# The Effect of Heavy-Duty Vehicle Crossings on the State of Stress of Buried Pipelines

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Results of Strain Gauge Measurements

_{1}= 6540 kg and that of the rear axle was G

_{2}= 7560 kg. The wheel spacing was 1.99 m and the bogie wheelbase was 1.81 m. Each crossing was realized in two steps. Step I: the truck moved perpendicularly to the pipe axis at a speed of ~3 km/h and stopped when the front axle reached the pipe. Following Figure 1, the position of the truck was such that the left-hand wheels of the truck moved above section B. Step II: the truck moved forward by about 1.2 m and stopped. At this point, the front axle was 1.2 m ahead of the pipe axis, and the rear axle was about 0.61 m behind the pipe axis. After a few seconds the truck was moved back to its starting position.

_{φ}and axial stresses σ

_{x}according to Equations (1) and (2), respectively.

_{1}= 6540 kg and G

_{2}= 7560 kg, is negligible with regards to the state of stress of the pipe, provided that the backfill cover is 1.5 m or greater. This is particularly valid for pressurized pipes, as in the case of high-pressure gas pipelines. It is understood that a real gas pipeline, with its length being multiple times greater than that of the test pipe, will experience somewhat different boundary conditions. However, it can be assumed that the actual magnitudes of the surface stresses will not differ much from the results presented here. It is also clear that the effect of driving a heavy vehicle over a buried pipe will be greater the larger the mass of the vehicle and the smaller the backfill cover.

## 3. Engineering Estimation of the State of Stress of a Buried Pipe

#### 3.1. Backfilling of a Soil

_{z}, can be determined by Equation (3):

_{i}is mass density of the i-th soil constituent and h

_{i}is height of the i-th layer of the soil cover. Proceeding from the surface of the soil cover towards the test pipe, we shall consider magnitudes of the mass density and the height of the soil constituents shown in Table 6.

^{2}, we arrive at p

_{z}= 27,154 kg/m/s

^{2}= 0.02715 MPa. This pressure is only valid at the 12 o’clock position though. At the 6 o’clock position, the pressure will be higher by a magnitude of p

_{G}= 765 Pa, which corresponds to the weight of the test pipe. Therefore, the total pressure at the 6 o’clock position will be p’

_{z}= p

_{z}+ p

_{G}= 0.027915 MPa.

- Δy = vertical deflection of pipe, (mm)
- D = pipe outside diameter, (mm)
- d
_{l}= deflection lag factor (~1.0–1.5), - d
_{b}= bedding constant (~0.1), - p
_{z}= pressure on pipe due to soil load, (MPa) - (EI)
_{eq}= equivalent pipe wall stiffness as composed of the stiffness of the bare pipe (EI), lining (E_{L}I_{L}) and coating (E_{C}I_{C}) per mm of pipe length, (Nmm) - I = t
^{3}/12, [mm^{3}] - t = wall thickness of pipe, (mm)
- r = mean pipe radius, (mm)
- E′ = modulus of soil reaction, (MPa)

_{b}obtains the value 0.102, and the deflection factor d

_{l}obtains the value 1.0. The modulus of soil reaction is taken as E′ = 9.4 MPa. After substituting these values into Equation (4) we arrive at Δy/D = 0.00328. As a matter of interest, it can be determined that the vertical deflection of the pipe is Δy = 0.00328 × 508 = 1.67 mm. At the 6 o’clock position, the ratio Δy/D will be greater than that at the 12 o’clock position, namely by the ratio p’

_{z}/p

_{z}= 0.027915/0.02715, thus resulting at Δy/D = 0.00337. The bending stress σ

_{b}through the wall thickness due to ovalization of the pipe is given by Equation (5),

_{b}as calculated by Equation (5) is ±33.5 MPa at the 12 o’clock position and ±34.4 MPa at the 6 o’clock position.

#### 3.2. Crossing the Buried Pipe with the Vehicle

- p
_{V}pressure transmitted to the pipe, (MPa) - G concentrated load at the surface above pipe. (N)
- h depth of soil cover above the pipe, (mm)
- d offset distance from the pipe to the line of application of the surface load, (mm)

_{1}, and its magnitude is G

_{1}/2 = 6540/2 = 3270 kg = 32,079 N. Similarly, the mass load acting on a single wheel of the rear axle is denoted here by the symbol Q

_{2}, and its magnitude is G

_{2}/2 = 7560/2 = 3780 kg = 37,082 N.

#### 3.2.1. Step I

#### 3.2.2. Step II

_{V}) have the same effect locally as those of the backfill cover, so that at the 6 and 12 o’clock positions there is compression at the outside surface of the pipe and tension at the inside surface of the pipe.

_{b}in the buried pipe in step I and step II loading, the respective pressure p

_{V}transmitted to the pipe is substituted into Equation (4) to obtain the pipe ovality Δy/D, which is then substituted into Equation (5). Considering the following magnitudes: d

_{b}= 0.102, d

_{l}= 1.0, EI = 4.293 × 10

^{6}Nmm, r = 251 mm, and E′ = 9.4 MPa, we can arrive at

- ${\sigma}_{b}=\pm 9.42\mathrm{M}\mathrm{P}\mathrm{a}$ for step I loading${\sigma}_{b}=\pm 9.06\mathrm{M}\mathrm{P}\mathrm{a}$ for step II loading

#### 3.3. Summary

_{φ}are concerned.

## 4. Conclusions and Observations

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 17.**Illustration of positions of the left-hand wheels at step I and step II loading. (Dimensions are in meters).

R_{t0.5} (MPa) | R_{m} (MPa) | KV (J) |
---|---|---|

400 | 578 | 72 |

Position (h) | 12 | 3 | 6 | 9 | ||||
---|---|---|---|---|---|---|---|---|

Strain (10^{−6}) | Hoop | Axial | Hoop | Axial | Hoop | Axial | Hoop | Axial |

no load | −165 | 43 | 159 | −22 | −159 | −27 | 141 | 11 |

step I | −173.4 | 26 | 174.6 | −7.2 | −170.2 | −10.5 | 154.1 | 28.1 |

step II | −189.2 | 17.2 | 187.6 | −0.7 | −178.8 | −8.7 | 168.5 | 32.6 |

Position (h) | 12 | 3 | 6 | 9 | ||||
---|---|---|---|---|---|---|---|---|

Strain (10^{−6}) | Hoop | Axial | Hoop | Axial | Hoop | Axial | Hoop | Axial |

no load | 890 | 308 | 829 | 215 | 1028 | 229 | 964 | 208 |

step I | 896 | 296.5 | 832 | 215 | 1020.5 | 241 | 965 | 218.5 |

step II | 902 | 313.5 | 832 | 218 | 1029.5 | 239.5 | 958.5 | 220.5 |

Position (h) | 12 | 3 | 6 | 9 | ||||
---|---|---|---|---|---|---|---|---|

Strain (10^{−6}) | Hoop | Axial | Hoop | axial | HOOP | Axial | Hoop | Axial |

no load | 843 | 278 | 688 | 183 | 988 | 186 | 876 | 181 |

step I | 828 | 259 | 700.5 | 188.5 | 979.5 | 202 | 885.5 | 194.5 |

step II | 837 | 266 | 696 | 184 | 981 | 201 | 883 | 191 |

Loading | Range of Differential Stresses | |
---|---|---|

Hoop Stress (MPa) | Axial Stress (MPa) | |

crossing I (p = 0 MPa) | (−7; 8) | (−7.5; 7) |

crossing II (p = 5.5 MPa) | (−1; 3) | (−2; 2) |

crossing III (p = 5.2 MPa) | (−4.5; 3) | (−5.5; 3.5) |

Layer | Mass Density (kg/m ^{3}) | Height (m) |
---|---|---|

backfill soil | 1730 | 0.6 |

agregate | 1900 | 0.5 |

compacted earth | 2000 | 0.2 |

sand | 1900 | 0.2 |

Loading | Hoop Stresses σ_{φ} (MPa) Determined by | |
---|---|---|

Soil Mechanics | Strain Gauge Measurement | |

backfill | −33.5 | −34.4 |

step I | −9.4 | −3.1 |

step II | −9.1 | −7.2 |

p = 5.5 MPa | 221.7 * | 222.4 |

p = 5.2 MPa | 209.7 * | 209.7 |

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**MDPI and ACS Style**

Gajdoš, Ľ.; Šperl, M.; Kec, J.; Crha, P.
The Effect of Heavy-Duty Vehicle Crossings on the State of Stress of Buried Pipelines. *Metals* **2022**, *12*, 153.
https://doi.org/10.3390/met12010153

**AMA Style**

Gajdoš Ľ, Šperl M, Kec J, Crha P.
The Effect of Heavy-Duty Vehicle Crossings on the State of Stress of Buried Pipelines. *Metals*. 2022; 12(1):153.
https://doi.org/10.3390/met12010153

**Chicago/Turabian Style**

Gajdoš, Ľubomír, Martin Šperl, Jan Kec, and Petr Crha.
2022. "The Effect of Heavy-Duty Vehicle Crossings on the State of Stress of Buried Pipelines" *Metals* 12, no. 1: 153.
https://doi.org/10.3390/met12010153