Development of a Metamaterial-Based Foundation System for the Seismic Protection of Fuel Storage Tanks
Creators: name: Wenzel, Moritz
Publisher: name: Universit� degli studi di Trento
Year: 2020

description: Metamaterials are typically described as materials with ?unusual? wave propagation properties. Originally developed for electromagnetic waves, these materials have also spread into the field of acoustic wave guiding and cloaking, with the most relevant of these ?unusual? properties, being the so called band-gap phenomenon. A band-gap signifies a frequency region where elastic waves cannot propagate through the material, which in principle, could be used to protect buildings from earthquakes. Based on this, two relevant concepts have been proposed in the field of seismic engineering, namely: metabarriers, and metamaterial-based foundations. This thesis deals with the development of the Metafoundation, a metamaterial-based foundation system for the seismic protection of fuel storage tanks against excessive base shear and pipeline rupture. Note that storage tanks have proven to be highly sensitive to earthquakes, can trigger sever economic and environmental consequences in case of failure and were therefore chosen as a superstructure for this study. Furthermore, when tanks are protected with traditional base isolation systems, the resulting horizontal displacements, during seismic action, may become excessively large and subsequently damage connected pipelines. A novel system to protect both, tank and pipeline, could significantly augment the overall safety of industrial plants. With the tank as the primary structure of interest in mind, the Metafoundation was conceived as a locally resonant metamaterial with a band gap encompassing the tanks critical eigenfrequency. The initial design comprised a continuous concrete matrix with embedded resonators and rubber inclusions, which was later reinvented to be a column based structure with steel springs for resonator suspension. After investigating the band-gap phenomenon, a parametric study of the system specifications showed that the horizontal stiffness of the overall foundation is crucial to its functionality, while the superstructure turned out to be non-negligible when tuning the resonators. Furthermore, storage tanks are commonly connected to pipeline system, which can be damaged by the interaction between tank and pipeline during seismic events. Due to the complex and nonlinear response of pipeline systems, the coupled tank-pipeline behaviour becomes increasingly difficult to represent through numerical models, which lead to the experimental study of a foundation-tank-pipeline setup. Under the aid of a hybrid simulation, only the pipeline needed to be represented via a physical substructure, while both tank and Metafoundation were modelled as numerical substrucutres and coupled to the pipeline. The results showed that the foundation can effectively reduce the stresses in the tank and, at the same time, limit the displacements imposed on the pipeline. Leading up on this, an optimization algorithm was developed in the frequency domain, under the consideration of superstructure and ground motion spectrum. The advantages of optimizing in the frequency domain were on the one hand the reduction of computational effort, and on the other hand the consideration of the stochastic nature of the earthquake. Based on this, two different performance indices, investigating interstory drifts and energy dissipation, revealed that neither superstructure nor ground motion can be disregarded when designing a metamaterial-based foundation. Moreover, a 4 m tall optimized foundation, designed to remain elastic when verified with a response spectrum analysis at a return period of 2475 years (according to NTC 2018), reduced the tanks base shear on average by 30%. These results indicated that the foundation was feasible and functional in terms of construction practices and dynamic response, yet unpractical from an economic point of view. In order to tackle the issue of reducing the uneconomic system size, a negative stiffness mechanism was invented and implemented into the foundation as a periodic structure. This mechanism, based on a local instability, amplified the metamaterial like properties and thereby enhanced the overall system performance. Note that due to the considered instability, the device exerted a nonlinear force-displacement relationship, which had the interesting effect of reducing the band-gap instead of increasing it. Furthermore, time history analyses demonstrated that with 50% of the maximum admissible negative stiffness, the foundation could be reduced to 1/3 of its original size, while maintaining its performance. Last but not least, a study on wire ropes as resonator suspension was conducted. Their nonlinear behaviour was approximated with the Bouc Wen model, subsequently linearized by means of stochastic techniques and finally optimized with the algorithm developed earlier. The conclusion was that wire ropes could be used as a more realistic suspension mechanism, while maintaining the high damping values required by the optimized foundation layouts. In sum, a metamaterial-based foundation system is developed and studied herein, with the main findings being: (i) a structure of this type is feasible under common construction practices; (ii) the shear stiffness of the system has a fundamental impact on its functionality; (iii) the superstructure cannot be neglected when studying metamaterial-based foundations; (iv) the complete coupled system can be tuned with an optimization algorithm based on calculations in the frequency domain; (v) an experimental study suggests that the system could be advantageous to connected pipelines; (vi) wire ropes may serve as resonator suspension; and (vii) a novel negative stiffness mechanism can effectively improve the system performance.