# Monitoring the Dynamic Response of a Buried Polyethylene Pipe to a Blast Wave: An Experimental Study

^{*}

## Abstract

**:**

## 1. Introduction

## 2. The Experimental Setup

#### 2.1. PE Pipe Parameters

_{p}is the density, E

_{P}is the young modulus of the PE material, μ is the Poisson ratio, δ

_{b}is the ultimate strength, ξ% is the elongation, and α

_{s}is the relative stiffness coefficient of the pipe and the soil. When α

_{s}is less than 1, it means that the pipe is a flexible pipeline. The definition of α

_{s}is as follows:

_{0}is the average radius of the pipe. E

_{d}is the soil deformation modulus, and here, it is 8 MPa.

#### 2.2. Experimental Site and Pipe

#### 2.3. Strain Gages and Strain Indicator

#### 2.4. Velocity Sensor and Blasting Vibration Meter

## 3. Experimental Procedure

## 4. Strain Results and Analysis

#### 4.1. Dimensional Analysis

#### 4.1.1. Load Acting on the Pipe

_{s}represents the inertia of the soil. The parameters on both sides of the wave front should satisfy the law of conservation of mass and momentum. The relationship between the vibration velocity v

_{p}and the pressure p

_{w}on the wave front is as follows [28]:

_{max}acting on the pipe is a function of soil density, wave velocity, and peak particle velocity (PPV) v

_{max}as follows:

_{s}are constants. Here, v

_{max}was used to represent the load level and was calculated by the Sadowski formula:

#### 4.1.2. The Maximum Strain of the Pipeline

_{max}. The deformation of the pipeline was linear elastic. The maximum strain ε

_{max}can be determined by D, δ, ρ

_{p}, E

_{p}, ρ

_{s}, E

_{d}, c, and v

_{max}. These variables include the load, inertia, and compression effect of the pipeline and soil and geometric properties of the pipeline section. The function of stress on the outer surface of the PE pipe is given by:

_{p}, E

_{p}, ρ

_{s}, E

_{d}, and c were determined, v

_{max}was a variable, which was determined by Equation (5). Therefore, we adopted the power function form for the maximum strain of the pipeline, as shown in the following equation:

#### 4.2. Strain Analysis

#### 4.2.1. The Test Data of the Peak Strain

#### 4.2.2. Peak Strain Attenuation Law

#### 4.2.3. Influence of Waveform Conversion

#### 4.2.4. Dynamic Strain Spectrum Analysis

_{i}is the frequency of fast Fourier transform (FFT) spectrum and A

_{i}is the amplitude.

## 5. Vibration Velocity Results and Analysis

#### 5.1. GPPV and Pipe Peak Vibration Velocity (PPVV)

#### 5.2. Velocity Spectrum

#### 5.3. Correlation Analysis

## 6. Blasting Criterion for PE Pipe

#### 6.1. Stress–Strain Constitutive Relation

_{h}is hoop strain, ε

_{a}is axial strain, δ

_{h}is hoop stress, and δ

_{a}is axial stress.

#### 6.2. Blasting Criterion Establishment

_{1}is the first principal stress. δ

_{h}

_{1}is the hoop stress caused by the maximum working pressure, and it is 50% MRS for PE80 material according to the China national code. For the pipe used in this experiment, the maximum working pressure is 0.5 MPa. δ

_{h}

_{2}is the additional hoop stress caused by the blast wave. δ

_{2}is the second principal stress, which is the axial stress caused by the blast wave and other factors, such as the Poisson effect. δ

_{y}is the ultimate stress. Here, the hoop stress rather than the axial stress became the main controlling factor, because of its smaller pipe–soil relative stiffness coefficient. If the coefficient were larger, the additional axial stress might have been the major factor. Considering the importance of natural gas pipeline safety and durability, we propose that MRS should be used as the ultimate stress value instead of the PE material yield or strength limit, and the maximum safety threshold of δ

_{h}

_{2}should be 10% MRS. In fact, MRS is the minimum guaranteed value of the hoop tensile strength of PE pipe for a 50 year service life under the working pressure action at 20 °C, which is the material’s durability index and is far less than the yield limit of PE material. Under the short-term blasting load, the cumulative damage can be ignored. Therefore, there is no doubt that this is a safer criterion for a straight pipe, and it can be used with confidence. Thus, the total hoop stress can be up to 60% MRS, and the maximum total axial stress should be 55%, according to the inequality of Equation (15).

#### 6.3. Engineering Design and Safety Monitoring

## 7. Conclusions and Future Work

- When the scaled distance is in the range of 4–11, the PCS is generally larger than the PAS at the same test point. The hoop stress level is related to the pipe–soil relative stiffness and the mechanical properties of the material. The shape of the circular section of pipe changes and the local deformation characteristics are obvious. As the scaled distance increases, the blast wave transforms from a compression wave to a seismic wave. The difference between the PHS and PAS value decreases progressively, the local deformation effect steadily weakens, and the overall deformation effect is relatively enhanced and gradually begins to dominate [35]. Therefore, the hoop stress should be fully considered in the safety check in the near and middle field of the blast wave.
- The peak strain and scaled distance have a good power attenuation relationship as demonstrated by dimensional analysis and experimental data analysis.
- According to the strain and velocity spectrum analysis, all of the average frequency is between 10–50 Hz and the vibration frequency is low. The average frequency of strain has a power attenuation relationship with the increase in the charge mass. Additionally, the average frequency of velocity is attenuated with the increase in the scaled distance, and inversely proportional with the blasting cavity factor.
- There was a strong linear correlation between the peak strain, PPVV, and GPPV in this experiment. Thus, we determined that GPPV can directly and effectively reflect the stress level. Moreover GPPV monitoring has the advantages of simple operation, reliable testing, and so on. Therefore, GPPV monitoring should be adopted and promoted as a technical means of on-site monitoring of buried pipelines.
- A single velocity criterion does not reflect the complex influence of various factors, such as pipe type, pipe material, soil properties, blasting source, and so on. Therefore, it is more reasonable to adopt 10% MRS of PE pipe as the blasting criterion. This criterion is accurate and easy to calculate.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 11.**Typical strain waveform before and after filtering: (

**a**) The original and filtered signals; (

**b**) the fast Fourier transform (FFT) spectra of the original and filtered signals.

**Figure 18.**The correlation between peak strain and PPVV or GPPV (R = 3.75 m and R = 2.7 m): (

**a**) the peak strain and PPVV; (

**b**) the peak strain and GPVV.

L (m) | D (mm) | δ (mm) | MRS (MPa) | ρ_{p} (kg·m^{−3}) | E_{P} (MPa) | μ | σ_{b} (MPa) | ξ% | α_{s} |
---|---|---|---|---|---|---|---|---|---|

4.8 | 314.9 | 18.4 | 8 | 936 | 834.9 | 0.38 | 31.6 | 116 | 0.20 |

H (m) | R (m) | Q (g) | ||||||
---|---|---|---|---|---|---|---|---|

1.5 | 2.7 | 50 | 75 | 100 | 125 | 150 | 175 | 200 |

3.2 | 50 | 75 | 100 | 125 | 150 | 175 | 200 | |

3.75 | 50 | 75 | 100 | 125 | 150 | 175 | 200 |

Point | The Peak Tensile Strain (PTS) and Peak Compressive Strain (PCS)/10^{−6} | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

50 (g) | 75 (g) | 100 (g) | 125 (g) | 150 (g) | 175 (g) | 200 (g) | ||||||||

$\overline{\mathit{R}}=7.3$ (m/kg ^{−1/3}) | $\overline{\mathit{R}}=6.4$ (m/kg ^{−1/3}) | $\overline{\mathit{R}}=5.8$ (m/kg ^{−1/3}) | $\overline{\mathit{R}}=5.4$ (m/kg ^{−1/3}) | $\overline{\mathit{R}}=5.1$ (m/kg ^{−1/3}) | $\overline{\mathit{R}}=4.8$ (m/kg ^{−1/3}) | $\overline{\mathit{R}}=4.6$ (m/kg ^{−1/3}) | ||||||||

PTS | PCS | PTS | PCS | PTS | PCS | PTS | PCS | PTS | PCS | PTS | PCS | PTS | PCS | |

21H | 46 | 121 | 86 | 151 | 73 | 160 | 99 | 239 | 143 | 318 | 162 | 340 | 182 | 356 |

21Z | 42 | 79 | 56 | 116 | 68 | 90 | 71 | 109 | 75 | 119 | 78 | 114 | 76 | 121 |

23H | 40 | 153 | 62 | 82 | 65 | 210 | 94 | 315 | 129 | 419 | 115 | 345 | 177 | 480 |

23Z | 137 | 103 | 139 | 97 | 141 | 107 | 200 | 154 | 256 | 197 | 178 | 169 | 292 | 232 |

31H | 43 | 109 | 56 | 115 | 64 | 144 | 87 | 202 | 122 | 271 | 136 | 286 | 158 | 296 |

31Z | 95 | 84 | 62 | 79 | 113 | 109 | 137 | 171 | 159 | 216 | 164 | 235 | 159 | 254 |

32H | 121 | 70 | 247 | 247 | 167 | 90 | 263 | 145 | 341 | 259 | 371 | 313 | 442 | 365 |

32Z | 83 | 96 | 216 | 311 | 107 | 139 | 131 | 209 | 193 | 290 | 248 | 341 | 296 | 395 |

33H | 41 | 201 | 174 | 333 | 91 | 279 | 158 | 403 | 271 | 554 | 333 | 614 | 420 | 657 |

33Z | 141 | 95 | 303 | 295 | 192 | 125 | 256 | 180 | 339 | 224 | 370 | 243 | 387 | 256 |

34H | 74 | 90 | 211 | 185 | 105 | 97 | 183 | 105 | 279 | 152 | 329 | 202 | 377 | 274 |

34Z | 117 | 113 | 171 | 220 | 135 | 145 | 171 | 202 | 215 | 243 | 246 | 260 | 239 | 283 |

Item | Peak Velocity (mm·s^{−1}) | ||||||
---|---|---|---|---|---|---|---|

50 (g) | 75 (g) | 100 (g) | 125 (g) | 150 (g) | 175 (g) | 200 (g) | |

PPVV | 35 | 47 | 44 | 62 | 78 | 83 | 87 |

GPPV | 90 | 119 | 114 | 152 | 194 | 229 | 247 |

Ratio | 38.9% | 39.9% | 38.7% | 40.6% | 40.3% | 36.1% | 35.4% |

Blasting Source Distance | MRS | Maximum Allowable Hoop Stress | Maximum Allowable PHS | Minimum Scaled Distance | Allowable Charge Mass | Allowable GPPV |
---|---|---|---|---|---|---|

5 m | 8 MPa | 0.8 MPa | 820 (×10^{−6}) | 2.92 m kg^{−1/3} | 5.02 kg | 291 mm/s |

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## Share and Cite

**MDPI and ACS Style**

Zhong, D.; Gong, X.; Han, F.; Li, L.
Monitoring the Dynamic Response of a Buried Polyethylene Pipe to a Blast Wave: An Experimental Study. *Appl. Sci.* **2019**, *9*, 1663.
https://doi.org/10.3390/app9081663

**AMA Style**

Zhong D, Gong X, Han F, Li L.
Monitoring the Dynamic Response of a Buried Polyethylene Pipe to a Blast Wave: An Experimental Study. *Applied Sciences*. 2019; 9(8):1663.
https://doi.org/10.3390/app9081663

**Chicago/Turabian Style**

Zhong, Dongwang, Xiangchao Gong, Fang Han, and Linna Li.
2019. "Monitoring the Dynamic Response of a Buried Polyethylene Pipe to a Blast Wave: An Experimental Study" *Applied Sciences* 9, no. 8: 1663.
https://doi.org/10.3390/app9081663