# Control and Interception Characteristics of the Debris-Flow Flexible Net Barrier Based on Orthogonal Design

^{1}

^{2}

^{*}

## Abstract

**:**

^{3}and the relative volume was 2/3. The form of blocking ratio with minimum value was as follows: the flume slope was 6°, the net barrier interval was 50 mm, the bulk density was 12 kN/m

^{3}and the relative volume was 1/2. The form of velocity reduction ratio with maximum value was as follows: the flume slope was 12°, the net barrier interval was 18 mm, the bulk density was 17 kN/m

^{3}and the relative volume was 1. The form of bulk density attenuation ratio with maximum value was as follows: the flume slope was 12°, the net barrier interval was 30 mm, the bulk density was 17 kN/m

^{3}and the relative volume was 1/3.

## 1. Introduction

## 2. Experimental Situation

#### 2.1. Experimental Setup

^{2}. To effectively eliminate the influence of the fluid pressure of the hopper, the barrier model was mounted at a distance of 3.5 m from the hopper. The tailings pool measured 1.2 m × 1.0 m × 0.85 m (length × width × height) and collected material after the experiment. To capture the whole interaction process and phenomena, four video cameras (recording at 25 frames per second) were placed upstream and downstream of the barrier and at the front and on the side of the flume.

_{90}is equal to 11.7 mm (d

_{90}indicates that 90% of the particles are smaller than this diameter).

^{2}), h the flow depth (m), and θ is the channel slope (°).

#### 2.2. Experimental Design

#### 2.2.1. Main Factor Selection

_{90}is chosen as the research target. In addition, V

_{r}= V/V

_{total}, where V denotes the experimental debris-flow volume, and V

_{total}is the storage capacity of the dam.

#### 2.2.2. Experimental Scheme

_{r}, and 4 levels were considered for each variable (Table 1). For each control variable, four values are set, namely, levels. For example, for the control variable “Flume slope”, the four levels are 6°, 9°, 12°, and 15°; for the control variable “Net barrier interval”, the four levels are 18 mm, 30 mm, 38 mm, and 50 mm. Without considering the interaction between the various factors, a total of 256 groups would be required under the comprehensive experimental approach. However, under the orthogonal design method, the number of tests required was 16, and L

_{16}(4

^{5}) was selected to design the test scheme (Table 2); “16” stands for the orthogonal table rows, namely the number of experiments; “4” means the level of the factors; “5” represents the orthogonal array. Thus, the maximum number of factors can be arranged. There are only 4 factors in this experiment, and the extra blank column is used as the error term.

#### 2.3. Target Selection

_{b}is the blocked area after the debris flow passes the dam, mm

^{2}, and S

_{a}is the effective through-area of the flexible dam, mm

^{2}.

_{1}is the debris-flow velocity before the dam, m/s, and v

_{2}is the debris-flow velocity after the dam, m/s.

^{3}, and ${\gamma}_{2}$ is the debris-flow bulk density after the dam, kN/m

^{3.}

## 3. Analytical Methods of Experiment Results

#### 3.1. Range Analysis

#### 3.2. Variance Analysis

## 4. Results

#### 4.1. Range Analysis Results

#### 4.1.1. Interception Ratio

_{B}> R

_{C}> R

_{D}> R

_{A}was determined. Therefore, the primary and secondary factors influencing the interception ratio were the net barrier interval and the bulk density, relative volume and flume slope, respectively. In particular, R

_{Error}> R

_{A}, but these two values were very close. A possible explanation is that this was caused by an error in the test operation.

^{3}, the interception ratio reached its maximum value; and (4) at a relative volume of 2/3, the interception ratio was the highest. In summary, the interception effect was maximized under the working condition of B

_{1}C

_{4}D

_{3}A

_{2}.

#### 4.1.2. Blocking Ratio

_{B}> R

_{C}> R

_{A}> R

_{D}was determined. Therefore, the primary and secondary factors influencing the blocking ratio were the net barrier interval and the bulk density, relative volume and flume slope, respectively.

^{3}, the blocking ratio reached its lowest value; and (4) when the relative volume was 1/2, the blocking ratio was the lowest. In conclusion, when the level combination of all factors was B

_{4}C

_{1}A

_{1}D

_{2}, the blocking ratio was minimized.

#### 4.1.3. Velocity Reduction Ratio

_{B}> R

_{C}> R

_{D}> R

_{A}was determined. Hence, the primary and secondary factors influencing the velocity reduction ratio were the net barrier interval and the bulk density, relative volume and flume slope, respectively.

^{3}, the velocity reduction ratio reached its maximum value; and (4) at a relative volume of 1, the velocity reduction ratio was the highest. In summary, the velocity reduction ratio was the highest under the working condition of B

_{1}C

_{3}D

_{4}A

_{3}.

#### 4.1.4. Bulk Density Attenuation Ratio

_{A}> R

_{C}> R

_{D}> R

_{B}was determined. Therefore, the primary and secondary factors influencing the bulk density attenuation ratio were the flume slope and the bulk density, relative volume and net barrier interval, respectively.

^{3}, the bulk density attenuation ratio was the highest; and (4) when the relative volume was 1/3, the bulk density attenuation ratio reached its maximum value. In summary, the maximum bulk density attenuation ratio was obtained under the working condition of A

_{3}C

_{3}D

_{1}B

_{2}.

#### 4.2. Variance Analysis Results

_{0.1}(3,3) = 5.39, F

_{0.1}(3,6) = 3.29, F

_{0.05}(3,3) = 9.28, F

_{0.05}(3,6) = 4.76, F

_{0.01}(3,3) = 29.46, F

_{0.01}(3,6) = 9.78. Table 5 reveals that the SS values (sum of squared deviations) of the considered factors were all larger than the errors except for the interception ratio. In regard to the interception ratio, the SS value of factor A (the flume slope) was smaller than the error.

## 5. Discussion

## 6. Conclusions

_{1}C

_{4}D

_{3}A

_{2,}the block ratio has the minimum value under working condition B

_{4}C

_{1}A

_{1}D

_{2}, the velocity reduction ratio has the maximum value under working condition B

_{1}C

_{3}D

_{4}A

_{3}, and the bulk density attenuation ratio has the largest value under working condition A

_{3}C

_{3}D

_{1}B

_{2}.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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Level | A | B | C | D |
---|---|---|---|---|

Flume Slope θ (°) | Net Barrier Interval b (mm) | Bulk Density γ (kN/m^{3}) | Relative Volume V_{r} | |

1 | 6 | 18 | 12 | 1/3 |

2 | 9 | 30 | 15 | 1/2 |

3 | 12 | 38 | 17 | 2/3 |

4 | 15 | 50 | 21 | 1 |

No. | Factors | ||||
---|---|---|---|---|---|

θ (°) | b (mm) | Error | γ (kN/m^{3}) | V_{r} | |

1 | 6 | 18 | 1 | 12 | 1/3 |

2 | 6 | 30 | 2 | 15 | 1/2 |

3 | 6 | 38 | 3 | 17 | 2/3 |

4 | 6 | 50 | 4 | 21 | 1 |

5 | 9 | 18 | 2 | 17 | 1 |

6 | 9 | 30 | 1 | 21 | 2/3 |

7 | 9 | 38 | 4 | 12 | 1/2 |

8 | 9 | 50 | 3 | 15 | 1/3 |

9 | 12 | 18 | 3 | 21 | 1/2 |

10 | 12 | 30 | 4 | 17 | 1/3 |

11 | 12 | 38 | 1 | 15 | 1 |

12 | 12 | 50 | 2 | 12 | 2/3 |

13 | 15 | 18 | 4 | 15 | 2/3 |

14 | 15 | 30 | 3 | 12 | 1 |

15 | 15 | 38 | 2 | 21 | 1/3 |

16 | 15 | 50 | 1 | 17 | 1/2 |

No. | Targets | |||
---|---|---|---|---|

Interception Ratio (%) | Blocking Ratio (%) | Velocity Reduction Ratio (%) | Bulk Density Attenuation Ratio (%) | |

1 | 33.25 | 46.72 | 12.74 | 7.5 |

2 | 16.26 | 24 | 12.42 | 13.33 |

3 | 10.25 | 4.55 | 32.65 | 15.88 |

4 | 10.34 | 6.25 | 39.34 | 6.19 |

5 | 42.38 | 100 | 75.41 | 25.29 |

6 | 41.57 | 77.2 | 6.15 | 21.9 |

7 | 0 | 0 | 12.13 | 10 |

8 | 0 | 0 | 8.88 | 24.67 |

9 | 60.96 | 97.22 | 64.22 | 22.86 |

10 | 9.43 | 31.2 | 35.56 | 27.65 |

11 | 1.6 | 7.95 | 41.11 | 18.67 |

12 | 0 | 0 | 21.53 | 14.17 |

13 | 36.88 | 100 | 48.1 | 8.67 |

14 | 4.25 | 20 | 5 | 2.5 |

15 | 20.5 | 44.32 | 12.9 | 7.14 |

16 | 0 | 0 | 23.08 | 11.76 |

Targets | Range Analysis | Factors | ||||
---|---|---|---|---|---|---|

A | B | Error | C | D | ||

Interception ratio (%) | K1 | 70.10 | 173.47 | 76.42 | 37.50 | 63.18 |

K2 | 83.95 | 71.51 | 79.14 | 54.74 | 77.22 | |

K3 | 71.99 | 32.35 | 75.46 | 62.06 | 88.70 | |

K4 | 61.63 | 10.34 | 56.65 | 133.37 | 58.57 | |

k1 | 17.53 | 43.37 | 19.11 | 9.38 | 15.80 | |

k2 | 20.99 | 17.88 | 19.79 | 13.69 | 19.31 | |

k3 | 18.00 | 8.09 | 18.87 | 15.52 | 22.18 | |

k4 | 15.41 | 2.59 | 14.16 | 33.34 | 14.64 | |

R | 5.58 | 40.78 | 5.62 | 23.97 | 7.53 | |

Primary and secondary factors | B C D A | |||||

Blocking ratio (%) | K1 | 81.52 | 343.94 | 131.87 | 66.72 | 122.24 |

K2 | 177.20 | 152.40 | 168.32 | 131.95 | 121.22 | |

K3 | 136.37 | 56.82 | 121.77 | 135.75 | 181.75 | |

K4 | 164.32 | 6.25 | 137.45 | 224.99 | 134.20 | |

k1 | 20.38 | 85.99 | 32.97 | 16.68 | 30.56 | |

k2 | 44.30 | 38.10 | 42.08 | 32.99 | 30.31 | |

k3 | 34.09 | 14.21 | 30.44 | 33.94 | 45.44 | |

k4 | 41.08 | 1.56 | 34.36 | 56.25 | 33.55 | |

R | 23.92 | 84.42 | 11.64 | 39.57 | 15.13 | |

Primary and secondary factors | B C A D | |||||

Velocity reduction ratio (%) | K1 | 97.15 | 200.47 | 83.08 | 51.40 | 70.08 |

K2 | 102.57 | 59.13 | 122.26 | 110.51 | 111.85 | |

K3 | 162.42 | 98.79 | 110.75 | 166.70 | 108.43 | |

K4 | 89.08 | 92.83 | 135.13 | 122.61 | 160.86 | |

k1 | 24.29 | 50.12 | 20.77 | 12.85 | 17.52 | |

k2 | 25.64 | 14.78 | 30.57 | 27.63 | 27.96 | |

k3 | 40.61 | 24.70 | 27.69 | 41.68 | 27.11 | |

k4 | 22.27 | 23.21 | 33.78 | 30.65 | 40.22 | |

R | 18.34 | 35.34 | 13.01 | 28.83 | 22.70 | |

Primary and secondary factors | B C D A | |||||

Bulk density attenuation ratio (%) | K1 | 42.90 | 64.32 | 59.83 | 34.17 | 66.96 |

K2 | 81.86 | 65.38 | 59.93 | 65.34 | 57.95 | |

K3 | 83.35 | 51.69 | 65.91 | 80.58 | 60.62 | |

K4 | 30.07 | 56.79 | 52.51 | 58.09 | 52.65 | |

k1 | 10.73 | 16.08 | 14.96 | 8.54 | 16.74 | |

k2 | 20.47 | 16.35 | 14.98 | 16.34 | 14.49 | |

k3 | 20.84 | 12.92 | 16.48 | 20.15 | 15.16 | |

k4 | 7.52 | 14.20 | 13.13 | 14.52 | 13.16 | |

R | 13.32 | 3.42 | 3.35 | 11.60 | 3.58 | |

Primary and secondary factors | A C D B |

Targets | Factors | Sum of Squared Deviations | Degrees of Freedom | Mean Square | Values of F | α |
---|---|---|---|---|---|---|

Interception ratio | Flume slope | 63.48 | 3 | 21.16 | ||

Barrier interval | 3917.61 | 3 | 1305.87 | 54.79 | *** | |

Bulk density | 1338.31 | 3 | 446.10 | 18.72 | *** | |

Relative volume | 141.06 | 3 | 47.02 | 1.97 | ||

Error | 79.52 | 3 | 26.51 | |||

New error | 143 | 6 | 23.83 | |||

Total | 5539.98 | 15 | ||||

Blocking ratio | Flume slope | 1352.08 | 3 | 450.69 | 4.48 | |

Barrier interval | 16,638.29 | 3 | 5546.10 | 55.15 | *** | |

Bulk density | 3169.01 | 3 | 1056.34 | 10.50 | ** | |

Relative volume | 611.18 | 3 | 203.73 | 2.03 | ||

Error | 301.72 | 3 | 100.57 | |||

Total | 22,072.28 | 15 | ||||

Velocity reduction ratio | Flume slope | 843.59 | 3 | 281.2 | 2.29 | |

Barrier interval | 2790.39 | 3 | 930.13 | 7.56 | * | |

Bulk density | 1694.16 | 3 | 564.72 | 4.59 | ||

Relative volume | 1038.69 | 3 | 346.23 | 2.82 | ||

Error | 368.90 | 3 | 122.97 | |||

Total | 6735.73 | 15 | ||||

Bulk density attenuation ratio | Flume slope | 552.62 | 3 | 184.21 | 24.50 | ** |

Barrier interval | 31.53 | 3 | 10.51 | 1.40 | ||

Bulk density | 280.52 | 3 | 93.51 | 12.43 | ** | |

Relative volume | 26.56 | 3 | 8.85 | 1.18 | ||

Error | 22.56 | 3 | ||||

Total | 913.79 | 15 |

Targets | Rank | Range Analysis | Variance Analysis | |
---|---|---|---|---|

Interception ratio | 1 | Net barrier interval | = | Net barrier interval |

2 | Bulk density | Bulk density | ||

3 | Relative volume | Relative volume | ||

4 | Flume slope | Flume slope | ||

Blocking ratio | 1 | Net barrier interval | = | Net barrier interval |

2 | Bulk density | Bulk density | ||

3 | Flume slope | Flume slope | ||

4 | Relative volume | Relative volume | ||

Velocity reduction ratio | 1 | Net barrier interval | = | Net barrier interval |

2 | Bulk density | Bulk density | ||

3 | Relative volume | Relative volume | ||

4 | Flume slope | Flume slope | ||

Bulk density attenuation ratio | 1 | Flume slope | ≈ | Flume slope |

2 | Bulk density | Bulk density | ||

3 | Relative volume | Net barrier interval | ||

4 | Net barrier interval | Relative volume |

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## Share and Cite

**MDPI and ACS Style**

Xiong, Z.; Chen, X.-Q.; Chen, J.-G.
Control and Interception Characteristics of the Debris-Flow Flexible Net Barrier Based on Orthogonal Design. *Water* **2023**, *15*, 1809.
https://doi.org/10.3390/w15101809

**AMA Style**

Xiong Z, Chen X-Q, Chen J-G.
Control and Interception Characteristics of the Debris-Flow Flexible Net Barrier Based on Orthogonal Design. *Water*. 2023; 15(10):1809.
https://doi.org/10.3390/w15101809

**Chicago/Turabian Style**

Xiong, Zhen, Xiao-Qing Chen, and Jian-Gang Chen.
2023. "Control and Interception Characteristics of the Debris-Flow Flexible Net Barrier Based on Orthogonal Design" *Water* 15, no. 10: 1809.
https://doi.org/10.3390/w15101809