E3S Web of Conferences 415, 05007 (2023)
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https://doi.org/10.1051/e3sconf/202341505007

Reconstruction of debris flow in the Gerkhozhan-Su river valley
based on the chain modeling
Viktoriia Iudina (Kurovskaia)1*, Sergey Chernomorets1, Inna Krylenko1,2, Tatyana Vinodradova3 and Eduard
Zaporozhchenko4
1 Lomonosov Moscow State University, 119899 Moscow, Russia
2 Water Problems Institute, Russian Academy of Sciences, 119991 Moscow, Russia
3 JSC SPA Gidrotekhproekt, 175400 Valdai, Russia
4 Debris Flow Association, 357502 Pyatigorsk, RussiaAbstract. The paper presents the reconstruction of the most catastrophic debris flows in the GerkhozhanSu river valley (North Caucasus, Russia) based on a chain of mathematical models. Transport-shift model
was applied for 6 sections of debris flow formation or intense material increment, while for the rest the FLO2D hydrodynamic model was used. A number of numerical experiments were carried out in the transportshift model for a section of a debris flow origination site with a change in the parameters of a potential debris
flow-forming soils, such as initial moisture content and density. According to the simulation results, with arise in moisture content, the maximum debris flow discharge can increase by about 2.8 times. Modeling ofdebris flow in the Gerkhozhan-Su river valley was conducted for the case of low density debris flow. Basedon the results, debris flow wave hydrographs were obtained at 12 sections. The results of modeling are ingeneral agreement with the commonly accepted reconstructed pattern of the debris flow in 2000 and values
obtained by videomaterials.

1 Introduction
Debris flows are one of the most frequent mass
movement processes. Their high velocity, impact forces,
long runout, combined with poor temporal
predictability, cause debris flows to be one of the mosthazardous processes [1]. Numerical simulation is one of
the ways to estimate debris flows characteristics [2].
FLO-2D and RAMMS are one of the most popularhydrodynamic models for debris flows assessment [35]. Also, discrete models such as RocFall can be used[6]. These models are based on representation of debris
flows as a cluster of material points or solid bodies.
Previously, in the chosen valley debris flow of 2000year modeling was conducted with the use of discrete
DEBRIS model [7]. A one-dimensional two-phase
continuous Bozhinsky–Nazarov model based on theequations of motion and continuity was also used [8].
However, these works do not present the dynamics ofdebris flow discharge from the moment of its formation
to the top of the alluvial fan.
The aim of this paper was to apply model chain toreconstruct debris flows of 2000 year in theGerkhozhan-Su river valley. Transport-shift model,developed by Yu.B. Vinogradov [9], was used for debris
flow origination site and sections of intense materialincrement. For the areas between these sectionshydrodynamic FLO-2D model [10] was applied. In thispaper transport-shift model was for the first time
adapted for the sections of intense solid material

increment in the river course, whereas earlier it was used
only for debris flow origination site [11-12].

2 Study area
The Gerkhozhan-Su river watershed is located on thenorthern macroslope of the Central Caucasus on theterritory of the Kabardino-Balkarian Republic, Russia.
The Gerkhozhan-Su River is the right tributary of theBaksan River and flows into it 124 km from the mouth.
The length of the Gerkhozhan-Su River is 12 km, thebasin area is equal to 76.3 km2 [13]. The average slopeof the course is 7°. The average and maximum
watershed elevations are 2760 and 4149 m, respectively.
The Gerkhozhan-Su river itself begins after theconfluence of the Kayaarty-Su and Saakashil-Su
tributaries at an altitude of 1665 m.
The basin of Gerkhozhan-Su river is among theNorth Caucasian regions with highest debris flow
hazard [14]. The debris flows in 18-25 July 2000 werethe most catastrophic [15].

* Corresponding author: viktoriiakurovskaia@gmail.com© 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, 05007 (2023)
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flows in the Gerkhozhan-Su river valley [20]. The
results showed the effectiveness of these models. A
distinctive feature of the debris flows in 2000 was thecatastrophic incision of the river course. In total, 6sections of material increment were identified in theriver course: 1 - the main debris flow origination site, 2- the area between the sandrs, 3 - the Western Canyon,
4 - the Upper Gorge, 5 - the Lower Gorge, 6 - theBuzulgan landslide and the lower valley cutting in thearea of the destroyed dam and 6 sections of solidmaterial accumulation (fig.1). For the sections ofmaterial increment transport-shift model was applied,since this model allows taking into account theincrement of solid material during flow formation [9].
Hydrodynamic model FLO-2D [10] was applied for
sections of material accumulation. The simulated flow
discharge was subsequently used as an input data for thetransport-shift model and vice versa.

Fig. 1. Location scheme of the Gerkhozhan-Su riverwatershed: 1 - boundaries of sections, 2 – rivers, 3 - debris
flow cone of 2000 event, 4 - the Gerkhozhan-Su watershed, 5- city of Tyrnyauz, 6 – altitude scalar, m.

3.1 Transport – shift model

One of the reasons of debris flow formation in 2000
could be release of water from the interglacial cavities[16]. A distinctive feature of the debris flows in 2000
was the catastrophic incision of the river course. During
the passage of debris flows in the middle part of thevalley, a new debris flow cut was formed, in some areas
the depth reached 20 m [17].

The transport-shift model is a one-dimensional and isintended for calculating high-density flows in theorigination site. The model was developed by Yu. B.
Vinogradov during Chemolgan experiments in 1971–
1975 [9]. The experiments were conducted in order toperform artificial debris flows in nature. The results ofmodelling of these artificial flows are in agreement withthe observed values [9]. The model is based onstatement that the increment in the solid flow along thedebris flow origination site is directly proportional to theinstability coefficient of the potential debris flow body,the elementary potential flow capacity and the index of
mudflow mass mobility. The main equation of thismodel is:𝑄𝜌0ln(𝑄𝜌0 + (𝜁𝜌0 + 𝜌)𝐺)𝜁𝜌0 + 𝜌𝑄−ln(𝑄 + (𝜁 − 𝜃пп )𝐺)𝜁 − 𝜃пп
𝑄𝜌0 + (𝜁𝜌0 + 𝜌)𝐺0
𝑄 + (𝜁 − 𝜃пп )𝐺0𝑙=[𝐴Fig. 2. Debris flow origination site. Photo by S.
Chernomorets, July 2000

𝑡𝑔𝛼
𝑔 𝑆𝑖𝑛𝛼[𝑄𝜌0 (𝜁 − 𝜃пп ) + 𝑄(𝜁𝜌0 + 𝜌)]
𝑡𝑔𝜑+ 𝑙0](1)

where l is the distance by the thalweg of the debris flow
source, m; l0 is the distance to the current reach, m; G issolid material discharge, m3/s; G0 is the initial value ofvariable G for a certain section and the result ofcalculation for the preceding one (for the first upstream
section, G0 = 0), m3/s; α is the slope of the thalweg ofdebris flow source, deg; Q is water discharge, m3/s; θmlis the volume ratio of water to solid matter at the yield(rigidity) point of the mixture of water and debris flowforming soils; ζ is the volume ratio of water to solid
matter in the potential debris flow massif,
dimensionless; g is the acceleration of gravity, m/s2 ; ρ0is water density kg/m3 ; ρ is the density of debris flowforming soils , kg/m3 ; А is proportionality factor, m/s2kg. The simulation results include a debris flow wavehydrograph, the flow density and velocity.
Obtained hydrograph was applied in FLO-2D modelfor the next section. Then the simulated hygrograph wasagain used in the transport-shift model. The amount of

According to estimates [18], debris flows volume
was approximately 2.1 million m3. In the river mouth anextensive debris flow cone about 2 km long and 0.7 km2
in area was formed [16]. As a result, the Baksan Riverwas blocked with a subsequent formation of dammedlake 2 km long and 0.6 km wide within the city of
Tyrnyauz [19]. The area of the lake was 0.55 km2, andthe maximum depth was 12 m. According to [19], therewere 42 buildings and a number of small structures in
the flood zone.

3 Materials and methods
In this study, chain of mathematical models was used
to estimate debris flows characteristics. Previously thischain of mathematical models was implied to assess theeffect of the present position of the Buzulgan rockslideon the conditions for the passage of possible debris

2

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solid material discharge (Go) for the previous section,
where FLO-2D model was applied, was identifiedaccording to this formula [9]:𝑄𝑐 = 𝑄 + (1 + ζ) ∗ 𝐺𝑜 (2)Where Qc is debris flow discharge from FLO-2D model,m3/s; Q is water discharge from FLO-2D model, m3/s; ζis the volume ratio of water to solid matter in thepotential debris flow massif, dimensionless. In thisresearch, the transport-shift model equations wereimplemented into FLOVI program in Python.

modeling in the downstream valley, as it was thesmallest one. The simulated flow density was 1492
kg/m3.
Table 1. Cases of debris flow-forming soils parameters in thetransport-shift model.

3.2 FLO-2D modelFLO-2D is two-dimensional hydrodynamic model
developed by J. O’Brien [10]. It is based on solving
Saint-Venan equations, which are widely used in studies
of water flows [21]. The motion of debris flow in FLO2D model is simulated under the assumption that debris
flows move as Bingham (viscoplastic) liquid [22]. Inputhydrograph from transport-shift model was divided intowater and sediment according to following formula[10]:
𝑄 = 𝑄𝑐 − (𝑄𝑐 ∗ 𝐶𝑣) (3)Where Qc is debris flow discharge from transport-shiftmodel, m3/s, Q is water discharge, m3/s ; Cv is sedimentconcentration, dimensionless.

№123ζ, dimensionless

00.20

ρ, kg/m3

2600

2600

1600Qmax, m3/s

2674

22The average flow velocity in the source was about
9.7 m/s. For the sections lying downstream, the samecase of parameters was used.

3.3 Initial data
The data on the relief for the modeling were taken froma 1:25000 map reflecting the situation in the valley
before catastrophic debris flows in 2000. The meanslope in the sections of intense material increment variesfrom 18° for the origination site to 6 ° for the last section.
Data from field trips, that were carried out immediately
after the disaster, were used during input hydrographconstruction [16]. The maximum water discharge wasset as 4 m3/s. Also, a number of numerical experiments
were carried out in the transport-shear model with achange in the parameters of the debris flow-forming
soils. The debris flow volume concentration in the FLO2D model was taken as 25%. Due to the fact that for thisbasin there are no measured values of rheologicalparameters required for modeling in FLO-2D, such as
viscosity and yield stress, we chose the parameters ofAspen Natural Soil, proposed by the authors [22].

Fig. 3. Simulated hydrographs at the selected sections: dottedlines – transport-shift model, continuous lines – FLO-2Dmodel.

There is a sharp increase in discharges already forthe 7 section and is approximately 231 m3/s. Further, forthe 9 and 11 sections an increase in maximum
discharges by about 1.8 times is observed.
At the top of the alluvial fan the maximum
discharge reaches 1007 m3/s (12 line). In [8], maximum
discharges were calculated using the flow cross-sectionin the contuit and flow velocity from the videomaterial;
the obtained discharges were 1356 m3/s at the meanvelocity of 11.3 m/s, 1764 m3/s at maximal velocity of
14.7 m/s and 936 m3/s at minimum velocity of 7.8 m/s.
The relative error between discharge obtained for theminimum velocity and the simulated maximum at thetop of the alluvial fan will be 8%. Difference between
simulated maximum discharge and value estimated at
the maximum velocity will be 757 m3/s, the averagevelocity will be 349 m3/s/. However, discharges
obtained from video material were determined for themost powerful waves observed on July 19th. Thus, thesimulated discharge value could be observed from 18 to
25 July. On the whole, the obtained results correspond

4 Results and discussion
Initial data for transport-shift model includes values ofa potential debris flow-forming soils, such as initialmoisture content (ζ) and density (ρ). Due to the fact thatthese data are not available, numerical experiments werecarried out for debris flow origination site (table 1).
According to the simulation results initial moisture
content of a potential debris flow-forming soils has thegreatest influence on the maximum value of debris flow
discharge. Maximum discharges for absolutely dry
massif and a massif filled with water differ by almost
2.8 times. An increase in the density of a potential debris
flow-forming soils by 600 kg/m3 leads to growth indischarges by 4 m3/s. The 3rd case was chosen for3

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to the generally accepted reconstructed flow pattern[16].

10. J.S. O'Brien, P.Y. Julien, W.T. Fullerton, J.
Hydraul. Eng. 119, 2 (1993)
11. V.A. Kurovskaia, S.S. Chernomorets, T.A.
Vinogradova, I.N. Krylenko, A.G. Gulomaydarov,
Y.Kh Raimbekov, IOP Conf. Ser.: Earth Environ.
Sci. 834, 012009 (2021)
12. V.A. Kurovskaia, S.S. Chernomorets, T.A.
Vinogradova, I.N. Krylenko, Kriosfera Zemli 26, 3(2022)
13. Surface water resources of the USSR:
Hydrological coverage, 8 North Caucasus(Gidrometeoizdat, 1964)
14. V. Perov, S. Chernomorets, O. Budarina, E.
Savernyuk, T. Leontyeva, Natural Hazards 88 (1Suppl.), (2017)15. I.B. Seinova, V.V. Popovnin, Ye.A.Zolotaryov,
Landslide News 14/15, (2003)
16. S.S. Chernomorets, Origination sites of debris
flow disasters: before and after (Scientific World,2005)
17. E.V. Zaporozhchenko, Coll. of sci. works of OJSC
“Sevkavgiprovodkhoz”, 15 (2002)
18. D.A. Petrakov, O.V. Tutubalina, S.S.
Chernomorets, I.V. Krylenko, Kriosfera Zemli 8, 3(2004)
19. I.V. Krylenko, D.A. Petrakov, O.V. Tutubalina,
S.S. Chernomorets, P.G. ZHuravleva, Materials of
glaciological studies, 96 (2004)
20. V.A. Kurovskaiaa, S.S. Chernomoretsa, I.N.
Krylenko, T.A. Vinogradova, M.D. Dokukin, E.V.
Zaporozhchenko, Water Resources 49, 1 (2022)
21. J.A. Cunge, F.M. Holly, Jr., A. Verwey. Practicalaspects of computational river hydraulics (Pitman
Advanced Pub. Program, 1980)
22. J.S. O’Brien, P.Y. Julien, J. Hydraul. Eng. 114, 3(1988)

5 Conclusions
The study assessed the possibility of chain modeling tocalculate discharges of catastrophic debris flows in theGerkhozhan-Su river valley in 2000. The river course
was divided into 12 sections depending on the observed
processes. Transport-shift model was applied for debris
flow origination site and sections of intense materialincrement, FLO-2D was used for the accumulation ones.
Several numerical experiments with various
parameters of a potential debris flow-forming soils wereconducted in the transport-shift model. According to thesimulation results initial moisture content plays the mostimportant role in the maximum discharge formation. In
this work modeling was conducted for the case ofabsolutely dry and low density a potential debris flowforming soils.
In general, the simulation results are in agreementwith the estimations of debris flows in 2000. Thus, thepossibility of applying the transport-shift model for
sections of intense material increment is confirmed. In
the future, the authors plan to model high-density debris
flows using various rheological parameters of the debris
flow block in the FLO-2D model.
The study was supported by the Russian Foundation for Basic
Research, project 20-35-90006 “Modeling of debris flows: acase study of the Pamir Mountains”, and was carried out under
State Assignment to Lomonosov Moscow State University(sections I.7 TsITIS 121051300175-4, I.10 TsITIS121051400038-1), Water Problems Institute, Russian
Academy of Sciences (0147-2019-0001 (TsITIS AAAAA18118022090056-0))

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