# Experimental Study of the Effect of Backfill Conditions on Soil Responses around a Pipeline under Wave–Current Load

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Setup

## 3. Dynamic Response around the Pipeline with Different Backfill Depth

#### 3.1. Dynamic Response around the Pipeline

#### 3.2. Dynamic Response Beneath the Pipeline

## 4. Dynamic Response around the Pipeline with Different Backfill Sands

#### 4.1. Effect of Backfill Sand

#### 4.2. Effect of Current Velocity and Direction

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Figure A1.**Variation of the dimensionless pore pressure amplitude around the pipeline with different backfill depths (e/D = 1/2, 3/2) and current velocities. (

**a**) e/D = 1/2; (

**b**) e/D = 3/2.

**Figure A2.**Variation of the dimensionless pore pressure amplitude around the pipeline with different backfill depths and current conditions (${U}_{c}=\pm $0.1 m/s, $\pm $0.2 m/s). (

**a**) ${U}_{c}$ = 0.1 m/s; (

**b**) ${U}_{c}$ = −0.1 m/s; (

**c**) ${U}_{c}$ = 0.2 m/s; (

**d**) ${U}_{c}$ = −0.2 m/s.

**Figure A3.**Variation of the dimensionless pore pressure amplitude beneath the pipeline with different backfill depths (e/D = 1/2, 3/2) and current conditions. (

**a**) e/D = 1/2; (

**b**) e/D = 3/2.

**Figure A4.**Variation of the dimensionless pore pressure amplitude beneath the pipeline under different backfill depths and current conditions (${U}_{c}=\pm $0.1 m/s, $\pm $0.2 m/s). (

**a**) ${U}_{c}$ = 0.1 m/s; (

**b**) ${U}_{c}$ = −0.1 m/s; (

**c**) ${U}_{c}$ = 0.2 m/s; (

**d**) ${U}_{c}$ = −0.2 m/s.

**Figure A5.**Variation of the dimensionless pore pressure amplitude around the pipeline with different backfill depths within the medium sand and silt seabed. (

**a**) ${\mathrm{d}}_{50}$ = 0.30 mm; (

**b**) ${\mathrm{d}}_{50}$ = 0.045 mm.

**Figure A6.**Variation of the dimensionless pore pressure amplitude around the pipeline under different current conditions within the medium sand and silt seabed. (

**a**) ${\mathrm{d}}_{50}$ = 0.30 mm; (

**b**) ${\mathrm{d}}_{50}$ = 0.045 mm.

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**Figure 3.**Variation curve of the dimensionless pore pressure amplitude around the pipeline under different backfill depths. (

**a**) P1; (

**b**) P2; (

**c**) P3; (

**d**) P4.

**Figure 4.**Variation of the dimensionless pore pressure amplitude around the pipeline with different backfill depths and current velocities. (

**a**) e/D = 0; (

**b**) e/D = 1; (

**c**) e/D = 2.

**Figure 5.**Variation of the dimensionless pore pressure amplitude around the pipeline with different backfill depths when ${U}_{c}$ = 0 m/s and $\pm $0.3 m/s. (

**a**) ${U}_{c}$ = 0 m/s; (

**b**) ${U}_{c}$ = 0.3 m/s; (

**c**) ${U}_{c}$ = −0.3 m/s.

**Figure 6.**Variation of the dimensionless pore pressure amplitude beneath the pipeline under different backfill depth and current conditions. (

**a**) e/D = 0; (

**b**) e/D = 1; (

**c**) e/D = 2.

**Figure 7.**Variation of the dimensionless pore pressure amplitude beneath the pipeline under different backfill depths when ${U}_{c}$ = 0 m/s and $\pm $0.3 m/s. (

**a**) ${U}_{c}$ = 0 m/s; (

**b**) ${U}_{c}$ = 0.3 m/s; (

**c**) ${U}_{c}$ = −0.3 m/s.

**Figure 8.**Variation of the dimensionless pore pressure amplitude around the pipeline with different backfill depths within the fine sand seabed.

**Figure 9.**Variation of the dimensionless pore pressure amplitude around the pipeline under different current conditions within the fine sand seabed.

Soil Parameter | Symbol | Fine Sand | Medium Sand | Silt |
---|---|---|---|---|

Median particle size | ${\mathrm{d}}_{50}$(mm) | 0.15 | 0.30 | 0.045 |

Relative weight of soil | ${\mathrm{s}=\mathsf{\gamma}}_{\mathrm{s}}/\mathsf{\gamma}$ | 2.68 | 2.67 | 2.61 |

Permeability Coefficient | $K$ (cm/s) | 3.57 × 10^{−3} | 2.68 × 10^{−2} | 3.20 × 10^{−7} |

Maximum Void Ratio | ${\mathrm{e}}_{\mathrm{max}}$ | 0.871 | 0.920 | 0.950 |

Minimum Void Ratio | ${\mathrm{e}}_{\mathrm{min}}$ | 0.411 | 0.514 | 0.523 |

Measured Void Ratio | e | 0.584 | 0.694 | 0.624 |

Natural Gravity | ${\mathsf{\gamma}}_{\mathrm{t}}$ (kN/m^{3}) | 16.90 | 17.2 | 16.17 |

Effective Gravity | ${\mathsf{\gamma}}^{\prime}$ (kN/m^{3}) | 10.34 | 9.819 | 11.05 |

Porosity | $\mathrm{n}=\mathrm{e}/(1+\mathrm{e})$ | 0.369 | 0.410 | 0.384 |

Relative Compactness | ${\mathrm{D}}_{\mathrm{r}}=\frac{{\mathrm{e}}_{\mathrm{max}}\text{}-\text{}\mathrm{e}}{{\mathrm{e}}_{\mathrm{max}}{\text{}-\text{}\mathrm{e}}_{\mathrm{min}}}$ | 0.624 | 0.557 | 0.763 |

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**MDPI and ACS Style**

Chen, H.; Guo, Y.; Yu, S.; Zhang, J.; Liu, S.
Experimental Study of the Effect of Backfill Conditions on Soil Responses around a Pipeline under Wave–Current Load. *J. Mar. Sci. Eng.* **2022**, *10*, 1384.
https://doi.org/10.3390/jmse10101384

**AMA Style**

Chen H, Guo Y, Yu S, Zhang J, Liu S.
Experimental Study of the Effect of Backfill Conditions on Soil Responses around a Pipeline under Wave–Current Load. *Journal of Marine Science and Engineering*. 2022; 10(10):1384.
https://doi.org/10.3390/jmse10101384

**Chicago/Turabian Style**

Chen, Hao, Yakun Guo, Shiqi Yu, Jisheng Zhang, and Sheng Liu.
2022. "Experimental Study of the Effect of Backfill Conditions on Soil Responses around a Pipeline under Wave–Current Load" *Journal of Marine Science and Engineering* 10, no. 10: 1384.
https://doi.org/10.3390/jmse10101384