Concrete Structures in Earthquake

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The concept of seismic base isolation has been developed over decades and has matured into practical applications around the world (Naeim and Kelly 1999). The developed base isolation systems, such as rubber bearings and friction pendulum systems, work by introducing low lateral stiffness devices at the base of a superstructure to lengthen the natural period of the structural system, resulting in a reduction of the acceleration response of the structural system during vibrations. The developed isolation systems had proven to enhance the horizontal seismic performance of many isolated structural systems (Buckle and Mayes 1990). However, vertical earthquakes are still a main issue in the conventional isolation systems. Full-scale shake table tests conducted at the E-Defense facility in Japan show a great amplification in the vertical acceleration response of the isolated buildings when subjected to vertical earthquakes (Furukawa et al. 2013; Ryan et al. 2016). The vertical response amplification causes a wide variety of damages to the non-structural components inside the isolated buildings. To accommodate the seismic safety of critical structures such as medical facilities and nuclear power plants, researchers have proposed various devices to isolate earthquakes in both the horizontal and vertical directions. Devices such as rolling seal type air spring and hydraulic isolation systems can provide vertical isolation and are proposed to be combined with laminated rubber bearings for horizontal isolation (Inoue et al. 2004; Suhara et al. 2005, 2002). On the other hand, devices such as thick rubber layer bearings (Okamura et al. 2011) and GERB systems (Naeim and Kelly 1999) can simultaneously provide seismic isolation in both the horizontal and vertical directions. All of the proposed devices are based on the same concept as conventional isolation systems, i.e., introducing low lateral and vertical stiffness and subsequently lengthening the natural periods of the isolated structural systems to avoid damaging frequency content of input earthquakes. Researchers (Naeim and Kelly 1999; Takahashi et al. 2008) found these systems are prone to rocking when subjected to horizontal earthquakes. Consequently, rocking suppression devices are needed to control the rocking movement. This paper presents a novel concept of seismic isolation from the perspective of elastic waves propagation in periodic materials or phononic crystals. Periodic materials, originally developed in the solid-state physics, are artificially made by arranging contrasting materials in the periodic fashion. According to the number of directions where the unit cell is repeated, periodic materials can be classified as one-dimensional (1D), two-dimensional (2D) and three-dimensional (3D) periodic
materials, as shown in Fig. 1.1a, b and c, respectively. This metamaterial has the capability to block elastic waves from propagating through if the frequencies of these waves are within certain frequency bands. These frequency bands are termed as frequency band gaps or attenuation zones (Torres and Montero de Espinosa 2004). This concept is depicted in Fig. 1.2a and b. It is shown in Fig. 1.2a that the wave cannot propagate through the periodic material since the frequency of the wave falls within the range of the frequency band gap of the material. The opposite case is shown in Fig. 1.2b. The range of the frequency band gap can be engineered by design to cover any frequency of interest. Guided by the notion of frequency band gaps in periodic materials, researchers
have developed periodic material-based seismic isolation systems better known as periodic foundations (Xiang et al. 2012; Yan et al. 2014, 2015). This type of
foundation can support the superstructure and isolate the superstructure from the incoming seismic waves since it possesses frequency band gaps. Physical tests of 1D (Xiang et al. 2012), 2D (Yan et al. 2014) and 3D (Yan et al. 2015) periodic foundations were conducted in the feasibility study stage of the periodic foundations. In each of the tests, a simple structure supported by a periodic foundation was tested simultaneously with a non-isolated counterpart. The test results show that the structures isolated with periodic foundations have a much smaller acceleration response than that of the non-isolated structures. Inspired by the success of the feasibility study, we proceed with the application into the real engineering structures. In this study, a 3D periodic foundation is employed to isolate a small modular reactor (SMR) building model. The study reported in this paper begins with the theoretical derivation of the dispersion relation in the 3D periodic materials to design the frequency band gaps on the test specimens. The subsequent section then describes the design of the 3D periodic foundation. Finally, the shake table test results of the 3D periodic foundation structural system are presented and discussed.

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