# SPH Simulations of Real Sea Waves Impacting a Large-Scale Structure

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## Abstract

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## 1. Introduction

## 2. Study Case

#### 2.1. The Pont del Petroli Pier

#### 2.2. Storm Gloria: Description and Damage to the Pont del Petroli

## 3. Numerical Model

#### 3.1. The DualSPHysics Code

#### 3.2. Validation

#### 3.3. Model Set-Up

## 4. Results and Discussion

#### Derived Pile Axial Loads and Soil Bearing Capacity

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**1980s (

**left**) and 2017 (

**right**) aerial photos of the Pont del Petroli. Originally constructed for industrial purposes, the pier is now open to the public. (Sources: Concepció Riba).

**Figure 2.**Geometrical details and top view of the platform, beam and pile cap forming the Pont del Petroli pier. The sketches are extracted from the first design report and provided by the Maritime Engineering Laboratory of Universitat Politècnica de Catalunya-BarcelonaTech (LIM/UPC) for the present manuscript. The sketches belong to the original project deposited in the 1965 archive "Colegio de Ingenieros de Caminos, Canales y Puertos de Madrid", PN 9280/65, under José Entrecanales Ibarra.

**Figure 3.**Beach profiles at Pont del Petroli. The original beach profile from the design report is indicated by a blue line. In red, the two profiles surveyed by LIM/UPC before and after storm Gloria.

**Figure 4.**View of the Catalan coast between Barcelona and Capo Begur. (Map Data: Google Earth, SIO, NOAA, U.S. Navy, NGA, GEBCO).

**Figure 5.**A large wave hitting the platform of the Pont del Petroli during storm Gloria. (Source: Badalona City Council).

**Figure 6.**Sketch of the experimental layout. The 2-D numerical model mimics this layout to a great extent. Conversely, the 3-D model has an open boundary for wave generation at the inlet, i.e., at $x=50$ m.

**Figure 7.**Snapshots of the SPH horizontal velocity contours for the test case A1. (

**a**) Time: 10.350 s; (

**b**) Time: 10.800 s; (

**c**) Time: 10.975 s; (

**d**) Time: 11.100 s.

**Figure 8.**Snapshots of the SPH horizontal velocity contours for the test case B1. (

**a**) Time: 10.350 s; (

**b**) Time: 10.600 s; (

**c**) Time: 10.850 s; (

**d**) Time: 11.100 s.

**Figure 9.**Time history of the normalized (

**a**) horizontal and (

**b**) vertical forces on the pier platform for different tested wave conditions.

**Figure 10.**Time history of the normalized forces on the beam and pile cap for different tested wave conditions: (

**a**) horizontal force on the pier beam, (

**b**) vertical force on the pier beam, (

**c**) horizontal force on the pile cap and (

**d**) vertical force on the pile cap.

Element | Main Exposed Area (Volume) | Self-Weight | Distributed Vertical Load (Self-Weight + Accidental Load) | Final Design Vertical Load |
---|---|---|---|---|

Platform | 9.75 m × 6.75 m | 32.90 tons | 2.00 tons/m${}^{2}$ | 131.62 tons |

$\pi $-shaped beam | 15.00 m × 3.20 m | 29.25 tons | 3.60 tons/m${}^{2}$ | 54.00 tons |

Pile cap (2 piles) | 4.40 m × 0.8 (×1.2) m | 9.12 tons | 12.30 tons/m${}^{2}$ | 54.12 tons |

Pile cap (4 piles) | 4.40 m × 0.8 (×2.0) m | 15.20 tons | 15.80 tons/m${}^{2}$ | 60.20 tons |

Test Case | Wave Conditions at Generation in 2-D (in Prototype Scale) | Scaling Factor for $\mathit{u}\left(\mathit{t}\right)$ from Equation (6) |
---|---|---|

A1 | $H=6.5$ m, $T=12.0$ s | 1.00 |

A2 | 1.05 | |

A3 | 1.10 | |

B1 | $H=8.2$ m, $T=12.7$ s | 1.00 |

B2 | 0.95 | |

B3 | 1.05 |

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**MDPI and ACS Style**

Altomare, C.; Tafuni, A.; Domínguez, J.M.; Crespo, A.J.C.; Gironella, X.; Sospedra, J. SPH Simulations of Real Sea Waves Impacting a Large-Scale Structure. *J. Mar. Sci. Eng.* **2020**, *8*, 826.
https://doi.org/10.3390/jmse8100826

**AMA Style**

Altomare C, Tafuni A, Domínguez JM, Crespo AJC, Gironella X, Sospedra J. SPH Simulations of Real Sea Waves Impacting a Large-Scale Structure. *Journal of Marine Science and Engineering*. 2020; 8(10):826.
https://doi.org/10.3390/jmse8100826

**Chicago/Turabian Style**

Altomare, Corrado, Angelantonio Tafuni, José M. Domínguez, Alejandro J. C. Crespo, Xavi Gironella, and Joaquim Sospedra. 2020. "SPH Simulations of Real Sea Waves Impacting a Large-Scale Structure" *Journal of Marine Science and Engineering* 8, no. 10: 826.
https://doi.org/10.3390/jmse8100826