Shaking Table Tests to Validate Inelastic Seismic Analysis Method Applicable to Nuclear Metal Components

Abstract

The main purpose of this study is to perform shaking table tests to validate the inelastic seismic analysis method applicable to pressure-retaining metal components in nuclear power plants (NPPs). To do this, the test mockup was designed and fabricated to be able to describe the hot leg surge line nozzle with a piping system, which is known to be one of the seismically fragile components in nuclear steam supply systems (NSSS). The used input motions are the displacement time histories corresponding to the design floor response spectrum at an elevation of 136 ft in the in-structure building in NPPs. Two earthquake levels are used in this study. One is the design-basis safe shutdown earthquake level (SSE, PGA = 0.3 g) and the other is the beyond-design-basis earthquake level (BDBE, PGA = 0.6 g), which is linearly scaled from the SSE level. To measure the inelastic strain responses, five strain gauges were attached at the expected critical locations in the target nozzle, and three accelerometers were installed at the shaking table and piping system to measure the dynamic responses. From the results of the shaking table tests, it was found that the plastic strain response at the target nozzle and the acceleration response at the piping system were not amplified by as much as two times the input earthquake level because the plastic behavior in the piping system significantly contributed to energy dissipation during the seismic events. To simulate the test results, elastoplastic seismic analyses with the well-known Chaboche kinematic hardening model and the Voce isotropic hardening model for Type 316 stainless steel were carried out, and the results of the principal strain and the acceleration responses were compared with the test results. From the comparison, it was found that the inelastic seismic analysis method can give very reasonable results when the earthquake level is large enough to invoke plastic behavior in nuclear metal components.

1. Introduction

In the current seismic design of nuclear power plants (NPPs), the peak ground acceleration (PGA) level of safe shutdown earthquake (SSE) is generally taken to be 0.3 g as a design-basis earthquake. Recently, there have been attempts to increase the PGA level above 0.3 g to enhance the seismic safety of NPPs. Furthermore, after the Fukushima NPP accident, the consideration of the beyond-design-basis earthquake (BDBE) became one of the big issues at the design stage, especially for safety-related nuclear facility components having small seismic margins. In fact, it is true that increasing the value of the SSE level is a big burden for the seismic design of NPPs. There have been many research and development efforts to resolve BDBE issues for the seismic design of NPPs. As one of the hardware approaches to accommodate large earthquakes, seismic isolation design has been studied by many countries for a whole nuclear island building isolation [1,2] or an individual facility component isolation [3,4]. Additionally, seismic energy absorbers such as tuned mass and dampers (TMDs) have been studied for application to seismic fragile piping systems or any other safety-related facilities [5].

Recently, as one of the approaches against large earthquakes, studies on the new seismic design acceptance criteria for large earthquakes have been actively conducted for the application of nuclear metal components [6,7,8,9]. The main concept of this design criteria provides strain-based design limits to protect the pressure-retaining nuclear metal components against an inelastic strain-induced failure mode. Actually, current design criteria in nuclear codes and standards such as ASME BPVC III [10] and RCC-MR [11] provide the stress-based design limits for the elastically calculated stress values. Therefore, they may not provide adequate limits for actual seismic failure modes in cases when the reversing dynamic plastic responses are significant.

In the previous studies on the new strain-based seismic design criteria, the feasibility of this approach was investigated for the nuclear pipe and nozzle. The most important thing when applying this approach is to calculate accurate inelastic strain values using inelastic seismic analysis [12,13]. Then, seismic shaking table tests are inevitably required in order to validate the inelastic seismic analysis method. There has been research on seismic shaking table tests for the piping system [14,15].

In this study, the test mockup for simulating the hot leg surge line nozzle, which is known as one of the fragile components in nuclear steam supply systems (NSSS), is designed and tested on a shaking table for two earthquake levels of PGA = 0.3 and 0.6 g. For validation of the inelastic seismic analysis method, the finite element model using the ANSYS program [16] is established with material constitutive equations of the Chaboche kinematic hardening model and the Voce isotropic hardening model for Type 316 stainless steel. Through the investigation of the test results and the comparison of seismic time history responses such as the principal strain and accelerations between the measured data and the inelastic seismic analysis results, the inelastic seismic analysis method for large earthquakes was validated and confirmed to be useful for the seismic design of nuclear metal components.

2. Design of Seismic Test Mockup

2.1. Configuration and Dimensions

In this study, the seismic test mockup is designed to be able to simulate the actual nuclear component installed in the in-structure building. This will be consistent with the purpose of validating the strain-based seismic design method developed in previous studies [9,13]. To do this, the metal component nozzle, which is known as one of the seismically fragile components in nuclear steam supply systems (NSSS), was selected as the reference for the test mockup. Specifically, the hot leg surge line nozzle connecting the hot-leg pipe and the surge line piping system, which is installed at the elevation of 136 ft in the in-structure building, is referenced in this test mockup design.

The main design concept of the test mockup is to configure the piping layout, resulting in the maximum accumulated plastic strain at the safe-end region connecting the nozzle and the piping system in the same condition as the actual hot-leg surge line nozzle in NSSS. Figure 1 presents the designed overall configuration and seismic directional axis of the test mockup. As shown in the figure, the test mockup consists of a target nozzle, horizontal and vertical pipes, one elbow, and two added masses. The total height of the test mockup is 1132 mm, and the total mass is about 158 kg.

Table 1. Summary of test mockup design parameters.

Design Parameters	Design Value
Pipe Outer Diameter (mm)	89.1
Pipe Thickness (mm)	7.6
Vertical Pipe Length (mm)	850
Horizontal Pipe Length (mm)	550
Elbow Curvature (mm)	114.3
Added Mass-1 (kg)	80
Added Mass-2 (kg)	40
Total Height of Nozzle (mm)	167.35
Nozzle Outer Diameter (mm)	133.34

reveals the summary of the design parameter values of the test mockup.

The used material of the test mockup is Type 316 stainless steel, which has an elastic modulus of 190 GPa, a density of 7970 kg/m³, and a Poison’s ratio of 0.27 at room temperature.

2.2. Analysis Model and Dynamic Characteristics of Test Mockup

To derive an appropriate plastic strain in the nozzle part, enough to validate the inelastic seismic analysis method, the test mockup is designed to have dominant dynamic characteristics resonant in the peak spectral frequency band of the seismic input motions. Figure 2 presents the target required response spectrum, representing those at the elevation of 136 ft in the in-structure building (ISB) of NSSS. As shown in the figure, the peak spectral frequency band is 9 to 12 Hz for the EW (east–west) direction, 5 to 20 Hz for the NS (north–south) direction, and 15 to 21 Hz for the V (vertical) direction.

The dynamic characteristics of the test mockup are investigated by the modal analysis by using the ANSYS [16] commercial finite element program. Figure 3 shows the finite element seismic analysis model of the test mockup. As shown in the model, the element type of the nozzle is a three-dimensional solid element of SOLID185. For the piping system, the three-dimensional pipe elements of PIPE289 and ELBOW290 are used for the straight run section and for the elbow, respectively. To rigidly couple the solid element of the nozzle and the line element of the pipe, the element type of MPC184 is used. The added masses in the test mockup are modeled with a structural mass element of MASS21, including the effects of the rotary moments of inertia.

Related to the boundary conditions, it is assumed that the seismic input motions are applied to the nozzle bottom surface as the design response spectrum is specified at the hot-leg piping system. Then, the modal analysis is carried out with the fixed condition of the nozzle bottom surface.

Table 2. Summaries of modal analysis.

Mode No.	Frequencies (Hz)	Modal Participation Factors			Effective Mass
		EW	NS	V	EW	NS	V
1	11.74	0.00	10.07	0.00	0.00	101.46	0.00
2	11.99	−8.74	0.00	4.35	76.30	0.00	18.96
3	25.89	0.00	5.47	0.00	0.00	29.94	0.00
4	27.63	7.74	0.00	5.05	59.84	0.00	25.54
5	101.61	0.00	0.07	0.00	0.00	5.81	0.00

presents the summary results of the modal analysis. For the horizontal directions, the dominant fundamental frequency is 11.74 Hz for the NS direction and 11.99 Hz for the EW direction. Additionally, the dominant natural frequency in the vertical direction is 27.63 Hz, slightly apart from the vertical target peak response frequency band. From the modal analysis, it is confirmed that the dynamic characteristics of the test mockup will meet the intended design goal, deriving the sufficiently inelastic strains at the nozzle.

Figure 4 presents the results of the mode shapes for dominant natural frequencies. From the results, it is expected that Mode 1 and Mode 3 will contribute to the torsional seismic response at the nozzle, and Mode 2, Mode 4, and Mode 5 will contribute to the bending seismic responses at the nozzle.

The deadweight effect of the added masses attached to the pipe was examined and included in the modal analysis, but it was found that it has minimal effects on the dynamic characteristics of the test mockup.

3. Seismic Shaking Table Tests

3.1. Performance of Shaking Table Test Facility

Table 3. Shaking table performance.

Item	Performance
Max. Loading (kg)	2000
Table Size (mm)	2209 × 2173
Excitation Axes	6 DOF (Translation 3 axes, Rotational 3 Axes)
Max. Displacement (mm)	Hor. (X, Z) = (±125, ±140), Ver. (Y) = ±110
Max. Accel. for bare table (g)	Hor. (X, Z) = 17, Ver. (Y) = 21
Max. Accel. with max load (g)	Hor. (X, Z) = 4.9, Ver. (Y) = 6.0
Frequency Range (Hz)	0.8~100
Excitation Mechanism	Electro-hydraulic Servo, 3 Variable Control
Control Software	354.20/MTS

shows the performance information of the MTS shaking table (2209 × 2173 mm) used in tests. As shown in the table, the test facility can perform the maximum excitation level of 4.9 g for the horizontal direction and 6.0 g for the vertical direction with the loaded maximum of 2000 kg on the table. The frequency range for excitation is 0.8 to 100 Hz.

3.2. Description of Test System and Sensors

As shown in Figure 5, the nozzle bottom flange is connected to the adapter flange by bolts, and then the adapter flange is installed on the shaking table by the bolted connection. Then, it can be assumed that the bolted connection of the test mockup with the shaking table is strong enough to assure the fixed boundary condition, as intended. In order to apply appropriate seismic inertia load on the nozzle, two added masses are attached to the pipes. These masses, Added Mass-1 and Added Mass-2, are composed of eight and four plates combined by bolts, respectively.

For the measurement of seismic strain responses, five strain gauges are attached to the nozzle safe end region where the maximum plastic strain responses are expected. They are almost equally spaced in the circumferential direction at the location of the safe-end region, as shown in Figure 6a. Figure 6b shows the pattern of the general-purpose foil strain gauge type used in this test.

Table 4. Specifications of the used strain gauge.

Item	Specifications
Model Name	KFGS-1-120-D17-11L15M3S (KYOWA)
Gauge Length (mm)	1
Gauge Resistance (Ω)	120 ± 0.7%
Gauge Pattern	Triaxial 0°–45°–90° Rosette, Round base
Adoptable Thermal Expansion	11.7 × 10−6/°C
Applicable Adhesive	CC-33A, EP-340

presents the specification of the used strain gauge.

As shown in Figure 5, three accelerometers are installed at the test system (one on the shaking table and two on the piping system) to measure the seismic acceleration responses. Since the seismic inelastic strain responses at the nozzle depend on what the seismic responses are at the piping system, it is important to investigate the acceleration responses. The accelerometer installed on the shaking table is to measure the input seismic motions needed for the inelastic seismic analyses.

Table 5. Specifications of the used accelerometers.

Item	Specifications
Model Name	Type 8396A (KISTLER)
Sensing Type	MEMS Variable Capacitance, Silicon Sensing Element
Measuring Range (g)	50
Measuring Axis	Triaxial
Measuring Freq. Range (Hz)	0.5~5000
Operating Temperature (°C)	−55~125

presents the specifications of the used accelerometers.

3.3. Results of Shaking Table Tests

3.3.1. Strain Time History Seismic Responses

From the measured strain data (ε_a, ε_b, and ε_c) obtained from the triaxial 0°–45°–90° rosette strain gauges, as conceptually described in Figure 7, the maximum principal strain (ε_max), the minimum principal strain (ε_min), the maximum shear strain (τ_max), and the directional angle of the principal strain (θ) can be calculated using the equations, as follows [17]:

$${\epsilon }_{\max }=\frac{1}{2}\left[{\epsilon }_{\mathrm{a}}+{\epsilon }_{\mathrm{c}}+\sqrt{2\left\{{\left({\epsilon }_{\mathrm{a}}-{\epsilon }_{\mathrm{b}}\right)}^2+{\left({\epsilon }_{\mathrm{b}}-{\epsilon }_{\mathrm{c}}\right)}^2\right\}}\right]$$

(1)

$${\epsilon }_{\min }=\frac{1}{2}\left[{\epsilon }_{\mathrm{a}}+{\epsilon }_{\mathrm{c}}-\sqrt{2\left\{{\left({\epsilon }_{\mathrm{a}}-{\epsilon }_{\mathrm{b}}\right)}^2+{\left({\epsilon }_{\mathrm{b}}-{\epsilon }_{\mathrm{c}}\right)}^2\right\}}\right]$$

(2)

$${\tau }_{\max }=\sqrt{2\left\{{\left({\epsilon }_{\mathrm{a}}-{\epsilon }_{\mathrm{b}}\right)}^2+{\left({\epsilon }_{\mathrm{b}}-{\epsilon }_{\mathrm{c}}\right)}^2\right\}}$$

(3)

$$\theta =\frac{1}{2} {\tan }^{-1}\left(\frac{2{\epsilon }_{\mathrm{b}}-{\epsilon }_{\mathrm{a}}-{\epsilon }_{\mathrm{c}}}{{\epsilon }_{\mathrm{a}}-{\epsilon }_{\mathrm{c}}}\right)$$

(4)

In the above equation, the angle, θ, is the angle of the maximum principal strain to the ε_a axis when ε_a > ε_c or the angle of the minimum principal strain to the ε_a axis when ε_a < ε_c.

The accurate coordinates of the five strain gauges attached at the nozzle region and their corresponding node numbers in the seismic analysis model of Figure 3 are listed in

Table 6. Coordinates of the attached strain gauges.

Strain Gauge ID	X (EW) (mm)	Y (V) (mm)	Z (NS) (mm)	Corresponding Node (1)
SG-1	26.2	156.0	36.0	19118
SG-2	40.7	156.0	18.1	19125
SG-3	44.5	156.0	0.0	137
SG-4	40.7	156.0	−18.1	851
SG-5	26.2	156.0	−36.0	858

The origin global coordinates (X = 0, Y = 0, Z = 0) are at the center of the nozzle bottom surface. ⁽¹⁾ The detailed node locations are described in Figure 17(b) below.

.

Figure 8 and Figure 9 present the test results of the principal strain time history responses for PGA = 0.3 and 0.6 g, respectively. These are calculated from the measured strains of ε_a, ε_b, and ε_c using Equations (1) and (2). As shown in the figures, the strain response time histories of the maximum principal strain and the minimum principal strain are almost symmetric. This means that the seismic strain responses at the nozzle have fully reversing characteristics with almost the same tension and compression behavior. Among the strain gauges, we can see that SG-5 shows the most significant seismic strain responses.

3.3.2. Acceleration Time History Seismic Responses

Figure 10, Figure 11 and Figure 12 present the measured acceleration time history responses for PGA = 0.3 g. As shown in Figure 10, measured at the shaking table, the maximum values are 1.74 g for EW, 1.52 g for NS, and 1.92 g for the vertical direction. These measured data will be used for the validation of the inelastic seismic analysis as input motions.

Table 7. Test results of ZPA responses.

Directions	PGA	Target Input Motions		Shaking Table (Accelerometer-1)		End of Pipe (Accelerometer-3)
		ZPA (g)	ZPA Ratio *	ZPA (g)	ZPA Ratio	ZPA (g)	ZPA Ratio
EW (X)	0.3 g	1.18	2.0	1.71	1.95	5.55	1.57
	0.6 g	2.35		3.33		8.76
NS (Z)	0.3 g	0.86	2.0	1.47	2.12	9.26	1.37
	0.6 g	1.75		3.13		12.70
V (Y)	0.3 g	1.33	2.0	1.86	1.95	6.23	1.58
	0.6 g	2.65		3.62		9.88

* The ZPA ratio represents the ratio of ZPA responses corresponding to PGA = 0.6 g and PGA = 0.3 g.

presents the test results of the zero-period acceleration (ZPA) obtained from the shaking table tests of two scale input motions (PGA = 0.3 g and PGA = 0.6 g) and the ZPA ratio of the two cases for each exciting direction. As shown in the table, the ZPA values of target input motions for PGA = 0.6 g are linearly set to be two times those of PGA = 0.3 g. Then, the ZPA ratio measured at the shaking table is almost 2.0, the same as the target ZPA ratio. However, the ZPA ratio values measured at the end of the pipe are much less than 2.0. These results mean that significant plastic behavior might be occurring in the piping system during the PGA = 0.6 g scale seismic shaking table test. Since this plastic behavior in the piping system has a role in energy dissipation in the seismic responses, the acceleration responses do not increase linearly two times even if the input motions increase two times. From these results, it can be seen that in the case of an earthquake level large enough to exceed the design level, a more accurate seismic response can be obtained using the inelastic seismic analysis method, and the effect of reducing the seismic response can be obtained. This will be discussed in the results of the inelastic analysis in the section below.

4. Validation of Inelastic Seismic Analysis

To validate the inelastic seismic analysis method, which can be used for strain-based seismic design, inelastic seismic time history analyses were performed, and their results were compared with those of the tests.

4.1. Analysis Modeling

4.1.1. Dynamic Characteristics

The used finite element model for the test mockup is shown in Figure 3. To confirm the dynamic characteristics of the analysis model, resonance searching tests were carried out, with the random input motions having the frequency range of 1.0 to 100.0 Hz. Figure 13 presents the frequency response functions measured by Accelerometer-3 (shown in Figure 5).

As shown in Figure 13, the measured dominant resonance frequencies are about 11.75 Hz for the 1st mode and 28 Hz for the 2nd mode.

Table 8. Comparison of resonance frequencies between tests and analyses.

Directions		Mode 1 (Hz)	Mode 2 (Hz)
EW (X)	Test	11.75	28.75
	Analysis	11.99	27.63
NS (Z)	Test	11.75	27.38
	Analysis	11.74	25.89
V (Y)	Test	11.56	28.56
	Analysis	11.99	27.63

presents the comparison of the resonance frequencies between tests and analyses.

As shown in Table 8, the dominant modes for EW and NS directions are almost the same in the tests but slightly different in the modal analysis results. In the test results, the frequency of Mode 1 is the same in both directions because it is not easy to separate such a closed mode in the test. However, it is confirmed that the used seismic analysis model describes the dynamic characteristics of the test mockup in good agreement.

4.1.2. Structural Damping Value

To be used for inelastic seismic analyses, the actual structural damping value corresponding to the test mockup is required. As shown in Figure 13, the test mockup is considered to be a very light damped system with dominantly well-separated modes. Therefore, the well-known half-power bandwidth method [18] can be used to identify the structural damping ratio. Figure 14 illustrates the concept for the dominant first natural frequency of the EW direction. In this method, it is assumed that half the total power of dissipation in this mode occurs in the frequency band between f₁ and f₂, where f₁ and f₂ are the frequencies corresponding to an amplitude of $f_{\mathrm{c}}/\sqrt{2}$.

As illustrated in Figure 14, the critical damping ratio, ξ can be approximately determined by the following relationship;

$$\xi =\frac{f_1-f_2}{2f_{\mathrm{c}}}$$

(5)

From Equation (5), the obtained critical damping values based on the first natural frequency mode for each direction are 0.5% for EW, 0.4% for NS, and 0.8% for the vertical direction. Then, the averaged value of 0.57% for the three directions is used in this study.

4.1.3. Inelastic Material Model

For inelastic seismic analyses, the well-known constitutive equations of Chaboche’s kinematic hardening model [19,20] is used as follows:

$${\dot{\alpha }}_{ij} = {\displaystyle \sum _{k=1}^3\left[\frac{2}{3}{C}_k{\dot{\epsilon }}_{ij}^p - {\gamma }_k{\left({\alpha }_{ij}\right)}_k\dot{p}\right]}$$

(6)

where ${\dot{\alpha }}_{ij}$ and $\dot{p}$ indicate the revolution of back stress and an accumulated plastic strain, respectively. Additionally, C_k and γ_k (k = 1~3) are material constants to be used in the ANSYS program.

For the isotropic hardening model, the inelastic Voce model [21] is used as follows:

$$\dot{R} = b \left[Q - R\right] \dot{p}$$

(7)

where $\dot{R}$ indicates the revolution of drag stress. Additionally, b and Q are material constants.

Table 9. Material constants for inelastic material models.

Material	σyo × 106 (Pa)	E × 109 (Pa)	C1 × 109	C2 × 109	C3 × 109	γ1 × 103	γ2 × 103	γ3	b	Q × 106
Type 316SS	135	190	120	20.2	10.67	1.0	1.0	1.0	45.0	85

presents the used material constants required in Equations (6) and (7) for Type 316 stainless steel [22].

4.1.4. Seismic Input Motions

Figure 15 presents the displacement time history input motions used for the inelastic seismic analyses, which are measured at the shaking table. The correlation coefficients are 0.015 between EW and NS, 0.0015 between NS and V and 0.0003 between V and EW, which are much less than the criteria value of 0.16 required for the seismic input motions [23]. Therefore, since the independence of the input motions is guaranteed, the inelastic seismic analyses can be performed by applying them simultaneously.

The time interval (Δt) used in the inelastic seismic analysis is 3.91 ms; then, the cut-off frequency (1/2Δt), 128 Hz, can sufficiently cover the seismic cut-off frequency of 33 Hz in NPP seismic design. The total analysis duration is 32 s. Figure 16 presents the test response spectrum (TRS) calculated from the measured shaking table motions of Figure 15. Compared with the target required response spectrum in Figure 2, it is confirmed that the TRS envelops the target response spectrum.

4.2. Results of Inelastic Seismic Analyses

4.2.1. Validation of Strain Time History Responses

Figure 17 presents the inelastic seismic time history analysis results, representing the accumulated equivalent plastic strain distribution at the end time of PGA = 0.3 g in the nozzle. As shown in the results, we can see that the maximum seismic strain responses occur in the region of the nozzle’s safe end, as expected in the test mockup design. This result is considered to be dominantly caused by the bending motions of the piping system. In addition, the frequencies of Mode 1 (11.74 Hz, torsional) and Mode 2 (11.99, bending) are in a closed mode. It is judged that these closed bending and torsional modes strongly influence the determination of the location where the maximum strain response occurs.

If we look more closely in Figure 17b, which shows the inelastic strain distribution in the cross-section where the maximum strain occurs, the largest inelastic strain occurs along the (EW, NS) direction. From the sectional view, it is expected that the largest seismic responses will occur at the SG-5 location among the strain gauges in tests.

Figure 18 presents the material hysteretic responses at the location of the maximum accumulated equivalent plastic strain in Figure 17.

To compare the inelastic seismic analysis results with the test results, the maximum and minimum principal strains are calculated at each node, corresponding to the locations of the strain gauges, as shown in Figure 17b. Figure 19 and Figure 20 present the analysis results of the principal strains for PGA = 0.3 and 0.6 g, respectively. As expected from the inelastic seismic analysis, the largest strain responses occur at SG-5.

When compared, the seismic strain time history responses of Figure 19 and Figure 20 with the test results of Figure 8 and Figure 9, the overall strain wave shapes and amplitudes are similar. Specifically, we can see that the largest strain responses occur at the same location of SG-5 in the tests and analyses, as expected in Figure 17. In general, the maximum accumulated equivalent plastic strain, which can be a failure mode in strain-based seismic design criteria, occurs at the location where the maximum value of the time history response occurs, but this is not always the case.

Table 10. Comparison results of principal strain responses.

Strain Gauge ID	Tests (%)				Inelastic Seismic Analysis (%)
	PGA = 0.3 g		PGA = 0.6 g		PGA = 0.3 g		PGA = 0.6 g
	Max(εmax)	Min(εmin)	Max(εmax)	Min(εmin)	Max(εmax)	Min(εmin)	Max(εmax)	Min(εmin)
SG-1	0.139	−0.144	0.185	−0.202	0.101	−0.139	0.184	−0.247
SG-2	0.125	−0.119	0.212	−0.211	0.123	−0.120	0.199	−0.197
SG-3	0.139	−0.158	0.249	−0.262	0.119	−0.099	0.255	−0.189
SG-4	0.148	−0.161	0.217	−0.239	0.127	-0.128	0.273	−0.194
SG-5	0.152	−0.168	0.228	−0.230	0.165	−0.167	0.290	−0.216

presents the comparison results of the maximum principal strain values of the time history responses between the tests and inelastic seismic analyses for the case of PGA = 0.3 g and PGA = 0.6 g. As shown in the table, the results of the inelastic strain responses are in good agreement with the test results.

4.2.2. Validation of Acceleration Time History Responses

The investigation of the acceleration time history responses at the pipe is important in pointing out that the seismic strain responses in the nozzle depend on the piping’s seismic behavior. Figure 21 and Figure 22 present the acceleration time histories at the locations of Accelerometer-2 and Accelerometer-3 (see Figure 5). As shown in the figures, the overall response waveforms are very similar to the test results of Figure 11 and Figure 12. The largest acceleration response occurs in the NS (Z) direction. This will dominantly excite Mode 1 and Mode 3, invoking torsional responses at the nozzle.

Table 11. Comparison results of ZPA responses at the pipe end (Accelerometer-3).

Directions	PGA (g)	Tests (g)	Inelastic Seismic Analysis (g)
EW	0.3	5.55	6.17
	0.6	8.76	9.90
NS	0.3	9.26	12.68
	0.6	12.70	16.80
V	0.3	6.23	8.71
	0.6	9.88	12.60

presents the comparison of ZPA values between the tests and analyses at the pipe end (Acceleration-3). The ZPA value corresponds to the maximum amplitude in the acceleration time history responses. As shown in the table, the analysis results reveal slightly larger values compared with the test results, but we can see that overall response characteristics are in good agreement.

Figure 23 presents the comparison results of the response spectrum, calculated from the acceleration time history responses at the pipe end (Accelerometer-3). As shown in the figure, the results obtained from the inelastic seismic analysis reveal good agreement with those of the tests.

5. Conclusions

In this study, shaking table tests are performed to validate the inelastic seismic analysis method applicable to the nuclear metal components. To do this, a test mockup, which can simulate the hot leg surge line nozzle, known as one of the nuclear seismic fragile components in NSSS, was designed and tested on the shaking table with seismic input motions corresponding to design-basis earthquake (PGA = 0.3 g) and beyond-design-basis earthquake (PGA = 0.6 g) levels. To validate the inelastic seismic analysis method, detailed comparisons of seismic responses between the tests and inelastic seismic analyses were carried out, especially for the seismic responses of the principal strains at the nozzle and the accelerations at the pipe. From this study, some meaningful conclusions have been derived, as follows:

• The seismic responses obtained from the inelastic seismic time history analyses with an accurate inelastic material model using Chaboche’s kinematic hardening model and the Voce isotropic hardening model for Type 316 stainless steel are in good agreement with those of the seismic shaking table tests.
• From the comparison of the seismic strain time history responses at the nozzle between the tests and inelastic analyses, the location of the maximum strain responses from the inelastic analyses was found to be almost the same as the locations in the test results.
• The structure damping value for the piping systems, recommended in the US NRC RG 1.61 [24], is 4% for the SSE level. However, in this study, the piping system made of Type 316 stainless steel revealed a much lighter damping value of about 0.57%.
• For earthquakes large enough to result in inelastic behavior at the nuclear metal components, the inelastic seismic analysis is useful for reducing the seismic responses by energy dissipation due to hysteretic damping.
• From the validation results obtained from the test mockup simulating the actual nuclear component in this study, it is assured that the inelastic seismic analysis method can be used for the seismic design of nuclear metal components in large earthquake scenarios such as the beyond-design-basis earthquake, which can cause significant plastic deformations.