH, while in RAMMS, it is
about 33 m/s. Since there are no field measurements during the process, these results are
assumed.
The cross-section shows different thicknesses according to the position of the ERT5
profile. For the ERT5 profile, the thickness is shown relative to the lower surface, i.e., the
depth of the channel predicted by geophysical investigations (Figure 11). For the models
obtained using RAMMS and SPH, the thickness is defined based on the input surface of
the DTM. All models predict greater material deposition on the right side of the flow dep-
osition compared to the ERT5 cross-section. The SPH model predicts greater thicknesses
throughout the area but is more representative in the sense that the majority of the mate-
rial is deposited within the deposition zone. In contrast, the RAMMS model predicts a
large amount of overflow material, as seen in the final model (Figure 9c), where the
amount of overflow material is significantly greater than the deposited material.
The differences in the estimation of deposition depth and calibrated parameters are
linked to the distinct solution algorithms on which these two programs are based. The
calibration of the turbulence parameter is the same for both flows, while the differences
arise in the calibration of the friction parameter. In the case of Selanac, the importance of
two-phase flow modeling becomes evident. By using the two-phase SPH model, the de-
posited material was contained within the deposition zone, unlike in the RAMMS model,
where it was not possible to prevent the material from spreading significantly beyond the
deposition zone.
Figure 11. Comparative view of final material depths at position of ERT 5 profile.
Figure 11. Comparative view of final material depths at position of ERT 5 profile.
The differences in the estimation of deposition depth and calibrated parameters are
linked to the distinct solution algorithms on which these two programs are based. The
calibration of the turbulence parameter is the same for both flows, while the differences
arise in the calibration of the friction parameter. In the case of Selanac, the importance
of two-phase flow modeling becomes evident. By using the two-phase SPH model, the
deposited material was contained within the deposition zone, unlike in the RAMMS model,
where it was not possible to prevent the material from spreading significantly beyond the
deposition zone.
4. Conclusions
This research shows the results of the detailed field investigation, with a comparison
of two numerical models of the Selanac debris flow. For comparison, different numerical
approaches are chosen, one FVM-based (RAMMS DBF program) and the other a meshless
method (SPH code). A field investigation was first made using geophysical methods
considering how huge debris flows are. Then, a detailed DEM was made to compare two
epoch DTMs; the RAMMS model was made continuously for a longer period, in different
versions of the program, using different-quality DTMs [
43
]; the SPH code gives more
possibilities in modeling, including different rheology laws. For comparison, here, we
use the same constitutive, rheology model. The selected source area is the same, with
the possibility to use different depths in SPH since the model is defined in points. For
comparison, we used the same position of the profile as profile 5 for ERT investigation
(about 20 m).
The Voellmy rheological law was used to ensure the most accurate comparison among
the results. The most suitable parameters for the Selanac model were 0.35 and 500 m/s
2
,
which provide the most realistic representation of material propagation. The validation
was performed by comparing a single cross-section, as well as in the case of the RAMMS
model, by comparing it with the ERT5 profile and the elevation difference model.
Appl. Sci. 2024,14, 9059 17 of 19
The modeling was significantly more influenced by the prediction of the frictional
parameter compared to the turbulence parameter. The final values of the deposited material
depth were overestimated in the SPH program compared to the measurements conducted
through ERT investigations. On the other hand, the RAMMS model shows a large amount
of material flowing through the Selanac River (up to 2/3 of the total material).
The differences in the estimated depth of material deposition and the calibrated
parameters are linked to the different solution algorithms on which these two programs are
based. The calibration of the turbulence parameter is the same for both flows, while there
are differences in the calibration of the friction parameter for both flows. In the case of the
Selanac model, the importance of modeling two phases in flows is observed. By using the
two-phase SPH model, the deposited material is stopped in the deposition zone, unlike
in the RAMMS model, where it was not possible to model the material to prevent it from
flowing significantly beyond the deposition zone. These findings indicate that utilizing
multiple simulation codes is essential for accurately predicting specific events, evaluating
potential risks, and developing appropriate countermeasures.
In the previous study [
45
,
46
], various methods were applied to assess the susceptibility
to instability in the Ljubovija municipality area. This resulted in susceptibility maps for
instability occurrences and a comparison of the accuracy of the applied methods. The
Selanac debris flow was activated in areas of mass flow occurrence following extreme
rainfall in 2014. The potential for flow development in a broader area, based on defined
potential initiation zones and using one of the susceptibility assessment methods, along
with rheological parameters established for the Selanac debris flow, provides the possibility
to estimate propagation in other potential areas. This could help prevent negative impacts
in the future.
Author Contributions: Conceptualization, J.K.; methodology, J.K. and M.P.; software, M.P.; validation,
J.K. and S.M.T.; formal analysis, S.M.T. and M.S.-P.; investigation, J.K. and D.D.; resources, T.D.;
data curation, J.K.; writing—original draft preparation, J.K.; writing—review and editing, J.K.;
visualization, M.S.-P. and M.M.; supervision, M.P. and B.A.; project administration, B.A.; funding
acquisition, B.A. All authors have read and agreed to the published version of the manuscript.
Funding: Field research was part of the project ‘BEyond Landslide Awareness’ (BEWARE), funded
by the People of Japan and the UNDP Office in Serbia (grant no. 00094641). All activities are also part
of Project TR36009, funded by the Ministry of Education, Science, and Technological Development of
the Republic of Serbia.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: The original contributions presented in this study are included in the
article; further inquiries can be directed to the corresponding authors.
Acknowledgments: The research results would not have been possible without the ERASMUS+
program between the Polytechnic University of Madrid, Spain, and the University of Belgrade, Serbia.
This investigation is included in the PhD dissertation [47].
Conflicts of Interest: The authors declare no conflict of interest.
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