Experimental Approach for the Failure Mode of Small Laminated Rubber Bearings for Seismic Isolation of Nuclear Components

Abstract

Response characteristics of small-sized laminated rubber bearings (LRBs) with partial damage and total failure were investigated. For nuclear component seismic isolation, ultimate response characteristics are mainly reviewed using a beyond design basis earthquake (BDBE). Static tests, 3D shaking table tests, and verification analyses were performed using optional LRB design prototypes. During the static test, the hysteresis curve behavior from buckling to potential damage was observed by applying excessive shear deformation. The damaged rubber surface of the laminated section inside the LRB was checked through water jet cutting. A stress review by response spectrum analysis was performed to simulate the dynamic tests and predict seismic inputs’ intensity level that triggers LRB damage. Shaking table tests were executed to determine seismic response characteristics with partial damage and to confirm the stability of the superstructure when the supporting LRBs completely fail. Shear buckling in LRBs by high levels of BDBE may be quickly initiated via partial damage or total failure by the addition of torsional or rotational behavior caused by a change in the dynamic characteristics. Furthermore, the maximum seismic displacement can be limited within the range of the design interface due to the successive slip behavior, even during total LRB failure.

1. Introduction

Recent strong earthquakes in Korea have shocked and affected people and the government due to the nature of damages inflicted on urban facilities and raised awareness that the country may no longer be a safe seismic area.

As a result of increasing concerns, technical research is encouraged to enhance the seismic capacity of nuclear power plants (NPPs). One of these measures is the application of seismic isolation techniques to plant structures. The idea is to limit the application objects to fragile and safety-related nuclear components instead of building structures, which might be more practical and economical for operating plants. However, applying a customized seismic isolator to individual NPP facilities requires optimal design and verification through analyses and tests. For reference, in Japan, a national project has been carried out since 2008 to design a large lead-inserted rubber bearing for seismic isolation evaluation of NPPs, and a feasibility study on the seismic design of a nuclear reactor building [1]. Some shear failure experiments were performed in this study, but they mostly used reduced laminated rubber bearings (LRBs) [2,3,4,5]. To date, there have been many studies on the shaking table test of LRBs for seismic isolation of buildings, but most of these have been conducted with downscaled LRBs. In addition, there are few studies on shaking table tests on full-size LRBs for NPP facilities or equipment models [6,7,8]. The acronyms used in the paper are shown as below near the end.

For the practicality of the study, it is targeted and planned to apply the results to the standard design of Korean nuclear plants for export, APR1400. The seismic plant capacity is known to have a safe shutdown earthquake (SSE) having a level of 0.3 g as a design basis earthquake (DBE) and a corresponding seismic performance of a 0.5 g level. In general, the seismic capacity of NPPs has been discussed at the plant level. Recently, however, the seismic performance of individual safety-related components, such as control panels, emergency diesel generators, remote stop consoles, battery packs, and spent nuclear fuel racks, has become more important in determining the seismic safety of NPPs. In particular, when the potential intensity of an earthquake is greater than the design level, plant and component safety should be reviewed and maintained to a reasonable extent. This is why a small-sized seismic isolation bearing is developed and the failure mode of the bearing investigated in the BDBE condition.

Therefore, major research issues are the development of an optimal design of a small lead-inserted LRB for seismic isolation of fragile nuclear components, and upgrading of the seismic capacity to a reasonable level in BDBE that can be applied to operating plants [2,3]. If the earthquake acting on the structure is much greater than the design level, buckling or damage to the seismic isolation bearing cannot be avoided. However, it is important to predict the potential impact on surrounding safety-related facilities by identifying the characteristics of extreme behavior and maximum response after failure. This could be caused by proper estimation of the bearing integrity in the BDBE for the enhancement of seismic performance. It can be a reference for re-evaluating the seismic performance of a structure through a review of response records before and after an actual earthquake. Hence, analyses and tests using prototype specimens were performed to determine the working capacity under ultimate loading. In addition to the work on seismic performance verification, a close investigation into the failure process of LRBs may be very useful to check the internal condition and performance reliability of the LRB after an actual BDBE. Therefore, in the current study, some approaches were attempted to investigate the response characteristics and failure mode from buckling via partial damage to a total failure of the LRB under ultimate seismic load conditions [9,10]. Some ultimate tests and simulation analyses for the intended failure were executed with detailed observation of the damaged surfaces and post-failure behavior. Hence, the stress during BDBE was observed through finite element analysis of a small LRB designed to have a unit capacity of 1 ton. In addition, static tests required by the design standards and a dynamic test using a 3-axis shaking table were performed. From these analyses and tests, the damage response characteristics of seismic isolation bearings for small facilities and seismic safety before and after breakage were reviewed. The results of failure mode analysis may be a reference for the application of small LRBs to the operating nuclear plant components.

2. Small-Sized Laminated Rubber Bearing Design for BDBE

2.1. Design of Lead Rubber Bearings

Analysis of the previous bearing designs confirmed that the low-damping small-sized LRB was less effective in dissipating seismic energy than the larger bearings for buildings. This is mainly because of the manufacturing difficulty of the thin rubber plate for small-sized isolation bearings [3]. Therefore, the design was modified in the form of an LRB with a lead core inserted in the center of the seismic isolator to supplement the damping performance.

In this study, the unit support weight of the small-sized LRB was designed to be 1 ton. Two design options (OPT1, OPT2) with different natural frequencies and shapes were initially prepared. First, the designs focused on enhancing the seismic isolation effect while considering the limitations of small seismic isolation bearings. In the case of the first design (OPT1), for a low natural frequency (2.0 Hz), the shape factor was lowered, resulting in poor stability. The second design (OPT2) was designed to improve the shape factor, whose fundamental natural frequency was slightly increased to approximately 2.3 Hz. The cross-sectional shape and design specifications of the LRB used in this study are compared in Figure 1 and

Table 1. Design options of the LRB for nuclear components.

Properties	OPT1	OPT2
Design Load [ton]	1	1
Outer Diameter [mm]	76	100
Design Hori. Freq. [Hz]	2.0	2.3
Shape Factor, S1	7.6	9.9
Shape Factor, S2	4.4	5.0

, respectively.

Table 2. Material properties of equipment LRB.

Material	Properties	Value
Rubber	Shear Modulus [MPa]	0.3
	Bulk Modulus [GPa]	1.96
	Tensile Strength [ksi]	2.5~3.5
	Density [g/cm3]	0.93
Lead	Shear Modulus [MPa]	8.33

shows the physical properties of the rubber and lead used in the manufacture of small-sized LRBs. These properties are similar to those of natural rubber and pure lead. The details of the design options were described in [2,3].

2.2. Design Seismic Inputs

The design earthquake for a domestic export-type NPP, APR1400, was used to simulate the damage and breakage of the seismic isolation bearing through analysis. The floor response acceleration spectra of the 137 ft high SSE in the auxiliary building were selected for analysis because several safety-related devices were located near this level. The input earthquakes of the SSE are based on a DBE of 0.3 g. In addition, the zero period acceleration (ZPA) of the operating basis earthquake (OBE) was assumed to be 1/3 of the SSE.

To verify the experimental results, the same response spectra were applied in the analysis. Figure 2 compares the shapes of the required response spectrum (RRS), test response spectrum (TRS), and floor response spectrum (FRS) used for the analysis. It is interesting that the acceleration level of the FRS used as an input is already amplified from ZPA of 0.3 to 1.3 g at a height of 137 ft using a plant building structure model. As shown in Figure 2, the value of TRS measured on the vibration table covers the RRS and FRS in most frequency ranges. The frequency characteristics of the floor response spectrum show that the peak appears near 10 Hz.

To simulate the damage response characteristics and failure behavior in the case of an earthquake exceeding the design, the input earthquake is shown in Figure 2. Three additional earthquakes of 0.4, 0.5, and 0.6 g were prepared by adjusting the scale of the design earthquake of 0.3 g of the floor response spectrum and time history in Figure 2.

3. Observation of LRB Failure Mode through Static Test

3.1. Static Test Setup and Procedures

The static test was conducted according to the Korean Standard KS M ISO 22762, which is similar to the international code. The experiment was a shear test of seismic isolation bearings, and shear displacement was applied while a constant vertical compressive load corresponding to the load capacity was applied to the specimen. For reference, Figure 3 shows a schematic diagram of the experimental apparatus. The test method applies a standard shear displacement to the specimen. At this time, the standard test frequency should be the seismic isolation frequency or a value of 0.5 Hz or less, as suggested in the standard [11,12,13].

Here, for the static ultimate test for a small-sized LRB, assuming that 100% of shear strain is defined as the total height of the rubber layer (17.5 mm), the predetermined ultimate strains exceeding the design limit would be 300% and 400%. The shear test was performed by increasing the strain in a step-by-step manner.

3.2. Observation of Failure Characteristics in Static Test

The static test of OPT1 of the small-sized LRB for equipment shows that the force-displacement response curve has hysteresis characteristics similar to the typical shear deformation behavior of the LRB for large structures until the shear strain reaches 300%, as shown in Figure 4. However, the shear force no longer increases near the shear displacement of approximately 60 mm (350% of shear strain), and the load decreases sharply without any strain change near a displacement of approximately 70 mm (400% of shear strain). This was considered to be caused by the initiation of buckling. However, in the opposite direction, the slope of the graph does not appear symmetrical, and the shear load hardly changes at a specific displacement range. When a shear force is applied in the opposite direction after a half cycle, the curve changes to show a negative shear stiffness from approximately 150% of shear displacement. Such a response trend indicates partial damage to the rubber part, when referring to a detailed review of the test video and internal fracture surface. This could be supplemented by observing the vertical section of the laminated surface of the tested specimens by water jet cutting after the test.

In summary, in the case of the 400% shear test of LRB OPT1, which has a low shape factor, the initiation of internal buckling was estimated when the shear displacement reached approximately 350% of the design shear, but partial damage was assumed to occur in the sequential backward shear test.

In contrast, the force-displacement response of OPT2 (Figure 5) shows typical hysteretic response characteristics with up to 500% shear displacement. OPT2 exhibits better response repeatability in the hysteresis curve than OPT1 due to the improved shape factor. In the 600% shear test, where the effect of bending moment by the vertical load is expected to increase significantly, the force-displacement response started to exhibit an asymmetric trend similar to the 400% case of OPT1. In the course of the 600% shear test, the shear force decreases sharply over 500% displacement and changes unstably as the bearing suffered partial damage inside, showing a non-linear negative stiffness before it reaches the maximum deformation. Near 100 mm (approximately 570%) shear displacement, the damaged area rapidly expanded along with buckling of the rubber disc inside the LRB laminate, leading to an almost zero slope in the opposite direction test. A similar response trend was observed in the shear test of other OPT2 specimens. This implies that the overall damage to the rubber laminate may proceed rapidly without prior signs and processes of partial buckling, and caution is required in the ultimate case, such as 600% shear in a BDBE. Detailed investigation of LRB sections with damaged surfaces by water jet cutting and test video review after the test supplements this estimation of the damage process. As shown in Figure 6a,b, in the damaged LRB, traces such as partial failure of the rubber disc of the laminate, excessive deformation of the steel plate, and plastic deformation of the lead core can be compared to the undamaged cross section. In conclusion, compared to OPT2, the excessive P-δ effect due to the poor shape factor brings forward the initiation of buckling earlier in OPT1. The dissipated energy in OPT2 shear test is estimated to be larger than that in OPT1 test because the area of hysteresis curve increased by the shear displacement and size.

4. Observation of LRB Failure Mode through Dynamic Test

4.1. Simulation of Dynamic Test through FE Analysis

Response spectrum analysis was performed for the stress evaluation of small-sized LRBs. The modeling was performed as shown in Figure 7 using a commercial program, ANSYS 2021 R2 [14]. A finite element (FE) model was prepared and analyzed to simulate the seismic test using a shaking table. As shown in Figure 7a, the 4-ton dummy mass model is supported by the four LRBs shown in Figure 7b at each square corner. It is a laminated structure composed of thin steel discs on every other rubber disc in the middle, similar to the model in Figure 7b, with thick steel end plates and rectangular flanges at the top and bottom, and a lead core inserted in the vertical center hole. All of these were modeled with a 3D solid element.

As boundary conditions for analysis, all the degrees of freedom of the bottom surfaces of the LRB model in the four corners are fixed. In addition, it is assumed that the lead core, steel plates, and rubber plates are bonded together.

The results of the modal analysis show that the dynamic characteristics of the LRB for small facilities, as shown in

Table 3. Comparison of designed LRB natural modes with analysis results.

Mode No.	1	2	3	4	5	6
Modal analysis results [Hz]	2.3	2.3	3.4	37.4	51.3	54.0
Design natural frequencies [Hz]	2.3	-	-	36.9	-	-

, are in good agreement with the design frequencies of 1st horizontal and 4th vertical modes.

Figure 8 shows a representative result of the response spectrum analysis for a BDBE of 0.6 g. Regarding the lead core of the LRB, it is concluded that large plastic deformation occurred in excess of the yield strength in all areas. Shear deformation contributes to the seismic energy dissipation of the LRB system. In the case of the steel layer, it was calculated that plastic deformation occurred at the edges facing around the lead core and was similar to the trend of the actual buckled LRB. In the case of the rubber layer, the yield strength of rubber does not appear clearly because of the characteristics of non-metallic materials. Here, with reference to the literature, the shear strength of natural and vulcanized rubber has a wide application range of approximately 1 to 6 MPa [4].

Table 4. Analysis results of max. equivalent stress on the rubber and steel layers.

ZPA [g] of FRS (BDBE)	Rubber Layer [MPa]	Steel Layer [MPa]
1.7 (0.4)	3.9	437.4
2.2 (0.5)	4.8	546.7
2.6 (0.6 g)	5.8	656.0

describes the maximum stresses of the rubber and steel layers under three different seismic BDBE inputs of 0.4, 0.5, and 0.6 g. It can be roughly estimated that rubber and steel experienced yielding near the edge of the lead core at 0.6 g of DBE, as shown in Figure 8. The maximum shear strength at rubber failure can be estimated using Hook’s law of shear modulus in Table 2 times the maximum shear strain in Figure 5, to be approximately 1.8 MPa. Considering the results described in Table 4 with the reference value and estimation of shear strength, it is concluded analytically that local buckling or damage may have already started from the case of a BDBE of 0.4 g.

4.2. Investigation of Damaged LRB Response through Dynamic Tests

The simulation of the ultimate dynamic test through BDBE analysis using the finite element model is discussed in the previous paragraph. In this paper, the observation results of the failure mode in the dynamic test using a 3-axis shaking table were examined to determine the actual dynamic response characteristics before and after the failure in the ultimate load condition by BDBE. For reference, the shaking table used in the test is a vibration table with a capacity of 30 tons for 3-axis dynamic test. The detailed specifications are listed in

Table 5. Performance and specification of 3D shaking table.

Item	Performance
Size [m]	4.0 × 4.0
Max Loading (Force/Moment)	300 kN/1200 kN-m
Frequency Range	0.1–60 Hz
Control Axes	6 DOF
Acceleration at Full Payload [g]	X	Y	Z
	1.2	1.2	0.8
Maximum Stroke [mm]	X	Y	Z
	±300	±200	±150

.

To observe the dynamic characteristics and extreme behavior of the LRB isolating a small rigid structure against a BDBE, shaking table tests were performed [15,16]. The overall schematic of the test is shown in Figure 9. As explained in the paper for the simulation and verification analysis, four LRB mockup bearings are set at the bottom corners to support a 4-ton dummy mass expressing a small lumped-mass-type superstructure.

The shaking table tests were performed using two types of approaches with different purposes. Test-I was used to observe the response characteristics of the LRB with partial damage during a BDBE. In contrast, Test-II was used to investigate the maximum seismic response, behavioral stability, and potential influence on the surrounding equipment due to excessive displacement when the entire LRB fails [17,18,19]. In Test I, the input earthquake was scaled down to limit the maximum displacement to less than the design earthquake at the operating floor level. The acceleration–time history in Figure 2 was applied as an input earthquake for the dynamic test. As shown in

Table 6. Shaking table test-I procedures.

No.	Seismic Input [137 ft]	ZPA [g] of FRS
1	OBE-X	1.3
2	OBE-Y	1.3
3	OBE-Z	0.4
4	OBE 3-Axis	-
5	SSE-X	2.6

, the ZPAs of the input earthquake applied to Test I have an acceleration range of 0.3–1.0 g, which were amplified through the building structure model from the ground level OBE and SSE. The input earthquake ZPA in Test-II is greatly amplified up to approximately 1.3 g. OPT 1 was used for Test-I, whereas OPT2 was used for Test-II.

4.3. Review of Shaking Table Test-I

As explained in the previous section, the 1st shaking table test was conducted in the order of three uniaxial and one triaxial OBE tests, and a uniaxial SSE test, as shown in Table 6. In particular, the fifth experiment enabled observation of the response characteristics to extreme loads before failure. Figure 10 shows a graph comparing the results of the resonance test before and after the experiments.

In Figure 10a, there is little change in the natural frequency in the X-direction before and after the tests. However, after the tests, the acceleration response at the top of the dummy mass was amplified in the peak region, and the acceleration at the bottom decreased, as shown in Figure 10b. This seems to be caused by the influence of rocking behavior on the X-direction translational response. In contrast, when comparing the responses before and after the whole test, the peak of the Y-directional acceleration moved to a lower value, indicating a decrease in stiffness due to damage. The observation of the specimen cross-sections by water jet cutting after the experiment shows some cracked areas in the rubber laminated surface inside the LRB. These response characteristics can be a good reference for evaluating the internal health and integrity of LRBs by analyzing the response records of seismically isolated facilities after an actual BDBE.

Figure 11 shows the displacement response of the uniaxial SSE shaking table test. Figure 11a depicts the responses of the seismically isolated dummy mass in the horizontal X- and Y-axes before the main test. As anticipated, the Y-axis response is almost zero, indicating that it is hardly affected by the X-axis excitation. However, once the LRB has been damaged through the ultimate test of a one-directional SSE, the Y-axis displacement response is non-zero, as shown in Figure 11b, due to the inequality and eccentricity of stiffness inside the LRB in the X-direction. In the case of the isolated dummy mass displacement, the response of the damaged LRB in the orthogonal direction is no longer independent of the effect of rotational behavior. This is unlike the response trend between the two horizontal axes of the shaking table. Therefore, if the acceleration and displacement response can be relatively checked between the two horizontal axes after a BDBE, it may provide useful information about the structural integrity inside the LRB. A comprehensive review of the response correlation trend can determine the continuous reusability of LRBs for the residual design life and improve the estimation reliability of possible partial damage inside the LRB.

4.4. Review of Shaking Table Test-II

As explained in Section 3.1, the seismic input was adjusted for the LRB to lead to crack initiation at the laminated rubber surface and to investigate the response trend in the partially damaged LRB. The second table test was performed to understand the response characteristics of the entire isolation system from partial damage to complete failure of the LRBs. For this purpose, BDBE inputs at the 137 ft level were directly applied to the 3D shaking table. The floor response in this case was already amplified through the building analysis model of a Korean standard nuclear plant. In the second experiment, three designed beam structures were additionally installed on the shaking table and on the upper surface of the dummy mass to examine and compare the seismic response characteristics of the secondary structures inside the isolated facility. The test on the shaking table is shown in Figure 12, which includes the dummy mass supported by four LRBs in the bottom corners, and serial numbers of acceleration sensors with predetermined natural frequencies in parenthesis. To observe the seismic isolation effect on the secondary structures, two sets of beam structures with natural frequencies of 5, 10, and 20 Hz were installed on the shaking table bottom and on the upper part of the isolated primary structure. The accelerometer attached at the top of the beam compares the seismically isolated and non-isolated beam responses. The experimental sequences are listed in

Table 7. Shaking table Test-II procedures and X-dir. seismic inputs [137 ft].

No.	LRB ID	ZPA [g] of FRS
1	OPT-2A	2.2
2		1.3
3		0.4
4	OPT-2B	2.2
5		1.3
6		0.4
7	OPT-2C	2.6

.

The second shaking table test was used to observe the behavioral characteristics before and after the isolation system failure during BDBE. The input earthquake for the test was the same as that given in Figure 2, whose ZPA was highly amplified from the 0.3 g DBE to 1.2 g. As shown in Table 7, the experimental sequence proceeded using two identical sets of specimens (OPT-2A, OPT-2B) for three input earthquakes of 0.4, 1.3, and 2.2 g of ZPA, followed by another identical specimen (OPT-2C) tested by applying the largest ZPA of a 2.6 g earthquake as a BDBE. The test was performed with a one-axis excitation in the X direction.

Figure 13 shows a comparison of the acceleration response measured on the shaking table for the DBE 0.3 g (ZPA of FRS: 1.3 g) test of OPT-2A with the response measured on the isolated dummy mass. As expected, the peak of acceleration response of the dummy mass appears around 2.3 Hz, which is the design frequency of the LRB. It gradually decreases to around 20 Hz, and then maintains a stable acceleration response in the remaining frequency range. The maximum acceleration of the dummy mass as a superstructure largely decreased in the range of about 4.5 to 100 Hz by seismic isolation, as intended.

Figure 14 shows the seismic isolation effect of the beam structures installed on the shaking table and dummy mass. Figure 14a,b shows the acceleration spectrum and time history of the secondary structure at 10 Hz in the facility. Again, as expected, a peak appears at 9 Hz, which is near the design natural frequency, and, except for the region below 3.5 Hz, which is slightly higher than the isolation frequency of the LRB, the isolating effect of reducing the response is significant. The response reduction rate is relatively larger than that of the 5 Hz beam. The characteristic of the acceleration response versus frequency is similar to that of the 5 and 20 Hz beams; a peak appears near the design natural frequency, and the seismic isolating effect of reducing the response appears reasonable.

Summarizing the above results, the seismic isolation performance of the LRB for small facilities developed in this study were confirmed once again, because the acceleration response of the secondary structure showed a seismic isolation effect similar to that of the primary structure. Figure 15 shows an example of the acceleration response history of beams when the primary structure experiences partial and complete failure in the isolation system owing to the ultimate load. The figure shows the acceleration–time history measured at the top of the beam, which indicates the secondary structure in the seismic isolation facility [20]. The dotted line indicates the buckling time of the LRBs confirmed through the video review. The overall response of a 10 Hz beam on the dummy mass is not significantly affected by the total isolation system break. The response trends of the three installed beam structures were similar.

4.5. Discussion of Failure Response Characteristics in Dynamic Test

To observe LRB dynamic characteristics due to the extreme load, shaking table tests as the last step of Test-II in Table 7 were conducted for the uniaxial seismic input at the upgraded level of 0.6 g simulating the BDBE. In this case, ZPA level of FRS for the working floor 137 ft high was amplified to almost 2.6 g by the plant building model. Figure 16 shows the displacement–time history, including the slip behavior, of the dummy mass following the test, and explains its behavior after the total break of the LRBs. The dotted line indicates the estimated time of failure initiation. Under the influence of a large input earthquake, partial failure among the LRBs by excessive shear displacement is detected at an early stage, at approximately 13 s. After a few seconds, the all of the LRBs supporting the dummy mass completely ruptured and slipped in a limited range on the table. The maximum shear displacement of the dummy mass before the break was approximately 100–110 mm (over 600% of the designed shear) and was reciprocated. The post-rupture behavior showed a slip response of approximately 70 mm in both directions on the shaking table after the center of mass moved approximately 80 mm. A detailed review of the experimental video record shows that the post-rupture behavior agrees with the response trend in Figure 16, and a small noise occurs near the point of complete break. The image in Figure 17 shows the seismic isolator LRBs supporting the dummy mass completely ruptured and moved with some rotation from the original position.

It is noteworthy that, even after the LRB was completely broken, the dummy mass continued to slip within a limited range due to friction. Therefore, even if the LRB is fractured due to the occurrence of a large earthquake exceeding the DBE, there is an additional secondary seismic isolation effect due to the slip. Therefore, this should be considered in the design of isolation systems, including LRBs, superstructures, and moat margins to ensure seismic safety, and prevent potential impact with interfacing neighboring structures [21].

Figure 18 shows the cross-section shape of the fully fractured LRB after the extreme dynamic test. Figure 18a is a side view of the failed LRB with cracked cover rubber, and Figure 18b shows the different colors of the scratched surface, which are friction traces due to the slip after a fracture. Similar observations were made on the cut surfaces of the deformed lead core and rubber plate. The fractured laminate occurs near the top of the LRB laminate, which is similar to the point of maximum stress in the simulation analysis in Section 4.1.

4.6. Simulation of After-Failure Response by Slip Analysis

The shaking table tests confirmed that the dummy mass continued to slip within a limited range by friction, even after the LRB was completely broken. This behavior indirectly ensures the seismic safety of an isolated system using LRBs, even during BDBE. To verify the maximum displacement response resulting from the test, tests measuring the actual friction coefficient of the failed LRB and simulation slip analysis based on Equation (1) were performed for a simple block slip model and equation of motion on a friction surface shown in Figure 19. To obtain the actual friction coefficient in the case of total LRB rupture, static slip tests using inclined steel plates and dynamic tests were undertaken using a 1D shaking table. The experiments were repeated more than 10 times to ensure precision. The test averages of the static and dynamic friction coefficients μ_s and μ_d are 0.66 and 0.54, respectively. Figure 20 shows the displacement-time history of the sliding rigid block for this range of friction coefficients.

$$\mathrm{m}\ddot{x}+\mathsf{\mu }·\mathrm{m}·\mathrm{g}·\mathrm{sgn}\left(\dot{x}\right)=-m{\ddot{x}}_g$$

(1)

Figure 20 shows the results of the block slip analysis as the displacement–time history. The maximum displacements were approximately 42, 25, and 22 cm for friction coefficients of 0.5, 0.6, and 0.7, respectively. This does not show a significant difference, considering that the actual slip displacement of ~25–30 cm appeared immediately after the dummy mass was completely damaged in the shake table test for the floor response seismic input corresponding to a DBE of 0.6 g. That is, considering that the friction coefficient with the floor was estimated as ~0.5–0.7 through static and dynamic friction tests, it was concluded that the slip displacement until the time when the test was stopped due to buckling of the entire seismic isolation bearing was similar to the analysis result. In general, these data determine the horizontal margin distance between the superstructure and moat wall to prevent collisions with neighboring structures during a BDBE. The study suggests that safety issues such as interference with surrounding structures can be mitigated even with a complete failure of the LRB in small facilities due to a BDBE.

5. Conclusions

In this study, approaches to measure the failure response characteristics of LRBs to extreme loads such as a BDBE for small facilities or devices were proposed. A small LRB was developed and tested to improve seismic performance in the case in which an earthquake exceeds the DBE of safety-related structures in NPPs. Static and dynamic experiments and verification analyses were performed. The amplified floor response was applied to analyze and test the buckling behavior of the extreme response. To understand the actual LRB damage characteristics, shaking table tests were conducted, and the fracture surface was observed. In addition, stress and slip analyses were simulated with video and cut view reviews to verify the results. The following conclusions were drawn from this study:

• The results of the seismic analysis of the LRB for BDBE input can simulate the failure initiation and process in the shaking table test. It matches well with the plastic deformation of the lead core, laminated rubber, and steel plate.
• The results of the static test and fracture surface observation of a small LRB show that buckling or partial damage starts at the part where the asymmetry and inverse slope of the hysteresis curve appears. The overall damage to the rubber laminate can proceed rapidly from partial buckling without signs of gradual propagation.
• It is useful to evaluate the internal soundness of the LRB and estimate the partial damage by comparing the natural frequency and orthogonal response of the seismic isolator before and after the occurrence of a BDBE.
• Even when the seismic isolation bearings supporting the facility are completely broken, additional isolation by slip behavior can maintain the superstructure within the interface limit without impacting the surrounding facilities.
• The small-sized LRB studied in the paper can be a good option among seismic isolation devices for the seismic enhancement of the selective safety-related equipment of operating nuclear plants.