E3S Web of Conferences 415, 06016 (2023)
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https://doi.org/10.1051/e3sconf/202341506016

Coupled Eulerian-Lagrangian Debris Flow Model with Flexible
BarrierShiyin Sha1, Ashley P. Dyson1, Gholamreza Kefayati1, and Ali Tolooiyan1*
1 Computational Engineering for Sustainability Lab (CES-Lab), School of Engineering, University of Tasmania, Hobart, 7005,

Australia

Abstract. Natural hazards such as large debris flow events can have catastrophic effects on theenvironment and critical infrastructure, posing a significant threat to human life. Debris flows often exhibithigh velocity, high-pressure discharges due to their bulk volume, and the capacity to transport considerable
volumes of large rocks, boulders, and woody debris. Although debris flow run-out simulations arecommonly performed using hydraulic modelling software, these environments are seldom capable ofassessing the interaction between the debris fluid, transported material, and protective structures. In thisresearch, large deformation numerical models are calibrated using input parameters from hydraulicmodelling software. Due to the computational cost of the large deformation models involving fluid-solidstructure simulation with flexible net barriers, an equivalent stiffness method is implemented to provide
comparable performance through a membrane structure. The Coupled Eulerian-Lagrangian Finite Element
method is used to model the impact forces of rocky boulders on the membrane, exhibiting damage
characteristics consistent with flexible ring-net protective structures. The Coupled Eulerian-Lagrangianmodel results highlight the performance of the simplified membrane, as shown through a benchmark
simulation of debris flow with boulders.

1 Background
Debris flow events are a perilous form of landslide dueto their high velocity, considerable impact forces andlong-runout distances. It is considered to be a mixture ofsoil and water, coupled with detritus such as gravel,boulders and driftwood. To mitigate potential debris
flow hazards, two categories of protective structures arecommonly implemented: rigid structures such as checkdams, fences and racks, and flexible barriers such as
wire ring nets, hexagonal nets, and water drop-shaped
meshes.
In recent times, advanced Finite Element Method(FEM) techniques have been developed to overcome
convergence issues for large deformation analysis bycombining Lagrangian and Eulerian methods. At areasonable computational cost, numerical methods suchas Coupled Eulerian-Lagrangian (CEL) can evaluate
large deformation behaviour while accurately capturing
fluid-structure interactions. The CEL method has been
applied to a range of geotechnical applications,including soil slope stability analysis [1], in-situ cone
penetration tests [2] and large deformation geotechnicallaboratory tests [3]. Several studies have employed CEL
to simulate debris flow, including Crosta et al. [4] andSha et al. [5], where the advantages of the CEL method
were demonstrated for debris flow simulations, avoiding
mesh distortion and modelling multiple materials.
Similarly, Jeong and Lee [6] employed the CEL method

to simulate a check dam subjected to debris flow, taking
into account the entrainment of the sediment, whereby it
was concluded that the method performs well in
simulating the dynamic impact force acting on the rigid
or deformable structures. It is worth noting that current
research has predominantly focused on flow behaviour
and entertainment within the sedimentary soil layer
rather than fluid-structure interaction. In terms ofmodelling flexible barriers, a number of scholars haveintroduced several approaches to simplify complicatedmodels by using shell or membrane elements [7-10].
However, these simplified models are rarely wellstudied and developed, especially for the simulation offlexible ring nets subjected to debris flow with various
shapes of boulders.
In this research, an equivalent simplified numericalmodel using membrane elements (referred to as amembrane model) is proposed as an efficient alternativeto the more traditional numerical model using beam
elements (called a ring net model). Several benchmark
analyses, including direct tensile tests, sphere/cylinder
loading tests, and sphere drop tests, were performed on
the ring net model to map the deformation-force curves
and the failure loads for calibration and validation of themembrane model. The CEL method was employed tosimulate the interaction between debris flow material
and the flexible barrier in the ABAQUS/Explicit [11]modelling environment. The performance of the flexible
barrier with membrane elements subjected to debris* Corresponding author: Ali.Tolooiyan@utas.edu.au© 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, 06016 (2023)
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flow incorporating boulders was investigated, indicatingthat such a numerical approach can be efficientlyapplied, replacing complex models of flexible ring nets
while significantly reducing the computational cost.

2 Numerical Models and Validation
2.1 Modelling of debris flow
The initial model geometry for the CEL debris flow
model to be simulated is provided in Fig. 1, material
parameters summarised in Table 1 [5]. The debris flow
is modelled with the Bingham visco-plastic material,
behaving as a solid at low stresses and a viscous fluid at
higher stress levels. The bedrock over which the debris
flows is modelled as a rigid body, while the check dam
in the path of the viscous fluid is considered linear
elastic, with a fixed base tied to the bedrock. In thesimulation of both the bedrock and check dam,ABAQUS Explicit type C3D8R 8-node linear brickreduced elements were used. EC3D8R 8-node Eulerianlinear brick reduced elements were implemented tosimulate CEL Eulerian behaviour.
To examine the performance of the simulation
methods, the results of CEL simulations were comparedwith numerical simulations performed by Joeng and Lee[6]. As shown in Fig. 2, the impact pressures wereobtained from 16 nodes with an interval of 0.05 m
placed along the central line on the check dam atsimulation times of 2.5 seconds for the CEL simulations,providing good agreement with the results of Joeng andLee.

Fig. 2. Comparison of model impact pressures with Jeongand Lee [6].

2.2 Modelling of flexible ring net
The modelled flexible ring net is made of 11 × 11 plus
10 × 10 steel wire rings (221 rings in total) with a single
ring diameter (d0) of 14.6 mm and an internal diameter(D) of 300 mm. Each wire ring is modelled using 8elements beam elements and is attached to four separate
rings within the net by 8 nodes, in which 4 nodes arefrom the ring itself, and the other 4 are from the fourattached rings, as shown in Fig. 3a to 3c. To simulate thering-to-ring contact properly, the pin type of MultiplePoints Constraint (MPC) is used to connect the twopoints between every two rings. This type of MPC
provides a pinned joint between two nodes, making theglobal displacements equal but leaving the rotation.
As discussed, finite membrane elements have beenpreviously used to simulate flexible ring nets [10, 12,13]. To do so, the equivalent model is idealised as aclosed homogeneous surface discretised with planestress finite membrane elements. As shown in Figure 3d,
the nodes (shown in red) are defined as boundary points
at which translation fixities are applied. Therefore, thered dashed square region can be considered as theeffective area of the ring net that undergoes impact loads
and deformation. Hence, the length of the effective area
(Le=4.455 m) can be used as the geometrical size of themembrane model (Fig. 3e). The key geometry andmaterial parameters for the ring net model and themembrane model are referred to [14].
Based on the performance of the ring net model, themembrane model is calibrated and verified through aseries of analyses, including direct tensile tests,
sphere/cylinder loading tests, and sphere drop tests. The
equivalent elastic modulus and tensile strength of themembrane model are calibrated based on the results of
the reaction force and deformation obtained from FEM
analyses of the ring net model, providing a good
agreement with the behaviour of the membrane and ringnet models, as shown in Fig. 4.
To investigate the computational efficiency of themembrane model, the processing time of the simulation
for the two models is compared in Fig. 5. As shown inthis figure, the simulation of the membrane model isalmost 9 times more cost-efficient than the ring net
model. Considering the agreements between the ring net

Fig. 1. The geometry of the debris flow model.
Table 1. Material parameters [5].
Material parameter

Debris flow

BedrockCheckdamConstitutive model

Bingham

RigidbodyLinearelastic

Density ρ (kg/m3)
Young’s Modulus E(GPa)Poisson’s ratio ν
Yield stress τy (Pa)Viscosity η (Pa·s)

1500-2500--

24100
100-

0.25-

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and membrane models found from the direct tensile,loading and drop tests, also considering the substantial
computational efficiency of the membrane model, it isconcluded that the proposed membrane model can beused as a reliable, accurate and efficient alternative forthe simulation of flexible ring net barriers.

Fig. 5. Comparison of the computational cost between thering net and membrane models in the sphere drop test.

3 Benchmark Simulations of Debris
Flow Incorporating Boulders
The geometry for the CEL debris flow model with arandomised assortment of boulder shapes, orientations
and locations is provided in Fig. 6. As discussed inSection 2.1, the debris flow is modelled with theBingham visco-plastic material, behaving like a solidwhen stresses are low and a viscous fluid when the yieldstress is reached. The ramp and boulders are modelled
as rigid bodies, while the membrane barrier is identicalto the membrane model discussed in Section 2.2. To
simulate both the ramp and boulders, Abaqus Explicit
type R3D4 4-node 3-D bilinear rigid quadrilateralelements were employed. EC3D8R 8-node linear
Eulerian brick elements with reduced integration andhourglass control were used to simulate CEL Eulerian
behaviour.
The membrane barrier is treated as a flexible ring net
barrier. In this case, it is assumed that there is nointeraction between the debris flow and the membranebarrier, which means the debris flow can pass throughthe barrier, as is expected for a ring-net barrier.
Furthermore, these two components indirectly interact
through a proxy interaction with the boulders, as eachcomponent exhibits a boulder contact definition, thereby
transmitting hydrodynamic forces to the protectivestructure. A contact penalty definition with a friction
coefficient of 0.1 was chosen for the contact between theboulders and both the debris flow and membrane barrier.
A gravity load was applied to the model. To investigate
the impact of the flow velocity on the performance ofthe membrane model, continuous initial flow velocitiesof 1 m/s, 3 m/s and 5 m/s were applied in threesimulations. A duration of 6 seconds was simulated foreach case.
Fig. 7 presents the reaction forces imposed by theboulders on the barrier at three different flow velocities.
From this Figure, the peak impact force generated byboulders is 29, 69, and 103 kN at the simulation time of
5.8, 2.7, and 2.1 seconds for the cases with flow
velocities of 1, 3 and 5 m/s, respectively. Based on thesimulation results, the faster the flow velocity acted on
the boulders, the higher the impact force imposed on thebarrier. However, as the boulders vary in size, weight,Fig. 3. Specifications of the ring net model: (a) Single wirering; (b) Ring-to-ring contact; (c) Flexible ring net (L=4.543m); (d) Effective area of the ring net model (red dashedsquare, Le=4.455 m); (e) Equivalent simplified model(membrane model).

Fig. 4. Comparison of the force and deformation response of
the ring net model and the membrane model: (a) the direct
tensile test; (b) the loading test; (c) the sphere drop test.

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and location, the reaction forces obtained from each caseshow irregular fluctuations with time.

faster the flow velocity acted on the boulders, the higher
the peak impact force imposed on the barrier.
Financial support for this research has been provided by
Natural Disaster Risk Reduction Grants Program (NDRRGP)
as part of the Australian Government National Disaster Risk
Reduction Framework (NDRRF) and the Tasmanian
Government Disaster Resilience Strategy, in partnership withthe Tasmanian State Emergency Services (TSES). The firstauthor is funded by the Australian Government ResearchTraining Program (RTP).

ReferencesFig. 6. Geometry of debris flow with boulders model.

1.
2.
3.
4.
5.
6.
7.

Fig. 7. Reaction force versus time at various flow velocities:(a) 1 m/s; (b) 3 m/s; (c) 5 m/s.

8.

4 Conclusions

9.

Numerical simulation of large deformation problems fordebris flow is a challenging task that often requires
complex numerical methods commonly attributed tocomputational fluid dynamics such as CEL. As one ofseveral protective structure types applied for mitigating
debris flow, flexible netting barriers exhibit complex
nonlinear behaviour when subjected to dynamic
impacts. Although flexible barriers are widely used inengineering practice, the analysis of flexible netting
models using an equivalent simplified model has notbeen well studied in the literature. In particular, theinteraction between flexible barriers, debris flow fluids
and boulders has been rarely investigated. In thisresearch, a simplified model for the simulation offlexible net barriers was proposed, and its performance
was studied comprehensively through several numericalanalyses.
The simulation results highlight the performance ofan equivalent stiffness model using membrane elements,
showing good agreement with the ring net model
regarding force-displacement response. Based on theperformed fully dynamic sphere drop test, the proposed
membrane model can be efficiently applied to replacecomplex models of flexible ring nets and significantly
reduce the computational cost. In addition, a benchmark
analysis was conducted to investigate the proposed
membrane model subjected to debris flow with boulders
at various flow velocities. The results showed that the10.
11.
12.
13.
14.

4

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