# Effect of Ovality Length on Collapse Strength of Imperfect Sandwich Pipes Due to Local Buckling

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Validation of the Finite Element Calculations

_{o}) and that of the inner pipe (R

_{i}) of the three cases are very similar. The thickness of the outer pipe (t

_{o}) is set to be the same in three cases, as well as that of the inner pipe (t

_{i}). The difference between the three cases is the ovality of the outer (Δ

_{o}) and inner (Δ

_{i}) pipe is changeable.

_{e}) measured in experiments from [6] and the collapse strength (P

_{co}) from FEM calculation in this research.

## 3. Effect of Ovality Shape in the Circumferential Direction

_{0}is the maximum amplitude;

_{c}is the number of half-waves in the circumferential direction;

_{c}is selected to be 2, 3, and 4. In this section, half of the whole circle is modelled in each case instead of one quarter in the previous because of the case Nc3. The cross-sections of three patterns are shown in Figure 4, with a scale factor of 100 for a clear illustration. The comparison result of the collapse pressure of the sandwich pipes is shown in Table 5.

_{c}= 2 is the most severe situation. Therefore, in this paper, the half wave number in the circumferential direction is set to be 2 for the parametrical study.

## 4. Parametric Study

_{o}/R

_{i}is almost evenly distributed between 1.2 and 2.0. In this section, the ovality of the outer and inner pipe is selected to be of the same value, unlike that in [18], since the effect of ovality is not the principal task in this research.

_{o}is selected, this parameter means the gradient of an ovality in SPs axial direction. In this regard, 240 cases are calculated in each group. The case name is represented by a five-number ‘abcde’, as shown in Table 7. In detail, ‘a’ means the group, ‘b’ means the ratio of radius and thickness of the outer pipe, ‘c’ means the ratio of radius and thickness of the inner pipe, ‘d’ means the ovality length, and ‘e’ means the ovality.

_{co}) and ovality (Δ) and ovality length (λ) are shown in Figure 5 and Figure 6, respectively.

_{o}describe the features of ovality, R

_{o}/t

_{o}, R

_{i}/t

_{i,}and R

_{o}/R

_{i}describe the collapse strength of intact SPs.

_{fit}) contains several constants. These constants are regarded as the effect of material properties of SPs.

_{o}is too large, for example, when λ = 1200 mm, the value of λ/R

_{o}is 20. A large value of λ/R

_{o}means the ovality area occurred to a large part of SPs. The issue discussed in this research focuses on the local buckling so that the cases with λ/R

_{o}ratios large than 16 are removed. Therefore, 1136 cases are summarized. The comparison result of the other cases between fitted equation and calculation is shown in Figure 7, in which good agreement is achieved.

_{o}are the features to describe the ovality. Except for these two parameters, the other two variables, R

_{o}/R

_{i}and R/t, describe the geometrical property of the SP It is concluded that the R/t ratio is a dominant factor not only in the collapse strength of the single-walled pipes but also in the collapse strength of SPs. The influence of the core layer is described by R

_{o}/R

_{i}, a higher value of it means a thicker layer of the core material. There are several constant values included in Equation (3) controlled by the physical properties of SP, since the material has not been changed in this research. The influence of the physical properties is worth to be investigated in the future.

_{o}/R

_{i}and decrease in R/t can both lead to the improvement of the collapse strength of imperfect SPs.

## 5. Discussion

_{o}/R

_{i}is set, that means for a certain SP, the effect of ovality is a more dominant factor of ovality to reduce the loading capacity when the SP is acted by external pressure.

_{o}/R

_{i}is shown in Figure 9. In both figures, the ovality is the same with the parameter λ/R

_{o}= 2.0 and Δ = 0.2%. It is clear that the collapse strength is greater of SPs with a higher value of R

_{o}/R

_{i}or a lower value of R/t. The changing rates of the curves are almost the same in both figures. However, it is concluded from the expression of C in Equation (3) that the influence of R/t is greater than that of R

_{o}/R

_{i}by checking the partial derivatives of both parameters. Due to the material strength of the metal pipe that is much higher than that of the core layer, the improvement of strength of both outer and inner pipes results in significant promotion of the collapse strength of SPs. Thus, in order to obtain SPs with a higher carrying capacity of external pressure, it is recommended to increase the strength of metal pipes, especially the inner pipe.

_{o}greater than 16 are taken out of consideration. From the comparison result of calculation and Equation (3), the error of most cases is smaller than 20%, except for 51 cases out of 1136. The average value of error is only 4.4%, which indicates a good fit.

## 6. Conclusions

_{o}/R

_{i}in the range of 1.2 to 2.0, ratios of R

_{o}/t

_{o}and R

_{i}/t

_{i}in the ranges of 20 to 50, and the ratio of λ/R

_{o}in the range of 0.5 to 15. The relationship between the collapse strength and ovality length and ovality follows a power function. Fitting 1200 cases of numerical calculations, Equation (3) is derived. Good agreement is achieved between Equation (3) and calculation results, leading to the conclusion that the proposed simplified model can be efficiently used in the evaluation of the collapse pressure of subsea pipelines.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Silva, L.M.R.; Teixeira, A.P.; Guedes Soares, C. A methodology to quantify the risk of subsea pipeline systems at the oilfield development selection phase. Ocean Eng.
**2019**, 179, 213–225. [Google Scholar] [CrossRef] - Silva, L.M.R.; Guedes Soares, C. Oilfield development system optimization under reservoir production uncertainty. Ocean Eng.
**2021**, 225, 108758. [Google Scholar] [CrossRef] - Wang, Z.K.; Guedes Soares, C. Upheaval thermal buckling of functionally graded subsea pipelines. Appl. Ocean Res.
**2021**, 116, 102881. [Google Scholar] [CrossRef] - Castello, X.; Estefen, S.F. Limit strength and reeling effects of sandwich pipes with bonded layers. Int. J. Mech. Sci.
**2007**, 49, 577–588. [Google Scholar] [CrossRef] - An, C.; Castello, X.; Duan, M.; Toledo Filho, R.D.; Estefen, S.F. Ultimate strength behaviour of sandwich pipes filled with steel fiber reinforced concrete. Ocean Eng.
**2012**, 55, 125–135. [Google Scholar] [CrossRef] - An, C.; Duan, M.; Toledo Filho, R.D.; Estefen, S.F. Collapse of Sandwich Pipes with PVA Fiber Reinforced Cementitious Composites Core under External Pressure. Ocean Eng.
**2014**, 82, 1–13. [Google Scholar] [CrossRef] - Gong, S.; Wang, X.; Zhang, T.; Liu, C. Buckle propagation of sandwich pipes under external pressure. Eng. Struct.
**2018**, 175, 339–354. [Google Scholar] [CrossRef] - Netto, T.A.; Santos, J.M.C.; Estefen, S.F. Sandwich pipes for ultra-deep waters. In Proceedings of the 4th International Pipeline Conference, Calgary, AB, Canada, 29 September–3 October 2002; Volume 36207, pp. 2093–2101. [Google Scholar] [CrossRef]
- Xia, M.; Kemmochi, K.; Takayanagi, H. Analysis of filament-wound fiber-reinforced sandwich pipe under combined internal pressure and thermomechanical loading. Compos. Struct.
**2001**, 51, 273–283. [Google Scholar] [CrossRef] - Paz, C.M.; Fu, G.; Estefen, S.F.; Lourenço, M.I.; Chujutalli, J.A.H. Sandwich pipe: Reel-lay installation effects. In Proceedings of the ASME 34th International Conference on Ocean, Offshore and Arctic Engineering, St. John’s, NL, Canada, 31 May–5 June 2015. OMAE2015-41089. [Google Scholar] [CrossRef]
- Xu, Q.; Gong, S.; Hu, Q. Collapse analyses of sandwich pipes under external pressure considering inter-layer adhesion behaviour. Mar. Struct.
**2016**, 50, 72–94. [Google Scholar] [CrossRef] - Arjomandi, K.; Taheri, F. Stability and post-buckling response of sandwich pipes under hydrostatic external pressure. Int. J. Press. Vessel. Pip.
**2011**, 88, 138–148. [Google Scholar] [CrossRef] - Jin, Z.; Shen, X.; Yan, S.; Ye, H.; Gao, Z.; Chen, Z. A three-dimensional analytical solution for sandwich pipe systems under linearly varying external pressures. Ocean Eng.
**2016**, 124, 298–305. [Google Scholar] [CrossRef] - Hastie, J.C.; Kashtalyan, M.; Guz, I.A. Analysis of filament-wound sandwich pipe under combined internal pressure and thermal load considering restrained and closed ends. Int. J. Press. Vessel. Pip.
**2021**, 191, 104350. [Google Scholar] [CrossRef] - Chen, B.Q.; Guedes Soares, C. Experimental and numerical investigation on welding simulation of long stiffened steel plate specimen. Mar. Struct.
**2021**, 75, 102824. [Google Scholar] [CrossRef] - Yang, J.; Paz, C.M.; Estefen, S.F.; Fu, G.; Lourenço, M.I. Collapse pressure of sandwich pipes with strain-hardening cementitious composite-Part 1, Experiments and parametric study. Thin-Walled Struct.
**2020**, 148, 106605. [Google Scholar] [CrossRef] - Yang, J.; Estefen, S.F.; Fu, G.; Paz, C.M.; Lourenço, M.I. Collapse pressure of sandwich pipes with strain-hardening cementitious composite-Part 2, A suitable prediction equation. Thin-Walled Struct.
**2020**, 148, 106606. [Google Scholar] [CrossRef] - Li, R.; Chen, B.; Guedes Soares, C. Design equation for the effect of ovality on the collapse strength of sandwich pipes. Ocean Eng.
**2021**, 235, 109367. [Google Scholar] [CrossRef] - Li, R.; Guedes Soares, C. Numerical study on the effects of multiple initial defects on the collapse strength of pipelines under external pressure. Int. J. Press. Vessel. Pip.
**2021**, 194, 104484. [Google Scholar] [CrossRef]

**Figure 1.**Strain–stress relationship of SPs materials in the experiment by An et al. [6].

**Figure 4.**Half-wave numbers in the circumferential direction with the value of Δ is 0.2% (scale factor: 100).

**Figure 7.**Comparison between the results obtained by using the fitted equation and from the calculation.

**Figure 9.**The relationship between collapse strength and parameter R

_{o}/R

_{i}(λ/R

_{o}= 2.0, Δ = 0.2%).

**Table 1.**Geometrical parameters of cases performed by An et al. [6] in experiments.

Case | R_{o} (mm) | R_{i} (mm) | t_{o} (mm) | t_{i} (mm) | Δ_{o} (%) | Δ_{i} (%) |
---|---|---|---|---|---|---|

SP1 | 101.4 | 76.2 | 2.0 | 1.8 | 0.41 | 0.32 |

SP2 | 101.5 | 76.3 | 2.0 | 1.8 | 0.47 | 0.22 |

SP3 | 101.5 | 76.3 | 2.0 | 1.8 | 0.39 | 0.23 |

**Table 2.**Comparison of FEM calculation and experiment results from [6].

Case | Results in [6], P_{e} (MPa) | Results from FEM, P_{co} (MPa) | Error (%) * |
---|---|---|---|

SP1 | 30.5 | 29.9 | −1.97 |

SP2 | 30.6 | 30.0 | −1.96 |

SP3 | 29.7 | 30.0 | 1.01 |

_{co}− P

_{e})/P

_{e}× 100%.

Case | Axial Direction (Half-Length) | Circular Direction (1/4 Circle) | Thickness Direction for Core Layer | Thickness Direction for Metal Pipe | ||||
---|---|---|---|---|---|---|---|---|

Number of Elements | Element Size (mm) | Number of Elements | Element Size (°) | Number of Elements | Element Size (mm) | Number of Elements | Element Size, o/i (mm) | |

N16 | 100 | 6 | 16 | 5.625 | 3 | 7.73 | 1 | 2/1.8 |

N20 | 120 | 5 | 20 | 4.5 | 4 | 5.8 | 1 | 2/1.8 |

N30 | 120 | 5 | 30 | 3 | 6 | 3.87 | 1 | 2/1.8 |

N40 | 200 | 3 | 40 | 2.25 | 8 | 2.9 | 2 | 1/0.9 |

N60 | 300 | 2 | 60 | 1.5 | 12 | 1.93 | 3 | 0.67/0.6 |

Case | Results in [6], P_{e} (MPa) | N16 | N20 | N30 | N40 | N60 | |||||
---|---|---|---|---|---|---|---|---|---|---|---|

P_{co} (MPa) | Error (%) * | P_{co} (MPa) | Error (%) * | P_{co} (MPa) | Error (%) * | P_{co} (MPa) | Error (%) * | P_{co} (MPa) | Error (%) * | ||

SP1 | 30.5 | 30.2 | −0.98 | 29.9 | −1.97 | 29.8 | −2.30 | 29.1 | −4.59 | 28.8 | −5.57 |

SP2 | 30.6 | 30.2 | −1.31 | 30.0 | −1.96 | 29.8 | −2.61 | 29.0 | −5.23 | 28.8 | −5.88 |

SP3 | 29.7 | 30.3 | 2.02 | 30.0 | 1.01 | 29.9 | 0.67 | 29.0 | −2.36 | 28.8 | −3.03 |

_{co}− P

_{e})/P

_{e}× 100%.

Case | Results in [6], P_{e} (MPa) | Nc2 | Nc3 | Nc4 | |||
---|---|---|---|---|---|---|---|

P_{co} (MPa) | Error (%) * | P_{co} (MPa) | Error (%) * | P_{co} (MPa) | Error (%) * | ||

SP1 | 30.5 | 30.0 | −1.74 | 30.3 | −0.66 | 32.2 | 5.42 |

SP2 | 30.6 | 30.0 | −1.95 | 30.3 | −0.87 | 32.2 | 5.08 |

SP3 | 29.7 | 30.0 | 1.12 | 30.4 | 2.30 | 32.2 | 8.26 |

_{co}− P

_{e})/P

_{e}× 100%.

Group | R_{o} (mm) | R_{i} (mm) | R_{o}/R_{i} |
---|---|---|---|

1 | 60 | 50 | 1.2 |

2 | 100 | 70 | 1.43 |

3 | 80 | 50 | 1.6 |

4 | 90 | 50 | 1.8 |

5 | 100 | 50 | 2.0 |

a | Group | b,c * | R/t | d | λ (mm) | d | λ (mm) | e | Δ (%) |
---|---|---|---|---|---|---|---|---|---|

1 | 1 | 1 | 20 | 1 | 50 | 5 | 200 | 1 | 0.01 |

2 | 2 | 2 | 25 | 2 | 80 | 6 | 300 | 2 | 0.05 |

3 | 3 | 3 | 40 | 3 | 120 | 7 | 400 | 3 | 0.2 |

4 | 4 | 4 | 50 | 4 | 160 | 8 | 600 | 4 | 1 |

5 | 5 | 9 | 1200 |

_{o}/t

_{o}; c: R

_{i}/t

_{i}.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Li, R.; Chen, B.-Q.; Guedes Soares, C.
Effect of Ovality Length on Collapse Strength of Imperfect Sandwich Pipes Due to Local Buckling. *J. Mar. Sci. Eng.* **2022**, *10*, 12.
https://doi.org/10.3390/jmse10010012

**AMA Style**

Li R, Chen B-Q, Guedes Soares C.
Effect of Ovality Length on Collapse Strength of Imperfect Sandwich Pipes Due to Local Buckling. *Journal of Marine Science and Engineering*. 2022; 10(1):12.
https://doi.org/10.3390/jmse10010012

**Chicago/Turabian Style**

Li, Ruoxuan, Bai-Qiao Chen, and C. Guedes Soares.
2022. "Effect of Ovality Length on Collapse Strength of Imperfect Sandwich Pipes Due to Local Buckling" *Journal of Marine Science and Engineering* 10, no. 1: 12.
https://doi.org/10.3390/jmse10010012