From the Sea into the Sky

Abstract

Due to global warming and the subsequent rise of the sea level, scarcity of land to build on, the continues increase of the world’s population and a shift in population from rural areas to the city, there is a need for innovative projects to tackle or deal with the increase of needed liveable area. One of the solutions is floating cities. A component of a modern city is high-rise buildings. High-rise is an advantageous option to deal with the limited availability of ground surface on the floating platforms. The question is whether it is possible to realise these floating high-rise structures.
This research investigates whether it is possible to realise high-rise buildings on floating platforms with limited dimensions on the sea or ocean regarding stability. And if it is feasible, what the requirements are for the general dimensions of both the platform and the high-rise building. For this purpose, conditions were used from three representative locations. At these three locations, the floating high-rise is tested for four different wave situations: Tsunami, Growing waves, most extreme wave. And an Irregular wave field. The platform and building are tested whether the structure could meet the various requirements and regulations. These are divided into three forms of stability: Buoyancy, static stability and dynamic stability.
In this study, for both the platform and the building a square cross-section is used and both are prismatic in the direction of the height. The platform and the core of the building are made of concrete. Apart from the four parameters: height of the building and width, height and depth of the platform all other parameters are based on these four parameters. No stability systems in the building were used (except the core), nor methods to keep the platform in place, such as mooring systems.
For the buoyancy, mainly the relation between the mass and the depth of the platform is determined. This is a relationship that has been used extensively in static and dynamic stability. The mass of the building and platform pose few problems for staying afloat. In fact, extra ballast water can easily be used to make the platform heavier in order to achieve the desired mass or depth.
For the static stability a combination of hand calculations based on the GM-method and a model that can include deformations in the calculations as well is used. A linear relationship was found between the height of the building and the width of the platform for which the floating high-rise is stable.
The model is used to determine the minimum platform depth and height, as well as the rotation for different building heights and platform widths. It follows that there are platform widths for which the vertical force is minimal. This is when the width of the platform is equal to the wavelength of the wave or a multiple of it. In addition, there are platform widths for which the moment due to the wave force on the platform is minimal. These values are called "zero moment widths" because for these widths the wave moment, regardless of position or time, is approximately equal to 0 kNm. Therefore the rotation is minimal when these zero moment widths are used for the platform width. These widths are only optimal for the specific wavelength for which they are calculated. If the wavelength is different, the zero moment widths will be different.
For the dynamic stability, a model consisting of three point masses distributed over the height connected with a beam was used. The three point masses each have three degrees of freedom: vertical and horizontal translation and rotation. With this model the accelerations of the three possible motions for different heights of the building, platform widths and platform masses (this can be adjusted by including ballast water) are calculated. It follows that: The tsunami and the growing wave are not a problem and the most extreme wave or the irregular wave field is normative; The vertical acceleration is minimal when the width of the platform is equal to the wavelength or a multiple of it; The vertical acceleration is only normative for small building heights and platform widths, whereas it is the biggest cause of seasickness; The horizontal acceleration at the top of the building due to both the horizontal motion and the rotation is almost always normative. It is largely caused by the rotation of the platform; If the zero moment widths are used for the width of the platform, the rotation and thus the horizontal acceleration is minimal. This does not mean that the accelerations are below the limit.
In order to avoid resonance in the motion, and thus extreme accelerations, of the floating high-rise with an irregular wave field, graphs are made were the combination of the height of the building and the width of the platform that result in resonance are shaded.
Using the results of the static and dynamic analysis and a few case studies, it can be concluded that with the design choices and simplifications used, it is not possible to realise floating high-rise buildings on platforms with limited dimension at the North Sea and the North of the Atlantic ocean due to too extreme condition causing too high accelerations, especially in the horizontal motion. The static stability and the buoyancy are less of a problem. If one of these locations is chosen, platforms over 600 m wide are required that are so stable that the rotation of the platform is minimal and no resonance occurs in the rotation motion. In this case, the conditions are similar to those on land and the wind force becomes the governing factor. In those cases, the same approach and measures should be used as for high-rise buildings on land. Even with these sizes, it is advised to use the zero moment widths to limit the rotation as much as possible.
The location on the Atlantic Ocean around the equator is the only location that is promising. The results show that several building heights are possible on different platform dimensions for the highest wave, as long as the platforms have the zero moment widths dimensions. However, it appears that the accelerations become too high when these sizes for the building and platform are tested with different wave frequencies with lower wave heights. Therefore, this option might not be suitable either, but it is not excluded in this research. One option is found that meets the regulations for all possible wave frequencies is a 50 m building on a platform 223 m wide (a zero moment width) and 22.7 m deep for the location around the equator. This proves that it is possible to construct high-rise buildings on platforms of limited size with the design choices used, but that it is very difficult and the options are limited.
Despite the conclusion that it is almost impossible with the design choices, floating high-rise buildings on limited platforms are still expected to be possible as the design can be improved. The first next steps to investigate are other, better shapes for the platform and building to increase stability and reduce overall forces. In addition, it is recommended that other methods of increasing stability and reducing motion, such as building stabilisation systems and tuned mass dampers, are investigated. With these improvements floating high-rise is more feasible than found in this research.