E3S Web of Conferences 415, 07008 (2023)
DFHM8

https://doi.org/10.1051/e3sconf/202341507008

Tensile stress development and critical behavior of a flexible
barrier
Miao Huo1* , Fucheng Huang1, Maojun Yang1, and Chenjie Jiang1
一1College of Water Conservancy and Hydropower Engineering, Sichuan Agricultural University, Ya’an city 625014, China
Abstract. A DEM numerical approach is employed to illustrate the critical stress development of athree-supporting cable flexible barrier under a large scale stony debris movement impact. A proper
linear parallel bond is applied to build the flexible barrier model. Critical state is presented bylowering the tensile resistance of the flexible barrier and steepening the channel slope. The tensilestress of the supporting cables is primarily studied. Results mainly indicate that the particlestructure contact is essential to the stress development. The bottom cable always exhibits larger
tensile stress due to the massive collision and compressive force of particles and the tensile force
exerted by the vertical cable-net joint system. On the other hand, the intermediate cable receives
lower collision and compressive force, resulting in smaller tensile stress. The bottom cableindicating numerous direct particle-structure contact part performs brittle failure, which isanalogous to the concentrated load feedbacks. The loading of the intermediate one reaches ductile
failure, reflecting the desirable effect of dispersing loads. This study suggests that practicalengineering should try to avoid massive boulder impact or reinforce the bottom cable in order toimprove the hazard prevention design.

1 Introduction
The flexible barrier shows its broad prospect inpreventing mountainous hazards such as rock avalanche,
landslide and debris flow. The critical state of flexible
barrier is key to verify the reliability. Increasing
research works have been taking the structural failure
into account. Albaba [1] analyzed load transfering
process of the supporting cable under the action ofdebris flow particles by DEM numerical simulation andrevealed that the stress of the anchor foundation was
related to the installation site, the energy dissipator andthe interception. CFD-DEM has been adopted tosimulate the flexible barrier without supporting cablebearing the debris-flow impact and it indicates thebreakage at middle section and end of the bottom net isthe commerce of failure [2]. Albrecht and Volkwein [3]studied the dynamic response of a flexible barrier withrhombic net structure subjected to boulder-impact, andthe failure characteristics of the structure underconcentrated load are described.
Previous studies have paved a solid way for thecritical state verification of flexible barrier. This study
aims to perform a rapid numerical analysis on flexible
barrier under critical debris-flow impact and to estimate
the stress development from initiated to final process.

2 Methodology
Collision of particles without fluid on the flexible
barrier is mainly studied through Particle Flow Code inthree dimension i. e. PFC3D, due to the dominate role ofsolid fraction in the impact mechanism [4]. The impact
scenario is demonstrated by a total solid volume of 400
m3 (apparent volume) accelerating along a inclined
chute and hitting the flexible barrier at the end of thechute (Fig. 1 and Table 1). Here we employ the particleparticle parallel bond (abbreviated as p. b.) to build thecable-net structure and set the net before the cables toensure the transferal force on the cables. Constrainted
particle size distribution is introduced (Table 2),
constituting a stony debris flow, and energy dissipatorcomponent is not planted, for simplified calculation.
Three identical-spacing cabes are employed to support
the net structure (Table 2) due to the elusive postion of
one cable that uniformly bears the distributed impact
load, and the mesh size of the net is equal to the
maximum grain size of the debris material based on an
open-type dam [5]. The theory of the bond technology
can be reviewed in the literature [6]. The initiation of
the debris particle is a dam-break technique and thenproduces a laminar flow through the rectangle-sectionchute to impact the flexible barrier model. The stress of
one cable can be monitored by the p. b.-stress module
which is invoked in the software. The tensile strength ofthe cable is lower than the actual yield strength in order* Corresponding author: huomiao@sicau.edu.cn© 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, 07008 (2023)
DFHM8

https://doi.org/10.1051/e3sconf/202341507008

to meet the critical state efficiently (Table 2). Moreover,
we use a conventional expression of safety factor K to
depict the structural behavior, especially the criticalstate as follow.
 pb
(1)
K
t
Where σpb and σt are the tensile resistance of p.b. (500MPa) and detected normal tensile stress, respectively.
Length(km)
0.025

Table 1 Dimension of the chute
Width
CrossTotal initiation
Slope
(m)
section (m) volume (m3)
16
45°
16×16
400

Table 2 Dimension of flexible barrier and debris flow
Diameter of Diameter of Cable Mesh
DensityObjective
3 cable/maximum net/minimum spacing size
(kg/m )
grain (mm)grain (mm) (m) (m)Flexible
5300
32
10
4
1.6
barrier
Debris2500
1600
30
particles

3 Results
The calculation duration is short and the total compute
time of this simulation is around 3 hours. Right before
the impact, the debris particle flow is around 3.4 m inmean thickness and 1.5 m per second in mean velocity,
forming an impact energy of approximately 810 kJ.
Then the particle interception rate (in weight) of thestructure is 69.14%.
The factor K of every p. b. node in the structure isdisplayed in Fig. 2, and major part of the top, immediate
and bottom cable, including the net structure is in
critical state but some part of the net is still in stable i. e.
very great value of K. Furthermore, large-particle
collision with the bottom cable is notable, leading initial
tensile damage at the left lateral point of the bottom
cable. Breakage practically extends from bottom to theimmediate as the impact processing.
The tensile stress of the bottom cable is always
greater than that of the intermediate cable. The stressincrement and the rupture of bottom cable are sharp andinstant, respectively, while it takes a long time span(around 8 seconds) for the immediate cable to reach the
failure state (Fig. 3).

Fig. 1. Diagram of numerical simulation: (a) profile of overall
impact scene (b) cross-section of the flexible barrier model (c)the elevation view of the flexible barrier from downstream siteand (d) grain distribution of the debris material.

4 Conclusion and implication
The critical state mainly stems from the bottom cablethat receives massive particle-collision, earth pressure
and the tensile force exerted by the vertical cable-net
joint system, and subsequently extends to global
structure as the impact loading, ending up to overall
failure. Stress developments indicate that the bottom
cable performs brittle-like rupture, while theintermediate reaches ductile failure and reflects thedesirable effect of dispersing loads. In practice, thelateral part of the bottom cable, enduring the sum ofimpact load along the cable, deserves mechanical careor reinforcement. As one kind of tension structures, theflexible barrier subjected to debris particle impact
would perform evident geometric nonlinearity. This
numerical simulation limits the yield strength of thecable, which seems not rigorous in the similarity
theorem. But the loading developments (of strength
limitation or not) before failure share the same trend,
and this numerical framework enables us to analyze theload response and failure rapidly. What’s more, only
several parameters and dimensions would be retyped to
study other relevant engineering cases.

2

E3S Web of Conferences 415, 07008 (2023)
DFHM8

https://doi.org/10.1051/e3sconf/202341507008

Fig. 2. The safety factor K distributed in the structure: (a) the initial impact stage and (b) the later impact stage of the critical impact.

Fig. 3. Tensile stress development of the cables.

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