E3S Web of Conferences 415, 06010 (2023)
DFHM8

https://doi.org/10.1051/e3sconf/202341506010

Deciphering controls for the impact of geophysical flows on a
flexible barrier: Insights from coupled CFD-DEM modeling
Yong Kong1, and Mingfu Guan1*
1Department of Civil Engineering, The University of Hong Kong, Hong Kong, SAR, China.

Abstract. Geophysical flows impacting a flexible barrier can create complex flows and solid-fluidstructure interactions, which are challenging to quantify and characterize towards a unified description.
Here, we examine the common physical laws of multiphase, multiway interactions during debris flows,debris avalanches and rock avalanches against a flexible barrier system using a coupled computational fluid
dynamics and discrete element (CFD-DEM) method. This model captures essential physics observed inexperiments and fields. The bi-linear, positive correlations are found between peak impact load and Fr or
maximum barrier deflection, with inflection points due to the transitions from trapezoid- to triangle-shaped
dead zones. Our findings quantitatively elucidate how flow materials (wet versus dry) and impact dynamics(slow versus fast) control the patterns of the identified bi-linear correlations. This work offers a physicsbased reference and insights for improving widely-used impact solutions for geophysical flows against
flexible barriers.

1 Introduction

2 Methods and model setup

Flexible barriers are increasingly used to mitigate debris
flows, debris/rock/snow avalanches, and rockfalls [1-3].
Determining the impact load exerted on a flexible
barrier is a fundamental issue in hazard mitigation. Still,it has not been directly measurable in experiments orfields over the past three decades [4-6]. The difficulty isrooted in capturing the multiphase, multiway flowbarrier interactions, where many mechanisms can work
simultaneously. Understanding such impact is thus ofdeep engineering and scientific importance.
The impact loads of geophysical flows on flexible
barriers are typically estimated by simplified [2, 3, 7]
and Froude-number-related analytical [8, 9] solutions.
Nonetheless, impact loads estimated by simplified
solutions in physical tests lack scrutiny but are
frequently referred to as reliable data for calibrating Frrelated analytical solutions [8, 9]. Alternatively, many
numerical methods, including continuum-based [10],discrete-based [11] and coupled frameworks [12, 13],have been developed to explore the impacts on flexible
barriers by geophysical flows. However, simplificationsof the solid-liquid flow dynamics [10, 11] and 3D
nonuniform, permeable flexible barriers [12, 13] have
prevented a deeper understanding of the underlying
relations and mechanisms behind the flow-barrierinteractions.
Towards a unified description of the impacts when
geophysical flows of variable natures against a flexible
barrier system, this study scrutinizes underlying
relations and mechanisms for widely-used solutions
based on direct, numerical measures of flow-barrier
forces and barrier load-deflection relations.

A coupled computational fluid dynamics and discreteelement (CFD-DEM) method is employed to probe thedynamics during geophysical flows against a flexible
barrier. A flexible barrier is modeled by DEM (Fig. 1a),while a debris flow is simulated as a mixture of discrete
particles and a continuous slurry by DEM and CFD (Fig.
1d), respectively. A two-way coupling scheme offers aunified way to describe the solid-liquid interactions in a
debris flow and between barrier components and debris
liquid. The motions of a particle are governed by
Newton’s equations, and the fluid is controlled by the
locally-averaged Navier-Stokes equation for each fluid
cell with the finite-volume method. Further details canbe found in our previous work [8, 14]. This method has
been benchmarked with classic geomechanics problems[14] and various engineering conditions [13, 15, 16, 17].
2.1 Modeling a flexible ring net barrier
A flexible barrier typically consists of a ring net, brakeelements, and cables (Fig. 1a-upper). It is modeled byassembling the main ring net, ten brake elements, andfive supporting cables (Fig. 1a-lower). The bottom andlateral edges of the top and middle cables are fixed,
mimicking the anchored boundaries. The Parallel Bond
Model [18] implemented in DEM is employed to model
all barrier components as connected nodal particles. For
example, interlocking rings are idealized as connected
nodal particles (Fig. 1b). Fig. 1c displays the local
deformations of cable-ring-ring connections, consistent
with field observations [3].

* Corresponding author: mfguan@hku.hk© 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, 06010 (2023)
DFHM8

https://doi.org/10.1051/e3sconf/202341506010

unified design diagram for flexible, slit and rigid
barriers. By contrast, this work focuses on elucidating
how flow materials and dynamics affect underlying
relations for impacts of geophysical flows on a flexible
barrier. Herein, the initial heights of viscous slurries in
DF, DA and RA cases are set to 0.3 m, 0.15 m and 0 m,
respectively. Clear differences in flow redirection,
separation and overtopping dynamics, and barrier
responses among DF, DA and RA cases can be observed
from Videos S1, S2 and S3 that can be permanently
archived at https://doi.org/10.5281/zenodo.6779488.

3 Results and discussion
3.1 Flow-barrier interactions and forces
Figs. 2a, 2b and 2c compare three key flow-barrierinteractions for debris flows against flexible barriers
observed between a large-scale flume test [6] with areduced-scale flexible ring net barrier (0.6m-high, 2mwide) and a DF case under Fr similarity. The numericalpredictions well capture experimental observations on
the deformed barrier at stages II, a certain volume of thefluid and small particles passing through the barrier atstages II and III, and the curved flow path at stage III.

Fig. 1. Model setup and a typical impact scenario. (a), (b) and(c) present a comparison between field photos and numericalsnapshots for the barrier, interlocking rings and local
deformation characteristics, respectively. (d) shows a debris
flow impacting the barrier, where split views display debris
fluid and gap-graded particles (back half-space) as well as
fluid streamlines and interparticle contacts (front half-space).

2.2 Model setup and simulated dynamics
We perform systematic simulations of Debris Flows(DF), Debris Avalanches (DA) and Rock Avalanches(RA) impacting a flexible barrier. A broad range of Fr(0.5 ~ 8.7) is produced with a pre-impact flow depth of~ 0.3 m and varying initial velocities 𝑣int = 0.5 m/s ~ 14
m/s. Fig. 1d shows a typical debris flow impacting a
reduced-scale flexible barrier (0.9m-high, 1.8m-wide)
constructed on an inclined channel with a slope of 20°,
capturing critical physical processes, such as flow
climbing, silting and retaining, the cable-ring-ringsliding, dewatering and small particles passing through.
Details of model geometry, debris-flow materials,
barrier models and simulation conditions can be foundin our newly published paper [8], which has complied aFig. 2. Comparisons between experimental observations [1]and a representative DF case (𝒗𝐢𝐧𝐭 = 6m/s) on key flowbarrier interactions: (a) frontal impact, (b) runup and (c)overflow. (d) presents temporal evolutions of flow-barrier
forces in this DF case.

Further, both the in-flow solid and fluid can exert
loads on a barrier, including solid-barrier contact force𝐹s−b and fluid-barrier interaction force 𝐹f−b , resulting in2

E3S Web of Conferences 415, 06010 (2023)
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solutions [8,9,15], with inflection points due to the shifts
from trapezoid- to triangle-shaped dead zones (Figs. 3b~ 3d). The boundaries of dead zones (runup surfaces) areroughly determined according to a velocity threshold[19], and details are presented in supplementary Fig. S1(https://doi.org/10.5281/zenodo.6779488). We refer theshifts of dead zones to identify the slow-to-fasttransitions of flow impact dynamics, which occurs at ahigher Fr with a larger solid fraction of impinging flows.
Further, the slope of Fr- 𝐹bPeak relations in DF cases
under fast impact dynamics is 7.7 times that under slow
impact dynamics, whilst this ratio is around 3 for RA
cases. Dry flows undergo a smaller bulk density and alonger energy-dissipative runup surface than wet flows(Figs. 3b and 3d). Further, grain shear stress is
considered more effective in energy dissipation than
fluid viscous shearing [20], and the viscous slurry may
enhance flow velocity and impact pressures bydecreasing the inter-particle friction [21] and dampening
particle collisions [22]. Our results highlight that thediscriminants of flow types (DF, DA or RA) and impact
dynamics (slow or fast) are crucial for predicting Fr𝐹bPeak relations, thereby enable potential improvementsof the Fr-related analytical solutions.

the total impact load 𝐹b . This enables direct measurethat delineates load components to 𝐹b from individualdebris-flow phases. Fig. 2d indicates that the peak valueof the fluctuating solid-barrier contact forces (183.2 kN)
is around nine times larger than that of the smooth fluidbarrier interaction forces (20.3 kN, see inset in Fig. 2d).
Thus, 𝐹s−b is the dominant debris-flow load contributor
on a flexible barrier. Moreover, solid particles also
trigger the first peak during the frontal impact (Fig. 2d),wherein the peak barrier load commonly occurs for rigid
countermeasures [2, 8]. In contrast, 𝐹bPeak appears
during overtopping for a flexible barrier (Fig. 2d),wherein flowing layer coexists with dead zones [16, 19](Fig. 2c). Therefore, 𝐹bPeak should be calculated as thesum of loads from the flowing layer and dead zone,
especially in designing multi-level flexible barriers.

3.2 Barrier load-deflection relations
Understanding barrier load-deflection phenomena isvital for evaluating peak impact, barrier deformation,and retainment capacity for practical designs. Notably,
the spring solution given by 𝐹b = 𝑘bn 𝐷h are investigatedin the estimates of impact loads [3,7], where 𝑘bn and 𝐷hrepresent the equivalent barrier stiffness and maximum
barrier deflection in the flow direction. We also present
the complex 𝐹b -𝐷h relations in supplementary Fig. S2(https://doi.org/10.5281/zenodo.6779488).

Fig. 4. A diagram showing the effects of flow materials andimpact dynamics on Max(𝑫𝐡 )-𝑭𝐏𝐞𝐚𝐤and Fr-𝒌𝐧𝐛 relations. The𝐛slow-to-fast transitions are consistent with Fig. 3.

Fig. 3. A unified diagram (a) show how flow types andimpact dynamics affect Fr-𝑭𝐏𝐞𝐚𝐤
relations. (b), (c) and (d)𝐛display free surfaces of flowing layers (dash lines) andboundaries of dead zones (dash-dotted lines) measured atpeak impacts for DF, DA and RA cases near the slow-to-fasttransitions in (a), respectively. 𝒉𝐛 and 𝒙𝐛 denote the heightand x-axis location of the barrier, respectively.

Fig. 4 presents the influences of flow types andimpact dynamics on Max(𝐷h )-𝐹bPeak relations, revealing
the bi-linear, positive correlations. Max(𝐷h ) and 𝐹bPeak
are crucial designing factors and positively correlatedwith Fr. Further, fast impact dynamics witness a higher
slope of Max( 𝐷h )- 𝐹bPeak relations than slow impact
dynamics. Because trapezoid-shaped dead zones (slow)

Fig. 3a witness the bi-linear, positive Fr- 𝐹bPeak
relations that underpin widely-used Fr-related analytical3

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undergo longer energy-dissipative runup surface andlarger volume of trapped debris than the triangle-shaped
ones (fast, Figs. 3b ~ 3d). The slope of Max(𝐷h )-𝐹bPeak
relation in dry cases under either slow or fast impact
dynamics is around half that in wet cases, owing tohigher energy-sinking efficiencies of flowing layer anddead zone in dry flows. For DF and DA cases, similar
trends of Max(𝐷h )-𝐹bPeak relations are observed, while
the magnitudes of Max(𝐷h ) and 𝐹bPeak in DA cases are
smaller than in DF cases under similar Fr. These results
indicate that flow materials (wet or dry) primarily
control the trend of Max(𝐷h )-𝐹bPeak relations, while alarger bulk density in a wet flow produces moresignificant Max(𝐷h ) and 𝐹bPeak under similar Fr.
The inset in Fig. 4 also witnesses the bi-linear,positive correlations between Fr and 𝑘bn . Under fast
impact dynamics, 𝑘bn increases rapidly with increasing
Fr in all cases, wherein RA (dry) cases present theminimum slope. It indicates that 𝑘bn changes with flow
materials and Fr conditions under fast impact dynamics,
regardless of the same barrier. Under slow impact
dynamics, 𝑘bn is roughly constant in either dry (RA: ~0.26 MN/m) or wet cases (DF: ~ 0.39 MN/m; DA: ~0.38 MN/m). Thus, the hypothesis of constant 𝑘bn inspring solution is justified under slow impact dynamics,
whereas its rationality is not guaranteed under fast
impact dynamics or with different impinging flows.

2.

C. W. Ng, D. Song, C. E. Choi, L. H. D. Liu, J. S.
Kwan, R. C. H. Koo, W. K. Pun, Can. Geotech. J.
54(2), 188-206 (2017) doi: 10.1139/cgj-2016-0128
3. C. Wendeler, Debris-flow protection systems for
mountain torrents. WSL. (2016)
4. J. S. DeNatale, R. M. Iverson, J. J. Major, R. G.
LaHusen, G. L. Fiegel, J. D. Duffy, Open-File
Rep. 99-205 (1999) doi: 10.3133/OFR99205.
5. L. Bugnion, B. W. McArdell, P. Bartelt, C.
Wendeler, Landslides 9(2),179-187 (2012) doi:
10.1007/s10346-011-0294-4.
6. H. Vicari, C. W. Ng, S. Nordal, V. Thakur, W. R.
K. De Silva, H. Liu, C. E. Choi, Can. Geotech. J.
59(6) (2022) doi: 10.1139/cgj-2021-0119
7. W. Ashwood, O. Hungr, Can. Geotech. J. 53(10),1700-1717 (2016) doi: 10.1139/cgj-2015-0481
8. Y. Kong, M. Guan, X. Li, J. Zhao, H. Yan, J.
Geophys. Res. Earth. Surf. 127(6) (2022) doi:
10.1029/2021JF006587
9. D. Song, Zhou, X. Q. Chen, X. Q. J. Li, A. Wang,
P. Peng, K. X. Xue, Eng. Geol. 288 (2021) doi:
10.1016/j.enggeo.2021.106154
10. L. Zhao, J. W. He, Z. X. Yu, Y. P. Liu, Z. H.
Zhou, S. L. Chan, Landslides 17(12), 2723-2736(2020) doi: 10.1007/s10346-020-01463-x
11. A. Albaba, S. Lambert, F. Kneib, B. Chareyre, F.
Nicot, Rock Mech. Rock Eng. 50(11), 3029-3048(2017) doi:10.1007/s00603-017-1286-z
12. A. Leonardi, F. K. Wittel, M. Mendoza, R. Vetter,
H. J. Herrmann, Comput-Aided Civ. Inf. 31(5),323-333 (2016) doi: 10.1111/mice.12165
13. Y. Kong, X. Li, J. Zhao, Eng. Geol. 289, 335-349(2021) doi: 10.1016/j.enggeo.2021.106188
14. J. Zhao, T. Shan, Powder Technol. 239, 248-258(2013) doi: 10.1016/j.powtec.2013.02.003
15. X. Li, J. Zhao, K. Soga, Géotechnique 71(8), 674685 (2021) doi: 10.1680/jgeot.18.P.365
16. Y. Kong, J. Zhao, X. Li, Powder Technol. 386,
335-349 (2021) doi:10.1016/j.powtec.2021.03.053
17. X. Li, J. Zhao, J. S. Kwan, Comput. Geotech. 128(2020) doi: 10.1016/j.compgeo.2020.103850
18. D. O. Potyondy, P. A. Cundall, Int. J. Rock Mech.
Min. Sci. 41(8), 1329-1364 (2004) doi:
10.1016/j.ijrmms.2004.09.011
19. T. Faug, R. Beguin, B. Chanut, Phys. Rev. E 80(2)(2009) doi: 10.1103/PhysRevE.80.021305
20. J. Fang, L. Wang, Y. Hong, J. Zhao, Géotechnique
72(5), 391-406 (2022) doi: 10.1680/jgeot.19.P.160
21. H., Zheng, Z., Shi, T., de Haas, D., Shen, K. J.,
Hanley, B. Li, J. Geophys. Res. Earth. Surf. 127(3)(2022) doi: 10.1029/2021JF006488
22. R. Kaitna, M. C. Palucis, B. Yohannes, K. M. Hill,
W. E. Dietrich, J. Geophys. Res. Earth. Surf.
121(2) (2016) doi: 10.1002/2015JF003725
23. R. M. Iverson, M. E. Reid, M. Logan, R. G.
LaHusen, J. W. Godt, J. P. Griswold, Nat. Geosci.
4(2), 116-121 (2011) doi: 10.1038/ngeo1040

4 Conclusions
This work presents systematic simulations of a flexible
barrier system against geophysical flows of variable
natures to identify underlying relations and mechanismsof the multiphase, multiway interactions. The employed
fluid-solid coupling model captures essential physics
observed in experiments and fields.
Physics-based numerical measures of flow-barrier
forces and barrier load-deformation behaviors reveal thebi-linear, positive relations underpinning widely-used
impact solutions, with inflection points caused by thetransitions from trapezoid- to triangle-shaped deadzones. Specifically, the identified correlations relate thepeak impact load to Froude-number or maximum barrier
deformation. Our findings facilitate determining theimpact loads of geophysical flows on flexible barriers
based on flow materials (wet versus dry) and impact
dynamics (slow versus fast).
Future work may explore the existence of similar
relationships regarding the complexity of geophysicalflows, including huge boulders [1], varying flow heights[3], and erosion [23].
The research reported in this study is financially supported by
the National Natural Science Foundation of China (Project#51909227) and the University Grants Council of Hong Kong
(RGC/GRF Project #27202419).

References
1.

R. M. Iverson, Rev. Geophys. 35(3), 245-296(1997) doi: 10.1029/97RG00426

4