Application Studies for Static Condition

Accurate estimation of the bundle behaviour with static load is important for a manoeuvring plan as well as for structural safety. Since bundles are very flexible due to their inherent section properties, very small submerged weight and limited tensile forces, their behaviour may be highly influenced by slight external disturbances. This section is concerned with the structural behaviour with change in key parameters such as heading angle and offset, including the application of accurate hydrostatic pressure forces.

5.3.1 Influence of Hydrostatic Pressure Force

For most offshore structures, little attention has been paid to hydrostatic pressure forces. Conventionally the ‘effective weight’ from the simple summation of dry weight and classical buoyancy with submerged volume has been used during structural analysis. This approach is quite reasonable if the buoyancy is negligible compared to other load items and/or the structures are stiff enough to be little influenced by their buoyancy. In the case of towed bundles, however, this is totally the opposite - their buoyancy is comparable to other loads, such as dry weight, and these structures are very flexible. As discussed in Section 3.2, hydrostatic pressure forces control pipe curvature in a way similar to the tensile forces in the wall of the pipe. In this section, the effects of hydrostatic pressure forces are studied by comparing these analysis results with those obtained from analysis with effective weight. Since curvatures of the towed bundle are small, the formulae for straight pipes in Section 3.2.1 are used.

Firstly, consider the case without tow speed. Figures 5.26 to 5.28 respectively show vertical coordinates, bending moments and axial forces with and without hydrostatic pressure forces for this condition. The terms ‘with’ and ‘without’ pressure forces respectively mean the cases with the application of accurate hydrostatic pressure forces and without it, that is effective weight only. Figure 5.27 clearly shows the so- called curvature reversal due to the hydrostatic pressure forces. Also this force gives rise to a significant change in axial forces along the length of the bundle as shown in Figure 5.28.

Next, consider the case with a tow speed of three knots. Two heading conditions, 0° and 30°, are considered and the axial forces and bending moments are shown in Figures 5.29 and 5.30, respectively. These results show that the application of accurate hydrostatic pressure force is still important for the towing condition with 0° heading while it gives negligible influence to that with 30° heading. The latter is because the current from 30° heading produces normal drag forces which are very large compared to the hydrostatic pressure forces. However, considering that the tow must be performed with a small heading angle (for details, see next section), the application of the accurate hydrostatic pressure force is essential for tow analysis and it is considered in all subsequent analyses.

5.3.2 Influence of Heading Angle

If the bundle is subjected to side current, its lateral load from normal drag easily exceeds the vertical load on it. Therefore the bundle will move near to the horizontal plane. This phenomenon is checked by applying different heading angles and Figures 5.31 and 5.32 clearly show this pattern. In addition to this phenomenon, due to the limited towline length, the bundle will consequently float just near the still water surface for large heading angles. This condition is very dangerous and must be avoided because the bundle is then directly exposed to the severe wave action zone. Also with increase in heading angle, axial forces increase rapidly while bending moments decrease as shown in Figures 5.33 and 5.34 respectively. The

required tug forces for different heading angles and tow speeds are shown in Figure 5.35. In side current the normal drag force is very large compared to the tangential force and therefore tows with large heading angles require very large tug forces and very strong towlines, which are difficult and unrealistic.

Considering the above results, it is very important to keep the heading angle as small as possible except in some special cases, such as the changing of tow direction, which requires careful planning and operation. The following analyses, including dynamic cases, are for the tow with 0° heading angle unless otherwise mentioned.

5.3.3 Influence of Offset

Throughout the analysis and tow operation, the position of towheads, along with tow speed, provides much useful information such as sag, axial forces and bending moments along the bundle. This section is concerned with the structural behaviour to the changes in offset. Due to the special geometric characteristic of the towed bundle, that is very long with shallow sag, a slight disturbance of offset gives rise to large sag of the bundle as shown in Figure 5.36. If the tow is performed in limited water depth, careful planning and operation are necessary to avoid contact between the bundle and seabed. Figure 5.37 shows that as offset increases there is almost a proportional increase in maximum absolute bending moment around 400 metres along the bundle. Although it is well below the allowable bending moment of

1.63x10^ N-m, this increase shows it is very sensitive to offset compared to the variation of other factors as considered in previous sections. The required tug forces with change in offset and tow speed are shown in Figure 5.38. It shows that the larger the offset the higher the tug force that is required, except for offsets between one and two metres. This exception is due to the combined effect of the distribution of the weight and the hydrostatic pressure force. The above trend of the tug force variation is very different or almost contrary to that from the analysis without considering the hydrostatic pressure force, as shown in Figure 5.39.