# The Role of Soil Structure Interaction in the Fragility Assessment of HP/HT Unburied Subsea Pipelines

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## Abstract

**:**

## 1. Introduction

## 2. Numerical Model

^{−4}) to avoid problems associated with the equations system conditions. Vertical directions were restrained while longitudinal and transversal directions were set free to allow soil shear deformations. The performed soil mesh (200 m × 200 m, 25 m depth, Figure 2) was selected with a convergence study between several meshes that allowed to select the one presented herein. It is built up with 7450 modes and 6430 non-linear solid brick elements called ‘‘Bbar brick’’ [34,35]. These dimensions have been determined following the suggestions already applied in [36,37,38], and the discretisation was built up with relatively small elements around the pipeline and gradually larger toward the outer mesh boundaries. The wave propagation is realistically represented by adopting transmitting boundaries located (at 100 m from the centre of the mesh) as far as possible from the pipeline to decrease any effect on the response. In particular, base and lateral boundaries have been modelled to be impervious to represent a small section of a presumably infinite (or at least very large) soil domain and to allow the seismic energy to be removed from the site itself [36,37,38,39]. In order to validate these assumptions, the mesh was verified by comparing the acceleration at the top of the mesh with those calculated for free field (FF) conditions.

## 3. Pipeline Failure Criteria

_{Sd}is the design compressive strain, p

_{i}and pe are the internal and external pressures, respectively, and γ

_{ε}is the resistance strain factor. The burst pressure p

_{b}is calculated from:

_{gw}) is equal to 1 with D/t = 20. For the pipe studied herein with parameters represented in Table 1, ε

_{c}is equal to 0.06.1 mm/mm. The resistance strain factor γ

_{ε}for three different classes, low, medium, and high, are equal to 2.0, 2.5, and 3.3, respectively [48]. The design compressive strain ε

_{Sd}for different classes are represented in Table 3. The strain at failure (local buckling of the compressive side) from the FE analysis [6] is also given in Table 3. Fragility curves were applied in order to consider a probabilistic-based methodology that may consider the mutual interaction between soil deformability and the behaviour of HP/HT unburied subsea pipelines. In this regard, ref. [49] proposed a methodology for the derivation of fragility curves for existing structures. In the present paper, fragility curves were developed by considering predefined limit states (LS) of the maximum strains (Table 3) at which the probability of exceedance was calculated. The seismic scenario consisted of 17 input motions with different intensity measures (IMs) in order to assess a wide range of damage in the pipeline (more details in [6]). Figure 4 shows the spectra of the selected 17 input motions and the corresponding peak ground accelerations (PGAs), while the characteristics of the inputs are shown in Table 4. The compression at the crown of the pipeline was considered as the reference parameter to express the damage condition.

## 4. Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

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**Figure 1.**Pipeline and sleeper model used in the thermal buckling and seismic/thermal interaction analyses.

Property | Value |
---|---|

Length, L (m) | 2000 |

Outer diameter, OD (mm) | 254 |

Wall thickness, t (mm) | 12.7 |

Thermal expansion coefficient, α (°C^{−1}) | 1.01 × 10^{−5} |

Young’s modulus, E (MPa) | 206,000 |

Poisson’s ratio, ν | 0.3 |

Lateral imperfection ratio, h_{0}/l0 | 0.012 |

Submerged weight, q (N/m) | 1500 |

Seabed friction coefficient, µ_{1} | 0.5 |

Sleeper friction coefficient, µ_{2} | 0.3 |

Sleeper height, h (m) | 0.5 |

SOIL1 | SOIL2 | SOIL3 | |
---|---|---|---|

Mass density (Mg/m^{3}) | 2.0 | 1.7 | 1.5 |

Shear Modulus (kPa) | 7.2 × 10^{5} | 1.53 × 10^{5} | 6 × 10^{4} |

Bulk Modulus (kPa) | 1.56 × 10^{6} | 3.32 × 10^{5} | 3 × 10^{5} |

Cohesion (kPa) | 100 | 50 | 37 |

Shear wave velocity (m/s) | 600 | 300 | 200 |

ε_{Sd} (mm/mm) | |||||
---|---|---|---|---|---|

OD (mm) | t (mm) | f_{Y} (MPa) | Low Safety Class | Medium Safety Class | High Safety Class |

254 | 12.7 | 448 | 3.0 × 10^{−2} | 2.44 × 10^{−2} | 1.85 × 10^{−2} |

Input Motion | Station | PGA [g] | Duration [s] |
---|---|---|---|

1 | BORREGO | 1.24 | 40.00 |

2 | AZE | 1.66 | 40.00 |

3 | CAP | 5.01 | 40.00 |

4 | CNP | 3.53 | 25.00 |

5 | H-PVB | 3.68 | 40.00 |

6 | SCS | 6.00 | 40.00 |

7 | BLC | 0.66 | 40.00 |

8 | H-COS | 1.44 | 40.00 |

9 | H-CAL | 1.26 | 40.00 |

10 | A-KOD | 1.51 | 21.00 |

11 | Northridge | 8.57 | 15.00 |

12 | Takatori | 7.20 | 40.00 |

13 | Llolleo | 3.54 | 116.50 |

14 | Erzican | 4.33 | 18.00 |

15 | Lucerne Valley | 7.12 | 40.00 |

16 | Imperial Valley | 3.09 | 22.00 |

17 | Trinidad | 2.28 | 21.40 |

SOIL1 | LS1 | LS2 | LS3 | LS4 |
---|---|---|---|---|

β | 0.793 | 0.809 | 0.821 | 0.833 |

μ | 0.165 g | 0.176 g | 0.196 g | 0.207 g |

SOIL2 | LS1 | LS2 | LS3 | LS4 |
---|---|---|---|---|

β | 0.776 | 0.781 | 0.791 | 0.799 |

μ | 0.156 g | 0.169 g | 0.183 g | 0.196 g |

SOIL3 | LS1 | LS2 | LS3 | LS4 |
---|---|---|---|---|

β | 0.749 | 0.728 | 0.670 | 0.705 |

μ | 0.144 g | 0.149 g | 0.158 g | 0.168 g |

PGA = 0.30 g | LS1 | LS2 | LS3 | LS4 |
---|---|---|---|---|

SOIL1 | 0.77 | 0.73 | 0.70 | 0.68 |

SOIL2 | 0.80 | 0.78 | 0.72 | 0.70 |

SOIL3 | 0.84 | 0.83 | 0.81 | 0.79 |

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**MDPI and ACS Style**

Forcellini, D.; Mina, D.; Karampour, H. The Role of Soil Structure Interaction in the Fragility Assessment of HP/HT Unburied Subsea Pipelines. *J. Mar. Sci. Eng.* **2022**, *10*, 110.
https://doi.org/10.3390/jmse10010110

**AMA Style**

Forcellini D, Mina D, Karampour H. The Role of Soil Structure Interaction in the Fragility Assessment of HP/HT Unburied Subsea Pipelines. *Journal of Marine Science and Engineering*. 2022; 10(1):110.
https://doi.org/10.3390/jmse10010110

**Chicago/Turabian Style**

Forcellini, Davide, Daniele Mina, and Hassan Karampour. 2022. "The Role of Soil Structure Interaction in the Fragility Assessment of HP/HT Unburied Subsea Pipelines" *Journal of Marine Science and Engineering* 10, no. 1: 110.
https://doi.org/10.3390/jmse10010110