3.1. Design of Small Base Isolators for Nuclear Power Plant Equipment
As a measure to enhance the seismic performance of internal equipment and facilities in operational nuclear power plants during beyond-design-basis earthquakes (BDBE) exceeding the design seismic level, small base-isolation bearings specifically designed for nuclear plant equipment were developed [
13]. It should be noted that for export-standard nuclear power plants, the design-basis earthquake (DBE) is set at a safe shutdown earthquake (SSE) level of 0.3 g, and they are designed to have a seismic performance level of up to 0.5 g. However, in the event of a BDBE, some equipment vulnerable to earthquakes may be affected. To enhance the seismic performance of such earthquake-vulnerable equipment, research on the development of small lead–rubber bearings (LRB) for base-isolation devices was conducted.
When making small-sized LRBs, there are limitations in the manufacture of the stacked rubber in the baseplate, resulting in a lower shape factor. This leads to decreased stability compared with larger base-isolation devices for building structures, and the energy dissipation effect is somewhat insufficient. To address these issues and improve damping performance, lead cores are inserted at the center of the base-isolation devices to enhance their base-isolation performance.
In this study, the unit support weights of the small LRBs were initially manufactured with four different designs, 1-ton, 2-ton, 5-ton, and 10-ton LRBs, and static tests were conducted. Since much of the internal equipment in nuclear power plants is low-weight individual devices, the design was optimized primarily for 1-ton LRBs. The detailed design process is explained in reference [
13]. Low-capacity base-isolation bearings are highly necessary for technical development and have high applicability at nuclear plant sites, especially for components like nuclear plant instrumentation. Furthermore, among design approaches with different sizes and dynamic characteristics, base isolation performance, including natural frequencies and shape factors, was compared and evaluated to determine the optimal design. The design details, including cross-sectional shape and the design specifications of the LRB finally chosen and used in this study, are provided in
Figure 1 and
Table 1, respectively.
Table 2 indicates the mechanical properties of the rubber and lead materials used in the fabrication of small equipment LRBs. The properties of the rubber material are very similar to natural rubber, and pure lead-like materials were used for the lead core [
13].
3.2. Seismic Response Sensitivity of Base-Isolated Structures by Mass Eccentricity
In this paper, the response due to structural stiffness eccentricity is not considered. Therefore, a small base-isolation bearing designed for equipment, developed in previous studies, was applied, assuming a constant support stiffness. Consequently, a base-isolated cubic design with lumped mass was selected as the analysis model for the upper structure, which facilitates setting the mass eccentricity sensitivity of the seismic response.
To reduce the significant computational time required for seismic time history analysis when modeling small base isolators at full scale and performing nonlinear analysis, this study simplified the small base isolators by representing them as spring elements for sensitivity analysis.
For reference,
Figure 2a depicts the configuration where the four 1-ton base isolators developed earlier are positioned at the corners of the 4-ton cubic mass model’s underside for support.
Figure 2b shows the simplification for analysis efficiency, where each base isolator is modeled with one vertical (Z) and two horizontal (X, Y) spring elements, totaling 12 spring elements. The stiffnesses of the springs in the horizontal and vertical directions are calculated as follows.
(: Horizontal stiffness, : Vertical stiffness. : The total thickness of the rubber layer in the base isolator, : The Shear modulus of the rubber, : The elastic modulus adjusted based on compression characteristics, : Effective design area).
Figure 2.
Sensitivity analysis models for a base-isolated structure. (a) Dummy mass on the LRB model; (b) Dummy mass on the equivalent spring model.
Figure 2.
Sensitivity analysis models for a base-isolated structure. (a) Dummy mass on the LRB model; (b) Dummy mass on the equivalent spring model.
To investigate the changes in horizontal dynamic characteristics and response sensitivity due to the one-axis mass eccentricity of the structure, seismic analysis was conducted using code-based methods [
14]. In the sensitivity analysis, as shown in
Figure 3, the mass eccentricity was defined as 0% and 100% when the mass center of the upper structure (Dummy Mass) was positioned at the center and at the edge, respectively. In this context, the analysis was theoretically extended up to 100% eccentricity for the purpose of the study. However, in actual structural design, eccentricities exceeding 50% are very unusual.
It should be noted that the points from A1 to A4 in
Figure 3 represent the corner positions of the upper structure, which are the actual locations of the acceleration sensors used in subsequent vibration testing, as described later. By varying the upper structure’s mass eccentricity from 0% to 100% in 1% intervals, modal analysis and response spectrum analysis were conducted to observe the impact on displacement and acceleration seismic responses.
3.3. Results of the Sensitivity Analysis of Seismic Response by Mass Eccentricity
First, we aimed to examine the changes in the dynamic characteristics of the base-isolated structure as the eccentricity increased. Modal analysis results indicate that for 0% eccentricity (non-eccentric), the first, second, and fourth modes appear as translational (X, Y, Z) modes, the third mode as a horizontal torsional (rotation) mode, and the fifth and sixth modes as vertical rocking modes as shown in
Table 3. As mass eccentricity increases, when observing changes in the dynamic characteristics of the base-isolated upper structure, torsional modes appear in lower-order modes, and, in some translational modes, a mixed mode with torsional behavior becomes more evident.
As the mass eccentricity increases, the contribution of the torsional mode increases, leading to a mixed behavior of translational and torsional modes in the structure [
15]. To summarize, the changes in the natural frequencies of each mode as the horizontal single-axis mass eccentricity increases were observed and are presented in
Figure 4. As the mass eccentricity of the base-isolated upper structure increases from 0% to 100%, the natural frequency of the first mode does not decrease much; however, the source of mode behavior changes from translation to a combination of translation and rotation. This is likely due to the torsional behavior caused by mass eccentricity. The second mode remains unaffected by horizontal direction eccentricity, as expected. In the case of the third mode, the frequency actually increases from 3.3 Hz to 4.6 Hz. This is attributed to an increase in the contribution of the first mode due to eccentricity, coupled with a decrease in horizontal torsion due to no eccentricity. The fifth mode, similar to the second mode, remains unaffected by eccentricity, resulting in no change in its natural frequency. The fourth and sixth modes exhibit characteristics similar to the changes observed in the first and third modes. Therefore, when the upper structure of the base-isolated structure experiences mass eccentricity, the torsional mode becomes the dominant mode, leading to changes in dynamic behavior with increased contributions to the response.
Next, to examine structural response characteristics for the input of seismic motion, 3D seismic response analysis was conducted using the design response spectrum (DRS) applied in domestic export-standard nuclear power plants, as shown in
Figure 5. In
Figure 5a, the horizontal direction (EW) DRS is compared with the test response spectrum (TRS) and the required response spectrum (RRS). In
Figure 5b, the acceleration time history corresponding to the DRS is shown.
Next, to observe the seismic response impact of the eccentricity in a base-isolated structure, the average acceleration response at the center of the upper structure is analysed and reviewed. Within an eccentricity of 10%, both the X and Y directions show minimal changes in acceleration. However, beyond 10% eccentricity, the average acceleration in the X direction starts to decrease significantly, reaching a minimum acceleration that is about 20% lower than the initial value at around 50% eccentricity. Beyond 50% eccentricity, the X-direction acceleration gradually increases again.
In contrast, the Y-direction average acceleration shows a linear response increase of up to about 15% as eccentricity increases. The eccentricity sensitivity of horizontal acceleration response at the center of gravity is shown in
Figure 6.
In order to examine the changes in more detail, we checked the acceleration responses at the four corner points from A1 to A4, which correspond to the corner positions of the upper structure, as shown in
Figure 3. Since A2 and A1 are symmetrical with respect to the Y axis, we omitted some of them and present them in
Figure 7.
The acceleration response in the Y direction, which serves as the reference for mass eccentricity, exhibits the same response characteristics as the average acceleration in
Figure 8. However, as seen in
Figure 7a, as eccentricity increases, the X-direction acceleration at point A2, where the center of mass gets closer, initially increases due to the eccentricity of the mass, but then linearly decreases after about 20% eccentricity. This is because, as indicated by the earlier modal analysis results, as eccentricity increases, the contribution of the torsional mode rises, leading to an initial increase in acceleration due to the combined behavior of translation and torsion modes.
However, as shown in
Figure 7b, as eccentricity increases, the change in the center of mass’s position due to the change in the rotational center position results in variations in acceleration values at specific points. Due to this phenomenon, the X-direction acceleration responses at A2 and A4 exhibit opposite characteristics. Therefore, during the seismic design of structures with mass eccentricity, it is important to pay attention to such peak response characteristics at around 20% eccentricity depending on the upper structure’s position.
Nextl, the displacement sensitivity to mass eccentricity during seismic responses is examined. As shown in
Figure 8, the Y-directional displacement response exhibits a linear increase of up to 25% as eccentricity increases. In contrast, the X-directional displacement initially shows little change in response, but starting from around 50% eccentricity, it exhibits an approximately 30% increase. This indicates that special attention is required when dealing with significant eccentricities, particularly in the case of large eccentricities, in the context of X-direction displacement.
The sensitivity of displacement response for points A2 and A4, as shown in
Figure 9, indicates that, as eccentricity increases, there is an increase in the influence of torsional behavior, leading to an increase in displacement response. In other words, as eccentricity increases, the response at point A2, where the mass center is closer, increases due to the influence of torsion behavior. Conversely, the response at point A4, which is farther from the mass center, decreases in overall response due to the out-of-phase effect of increased X-direction displacement. For instance, at eccentricity of around 20%, the maximum displacement response can be observed to increase by approximately 20% or decrease by nearly 30%, depending on the location of the upper structure.
In summary, the analysis results for the response spectra based on mass eccentricity in the one-axis direction indicate that, as eccentricity increases, the combined behavior due to the increased contribution of torsion leads to varying acceleration or displacement responses at specific locations of the upper structure, depending on its position.
In the following analysis, a sensitivity analysis of seismic response due to 2D mass eccentricity in both horizontal directions was conducted. For the input of seismic motion, the EW direction design response spectrum from
Figure 5 was utilized, along with the NS direction DRS, to perform acceleration and displacement response spectrum analysis.
Figure 10 illustrates the changes in acceleration response for the X direction and Y direction while simultaneously increasing mass eccentricity in both horizontal directions. In
Figure 10a, it can be observed that, for X-direction acceleration, the response sensitivity due to 2D mass eccentricity, where both Y-direction and X-direction eccentricities exist, shows nonlinear variations. As seen in
Figure 10b, a similar trend is observed for Y-direction acceleration. In summary, the common feature is that, while in some regions the response may decrease, when mass eccentricity increases simultaneously in both horizontal directions, acceleration response can significantly increase. Thus, caution is required.
Figure 11 is similar to
Figure 10, showing the influence on displacement response for the X direction or Y direction while simultaneously increasing mass eccentricity in the horizontal direction. As shown in
Figure 11a, in the case of X-direction displacement, when Y-direction mass eccentricity is low, the displacement response linearly increases in proportion to the eccentricity. For X-direction non-eccentric cases, there is little effect from Y-direction eccentricity on displacement response until the X-direction eccentricity reaches around 50%, at which point the sensitivity to eccentricity increases significantly.
In
Figure 11b, Y-direction displacement demonstrates a different behavior. When X-direction mass eccentricity is low, the response sensitivity to Y-direction mass eccentricity remains relatively constant. As both horizontal mass eccentricities increase, Y-directional maximum displacement can increase by approximately 60%.