In this section the beam-model is used to simulate the backfilling of an offshore pipeline. It must be noted that this model has no time component. This implies that only a certain moment of the backfilling process can be observed and not the total dynamical process. The results of the 2DV model (‘multiple fixed inflow points’ method) are used as input for the beam-model.
5.5.1 Model setup
The model setup for these simulations is equal to the setup described in section 5.2.1, except for the soil-water density.
Soil-water density
The results of the ‘multiple fixed inflow points’ simulations (Section 4.4.2) are used to generate input for the beam-model. The density of the soil-water mixture is not constant over the entire modelled area. For instance, the slurry density will be higher close to the bed surface and lower close to the inflow point. The results from the
‘multiple fixed inflow points’ simulations are converted to a grid as displayed in Figure 48. With this approach, it is possible to incorporate the different densities as a function of the horizontal distance x(i) and the vertical pipe displacement w(i).
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1.5 m
20%
1 m
0% 45% 20% 45% 0%
0 m
0 m a b c d 2000 m Figure 48. Example of a typical density distribution of a soil-water mixture over the modelled area. This density distribution is based on the results displayed in Figure 33. A concentration of 0% corresponds with a density of 1025 kg/m3 (seawater). A concentration of 20% and 45%
corresponds with a soil-water mixture density of 1350 kg/m3 and 1756 kg/m3 respectively.
Figure 49 visualises the grid from Figure 48 combined with the results from Figure 33. The used grid seems very coarse. However, this is just an example to explain the used approach. The grid can be refined if this is necessary.
Figure 49. Example of a typical grid displayed on the result of the corresponding 2DV simulation (Figure 33).
5.5.2 Results
Figure 50 shows a result of the beam-model. The input for this simulation is acquired from a typical 2DV sedimentation test using the ‘multiple fixed inflow points’ method.
The results from this 2DV sedimentation test are converted to a grid similar to Figure 48.
This grid distributes the density of the soil-water mixture over the length and height of the modelled area.
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Figure 50. Example of a typical result of the beam-model. The distribution displayed in Figure 48 is used as input for this calculation. The seabed level is located at 0 m.
Next, the simulated pipeline displacement is verified. This verification is done by combining the results of Figure 50 and Figure 33. A visualisation of this verification is shown in Figure 51. This figure shows that upward pipeline displacement is present at places of high solid concentration. At locations with low solid concentration, upward pipeline displacement is minimal. Locations which are not covered with backfill, experience a downward deflection.
Figure 51. Visualisation of the result displayed in Figure 50 combined with the result of the
‘multiple fixed inflow points’ analysis in Figure 33. The seabed level in this figure is 0.5 meters higher compared to the seabed level in Figure 50.
It can be concluded that the beam-model provides a tool which can predict pipeline floatation. Before using the beam-model, it is necessary to acquire information on the distribution and evolution of the soil-water mixture. The beam-model simplifies the backfilling process to a quasi-static process. However, in reality, the backfilling processes is more than just a series of snapshots. It is an evolving process in which the pipeline has a history. The pipeline can already be partly buried or floating. The beam- model cannot be used as a tool to predict pipeline floatation, if the history of the pipeline is not included.
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6 Conclusions and recommendations
In this thesis pipeline floatation during dredge-based backfilling is subject of discussion.
A subsea pipeline should remain stable in all circumstances. This includes the backfilling operation of a subsea pipeline. It is not always clear if the in situ soil is suitable to be used as backfill. In the past this lack of knowledge sometimes resulted in pipeline floatation during backfilling. Also material was disposed, which would have been perfectly suitable as backfill. In this case material is supplied from elsewhere, which is an economic disadvantage. These two risks indicate the importance of accurately predicting the displacement of a pipeline during and short after backfilling. The main objective of this study was stated as:
How can pipeline floatation during dredge-based backfilling be prevented?
The research questions that have been investigated in this thesis are presented below (see also Section 1.5).
What is the sedimentation length of a particular soil-water mixture? To achieve this, it is necessary to know the density of the slurry, the gradation of the soil, the initial mixture speed and trailing speed of the Trailing Suction Hopper Dredger (TSHD).
How does the density of a soil-water mixture develop in time?
How does the strength of the deposited material develop? In case of coarse sand or gravel the strength development will be instantaneous. Strength development of a clayey soil-water mixture may take a few days.
The properties of the pipeline in combination with the three points above will provide an estimation whether the pipeline will remain stable during backfilling.
The conclusions of this study are presented in Section 6.1. These conclusions are evaluated using the previously stated research questions. Section 6.2 concludes with a list of recommendations. This section explains what is still missing and what topics need further research.
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