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# Scale Effect: Numerical Modeling of Net Barriers in Torrents

Shuo Li, Guillaume Piton, Franck Bourrier

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## To cite this version:

Shuo Li, Guillaume Piton, Franck Bourrier. Scale Effect: Numerical Modeling of Net Barriers in Torrents. 2018. hal-02871091

HAL Id: hal-02871091

https://hal.inrae.fr/hal-02871091

Preprint submitted on 17 Jun 2020

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Distributed under a Creative Commons Attribution 4.0 International License
SCALE EFFECT:
NUMERICAL MODELING OF NET
BARRIERS IN TORRENTS

LI Shuo

Supervisor: Bourrier Franck, Piton Guillaume

<figure><img src="image_4.png" /></figure>
[Abstract]

Some geohazards such as landslides and debris flow, which have already caused millions of
dollars in damage and thousands of deaths and injuries each year, are regarded as a serious
threat to humans and infrastructures. Therefore, studies on the design of structural mitigation
measures and the related numerical simulation on barriers deformation against debris flow is of
crucial importance in terms of engineering application. Motivated to clarify the mechanisms
underlying rope nets deformation behavior and further establish a theoretical model for
determining an appropriate material under experimental conditions, a series of numerical
simulations using an extensive open-source framework called Yade DEM along with its discrete
element method (DEM) is being performed by generating a rope net within certain physical
properties under different loading conditions on the net nodes. To further understand this
behavior, in this paper the scale effect and buckling effect are investigated by Bunkingham-pi
theorem and plastic structure respectively. It is found that, a consistent impact of simple load
on the net central deformation characteristics (e.g. absolute and relative displacement) under
different scales are observed. And the efficiency of basic model including five dimensionless
parameters to investigate the scale effect by similarity analysis is confirmable. And the net
deformation of a chosen material (PSU) under a small scale (1:30) is in accordance with that of
the theoretical material which is defined by basic model. In addition, it seems that, to improve
the performance of net barrier against debris flow, the plastic flat region as shown in strain-
stress curve should be larger than a certain value. Knowledge and evidence from this work
might be utilized for the development and verifications of theoretical model and barriers
structure design in the future.

[Keywords]: Debris flow; Net barrier; Numerical simulation; Similarity analysis; Discrete Element Method
# Contents

<table><tr><td>1. Introduction</td><td>1</td></tr><tr><td>2. Physical model and calculated conditions</td><td>3</td></tr><tr><td>2.1 Simulation method: Discrete element method</td><td>3</td></tr><tr><td>2.2 Determination of analytical geometry and theoretical model</td><td>5</td></tr><tr><td>2.3 Summary</td><td>8</td></tr><tr><td>3. Discussions of calculated results</td><td>9</td></tr><tr><td>3.1 Qualitative analyses of calculation</td><td>9</td></tr><tr><td>3.2 Quantitative analyses of net deformation without braking devices</td><td>10</td></tr><tr><td>3.3 Quantitative analyses of net deformation within braking devices</td><td>13</td></tr><tr><td>3.4 Summary</td><td>18</td></tr><tr><td>4. Conclusions and perspectives</td><td>19</td></tr><tr><td>References</td><td>21</td></tr><tr><td>Acknowledgements</td><td>22</td></tr><tr><td>Annex</td><td>23</td></tr></table>
# 1. Introduction

In mountain areas, some geohazards such as landslides and debris flow, which have already caused millions of dollars in damage and thousands of deaths and injuries each year, are regarded as a serious threat to humans and infrastructures [1-2]. In response to these catastrophic events, a series of physical experiments and numerical modeling of landslides and debris flows are carried out by researchers and engineers in order to understand the mechanism underlying this behavior. For the last few years, more and more rope net barriers, which has been regarded as a quite simple building structure including a few lightweight materials, are used to entrap woody and rocky debris in such some torrents [3]. The design of structural mitigation measures and the related numerical simulation on barriers deformation against debris flow is of crucial importance in terms of engineering application.

Unfortunately, over the past decades, although extensive studies have been performed on the rope nets deformation against debris flow (as depicted in Fig.1), most of them generally focused on the phenomenological studies and development of empirical models on the loading conditions [4-5]. Noticing that due to the existence of scale effect [6-7], during the rope nets deformation against debris flow, the traditional material using stainless steel under actual conditions could possibly not be in accordance with that of experimental conditions. Thus, during the rope nets deformation within a quite small scale, the scale effect should be clarified in detail and an appropriate material based on the developed theoretical model should be also taken into consideration.

<figure><img src="image_5.png" /><figcaption>Figure 1. Schematic view of rope nets barriers. [8]</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>Figure 2. A real metallic net structure within the braking device [9].</figcaption></figure>

In addition, it is instructive to note that, to dissipate a part of energy by friction and buckling effect, a specific protection system, called braking device, are dedicated in the net structure design as depicted in Figure 2. D. Bertrand et al. [9] are one of the representative authors who investigate this structure by a specific experimental setup. In their studies, the dynamic tensile test has been performed by dropping a boulder from a given height, and the evolution of force inside the cable as a function of displacement shows that the fluctuation of force corresponding to buckling of the steel tube appears once the force reaches a peak value (~100kN). Therefore, in our studies, we should also concentrate on the simulation of buckling effect on braking device.

Motivated to establish and verify a theoretical model for determining an appropriate material under experimental conditions, a series of simulation is being performed by generating a rope net within certain loading conditions on the net nodes. And an extensive open-source framework based on discrete element method (DEM) called Yade DEM is used. Here, it should point out that, according to Rimbock's work [8], as compared to hydro-static and dynamic pressure, the boulder impact load is not predominant in rope net barriers, thus in this study, only the effect of hydraulics is being considered in the load. The basic simulation methods and physical models are described briefly in Section 2. In Section 3, the obtained results and further similarity analyses are discussed in detail.
## 2. Physical model and calculated conditions

In this Chapter, a physical method DEM and the related calculated conditions are discussed in detail. In this project, we use Yade DEM, an extensible open-source framework, to achieve the whole simulation and mechanical postprocess by changing the material properties, geometry size and loading conditions, then Origin Pro to do the data analyses and curve display.

### 2.1 Simulation method: Discrete element method

Discrete element method was firstly introduced and extended by Cundall and Strack et al. [10] in 1979. In fact, to model the response of granular assemblies to dynamical or quasi-static loadings, there are a lot of difficulties by continuous approaches. Firstly, the continuous medium hypothesis in elastic mechanics is based on small deformation assumption, thus the traditional model could not be used in some cases in which some large strains and displacements are observed. Secondly, the continuous theory is difficult to handle with the contact and breakage problems by finite element method because of mesh generation limit. Besides, some constitutive models which could represent the local interactions is also complex. Thus, DEM is quite efficient to simulate the interaction between granular material.

<figure><img src="image_7.png" /><figcaption>Figure 3. General calculation cycle of discrete element method</figcaption></figure>

In DEM, a finite different scheme is used in which the position of the particles is calculated by integrating Newton’s second law over certain time steps. As shown in Fig. 3, the general calculation cycle could be divided into four steps: Firstly, after generating the calculated
geometry, the contact force applied on all particles begins to be detected. Secondly, the contact force is decomposed into a normal component acting in the direction of the normal vector and a tangential component acting in the contact plane, which will be updated to each body. Thirdly, the acceleration of each body is calculated by Newton's second law, then the velocity and displacement of each particle could be obtained. Finally, the particle position and existing contacts will be updated and redetected respectively, and the calculation cycle could start.

The Newton's law for each body could be expressed by the following equation:

$$F_i = m_i x_i$$

where $x_i$ and $F_i$ represent the position and resultant force of particle i respectively.

Then, the angular motion could be expressed:

$$M_i = I_i \ddot{\omega}_i$$

where is $M_i$ the resultant moment and $I_i$ is moment of inertia.

Then the explicit scheme is adopted to integrate the two parameters over a time step which could be expressed as following equations:

$$\dot{x}_{i,t+\frac{\Delta t}{2}} = \dot{x}_{i,t-\frac{\Delta t}{2}} + \frac{F_{i,t}}{m} \Delta t$$

and

$$\dot{\omega}_{i,t+\frac{\Delta t}{2}} = \dot{\omega}_{i,t-\frac{\Delta t}{2}} + \frac{M_{i,t}}{m} \Delta t$$

The new position of each particle is given by:

$$x_{i,t+\frac{\Delta t}{2}} = x_{i,t} + \dot{x}_{i,t+\frac{\Delta t}{2}} \Delta t$$

and

$$\omega_{i,t+\frac{\Delta t}{2}} = \omega_{i,t} + \dot{\omega}_{i,t+\frac{\Delta t}{2}} \Delta t$$

In the same ways, the contact law could be explained as the interaction between two spheres as following:

$$F_n = k_n u_n,$$

$$dF_s = k_s \dot{u}_s dt,$$

$$M_t = k_t \Omega_{12}^t,$$

$$M_b = k_b \Omega_{12}^b,$$

where $F_n$ is normal force, $dF_s$ is shear force increment, $M_t$ is twisting moment and $M_b$
is bending moment, $k_n, k_s, k_t$ and $k_b$ are the elastic stiffness associated respectively to the normal force, the shear force, the twisting moment, and the bending moment.

In the simulation presented in this paper, the moments are not considered for contacts between spheres ($k_t = k_b = 0$), and the normal and tangential stiffness are related to a macroscale stiffness:

$$k_n = \frac{2E_c R_1 R_2}{R_1 + R_2},$$

$$k_s = \alpha k_n,$$

where $\alpha$ is a non-dimensional factor, $R_1$ and $R_2$ are the radius of interacting particles.

In addition, it is convenient to define the maximum forces and moments with reference to shear and tensile strengths $\sigma_s^l$ and $\sigma_n^l$, which have the dimension of a stress. Therefore, the following conditions are imposed:

$$F_n \le \sigma_n^l A,$$

$$||F_s|| \le F_n \tan(\varphi_c) + \sigma_s^l A,$$

$$M_b \le \frac{I_b \sigma_n^l}{R_c},$$

$$M_t \le \frac{I_t \sigma_s^l}{R_c},$$

where $R_c$ is the minimal radius of interacting particles, $A$ is the reference surface area, $I_b$ and $I_t$ are the reference bending moment and polar moment of inertia respectively.

## 2.2 Determination of analytical geometry and theoretical model

Figure 4 illustrates the calculated geometry in the present simulation. A variety of physical quantities to determine net geometry is defined, including cell size $a$, rope diameter $d_{rope}$, net length $L$ and net height $h$. It should be noted that, to simplify the problem and model, the net height is considered the same as fluid height. To get a comprehensive understanding of net deformation, Buckingham-pi theorem is introduced, which is considered as a key theorem in dimension analysis.

For a physical system which could be described by a meaningful equation as following:

$$f(q_1, q_2, \dots, q_n) = 0,$$
where the $q_i$ are the $n$ physical variables, and they could be expressed by $k$ independent physical units, then the above equation could be restated as

$$F(\pi_1, \pi_2, \dots, \pi_n) = 0,$$

where the $\pi_i$ are dimensionless parameters constructed from the $q_i$ by $p (= n - k)$ dimensionless equations of the following forms:

$$\pi_i = q_1^{a_1} q_2^{a_2} \dots q_n^{a_n},$$

In this way, five dimensionless parameters could be defined as following:

$$\pi_1 = \frac{E}{v^2 \rho_e}, \pi_2 = \frac{gh}{v^2}, \pi_3 = \frac{L}{h}, \pi_4 = \frac{a}{h}, \pi_5 = \frac{d_{rope}}{h}$$

where E is the material stiffness, v is the fluid velocity, and is the gravity acceleration.

<figure><img src="image_8.png" /><figcaption>Figure 4. Analytical geometry used in the present simulation.</figcaption></figure>

The dimensionless parameters are used to define a theoretical material which could eliminate the scale effect, hence they should be constant when the dimension of rope net changes. Under actual conditions (scale 1:1), the stainless steel is generally used to constitute rope nets. As shown in Table 1, according to this basic model, a theoretical material in which some physical parameters (i.e. Young's modulus and net dimensions) varies as the scale of nets changes.
<table><caption>Table 1. Physical parameters according to basic model</caption><thead><tr><th>Case NO.</th><th>Scale ratio</th><th>Young's modulus<br><i>E</i> (MPa)</th><th>Fluid velocity<br><i>v</i></th><th>Fluid height<br><i>h</i> (m)</th><th>Net length<br><i>L</i> (m)</th><th>Cell size<br><i>a</i> (cm)</th><th>Rope diameter<br><i>d</i><sub>rope</sub> (mm)</th></tr></thead><tbody><tr><td>1</td><td>1:1</td><td>210000</td><td>6</td><td>4</td><td>5</td><td>20</td><td>10</td></tr><tr><td>2</td><td>1:10</td><td>21000</td><td>1.897</td><td>0.4</td><td>0.5</td><td>2</td><td>1</td></tr><tr><td>3</td><td>1:30</td><td>7000</td><td>1.095</td><td>0.133</td><td>0.167</td><td>0.667</td><td>0.333</td></tr><tr><td>4</td><td>1:50</td><td>4200</td><td>0.849</td><td>0.08</td><td>0.1</td><td>0.4</td><td>0.2</td></tr><tr><td>5</td><td>1:100</td><td>2100</td><td>0.6</td><td>0.04</td><td>0.05</td><td>0.2</td><td>0.1</td></tr></tbody></table>

On the other hand, we should also concentrate on the buckling effect due to existence of braking device. Figure 5 shown the calculated geometry of nets within braking devices, in which four horizontal cables are extended at extreme points of traditional rope net. Furthermore, these cables are used to dissipate a part of energy and avoid the abruptly mechanical rupture of net and the strain-stress curve could be presented as Fig. 6. According to Buckingham-pi theorem, two new dimensionless parameters could be defined as follows:

$$ \pi_6 = \frac{L_{frein}}{h}, \pi_7 = \varepsilon = \frac{\sigma_{max}}{E} $$

In addition, it should be noted that, according the work of [8], as compared to hydro-static and dynamic pressure, the effect of rock debris is not predominant. Thus, in our present simulation, the rope net is mainly buffeted by fluid without rocky debris and the existing loads are static and dynamic pressure, and they could be expressed by the following equations [11]:

$$ p_{static} = \rho_{water}gh_{node}, $$

$$ p_{dy} = c_D \rho_{water} v^2 $$

where $c_D$ is the drag factor which could vary between 0.7-2.0 depending on the mixture and the density of the flow. Here, we just choose the value of $c_D$ to 1. And the effect of woody debris will be simulated by some beams with certain diameters, thus it will not influence the distribution of hydraulic loads.

During our simulation, these loads will be applied to each node of rope net in the form of force, thus the average force in each cell, which depends on the fluid velocity, cell size and node height, was firstly calculated. Then, all the permanent force will be continuously set up to the whole rope net during our simulation until the system reached into a quite steady state. Finally, the distribution of displacement and stress could be obtained and discussed as shown in the next chapter.
<figure><img src="image_9.png" /><figcaption>Figure 5. Analytical geometry of nets within braking devices.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Figure 6. Strain-stress curve of braking devices in the present simulation.</figcaption></figure>

## 2.3 Summary

In this Chapter, discrete element method and its related calculated geometry are simply discussed. And an extensible and extensible open-source framework for DEM called Yade DEM and based on python language is chosen. Besides, to simulate the braking devices generally used in the last few years, the measured strain-stress relation is applied to four straight sticks located at extreme points of rectangular net. In this way, a series of simulation could be performed under different conditions in the next Chapter.
# 3. Discussions of calculated results

In this chapter, we concentrate on the net deformation behavior under different scales, different materials and different structures. Here, the effects of theoretical material, traditional material and PSU material are clarified, and the mechanical analyses of buckling effect are also discussed.

## 3.1 Qualitative analyses of calculation

Figure 7 shows some representative transient frames of a randomly selected run under scale ratio 1:30 without braking devices. From the change of rope net shape, it is evident that the rope net tends to be curved due to the loading conditions, and finally reach into a steady state.

<figure><img src="image_11.png" /><figcaption>Figure 7. Representative transient frames under loading conditions without braking devices.</figcaption></figure>

As for the case in which the extreme node of rope net barriers is buckled by braking devices, figure 8 shows some representative transient frames of a randomly selected run. During the rope net formation behavior, the length of energy dissipation structure has obviously been extended until a stationary regime of whole system is obtained, which is in a good agreement with the strain-stress curve as shown in Fig. 6.
<figure><img src="image_12.png" /><figcaption>Figure 8. Representative transient frames under loading conditions within braking devices.</figcaption></figure>

## 3.2 Quantitative analyses of net deformation without braking devices

For quantitative analysis of net deformation under certain loading conditions, to acquire the more comprehensive and more comparable results for understanding this behavior, in this section, the relative height $h_{relative}$ is defined as the ratio of the node z-displacement in the horizontal center of rope nets to the net length:

$$h_{relative} = \frac{\Delta h_{node}}{L_{net}}$$

Figures 9 depicts the change of two quantities which represent the absolute and the relative displacements under different scales. And as rope position increases, the displacements tend to increase until they reach a peak value, then they tend to decrease. Besides, from Fig. 9(b), the net central deformation is the same in all cases, which means that the scale effect is eliminated in our basic model.

However, it should be noted that, these two figures show only the scale effect of defined theoretical material which depend on net dimensions. To further understand the relation between the material and scale effect, the traditional material (stainless steel) are used in our simulation under different scales. As shown in Fig. 10, as net scale decreases, the defined two quantities (i.e. absolute and relative displacement in the central region of rope net) tends to decrease for each position of nodes, which means that the dimensionless number could not be constant. Thus, under the experimental conditions such as a scale of 1:30, the traditional material could not be used because of the different net deformation.
<figure><img src="image_13.png" /><figcaption>Figure 9. Absolute and the relative displacements of theoretical material under different scales.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>Figure 10. Absolute and the relative displacements of stainless steel under different scales.</figcaption></figure>

On the other hand, another material called PSU containing 20% Fiber glass is chosen under scale of 1:30, as shown in Table 2, as compared to theoretical material under scale of 1:30, the physical properties of PSU are in a good agreement. Figure 11 shows the comparison of relative height under different conditions, from this figure, it can be clearly seen that, the deformation curve of theoretical material (scale 1:30), traditional material and PSU under scale 1:30 is almost coincident, as compared to the deformation curve of PSU under scale 1:10 and 1:50. Hence, the PSU material could only be used under scale 1:30 to compare with traditional material under scale 1:1. However, it should be pointed out that, the error of theoretical material should not be much smaller than that of PSU because the scale effect has been eliminated in basic model theoretically. Table 3 shows some peak value of relative height under
the comparison of three materials (theoretical material, traditional material and PSU), to further understand the importance of different effects (e.g. scale effect, material properties), three different errors, namely respectively scale error, PSU error and actual error could be defined as follows:

$$ 
\begin{aligned}
\varepsilon_{scale} &= \Delta h_{relative,theoretical material}, \\
\varepsilon_{PSU} &= (h_{relative,steel 1:1} - h_{relative,PSU Scale 1:30}), \\
\varepsilon_{actual} &= \Delta h_{relative,steel}
\end{aligned}
$$

According to Table 3, the three errors could be calculated, and we obtain finally:

$$ 
\begin{aligned}
\varepsilon_{scale} &= 0.00162 = 0.162\%, \\
\varepsilon_{PSU} &= 0.00131 = 0.131\%, \\
\varepsilon_{actual} &= 0.08868 = 8.87\%
\end{aligned}
$$

Under comparison of three errors, it is evident that the PSU could reproduce the net deformation under the scale 1:30, which has the same order of magnitudes as that of scale effect.

<figure><img src="image_15.png" /><figcaption>Figure 11. Comparison of relative height under different conditions. Table 2. Physical properties of PSU (20% Fiber glass) and stainless steel.</figcaption></figure>

<table><tbody><tr><td rowspan="3">Theoretical material (Scale 1:30)</td><td>Young's modulus <i>E</i> (MPa)</td><td>7000</td></tr><tr><td>Density (kg/m<sup>3</sup>)</td><td>7800</td></tr><tr><td>Coefficient de Poisson <i>ν</i></td><td>0.3</td></tr><tr><td rowspan="3">PSU (20% Fiber glass)</td><td>Young's modulus <i>E</i> (MPa)</td><td>6860</td></tr><tr><td>Density (kg/m<sup>3</sup>)</td><td>1400</td></tr><tr><td>Coefficient de Poisson <i>ν</i></td><td>0.36</td></tr></tbody></table>
<table><caption>Table 3. Peak values of relative height under the comparison of three materials.</caption><thead><tr><th></th><th>Scale 1:1</th><th>Scale 1:10</th><th>Scale 1:30</th><th>Scale 1:50</th><th>Δh<sub>relative</sub></th></tr></thead><tbody><tr><td>max(h<sub>relative,steel</sub>)</td><td>0.19053</td><td>0.13094</td><td>0.10952</td><td>0.10185</td><td>0.08868</td></tr><tr><td>max(h<sub>relative,theoretical</sub>)<br>material</td><td>0.19053</td><td>0.19188</td><td>0.19184</td><td>0.19215</td><td>0.00162</td></tr><tr><td>max(h<sub>relative,PSU</sub>)</td><td>-</td><td>0.2313</td><td>0.19308</td><td>0.17832</td><td>-</td></tr></tbody></table>

### 3.3 Quantitative analyses of net deformation within braking devices

To further understand the scale effect of theoretical model which has been extended by two other terms, thus quantitative analyses will be shown in the same methodology.

To begin with, Figures 12 depicts the change of two quantities which represent the absolute and the relative displacements under different scales. And it can be seen that, as rope position increases, the displacements tend to increase until they reach a peak value, then they tend to decrease. Besides, Fig. 9(b) shows net central deformation is the same in all cases, which means that the scale effect is eliminated in our basic model.

<figure><img src="image_16.png" /><figcaption>Figure 12. Absolute and the relative displacements of theoretical material with braking devices under different scales.</figcaption></figure>

Secondly, from Fig. 13, the traditional material was used under different scales, as net scale decreases, the relative displacement in the central region of rope net tends to decrease for each position of nodes, which means that the dimensionless number could not be constant. Thus, in the modeling of rope net with braking devices, it is still impossible to apply the same material
under actual and experimental-reduced conditions.

<figure><img src="image_17.png" /><figcaption>Figure 13. Relative displacements of stainless steel with braking devices.</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>Figure 14. Comparison of relative displacements between different materials with braking devices.</figcaption></figure>

Thus, it is necessary to examine the difference of PSU and theoretical material under the scale ratio 1:30. As depicted in Figure 14, it could be observed, the deformation of PSU (Scale ratio 1:30), theoretical material (Scale ratio 1:30) and actual material (Scale ratio 1:1) are almost coincident. To quantify the difference of theoretical material, traditional material and PSU material, these three errors could be obtained in the same way as illustrated in Section 3.2.

<table><caption>Table 4. Peak values of relative height under the comparison of three materials.</caption><thead><tr><th></th><th>Scale 1:1</th><th>Scale 1:10</th><th>Scale 1:30</th><th>Scale 1:50</th><th>Δh<sub>relative</sub></th></tr></thead><tbody><tr><td>max(h<sub>relative,steel</sub>)</td><td>0.44211</td><td>0.40332</td><td>0.36562</td><td>0.35015</td><td>0.09196</td></tr><tr><td>max(h<sub>relative,theoretical</sub>)<br>material</td><td>0.44211</td><td>0.44362</td><td>0.44488</td><td>0.44385</td><td>0.00175</td></tr><tr><td>max(h<sub>relative,PSU</sub>)</td><td>-</td><td>0.45261</td><td>0.443</td><td>0.44269</td><td>-</td></tr></tbody></table>
Hence, we obtain the following numbers:

$$ \varepsilon_{scale} = \Delta h_{relative,theoretical material} = 0.175\%, $$

$$ \varepsilon_{PSU} = (h_{relative,steel 1:1} - h_{relative,PSU Scale 1:30}) = 0.089\%, $$

$$ \varepsilon_{actual} = \Delta h_{relative,steel} = 9.196\% $$

Thus, the same order of magnitude of PSU and actual material shows that PSU could also be used when the rope net is buckled by braking devices.

On the other hand, the design of braking device is aimed at dissipating a part of energy by friction and buckling effect that could be calculated by the integral in flat region of strain-stress curve. However, owing to the outward extension of simulated sticks, the final shape of rope net will be much different from that without braking devices. To further understand the dissipation effect of freins during deformation behavior, we concentrate on the quantitative comparison between the two cases as shown on Figure 15. From Fig. 15(a), the absolute height of each node at the central region of net is a function of nodes' horizontal ordinate. However, the spatial distribution of two curves is quite different because of the freins axial extension. Thus, to compare the relative difference of two curves, the smallest value of endpoints is set down to zero as illustrated in Fig. 15(b). It can be obviously seen that, due to the contribution of braking devices, the final net shape becomes much more narrow and prominent. This is probably because the plastic regime of sticks could have a comparable impact on nets stress distribution, which further change the final displacement of each node. And it seems that the narrower deformation we have obtained, a much more distinct dissipation effect observed, which could demonstrate the advantage of such a mechanical design in the protection of net barriers.

<figure><img src="image_19.png" /><figcaption>Figure 15. Comparison of node displacements under the condition of braking devices or not.</figcaption></figure>
To further provide more evidence of such tendency, we concentrate on the tangential force of each node in stationary regime as shown in Figure 16. From Fig. 16, it could be observed, the tangential forces of each node are much smaller than that without simulated sticks. Therefore, due to the existence of these simulated sticks, the displacement and force history become absolutely different until the whole system reached into a steady state, and the efficiency of our new introduced energy-dissipation devices seems to be confirmable.

Moreover, as node position increases, the tangential force tends to decrease until the central node, and then tends to increase. It seems that, in the design of net barriers against debris flow, the connection at extreme part of each sides should be carefully handled with just because of a comparably larger interne stress.

<figure><img src="image_20.png" /><figcaption>Figure 16. Comparison of tangential forces under the condition of braking devices or not.</figcaption></figure>

However, it is instructive to note that, the main advantage and physical reason of such design involving a plastic mechanical regime as shown in the strain-stress curve have not yet been discussed. Thus, in our following discussion, a series of mechanical analyses has been performed under different values of plastic dimension and pure elastic design, which means the horizontal ordinate of point 3 (i.e. $ε_3$) as shown in Fig. 6 and the length of simulated sticks without plasticity, respectively.

Figure 17 shows many curves under different conditions, to begin with, we just compare the effect of different freins length without plastic regime, as the length of sticks becomes twice as much, it seem that the related force of each node tends to be larger than before. However, if we apply the sticks with a plastic regime in which the sticks size could be elongated to be twice
(i.e. ε₃ = 1), which means the final length of simulated sticks of the two cases is almost the same. However, Fig. 17 shows that the interne force of nodes becomes much smaller than elastic case. Therefore, in the case of braking devices, the main advantage of such design is not the application of a simple stick, but the plastic region of those sticks. Here, it should be pointed out that, the only difference between simulation and reality is that in engineering application, the simulated sticks are replaced by a series of special structure which could show the same strain-stress curve as that of Fig. 6. On the other hand, if we change the value of ε₃ from 0 to 1, we could observe that, as ε₃ increases, all the curves tend to move down and becomes much smaller. Hence, the longer plastic region that the designed special structure has, the much better performance of the whole rope nets against debris flow. Besides, the force curve of no-freins is located between these different values of ε₃, which means a poor design of braking devices could possibly has a negative impact on the rope nets deformation behavior (e.g. a prematurely mechanical rupture of nets), and in reality, the measured value of maximum extension is bigger than 1, which finally maintain in accordance with our simulated results.

<figure><img src="image_21.png" /><figcaption>**Figure 17.** Comparison of tangential force under different conditions including plastic dimension and pure elastic design.</figcaption></figure>
**3.4 Summary**

In this chapter, to understand the net deformation behavior under hydraulic loads, a series of experiments is performed and their results are analyzed. And a series of preliminary results has been obtained, which is in a good agreement with the engineering application and theoretical model. In addition, some results shows that a new material PSU could be used under reduced experimental condition (Scale ratio 1:30) to reproduce almost the same deformation as actual case (Scale ratio 1:1).
# 4. Conclusions and perspectives

Studies on the design of structural mitigation measures and the related numerical simulation on barriers deformation against debris flow is still a challenging task in engineering application. In our preliminary studies, motivated to clarify the mechanisms underlying rope nets deformation behavior and further establish a theoretical model for determining an appropriate material under experimental conditions, a series of numerical simulations using an extensive open-source framework called Yade DEM along with its discrete element method (DEM) is being performed by generating a rope net within certain physical properties under different loading conditions on the net nodes. And it is observed a consistent impact of simple load on the net central deformation characteristics (e.g. absolute and relative displacement) under different scaled. And the efficiency of theoretical model including five or seven dimensionless parameters by similarity analysis is confirmable. In addition, the net deformation of a chosen material (PSU) under a small scale (1:30) is in accordance with that of the theoretical material which is defined by basic model. And plastic regime of braking devices is the main reason that could improve the performance of rope net design against debris flow. Knowledge and evidence from this work might be utilized for the development and verifications of theoretical model and barriers structure design in the future.

For future work, to achieve a more comprehensive understanding on rope net deformation, the following problems should be examined and clarified:

(1) Further calculation involving the woody conditions;

(2) Further simulation of rope nets deformation under different fluid velocities.

Firstly, the woody debris could be achieved by generating a bunch of beams within certain diameter and the same velocity as fluid flow. However, due to the time and manpower limit, the investigation of woody debris could not be accomplished in our present project, here we just show some representative transient frame of our further calculated model as depicted in Fig. 18. After generating of such bunch of beams, the similarity and mechanical analyses could be done by means of the same methodology. And the only problem is defining a new parameter which could represent the beams, such as physical properties, spatial position, generating rate etc.
<figure><img src="image_22.png" /><figcaption>Figure 18. Representative transient frames of rope nets against woody debris within braking devices.</figcaption></figure>

Secondly, the main purpose of such investigation is the simulated results could be
compared to our following experimental project which will be launched in this summer.
References

1. Hervás, J., et al., “Lessons learnt from landslide disasters in Europe,” European Commission, Joint Research Centre, Institute for the Protection and the Security of the Citizen, Technological and Economic Risk Management Unit, 2003.

2. Alibaba, A., “Discrete element modeling of the impact of granular debris flows on rigid and flexible structures,” *PhD thesis*, 2006.

3. Andreas, R., Theodor, S., “Loads on rope net constructions for woody debris entrapment in torrents,” *International Congress, Interpraevent 2002 in the Pacific Rim*, Matsumoto, Japan, Volume 2, pp. 797-807, 2002.

4. Hubel, J., Nagl, G., Suda, J., et al., “Standardized Stress Model for Design of Torrential Barriers under Impact by Debris Flow (According to Austrian Standard Regulation 24801), *International Journal of Erosion Control Engineering*, 10(1), 2017.

5. Bradley, J.B., Richards, D.L., Bahner, C.D., “Debris Control Structures: Evaluation and Countermeasures,” *Publication: Hydraulic Engineering Circular No. 9*, 2005.

6. HELLER, V., “Scale effects in physical hydraulic engineering models,” *Journal of Hydraulic Research*, 49(3), pp. 293-306, 2011.

7. Peakall, J., Ashworth, P., Best, J., “Physical modeling in fluvial geomorphology: Principles, Applications and Unresolved Issues,” *Scientific nature of geomorphology*, 1996.

8. Rimböck, A., “Design of rope net barriers for woody debris entrapment: introduction of a design concept,” in: *INTERPRAEVENT Conference Proceedings.*, pp. 265–276, 2004.

9. Bertrand, D., Trad, A., Limam, A., et al., “Full-Scale Dynamic Analysis of an Innovative Rockfall Fence Under Impact Using the Discrete Element Method: from the Local Scale to the Structure Scale,” *Rock Mech Rock Eng*, Volume 45, pp. 885-900, 2012.

10. Cundall, P., Strack, O., “Discrete numerical model for granular assemblies,” *Geotechnique*, 29(1), pp. 47-65, 1979.

11. Publication GD06/T06 EAD, “Flexible kits for retaining debris flows and shallow landslides/open slope debris flows,” *European Organization for Technical Assessment (EOTA)*, 2015.
**Acknowledgements**

My deepest gratitude goes first and foremost to my supervisors, Mr. Bourrier FRANCK and Mr. Piton GUILLAUME, for their constant encouragement and guidance. Without their consistent and illuminating instruction, this project could not have reached its present form.

I would like to appreciate Dr. LIU Jiaying for her constant guidance in the installation and application of Yade DEM.

I would also like to express my appreciation to École nationale supérieure de l'énergie, l'eau et l'environnement (ENSE3) and Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture (IRSTEA), for a half-year's systematic education in the field of nuclear and environmental engineering respectively.
# Annex

## Journal de bord

Projet Recherche_IRSTEA_Journal de Bord

<table><thead><tr><td>Date et heure</td><td>Lieu</td><td>Intervenants</td><td>Moyen de contact</td><td>Objet</td><td>Contenu</td><td>Attribution des tâches</td></tr></thead><tbody><tr><td>14h-17h30 07/02/2018</td><td>Bureau 024, IRSTEA</td><td>M. FRANCK<br>M. GUILLAUME<br>Shuo LI</td><td>Entretien en tête à tête</td><td>Compréhension de projet de recherche</td><td>1. Première rencontre avec le tuteur</td><td>1. Lire des articles scientifiques<br>2. Planifier le projet de recherche</td></tr><tr><td>8h30-12h00 09/02/2018</td><td>Bibliothèque, bâtiment de GreEn-ER</td><td>Shuo LI<br>Mme. LIU</td><td>E-mail</td><td>Etude du logiciel</td><td>1. Discussion sur les problèmes d'installation</td><td>1. Apprendre le logiciel Yade DEM et comprendre le code</td></tr><tr><td>8h00-17h00 10/02/2018</td><td>Studio 314, bâtiment de CROUS</td><td>Shuo LI</td><td></td><td>Etude du logiciel</td><td>1. Travail individuel</td><td>1. Apprendre le logiciel Yade DEM et comprendre le code</td></tr><tr><td>8h00-17h00 14/02/2018</td><td>Bureau 024, IRSTEA</td><td>M. FRANCK<br>Shuo LI</td><td>Entretien en tête à tête</td><td>Détermination sur la première tâche et étude du logiciel</td><td>1. Travail individuel<br>2. Discussion sur les problèmes techniques</td><td>1. Appliquer les codes connus par Yade DEM<br>2. Apprendre la méthode DEM</td></tr><tr><td>8h00-17h00 17/02/2018</td><td>Studio 314, bâtiment de CROUS</td><td>Shuo LI</td><td></td><td>Recherche des références et étude du logiciel</td><td>1. Travail individuel</td><td>1. Trouver les résultats connus dans des publications<br>2. Apprendre le langage python</td></tr><tr><td>14h00-18h00 26/02/2018</td><td>Studio 314, bâtiment de CROUS</td><td>Shuo LI</td><td></td><td>Etude du logiciel</td><td>1. Travail individuel</td><td>1. Résoudre les problèmes d'installation concernant le Yade DEM, VMWare et Ubuntu</td></tr></tbody></table>

Mr. Bourrier Franck

Mr. Piton Guillaume

Shuo Li

Projet Recherche_IRSTEA_Journal de Bord

<table><thead><tr><td>Date et heure</td><td>Lieu</td><td>Intervenants</td><td>Moyen de contact</td><td>Objet</td><td>Contenu</td><td>Attribution des tâches</td></tr></thead><tbody><tr><td>8h00-10h30 28/02/2018</td><td>Salle 2C005, bâtiment de GreEn-ER</td><td>Shuo LI</td><td>Entretien en tête à tête</td><td>Cour de projet recherche bibliographique</td><td>1. Moyens de recherche bibliographique</td><td></td></tr><tr><td>8h30-22h00 02/03/2018</td><td>Studio 314, bâtiment de CROUS</td><td>Shuo LI<br>M. FRANCK</td><td>E-mail</td><td>Analyse de similitude sous chargement simple</td><td>1. Travail individuel<br>2. Discussion sur un problème de chargement</td><td></td></tr><tr><td>04/03/2018-06/03/2018</td><td>Studio 314, bâtiment de CROUS</td><td>Shuo LI</td><td></td><td>Analyse de similitude sous chargement simple</td><td>1. Travail individuel</td><td>1. Analyser les résultats préliminaires<br>2. Préparer le PPT pour la soutenance intermédiaire</td></tr><tr><td>14h00-17h00 07/03/2018</td><td>Bureau 024, IRSTEA</td><td>Shuo LI<br>M. FRANCK</td><td>Entretien en tête à tête</td><td>Discussion du bilan de projet</td><td>1. Travail individuel<br>2. Discussion sur un problème du logiciel</td><td>1. Trouver une solution de rentrer les forces du corps</td></tr><tr><td>10/03/2018-11/03/2018</td><td>Studio 314, bâtiment de CROUS</td><td>Shuo LI</td><td></td><td>Comparaison des matériaux sous acharnement simple</td><td>1. Travail individuel</td><td>1. Appliquer les codes connus dans Yade DEM<br>2. Rajouter des phrases dans les codes</td></tr><tr><td>9h00-16h30 14/03/2018</td><td>Bureau 024, IRSTEA</td><td>Shuo LI<br>M. FRANCK</td><td>Entretien en tête à tête</td><td>Discussion de la simulation des filets avec les freins</td><td>1. Travail individuel</td><td>1. Appliquer un nouveau code dans Yade DEM<br>2. Rajouter des phrases dans les codes</td></tr></tbody></table>

Mr. Bourrier Franck

Mr. Piton Guillaume

Shuo Li
<table><thead><tr><td>Date et heure</td><td>Lieu</td><td>Intervenants</td><td>Moyen de contact</td><td>Objet</td><td>Contenu</td><td>Attribution des tâches</td></tr></thead><tbody><tr><td>8h00-18h30 17/03/2018</td><td>Studio 314, bâtiment de CROUS</td><td>Shuo LI</td><td></td><td>Simulation des filets avec les freins</td><td>1. Travail individuel</td><td>1. Appliquer un nouveau code dans Yade DEM<br>2. Rajouter des phrases dans les codes</td></tr><tr><td>14h00-17h00 28/03/2018</td><td>Bureau 024, IRSTEA</td><td>Shuo LI<br>M. FRANCK</td><td>Entretien en tête à tête</td><td>Discussion des problèmes de la simulation avec les freins</td><td>1. Travail individuel<br>2. Discussion sur un problème technique</td><td>1. Trouver une solution de la fausse déformation des filets pendant la simulation</td></tr><tr><td>8h00-22h00 01/04/2018</td><td>Studio 314, bâtiment de CROUS</td><td>Shuo LI</td><td></td><td>Analyse de résultats sous chargement simple</td><td>1. Travail individuel</td><td>1. Analyser les résultats secondaires<br>2. Préparer le PPT pour la deuxième soutenance intermédiaire<br>3. Rédiger le rapport</td></tr><tr><td>14h00-18h00 04/04/2018</td><td>Bureau 024, IRSTEA</td><td>M. FRANCK<br>M. GUILLAUME<br>Shuo LI</td><td>Entretien en tête à tête</td><td>Discussion du bilan de projet et méthodologie de rédiger le rapport</td><td>1. Travail individuel</td><td>1. Discuter les méthodes et les résultats généraux<br>2. Préparer les tâches de mai<br>3. Rédiger le rapport</td></tr><tr><td>10/03/2018- 11/03/2018</td><td>Studio 314, bâtiment de CROUS</td><td>Shuo LI</td><td></td><td>Comparaison des matériaux sous chargement simple</td><td>1. Travail individuel</td><td>1. Appliquer les codes connus dans Yade DEM<br>2. Rajouter des phrases dans les codes<br>3. Rédiger le rapport</td></tr><tr><td>16/04/2018- 17/04/2018</td><td>Studio 314, bâtiment de CROUS</td><td>Shuo LI</td><td></td><td>Analyse de résultats sous chargement simple</td><td>1. Travail individuel</td><td>1. Appliquer un nouveau code dans Yade DEM<br>2. Rédiger le rapport</td></tr></tbody></table>

Mr. Bourrier Franck
Mr. Piton Guillaume
Shuo Li

<table><thead><tr><td>Date et heure</td><td>Lieu</td><td>Intervenants</td><td>Moyen de contact</td><td>Objet</td><td>Contenu</td><td>Attribution des tâches</td></tr></thead><tbody><tr><td>14h00-16h30 18/04/2018</td><td>Bureau 024, IRSTEA</td><td>M. FRANCK<br>Shuo LI</td><td>Entretien en tête à tête</td><td>Discussion sur la courbe de traction des freins</td><td>1. Travail individuel<br>2. Discussion sur un problème technique</td><td>1. Appliquer un nouveau code dans Yade DEM</td></tr><tr><td>8h00-16h00 21/04/2018</td><td>Studio 314, bâtiment de CROUS</td><td>Shuo LI</td><td></td><td>Simulation des filets avec freins en appliquant la courbe de traction</td><td>1. Travail individuel</td><td>1. Changer le code dans Yade DEM<br>2. Rédiger le rapport</td></tr><tr><td>15h00-16h00 25/04/2018</td><td>Bureau 024, IRSTEA</td><td>M. FRANCK<br>Shuo LI</td><td>Entretien en tête à tête</td><td>Analyse des similitudes sur les filets avec freins</td><td>1. Travail individuel<br>2. Discussion sur un problème technique</td><td>1. Appliquer le modèle théorique dans Yade DEM<br>2. Appliquer le logiciel ORIGIN PRO pour faire la diagramme</td></tr><tr><td>14h30-16h30 02/05/2018</td><td>Bureau 024, IRSTEA</td><td>M. FRANCK<br>Shuo LI</td><td>Entretien en tête à tête</td><td>Analyse des mécaniques sur les filets avec freins</td><td>1. Discussion sur le bilan de projet en mai</td><td>1. Finir les analyses des filets avec freins<br>2. Rédiger le rapport systématiquement<br>3. Essayer d'appliquer les arbres dans la simulation si on aurait le temps</td></tr><tr><td>12/05/2018- 13/05/2018</td><td>Studio 314, bâtiment de CROUS</td><td>Shuo LI</td><td></td><td></td><td></td><td>1. Rédiger le rapport</td></tr><tr><td>9h00-19h00 20/05/2018</td><td>Studio 314, bâtiment de CROUS</td><td>Shuo LI</td><td></td><td></td><td></td><td>1. Finir de rédiger le rapport</td></tr></tbody></table>

Mr. Bourrier Franck
Mr. Piton Guillaume
Shuo Li
<table><thead><tr><td>Date et heure</td><td>Lieu</td><td>Intervenants</td><td>Moyen de contact</td><td>Objet</td><td>Contenu</td><td>Attribution des tâches</td></tr></thead><tbody><tr><td>14h30-16h30 22/05/2018</td><td>Bureau 024, IRSTEA</td><td>M. FRANCK Shuo LI</td><td>Entretien en tête à tête</td><td>Discussion sur les conclusions de projet et l'ouverture</td><td>1. Discussion sur des conclusions spéciales mécaniques.<br>2. Discussion sur l'avenir du projet.</td><td>1. Refaire la simulation dans quelques situations.<br>2. La vérification des résultats</td></tr><tr><td>26/05/2018- 27/05/2018</td><td>Studio 314, bâtiment de CROUS</td><td>Shuo LI</td><td></td><td>Simulation des filets avec freins en appliquant la courbe de traction</td><td>1. Travail individuel</td><td>1. Corriger le rapport avec quelques résultats étonnants.<br>2. Soumettre le « Draft Paper » du projet au tuteur.</td></tr><tr><td>14h00-24h00 28/05/2018</td><td>Studio 314, bâtiment de CROUS</td><td>Shuo LI</td><td></td><td></td><td>1. Travail individuel</td><td>1. Finir la dernière version de rapport du projet.</td></tr><tr><td>8h00-22h30 29/05/2018</td><td>Studio 314, bâtiment de CROUS</td><td>Shuo LI</td><td></td><td></td><td>1. Travail individuel</td><td>1. Préparer le PPT de soutenance.<br>2. Préparer et mémoriser les notes de présentation.</td></tr></tbody></table>

Mr. Bourrier Franck
Mr. Piton Guillaume
Shuo Li
Diagramme de GANNT

<figure><img src="image_23.png" /></figure>

<table><thead><tr><th>Nom</th><th>Date de début</th><th>Date de fin</th></tr></thead><tbody><tr><td>Préparation</td><td>01/02/18</td><td>21/02/18</td></tr><tr><td>Recherche des références</td><td>01/02/18</td><td>12/02/18</td></tr><tr><td>Etude du logiciel</td><td>13/02/18</td><td>21/02/18</td></tr><tr><td>Démarrage du projet</td><td>22/02/18</td><td>16/05/18</td></tr><tr><td>Analyses des similitudes sous chargement simple</td><td>22/02/18</td><td>06/03/18</td></tr><tr><td>Vérification du modèle principal pour les filets sans freins</td><td>22/02/18</td><td>27/03/18</td></tr><tr><td>Comparaison des matériaux théoriques et pratiques</td><td>28/03/18</td><td>10/04/18</td></tr><tr><td>Soutenance intermédiaire I</td><td>07/03/18</td><td>07/03/18</td></tr><tr><td>Rédaction du rapport de projet</td><td>07/03/18</td><td>16/05/18</td></tr><tr><td>Soutenance intermédiaire II</td><td>11/04/18</td><td>11/04/18</td></tr><tr><td>Application du modèle et simulation avec les freins</td><td>11/04/18</td><td>10/05/18</td></tr><tr><td>Analyse des résultats</td><td>11/05/18</td><td>16/05/18</td></tr><tr><td>Rapport et soutenance</td><td>17/05/18</td><td>29/05/18</td></tr><tr><td>Relecture et vérification du rapport</td><td>17/05/18</td><td>24/05/18</td></tr><tr><td>Préparation de la soutenance</td><td>25/05/18</td><td>29/05/18</td></tr><tr><td>Soutenance et soumission de rapport final</td><td>30/05/18</td><td>30/05/18</td></tr></tbody></table>

<figure><img src="image_24.png" /></figure>