Graduation of Mart-Jan Hemel

22 October 2019 15:30 - Location: Hall G, Faculty of EWI, Mekelweg 4, 2628 CD Delft - By: Webredactie

"Submerged floating tunnel. The dynamic response due to fluid structure interaction." | Professor of graduation: Prof. dr. ir. Wim Uijttewaal, supervisors: Dr. ir. Dirk Jan Peters (TU Delft / Royal Haskoning DHV), dr. ir. Karel van Dalen (TU Delft), dr. ir. Xuexue Chen (Royal Haskoning DHV).

The submerged floating tunnel (SFT), also known as the Archimedes bridge or suspended tunnel, is a conceptual idea for a tunnel that floats in the water, supported by its buoyancy. The tunnel would be placed underwater, not too deep in order to avoid high water pressures, but deep enough for it not to be exposed to extreme weather conditions or obstruct shipping traffic. The tunnel is kept in position with tethers that are anchored to the sea bed or floating pontoons at the water surface. This thesis focuses on the tether supported SFT. The dynamic response of a tether supported SFT, in a hydrodynamic environment, is different from the tunnels that are widely used nowadays. The SFT is always in contact with open water in which it is moving due to the hydrodynamic environment. The dynamic response of the tether supported SFT is still a gap in our engineering knowledge and this contributes to the fact that world-wide no tether supported SFT has ever been constructed. Many research has been performed in the last years. A broad range of models has been used to study the dynamic behavior of the tether supported SFT. The key in all these models is to capture the fluid structure interaction. Waves and current exert forces on the tunnel body but at the same time, the presence and motion of the tunnel body affects the wave-current environment.

To model the dynamic response of a tethered SFT incorporating fluid-structure interaction, a new model has been developed. The dynamic SFT model describes the cross sectional motion and tether forces of a rectangular tubular tunnel which is pinned down by two inclined tethers, excluding longitudinal effects. The tunnel is forced by waves and current only. When assuming the SFT system to be linear, the motion of the SFT can be seen as a superposition of the motion of the tunnel body in still water and the forces on the restrained tunnel body in waves and current. The tunnel motion in still water is modelled with a dynamic module while the hydrodynamic forces on a restrained tunnel body are computed with a wave force module. The two independent modules are combined in a coupling module which makes it possible to describe the dynamic response of a tether supported SFT in a wave-current environment. The advantages of this model choice are the fast computational time and the convenience of physical interpretation.

The wave force module computes the wave-current forces on the restrained tunnel body with a modified Morison formulation. This formulation is capable of computing, besides vertical and horizontal wave-current forces, the rotational wave force. Rotational wave forces are essential in the determination of tunnel roll motion and cannot be determined with the classical Morison theory. Just like the classical Morison theory, the modified Morison formulation does not take into account wave field deformation due to the presence of the tunnel structure. Therefore, for waves that are short compared with the dimensions of the SFT, diffraction effects cannot be taken into account. The absence of the diffraction effect is corrected for by integrating the dynamic pressures, water accelerations and water velocities with respect to the tunnel height and width. It should be noted that the applicability for short waves is only valid in case of structures that are submerged at a depth of at least 1.5-2 times the structure height. For shallowed submergence depths, the diffraction effects in combination with wave deformation become too large which cause prediction errors in the force determination. The force on the restrained SFT due to a uniform current can be modelled with the drag force expression from the classical Morison equation. To correct for the wave current interaction, the hydrodynamic mass coefficients are adapted as function of the Keulegan-Carpenter number.

The dynamic module describes the oscillation of the SFT, in still water, with a dynamic system. A free floating tunnel has three degrees of freedom which are roll, sway and heave. This dynamic system assumes the tunnel is connected with two in-extensible tethers. Adding two rigid constrains to the free floating tunnel reduces the SFT to a single degree of freedom system. This single degree of freedom system describes a coupled translational (sway) and rotational (roll) motion around an instantaneous rotational point which can be found at the intersections of the tether axes. When assuming small vibrations, the instantaneous rotational point remains fixed at the intersection of the tether axes when the tunnel is at rest. The moment of inertia of the SFT is obtained by using the Lagrangian approach which is based on energy conservation. Because the structure is submerged in water, added damping and mass terms are used in the equation of motion. The magnitude of these damping and mass terms is calibrated with physical model experiments. The coupling module combines the wave force module and the dynamic module, which makes it possible to formulate a full equation of motion, describing the oscillation of the SFT in a wave current environment. From the equation of motion the sway and roll motions, containing accelerations, velocities and displacements, can be obtained. Apart from the motions, the tether forces can be predicted. The dynamic SFT model is validated with physical model experiments.  

With this dynamic SFT model, a parametric study has been performed. The first part of the parametric study focuses on the motion of the SFT. The second part examines the tether forces. Furthermore, the slack-taut transition and the safety against fatigue have been investigated. The parametric study does not take into account current. The most important findings and implications are in summary:

  • Each SFT configuration has a different response to the wave environment. Hence, every configuration has a different critical wave length for which the dynamic response is maximum. This critical wave length is independent of the wave height. It should be noted that the dynamic response is a comprehensive term which consists of many variables. These are; tether forces, sway motions and roll motions of which both motions contain accelerations, velocities and displacements. The most dominant parameters to influence the dynamic response are the buoyance to weight ratio (BWR), tether angle and submergence depth.
  • The BWR increases the stiffness of the dynamic SFT system which causes a decrease in the roll motions and sway displacement. Due to the stiffness increase, sway accelerations and velocities become larger. The natural frequency of the SFT is increased by increasing the BWR, which makes it more sensitive to shorter waves.
  • Configurations with large tether angles have the character to be very flexible and sway dominant, while configurations with small tether angles are stiffer and roll dominant. Tether forces for configurations with large tether angles are more sensitive to long waves, while tether forces for configurations with small tether angles are more sensitive to short waves.
  • A decrease in submergence depth increases all tunnel motions and tether forces, as the tunnel becomes more exposed to the wave environment. The dynamic response of the SFT becomes more sensitive to short waves.
  • An increase in anchorage depth results in larger tunnel motions. The increase in tether forces is negligible.
  • Placing the tether connection sideways of the tunnel body results in smaller roll motions and larger sway motions. Lowering the tether connection with respect to the tunnel bottom is favourable for all tunnel motions. The manner of how the tether connection is orientated, with respect to the tunnel body, has small influence on the tether forces.
  • Increasing the BWR, submergence depth or both reduces the risk of snapping lines and tether fatigue. Configurations with small tether angles have a smaller risk of having line snapping and tether fatigue compared to configurations with large tether angles.

This study gives a supplement to the classical Morison theory. Morison’s theory is modified which makes it possible to compute rotational moments due to wave loading. Also the applicability to short waves is enlarged. A new dynamic schematization is developed which makes it possible to describe the dynamic response of a SFT as a single degree of freedom (SDOF) system. The advantages of this dynamic schematization are the fast computational time and the convenience of physical interpretation. The results obtained from this research study can be used as a preliminary design tool. In an early design stage, motions and tether forces can be predicted. Also measures to reduce these motions and tether forces can be investigated using the dynamic SFT model. Design graphs to estimate the snap-taut transition and for safety against tether fatigue are provided. It should be noted that this dynamic SFT model should not be used for detailed computations in later design stages.