# Seismic Dynamics of Pipeline Buried in Dense Seabed Foundation

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## Abstract

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## 1. Introduction

## 2. Coupled Numerical Model: FSSI-CAS 2D

## 3. Computational Domain, Boundary Condition, Seismic Wave and Parameters

_{L}= 9.0), is adopted as the input seismic wave (Figure 3). The input horizontal (E-W) and vertical (U-D) seismic acceleration wave are applied on the bottom of the seabed foundation simultaneously.

^{3}). Therefore, it can be modelled by elastic model. Here, the pipeline is considered as a kind of impermeable medium without porosity. The crude oil transported by the pipeline is considered as a kind of incompressible and fluidized elastic medium with a small value of Young’s elastic modulus. It means v = 0.5 and porosity n = 1.0. The density of crude oil is set as 0.85 g/cm

^{3}, which is significantly less than that of water. In computation, a great value of permeability 1.0 × 10

^{−1}m/s is given to the crude oil due to the fact that there is no a solid medium to block the flowing of crude oil in pipeline. In this study, the flowing process of crude oil in pipeline cannot be modelled in 2D condition. Consideration of the crude oil helps determine the effect of the crude oil mass on the seismic dynamics of pipeline-seabed system. In previous literature, such as Ling et al. [29], Luan et al. [30], and Zhang and Han [31], the pipeline is set as empty without any mass, resulting in that the effect of the mass of crude oil on the seismic dynamics of pipeline-seabed system is ignored. In this study, the consideration of crude oil in pipeline actually is an innovative point relative to previous studies.

^{3}, and the bulk modulus is 2.24 × 10

^{9}Pa. The saturation S

_{r}is set as 98% due to the fact that there are more or less NH3/CH4 or air bubbles in real seabed soil. It has been widely recognized and accepted that Biot’s equation can accurately describe the mechanical behavior of seabed soil when its saturation is greater than 95% by introducing a parameter, bulk of compressibility $\beta =\frac{1}{{\mathrm{K}}_{f}}+\frac{1-{\mathrm{S}}_{r}}{{p}_{w0}}$, where K

_{f}= 2.24 × 10

^{9}Pa is the bulk modulus of pure water, S

_{r}is the saturation of soil, and p

_{w0}is the absolute water pressure. Furthermore, the effect of temperature on properties of soil and pore water is not considered. Elastic modulus, permeability, and saturation of seabed soil are constant in computation, not depending on the confining pressure.

## 4. Results

#### 4.1. Initial Status

_{z}’ is not layered. However, the zone where the effective stress is affected by the pipeline is limited in the range x = 98 m to 102 m, and z = 16 m to 20 m. In the other zone, the distribution of effective stress is basically layered. Additionally, it is interesting to find that there is a small zone (labelled by red color) in the seabed beneath the pipeline where the effective stress is very small, comparing with that in the zone near to it. The physical mechanism is that some volume of pore water is expelled by the pipeline, resulting in an upward buoyancy applied on the pipeline. As a result, the effective stress in the seabed soil beneath the pipeline of course decreases. In the surrounding seabed soil of pipeline, the magnitude of shear stress is significant (greater than 5 kPa), and the distribution has symmetrical characteristics. Furthermore, there is also shear stress in the pipeline itself. However, there is no shear stress in the crude oil due to the fact that fluid cannot resist shear stress.

#### 4.2. Seismic Dynamics of Pipeline

_{1}on the two typical positions, A and B, labelled in Figure 2, are demonstrated. It is found that the wave form of the time histories on the two typical positions are basically the same, regardless of the pore pressure or the mean effective stress. They are all similar to the wave form of the input seismic wave on the bottom of seabed foundation. Due to the fact that the seabed soil is dense, poro-elastic model is used to describe the behavior of dense seabed soil in computation. There is only oscillatory pore pressure in seabed soil without the build-up of residual pore pressure. These characteristics are completely different compared to that in loosely deposited seabed soil [46,47].

#### 4.3. Effect of Lateral Boundary Condition

#### 4.4. Comparison with Pipeline-Gas System

^{3}). In this study, the seismic dynamics of pipeline-gas system buried in dense seabed foundation is also investigated under the same excitation of the input seismic wave. The time history of acceleration of the pipeline-gas system is demonstrated in Figure 11. Compared with the result of the pipeline-oil system shown in Figure 6, it is found that the difference of acceleration response between the two cases is not significant. The peak horizontal acceleration (0.242 g) of the pipeline-gas system is only slightly greater than that (0.225 g) of the pipeline-oil system. The peak vertical acceleration of the two systems are basically the same.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Sketch map of the pipeline-seabed system adopted in computation. A submarine pipeline is buried in the dense seabed foundation. Only the hydrostatic water pressure is applied on the surface of seabed, and the laminar boundary condition is applied on the two lateral sides.

**Figure 2.**Mesh system of the pipeline-seabed in computation (Noted: The crude oil in the pipeline is also considered, and only the mesh around the pipeline is shown).

**Figure 3.**Input seismic wave after wave filtering adopting the recorded seismic wave at the station MYGH03 (141.6412E, 38.9178N, buried depth = 120 m) at Karakuwa, Japan during 311 off-Pacific earthquake event. Noted: Noncausal butterworth filter is used; filtering range: f ≤ 0.03 Hz and f ≥ 30 Hz.

**Figure 4.**Displacement distribution of the pipeline-seabed in consolidated status. The effect of the pipeline on horizontal displacement is obvious, and the pipeline slightly subsides relative to its surrounding seabed soil.

**Figure 5.**Effective stress and pore pressure distribution of the pipeline-seabed in consolidated status. The distribution of the vertical effective stress σ

_{z}’ indicates that an upward buoyancy is applied on the pipeline.

**Figure 6.**Time history of acceleration of the pipeline responding to input seismic wave. It is shown that there is a significant resonance in horizontal direction.

**Figure 7.**Time history of displacement of the pipeline responding to input seismic wave. It is shown that there is a significant resonance in horizontal direction.

**Figure 8.**Time history of pore pressure and effective stress I

_{1}at the two typical position

**A**and

**B**in the seabed foundation labelled in Figure 2. There is no residual pore pressure built up in dense seabed soil.

**Figure 9.**Acceleration spectrum of the pipeline responding to input seismic wave. It is observed that there are two resonance periods (0.6 s and 1.85 s) for the pipeline-crude oil-seabed foundation system.

**Figure 10.**Effect of the fixed lateral side boundary on the dynamics of pipeline. It is shown that there is a significant adverse effect of the fixed lateral boundary condition on the horizontal dynamics.

**Figure 11.**Time history of acceleration of pipeline-gas system responding to input seismic wave. There is also a significant resonance if natural gas is transported by the pipeline.

**Figure 12.**Acceleration spectrum of pipeline-gas system responding to input seismic wave. It is shown that the difference of seismic dynamics of the pipeline-oil system and the pipeline-gas system is minor.

**Figure 13.**Amplification effect of the seabed soil along depth. It is confirmed that the seabed foundation has significant amplification effect to the input seismic wave in both horizontal and vertical direction.

Parameter | Seabed | Pipeline | Crude Oil |
---|---|---|---|

Elastic modulus E (MPa) | 20 | 200 × 10^{3} | 1 × 10^{−1} |

Poisson’s ratio v | 0.33 | 0.25 | 0.5 |

Porosity n | 0.4 | 0 | 1.0 |

Permeability k (m/s) | 1.0 × 10^{−5} | 0 | 1.0 × 10^{−1} |

Saturation Sr (%) | 98 | 0 | 100 |

Density ρ (g/cm^{3}) | 2.65 | 7.85 | 0.85 |

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**MDPI and ACS Style**

Zhang, Y.; Ye, J.; He, K.; Chen, S.
Seismic Dynamics of Pipeline Buried in Dense Seabed Foundation. *J. Mar. Sci. Eng.* **2019**, *7*, 190.
https://doi.org/10.3390/jmse7060190

**AMA Style**

Zhang Y, Ye J, He K, Chen S.
Seismic Dynamics of Pipeline Buried in Dense Seabed Foundation. *Journal of Marine Science and Engineering*. 2019; 7(6):190.
https://doi.org/10.3390/jmse7060190

**Chicago/Turabian Style**

Zhang, Yan, Jianhong Ye, Kunpeng He, and Songgui Chen.
2019. "Seismic Dynamics of Pipeline Buried in Dense Seabed Foundation" *Journal of Marine Science and Engineering* 7, no. 6: 190.
https://doi.org/10.3390/jmse7060190