New Structural Seismic Isolation for Nuclear Containment Structures

'e new Structural Seismic Isolation System (SSIS) intends to provide high safety for important structures such as nuclear power plants, offshore oil platforms, and high-rise buildings against near-fault and long-period earthquakes. 'e presented SSIS structure foot base and foundation contact surfaces have been designed as any curved surfaces (spherical, elliptical, etc.) depending on the earthquake-soil-superstructure parameters, and these contact surfaces have been separated by using elastomeric (lead core rubber or laminated rubber bearings with up to 4-second period) seismic isolation devices. It would allow providing inverse pendulum behavior to the structure. As a result of this behavior, the natural period of the structure will possess greater intervals which are larger than the predominant period of the majority of the possible earthquakes including near-fault zones. Consequently, the structure can maintain its serviceability after the occurrence of strong and long-period earthquakes.'is study has investigated the performance of the SSIS for the nuclear containment (SSIS-NC) structure. 'e finite element model of SISS-NC structure has been developed, and nonlinear dynamic analysis of the model has been conducted under the strong and long-period ground motions. 'e results have been presented in comparison with the conventional application method of the seismic base isolation devices for nuclear containment (CAMSBID-NC) and fixed base nuclear containment (FB-NC) structures. 'e base and top accelerations, effective stress, and critical shear stress responses of the SSIS-NC structure are 48.67%, 36.70%, and 32.60% on average lower than those of CAMSBID-NC structure, respectively. 'e result also confirms that the SSIS-NC structure did not cause resonant vibrations under long-period earthquakes. On the other hand, there is excessive deformation in the isolation layers of CAMSBID-NC structure.


Introduction
Seismic base isolation is indicated as a reliable tool for the protection of structures against strong earthquakes [1,2], and there are more than seven thousand seismically isolated buildings around the world. On the other hand, the number of active seismically isolated nuclear power plants is very low (only six) and they are located in the low seismic hazard risk regions. All are pressurized water reactors (PWR), four of them located in Cruas Meysse (France) and the remaining two in Koeberg (South Africa) [3]. e main reasons for limited usage of seismic isolation are related to decline of nuclear power plant construction from 1980 to 2010, construction of NPPs in regions with low seismic hazard risks, and lack of proper codes/standards for the design of NPPs with seismic isolation systems [4]. Another reason for sparse usage of the seismic isolation system for NPPs could be related to the fact that water reactors are the most common which are stiff structures containing rigid internal components with intrinsic robustness enough to overcome low ground motions (0.1 g peak) [5]. During the last two decades, various institutions such as the American Society of Civil Engineers published codes regarding analysis, design, and safety issues of nuclear structures called ASCE 4-16 [6]; the older version was included in ASCE 43-05 [7]. Based on this code, elastomeric (low damping and lead rubber) and friction pendulum sliding isolator are suggested for seismic protection of nuclear facilities [4]. e French Association for nuclear steam system supply equipment construction rules, AFCEN, developed regulations for the design of base-isolated structures using elastomeric bearings [8]. e Atomic Energy Research Institute of Korea aimed to develop a seismic design standard for seismic base-isolated nuclear power plant structures [3].
e Fukushima Daiichi nuclear disaster revealed the vulnerability of the nuclear power plants against strong earthquakes causing serious causalities and environmental problems [9]. ere are several studies regarding the seismic isolation of nuclear installations. For instance, Ostrovskaya and Rutman proposed a support-pendulum seismic isolation system for seismic protection of NPP structures; this system aims to isolate the vibration and shocks using pendulum bars and plastic dampers [10]. Studies of Whittaker et al. and Medel-Vera et al. on seismic protection of nuclear power plants also can be noted [4,11,12] as efforts to develop a seismic design standard for seismically isolated nuclear power plants in the United Kingdom. Kasimzade et al. [13][14][15] proposed and developed a new structural seismic isolation system named Structural Seismic Isolation System (SSIS) against strong and long-period earthquake ground motions, and it aims to eliminate the limitation and vulnerability of the conventional elastomeric (lead rubber or laminated rubber) base-isolated structures for the same excitations [16]. e SSIS system provides the possibility of keeping the natural period of the structure in a larger interval which is greater than the predominant period of the majority of possible earthquakes (including near-fault pulse) using currently existing conventional elastomeric isolators with up to 4 sec period. In this study, the finite element simulation of the dynamic performance of the SSIS with the spherical structure foot base and foundation contact surfaces for nuclear containment (SSIS-NC) structure was presented in comparison with a conventional application method of the seismic base isolation devices for nuclear containment (CAMSBID-NC) and fixed-base nuclear containment (FB-NC) structures, respectively.

Fundamentals of SSIS.
e main aim of the SSIS is to keep the period of structure beyond the period of the earthquake. is aim is approached by building structure foot base, and foundation contact surfaces have been designed as any curved surface (spherical, elliptical, etc.) depending on the earthquake-soil-superstructure parameters and these contact surfaces have been separated by using elastomeric (lead core rubber or laminated rubber bearings) seismic isolation devices. It would allow the curved surface structure foot base to turn around the gyration center through rubber bearing contact and maintain similar behavior to the superstructure. is will allow structures to overcome strong earthquakes including long-period and near-fault pulse. e governing equation and the mathematical model of the SSIS with the spherical structure foot base and foundation contact surfaces (see Figure 1) have been presented as follows [13][14][15]: with where [m], [c], and [k] are the mass, Rayleigh damping, and stiffness matrix of the superstructure, respectively, and were composed by FEM [17]. u is the relative displacement vector of the superstructure of the deformed state. _ u andü are the velocity and acceleration vector, respectively. F € ug stands for seismic force: Here, φ represents the absolute rigid structure's rotation angle around the gyration center, € u g is the ground motion excitation, F c0 = c b ρ 2 φ is the total damping, and F kb is the total stiffness forces of the seismic isolator deployed in the SSIS which possesses total damping coefficient and spherical radius (ρ 2 ). F c , eq = c d ρ 2 _ φ represents the sum of external dampers' equal damping force which contains the c d (damping coefficient), and φ is the solution of Equation (2): Here, h i (i = 1, n) is the z distance of the superstructure's i-th mass m i from the gyration center; m 0j and h 0j (j = 1, m) are the similar parameters for the underground part of the SSIS. e lateral displacement of the superstructure's base is indicated by u b which correlates to the contact surface of the foundation. u y stands for the yield displacement, k b for the total stiffness of the isolators, and α for the postyielding to preyielding stiffness ratio of seismic isolators commonly taken as 0.1. e ratios d r = u yb2 /u y = about 10 and f r = F yb2 / F y = about 2, respectively, as described in Figure 2. e parameterŻ refers to the dimensionless hysteresis displacement component that satisfies the nonlinear first-order [18,19] differential equation (5). F y and Q refer to the yield and characteristic strengths of the seismic isolator, respectively. By defining the F 0 parameter as presented in equation (10) with regard to the total weight of the structure W, the yield strength of the seismic isolator can be normalized: In some references, normalized stiffness has been expressed as where m i , m b , and m t are the mass of the story, base slab, and total mass of the building respectively. In equation (5), β, a, n, and c are the dimensionless parameters and affect the shape of the hysteresis loop; the value of these parameters is predicted through experiments. Here, the value of the abovementioned parameters are taken as n � 2; a � 1; and (β + c)/a � 1. e model of equation (5) decreases to a viscoplasticity model; in equation (5), u y refers to the yield displacement. e base and top absolute displacement and acceleration behavior of the SSIS-NC structure are described through the following equation: where, u b , u n ,ü b , andü n are the base and top relative displacement and acceleration and u 0n andü 0n are the top relative displacement and acceleration of the SSIS-NC structure as a rigid body. Assessment of the SSIS-NC structure has been conducted by MATLAB and Simulink programming tools using the presented governing equations by Kasimzade et al. [13][14][15] in the following section.

Assessment of SSIS for Nuclear Containment Structure.
A numerical assessment of the SSIS structure is presented with an example of reinforced concrete nuclear containment structure [20,21]. e structure is formed of a semispherical dome, a cylindrical shell wall, and at the bottom, a base-mat slab (see Figure 3 Table 1; the grade of the concrete is C50. e cooling system of the nuclear containment is located at the base of the structure. e distribution of the mass for SSIS-NC, CAMSBID-NC, and FB-NC structures based on references [20,21] are presented in Table 2, respectively. Assuming that the predominant period of the earthquakes in the area where FB-NC, CAMSBID-NC, and SSIS-NC structures are about 11 seconds, SSIS's required total Figure 2: Illustration of the hysteresis loop of the LCRB isolator and its geometric ratios [13]. elastomeric isolator horizontal stiffness for the first approximation was defined by equation (2) in case of free vibration as k b � 8.6834E + 7 N/m. Other parameters of the elastomeric isolator such as period, damping coefficient, and damping ratio were defined as T b � 4 s, C b � 1.6169E + 7 Ns/ m 2 , and ξ b � 0.15, respectively. Based on the above SSIS-NC structure's parameters and using governing equations for the SSIS from the previous section, the SSIS-NC structure's performance was preliminarily assessed to Tohoku 2011 Earthquake X-direction acceleration excitation, and base acceleration responses are presented in Figure 4.
As presented in Figure 4, the base-level acceleration of the SSIS-NC (about four times) was significantly reduced. Based on preliminary design parameters and assessment results presented in this section, detailed finite element modeling of the SSIS-NC structure compared with FB-NC and CAMSBID-NC structures are presented in the following section.

Finite Element Model of Nuclear
Containment Structure with SSIS e finite element model of the nuclear containment structure with the SSIS has been prepared using LS-DYNA software; in this model, solid and discrete beam elements have been used [22]. Fully integrated ten-node tetrahedron solid elements [23] have been selected for modeling the structure base and the superstructure of the SSIS-NC model. e size of the solid mesh ranges between 0.7 and 2 m. e elastomeric (lead core rubber bearing) seismic isolators have been modeled using discrete beam elements that exhibit nonlinear characteristics of elastomeric seismic isolators [23,24]. e size of the discrete beam element is 0.5 m (see Table 1: Material properties of reinforced concrete [21]. Density (kg/m 3 ) 2940.0 Tensile strength (N/m 2 ) 1.740E + 05 Young's modulus (N/m 2 ) 2.011E + 10 Shear modulus (N/m 2 ) 0.837E + 10   e mesh of the finite element model has been selected through a process of mesh convergence study. It is obvious that finer meshes procure more accurate results, but the finer the mesh becomes, the more the time and computer capacity needed for conducting the dynamic analysis. Figure 5 presents the different sizes of the meshes which have been proposed for the nuclear containment structure. Figures 5(a)-5(d) have a maximum mesh size of 5.5, 3.5, 2, and 1 meters, respectively. In this study, the third option ( Figure 5(c)) has been deemed as an optimum variant. e convergence of dynamic analysis is also affected by the characteristics of the excitations (earthquake timehistory records); earthquake records with high frequency (composed of heavily alternating ± acceleration values) require more solution time than low-frequency records. Because during the analysis in case of heavy changes in the value of acceleration from − to + and opposite, the solver will divide the original time step into subtime steps to catch the convergence of relevant points; consequently, it will considerably increase the duration of the analysis. For instance, the Duzce earthquake ( Figure 6(a)) time-history record has a lower frequency than the Kobe earthquake ( Figure 6(b)) with both having a similar duration (around 55 seconds), the same magnitude (around 7.8 m/s 2 ), and the same time step (0.01 second). Conducting the dynamic analysis of the concerned FE model under the effect of the Duzce earthquake required 39 hours and 8 minutes, while the same model has been analyzed under the effect of the Kobe earthquake in 50 hours and 16 minutes using the same computer capacity. Smaller time steps generate a more accurate result but require more analysis time. In this study, the time steps of the excitation are 0.01 second which is considered to be the optimum value for seismic analysis.

Preliminary Design of the Seismic Elastomeric Isolators.
e preliminary dimension and analytical parameters of the seismic isolators are calculated based on ASCE 7-16 [25] and ASCE 41-13 [26] codes. Yield force (Fv), yield displacement (u y ), damping ratio, and vertical stiffness (Kv) are the necessary analytical parameters for finite element modeling of the seismic isolator. Minimum horizontal stiffness and the     Science and Technology of Nuclear Installations design displacement of the isolator are calculated using equations (13) and (14), respectively: where W stands for the total weight on a single bearing, T D for the design period (here T D � 4 seconds), B D for the damping coefficient, g for the gravity, and S D1 for the spectral coefficient (the value of S D1 is based on 2011 Tohoku earthquake response spectra). e cross-section area of rubber (A r ) and postyielding stiffness are calculated using equations (15) and (16), respectively: Yield displacement (u y ) is 0.05∼0.1 times total rubber thickness (R T ) based on experimental data. f L is a factor that is commonly taken as 1.5. e characteristic strength (Q) of the elastomeric can be calculated using equation (17). en, the yield force (F y ) of the bearing can be calculated as equation (18):  Science and Technology of Nuclear Installations Finally, the vertical stiffness (Kv) of the elastomeric bearing is calculated via equation (19); here, E c , G, and K represent the compression of rubber-steel composite, shear, and bulk modulus of rubber, respectively. e value of K and G differs based on the type of rubber; the value of K can vary between 1000 and 2500 MPa and G between 0.45 and 1 MPa. S represents the hysteresis loop shape factor of the seismic isolator, and the value of S should range between 12 and 20 [27]. e parameters of the lead core rubber bearing (LCRB) for SSIS-NC and CAMSBID-NC structures are calculated as presented in Table 3: e final design of the elastomeric isolator parameters is implemented based on comparing the first iteration results K h � 9.67E + 5 * 86 � 83.162E + 6 N/m with the required total horizontal stiffness of the isolators k b � 86.834E + 6 N/m obtained from equation (2). en, it can be confirmed in

Numerical Study
Nonlinear dynamic analysis of the presented finite element model (see Figure 3) has been analyzed using two strong and long-period earthquakes; general characteristics of these earthquakes are presented in Table 4 and Figure 7. Time-history data of the ground motions are obtained from the PEER Berkeley Strong Ground Motion database [28]. e design spectrum presented in Figure 7 is used in the preliminary design of the isolator in Section 2.1. Tohoku and 2010 El Mayor earthquakes have been presented in Figures 9(a)-9(d), respectively. e top-level results indicate that the SSIS is more effective in mitigating earthquake energy in the top level of the nuclear containment structure compared to that of CAMSBID-NC and FB-NC. e top-level displacements of SSIS-NC, CAMSBID-NC, and FB-NC structures are presented in Figure 10.

Conclusions
e SSIS-NC, CAMSBID-NC, and fixed-base structures were analyzed under the effect of strong and long-period earthquakes listed in Table 4. e base acceleration responses of the SSIS-NC structure are 33.34% and 55.10% lower (on average) than the CAMSBID-NC structure, while there are 52.93% and 53.33% differences between the top-level acceleration response of SSIS and CAMSBID-NC structures in the X and Y directions, respectively (see Figures 16 and 17). e effective stress (Von-Mises) and critical shear stress (Tresca) responses of the SSIS-NC and CAMSBID-NC structures also confirm the effectiveness of the SSIS. As presented in Figure 18, the effective stress and critical shear stress response of SSIS structure are 36.70% and 32.60% lower (on average) than CAMSBID-NC structures, respectively. As presented in Figure 19, the general stress responses of SSIS-NC, CAMSBID-NC, and FB-NC structures also indicate the significant effect of the SSIS with a 76.28% reduction compared to the CAMSBID-NC structure. erefore, the following aspects can be noted about the SSIS: (i) e base and top accelerations, effective stress, and critical shear stress responses of the SSIS-NC structure are 48.67%, 36.70%, and 32.60% (on average) lower than CAMSBID-NC structures, respectively (ii) e seismic isolator showed maximum performance for the SSIS-NC case compared with CAMSBID-NC, while similar seismic isolator parameters were used in the CAMSBID-NC case as well (iii) ere is a possibility of the usage of additional seismic dampers for additional seismic dissipation purposes for extremely important buildings (iv) e SSIS-NC system can be highly effective and reliable for seismic protection of nuclear containment structure (v) e feasibility of the usage of this is not limited to nuclear containment structures; it could be used as a seismic protection system for other important structures such as high-rise buildings and offshore oil platform (vi) e significantly lower response of the SSIS-NC system compared with CAMSBID-NC and FB-NC systems allows to make it even lighter (in the presented study, approximately the same total mass for SSIS-NC, CAMSBID-NC, and FB-NC systems was used only for comparability of the responses)

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that they have no conflicts of interest. 14 Science and Technology of Nuclear Installations