An Experimental Study on Seismic Performance Evaluation of Multi-Ply Bellows Type Expansion Joint for Piping Systems

Abstract

Piping systems are a representative social infrastructure to provide oil, gas, and water. Damage to piping systems may cause serious consequences, such as fire, water outage, and environmental pollution. Therefore, piping systems need to be protected from natural disasters, such as earthquakes. Earthquakes may cause deformation that exceeds piping design criteria. For example, large relative displacements and liquefaction of the ground resulting in loss of strength and ground subsidence, and the side-sway of primary structures subjected to a strong ground motion may cause critical damage to piping systems. Therefore, expansion joints to maintain flexibility can be applied to locations where excessive deformation is expected to improve the seismic performance of piping systems. Metal bellows, a type of expansion joints, are flexible, so they are highly durable against deformation and fatigue loads. This indicates that metal bellows can be used as seismic separation joints for piping. In this study, experimental research was conducted to analyze the seismic performance of multi-ply bellows type expansion joints, a type of metal bellows. Monotonic loading tests and cyclic loading tests were conducted on 2-ply bellows and 3-ply bellows, and the results were compared. In the cyclic loading tests, multi-step increasing amplitude cyclic loading, which used the displacement history amplified in stages, and constant amplitude cycling loading with various magnitudes were considered. The test results showed no significant difference in bending performance for monotonic loading between the two types of multi-ply bellows. The 3-ply bellows, however, showed higher performance for low-cycle fatigue than 2-ply bellows.

1. Introduction

The frequency of earthquakes worldwide is increasing each year, and the scale of expected seismic damage is also increasing due to the urban population and the expanding size of facilities due to industrial development [1,2,3]. Piping has been widely used in most industries as the major equipment for providing gas or liquid. Thus, the integrity of a piping system is very important for maintaining its original function and for the safety of facilities. Strong external forces can cause seismic-induced damage or malfunction to the piping system. In particular, leakage can cause serious secondary damage, such as explosion or liquefaction. Therefore, pipes must have sufficient seismic performance to prevent damage against earthquakes that have been assumed during the design process.

In general, piping is buried underground or installed using the support of structures. Buried piping systems can be damaged by permanent ground deformation (PGD), such as soil liquefaction, fault, and ground subsidence [4,5]. Seismic damage to buried piping is mainly found at joints [6]. The piping installed in structures is damaged by the deformation and story drift of the structures as well as the relative displacement between the structures [7]. Damage occurs due to the concentration of nonlinear behavior on supports, joints, and fittings (elbow, tee) [8]. The main cause of seismic damage to piping is the relative displacement that exceeds the allowable displacement, with the joints and fittings as a critical damaged location. Therefore, experimental research to analyze the seismic behavior of piping with joints and fittings, as well as assess its seismic performance, has attracted significant attention of many researchers.

To evaluate the seismic performance of buried piping, tensile, compressive, and bending tests have been conducted on piping with various specifications. In particular, various studies have been conducted recently to analyze the seismic behavior of piping systems considering buried conditions [9,10,11,12,13]. Research on piping that is installed in structures has also been conducted in various industrial fields. Experimental studies were conducted to analyze the nonlinear behavior of piping elements under internal pressure and seismic loading conditions [14,15], and the low-cycle fatigue and limit state of the piping system was defined in these studies [16,17,18,19,20,21]. A program was also performed to analyze the gap between plastic collapse corresponding to the design standard consideration and leakage related to the actual failure observed through experimental tests and to simulate the extreme nonlinear behavior of piping [22]. In recent years, studies have been actively conducted to analyze the seismic behavior of non-welded joints or supports in piping [23,24,25,26]. Through-wall cracks were defined as failure criteria, and seismic fragility was analyzed in piping systems [27,28].

Seismic separation joints in piping are installed at locations where earthquake-induced deformation is concentrated to protect the piping [29]. Bellows-type expansion joints are devices that absorb the expansion and deformation of pipes caused by the temperature difference and to prevent the damage caused by mechanical vibration. They are highly adaptable to relatively large deformations due to their flexibility and low stiffness. As a result, well-designed bellows-type expansion joints can be applied to improve the seismic performance of piping [30]. However, very few studies of the current state of bellows piping joints have evaluated the structural performance or seismic performance of the expansion joints based on experimental data. Thus, an experimental study that considers the characteristics of seismic loads is required. In this study, bending tests were conducted to evaluate the seismic performance of bellows-type expansion joints. Monotonic loading tests and cyclic loading tests were conducted on two types of multi-ply metal bellows with multi-layered structures. The cyclic loading tests were divided into multi-step loading conditions with (1) increasing amplitude cyclic loading tests, which applied the displacement history amplified in stages, and (2) constant amplitude cyclic loading tests, which considered a constant amplitude in various magnitudes. Finally, the test results of the two types of multi-ply metal bellows were compared, and their seismic performance and low-cycle fatigue performance were predicted.

2. Test Specimen

Bellows forming methods can be mainly classified into mechanical and hydraulic forming methods. In mechanical forming methods, a tube is placed on a forming machine, and each convolution is formed using the pressure applied by the forming roll while rotating. In hydraulic forming methods, a tube is placed on a hydraulic press or forming machine, and a circular mold is arranged on the outside of the tube. The inside of the tube is then filled with water, and a product is formed by applying pressure until yielding in the circumferential direction occurs. Hydroforming is a representative hydraulic forming method. Bellows may exhibit the yielding of materials during the forming process, and the hardness may change. The bellows formed using the hydroforming method, however, can minimize the increase in hardness by work hardening compared to mechanical forming [31]. Therefore, in this study, tests were conducted on the multi-ply metal bellows type expansion joints fabricated using the hydroforming method.

Figure 1 shows multi-ply metal bellows. In general, bellows are formed using a single-layer steel sheet. To improve the low-cycle fatigue performance of bellows, 2-ply or 3-ply structures can be considered, as shown in Figure 1. In this study, 2-ply metal bellows type expansion joints were defined as 2-ply bellows, and in a similar manner, 3-ply metal bellows type expansion joints were defined as 3-ply bellows. The bellows of the test specimens were fabricated by overlapping STS 316L stainless steel sheets with a thickness of 0.3 mm. The thickness of the 2-ply bellows was 0.6 mm, and that of the 3-ply bellows was 0.9 mm.

In this study, it was assumed that multi-ply metal bellows type expansion joints were applied to gas systems piping. Carbon steel pipes for fuel gas piping have various standards [32]. In general, the standard piping of 100 mm or less is used for the supply to residential areas. For this study, test specimens were prepared considering piping with an outer diameter of 89.1 mm. Figure 2a,b shows the schematic designs and a photograph of a test specimen. The U-shaped bellows located in the center of the test specimen had six convolutions, a pitch of 15 mm, a height of 15 mm, and a length of 110 mm. The bellows were connected to 50 mm-long SS275 carbon steel pipes [33] by welding, and the ends of the straight pipes were finished with flanges.

Table 1. Material properties.

	Yield Strength (N/mm2)	Tensile Strength (N/mm2)	Elongation (%)
STS 316L	257	563	52.7

shows the material properties of STS 316L provided by the manufacturer.

3. Test Setup and Method

Figure 3a shows the test setup, and Figure 3b is a photograph of the setup. As shown in Figure 3a, one end of the test specimen was connected to the jig fixed at the bottom of the universal testing machine (UTM), while the other end was connected to the jig fixed at the actuator using a pin. This design describes the bending deformation caused by the external force applied in the direction perpendicular to the axis to be concentrated on the bellows. In addition, the degree of freedom in directions other than the loading direction was constrained using the LM guide. The inside of the specimen was filled with water, and a pressure of 0.4 MPa [34] was applied using a regulator and a pump before the experiment. The pressure was maintained until the end of the experiment. In this study, pipe damage was defined as leakage, and the experiment was performed until leakage occurred. This experiment was carried out using 1000 kN UTM in the Seismic Research and Test Center at Pusan National University.

Figure 4 shows the test procedure. First, the monotonic loading test is conducted. Then the multi-step increasing amplitude cyclic loading test is conducted by setting 25% of the minimum leakage displacement of the monotonic loading test as the initial amplitude. Based on the magnitude of the cycle that preceded the cycle where leakage occurred in the multi-step increasing amplitude cyclic loading test (minimum displacement of the two test results), the constant amplitude cyclic loading test is carried out. As shown in Figure 4, the objective of the monotonic loading test and multi-step increasing amplitude cyclic loading test are focused on the evaluation of the seismic performance of the bellows piping system, whereas the constant amplitude cyclic loading test is a low-cycle fatigue test.

The monotonic loading test was conducted until leakage occurred in the tension direction in Figure 3. The multi-step increasing amplitude cyclic loading test used the two-step displacement cyclic loading history, as shown in Figure 5, and this was continued until leakage occurred. The cyclic loading history was prepared by referring to ANSI/FM Approvals 1950 [35] and KS B 1528 [36]. ANSI/FM Approvals 1950, a test method to evaluate the seismic performance of a seismic sway brace in piping, proposes a cyclic loading test by a test frequency of 0.1 Hz or less. In this test method, the cyclic loading process is performed 15 times for the initial amplitude, and the magnitude of the amplitude is gradually increased. Here, the initial amplitude must be less than 50% of the expected damage load, and the 15 cycles mean one seismic event [37]. KS B 1528 suggests a test method for pipe joints by referring to ANSI/FM Approvals 1950. The cyclic loading history of this test method is similar to that of ANSI/FM Approvals 1950, but the amplitude is proposed as an angle to consider the deformation of piping by the story drift of the structure. For the initial amplitude, the deformation angle of the pipe joint by the story drift of the structure was considered. In the case of FEMA 461 [38], the cyclic loading history gradually increased by displacement control that takes into account the story drift of the structure. Since seismic separation joints are applied to locations where relative displacement may occur, it was determined that tests must be conducted with displacement control. Therefore, in this study, the cyclic loading history shown in Figure 5 was used. After applying cyclic loads 15 times for $x$, which is the initial amplitude and as shown in Equation (1), the amplitude is increased until leakage occurs according to Equation (2). Here, $\Delta l$ is the loading amplitude and $N$ is the number of cycles.

$$\mathsf{\Delta }l=x\hspace{1em}\hspace{1em}\hspace{1em}\mathrm{for} N\le 15 \mathrm{cycles}$$

(1)

$$\mathsf{\Delta }l=x\times {\left(\frac{15}{14}\right)}^{\frac{\left(N-15\right)}{2}}\hspace{1em}\hspace{1em}\hspace{1em}\mathrm{for} N>15 \mathrm{cycles}$$

(2)

The constant amplitude cyclic loading test was conducted to estimate low-cycle fatigue life. For the loading amplitude, the amplitude of the cycle before the minimum leakage displacement of the multi-step increasing amplitude cyclic loading test was defined as 100%, and 40% to 100% was applied at 10% intervals. Both the monotonic loading test and multi-step increasing amplitude cyclic loading test were performed twice, and the constant amplitude cyclic loading test was conducted once for each input amplitude. All the tests were conducted at a rate of 1 mm/s or less.

The deformation angle is a representative performance required for seismic separation joints [29,36,39]. In this study, the deformation angle was calculated using the center of the fixed flange and the center of the pin connection, as shown in Figure 6, and $l$ is the length of the test specimen and $\theta$ is the deformation angle.

4. Experiment Results and Analysis

Table 2. Test results of 2-ply bellows.

Test Method	No.	Leakage Point			$N_f$	Remarks
		Displacement (mm)	Angle (Degree)	Location
Monotonic	2P-M1	257.8	39.8	Pipe-bellows welding	-	Lowest leakage displacement: 237.1 mm
	2P-M2	237.1	37.5		-
Multi-step increasing amplitude cyclic	2P-MC1	113.6	20.2	Convolutions of bellows	34	Initial amplitude: 59 mm
	2P-MC2	113.6	20.2		34
Constant amplitude cyclic	2P-C1	44.0	8.1	Convolutions of bellows	592	Amp. 40%
	2P-C2	55.0	10.1		74	Amp. 50%
	2P-C3	66.0	12.1		43	Amp. 60%
	2P-C4	77.0	14.0		22	Amp. 70%
	2P-C5	88.0	15.9		17	Amp. 80%
	2P-C6	99.0	17.8		13	Amp. 90%
	2P-C7	110.0	19.6		6	Amp. 100%: Amplitude of cycle before minimum leakage displacement at multi-step increasing amplitude cyclic test

and

Table 3. Test results of 3-ply bellows.

Test Method	No.	Leakage Point			$N_f$	Remarks
		Displacement (mm)	Angle (Degree)	Location
Monotonic	3P-M1	237.0	37.5	Pipe-bellows welding	-	Lowest leakage displacement: 237 mm
	3P-M2	248.7	38.8		-
Multi-step increasing amplitude cyclic	3P-MC1	126.0	22.2	Convolutions of bellows	37	Initial amplitude: 59 mm
	3P-MC2	130.5	22.9		38
Constant amplitude cyclic	3P-C1	48.8	9.0	Convolutions of bellows	1949	Amp. 40%
	3P-C2	61.0	11.2		406	Amp. 50%
	3P-C3	73.2	13.3		153	Amp. 60%
	3P-C4	85.4	15.4		46	Amp. 70%
	3P-C5	97.6	17.5		10	Amp. 80%
	3P-C6	109.8	19.6		7	Amp. 90%
	3P-C7	122.0	21.5		4	Amp. 100%: Amplitude of cycle before minimum leakage displacement at multi-step increasing amplitude cyclic test

show the bending test results of 2-ply bellows and 3-ply bellows, respectively. When expressed to one decimal point for both 2-ply bellows and 3-ply bellows, 25% of the minimum leakage displacement in the monotonic loading test was 59.0 mm. Therefore, 59.0 mm was used as the initial amplitude of the multi-step increasing amplitude cyclic loading tests. In the monotonic loading test of 2-ply bellows, leakage displacements were 257.8 and 237.1 mm with a difference of 8.4%, while the leakage angles were 39.8° and 37.5° with a difference of 6.0%. In the multi-step increasing amplitude cyclic loading test, leakage displacement and leakage angle were found to be 113.6 mm and 20.2° in both tests. Therefore, the difference of the multi-step increasing amplitude cyclic loading test is 0.0%, as shown in

Table 4. Difference in leakage points.

	Difference in Leakage Point (%)
	2-Ply Bellows		3-Ply Bellows
	Displacement	Angle	Displacement	Angle
Monotonic	8.4	6.0	4.8	3.4
Multi-step increasing amplitude cyclic	0.0	0.0	3.5	3.1

. In the monotonic loading test of 3-ply bellows, the leakage displacements were 237.0 and 248.7 mm with a difference of 4.8%, while the leakage angles were 37.5° and 38.8° with a difference of 3.4%. In the multi-step increasing amplitude cyclic loading test, leakage displacements were 126.0 and 130.5 mm with a difference of 3.5%, while the leakage angles were 22.2° and 22.9°, with a difference of 3.1%. Table 4 shows the difference in leakage points between the 2-ply bellows and 3-ply bellows in the same test. The difference was calculated using Equation (3) with $E_1$ and $E_2$ as experimental values.

$$\mathrm{Difference} \left(\%\right)=\frac{\left|E_1-E_2\right|}{\frac{1}{2}\left(E_1-E_2\right)}\times 100$$

(3)

Table 2 and Table 3, the number of cycles to failure ($N_f$) increases as the magnitude of the input amplitude increases. For 2-ply bellows, $N_f$ is 74 cycles or less when the magnitude is 50% or higher and 592 cycles when it is 40%. In the case of 3-ply bellows, $N_f$ is 406 cycles or less when the magnitude is 50% or higher and 1949 cycles when it is 40%.

Table 5. Minimum leakage points comparison of monotonic and multi-step increasing cyclic loading tests.

Specimen Type	Leakage Displacement		Leakage Angle		Ratio (MC/M)
	Monotonic [M]	Multi-Step Increasing Cyclic Loading [MC]	Monotonic [M]	Multi-Step Increasing Cyclic Loading [MC]	Leakage Displacement	Leakage Angle
2-ply	237.1 mm	113.6 mm	37.5°	20.2°	0.48	0.54
3-ply	237.0 mm	126.0 mm	37.5°	22.2°	0.53	0.59
Difference	0.0%	10.4%	0.0%	9.4%	-	-

compares the minimum leakage points of the monotonic loading test and the multi-step increasing amplitude cyclic loading test. The ratio between the leakage displacement of the multi-step increasing amplitude cyclic loading test and that of the monotonic loading test is 0.48 for 2-ply and 0.53 for 3-ply. These become 0.5 when rounded to the first decimal place. The leakage angle ratio is 0.54 for 2-ply and 0.59 for 3-ply, and these become 0.6 or less when rounded to the first decimal place.

The difference in the minimum leakage point of the monotonic loading test between 2-ply bellows and 3-ply bellows is insignificant when expressed to the first decimal place. For the minimum leakage points of the multi-step increasing amplitude cyclic loading test, however, the leakage displacement is 10.4% higher, and the leakage angle is 9.4% higher for 3-ply bellows compared to 2-ply bellows.

Figure 7, Figure 8 and Figure 9 show the leakage in each test, with a yellow circle marking the leakage location. In the monotonic loading test, leakage caused by cracking in the bellows-pipe weld was observed. Figure 8 and Figure 9 show the leakage locations of the multi-step increasing amplitude cyclic loading test and constant amplitude cyclic loading test, respectively. The cyclic loading test results showed that leakage occurred due to the through-wall cracks generated in the loading direction in the convolution of the bellows. Water spray can be seen in the yellow circles of Figure 8 and Figure 9. Leakage locations vary between the monotonic loading test and the cyclic loading test. In the same test, however, the leakage locations of 2-ply bellows and 3-ply bellows are similar.

Figure 10a shows the load-displacement correlation measured from the monotonic loading test of 2-ply bellows. The load and displacement are the responses measured from the load cell and the displacement meter in the actuator of UTM. As shown in Table 4, the difference in leakage displacement is 8.4%. The maximum loads, however, are 38.1 and 31.5 kN, respectively, with a difference of 19.0%. Figure 10b shows the load-displacement correlation of 3-ply bellows. The difference in leakage displacement between the two test specimens is not significant (4.8%). The maximum loads, however, are 39.8 and 56.8 kN, respectively, with a difference of 35.2%. From Figure 10, it can be seen that the load at leakage is 8.3 kN (approximately 1.3 times) to 25.3 kN (1.8 times) higher for 3-ply bellows compared to 2-ply bellows. As shown in Figure 7 and Figure 10, it was estimated that the damage of the test specimen due to monotonic loading tests could not occur due to fatigue, but damage to the welded part occurred due to exceeding the limit displacement. Therefore, it is estimated that the damage displacement is similar, but the load could be higher with 3-ply bellows specimens.

Figure 11 shows the load-displacement hysteresis loops of the multi-step increasing amplitude cyclic loading test. For the 2-ply bellows shown in Figure 11a, the load tends to decrease in the initial 15-cycle section. This phenomenon, however, is not significant for 3-ply bellows. Figure 12 and Figure 13 show the load-displacement hysteresis loops of 2-ply bellows and 3-ply bellows in the constant amplitude cyclic loading test, respectively. The load tends to decrease as the number of cycles increases. In Figure 12, the load tends to decrease in all tests for 2-ply bellows. In the case of 3-ply bellows, however, the load tends to significantly decrease as the number of cycles increases at an input amplitude of 61 mm (50%) or less, as shown in Figure 13a.

Next, an additional study associated with the damage criteria of bellows piping system was proposed in this study. Fatigue failure is a phenomenon in which an object subjected to repeated small forces develops fractures due to cracking. Among the fatigue phenomena, fatigue failure with a low repetition frequency is defined as low-cycle fatigue. In Table 2 and Table 3, $N_f$ significantly increases when the input amplitude is 40% (44 mm) for 2-ply bellows. For 3-ply bellows, $N_f$ significantly increases when the input amplitude is 40% (48.8 mm). Therefore, in this study, the low-cycle fatigue curve was estimated for cases where $N_f$ was smaller than 500 cycles.

The low-cycle fatigue life of the seismic vulnerability components of piping could be estimated using the relationship between the loading amplitude and $N_f$ by the cyclic loading test [34,35]. Figure 14 shows the leakage displacement-$N_f$ relationship and the low-cycle fatigue curve of multi-ply bellows-type expansion joints. Here, the low-cycle fatigue of 2-ply bellows can be represented by Equation (4) and that of 3-ply bellows by Equation (5). Figure 15 shows the leakage angle-$N_f$ relationship and the low-cycle fatigue curve. Equations (6) and (7) present the low-cycle fatigue curves of 2-ply bellows and 3-ply bellows by the leakage angle-$N_f$ relationship, respectively. From Figure 15, it can be seen that 3-ply bellows have higher low-cycle fatigue performance than 2-ply bellows. For Equations (4)–(7), the coefficient of determination (${\mathrm{R}}^2$) is 0.97 or higher, indicating high reliability. Here, $\delta$ refers to the leakage displacement, and $\theta$ is the leakage angle.

$${\delta }_{2\mathrm{ply}}=192.18 N_f^{-0.286} {\mathrm{R}}^2=0.9723$$

(4)

$${\delta }_{3\mathrm{ply}}=143.14 N_f^{-0.139} {\mathrm{R}}^2=0.9807$$

(5)

$${\theta }_{2\mathrm{ply}}=33.497N_f^{-0.273} {\mathrm{R}}^2=0.9704$$

(6)

$${\theta }_{3\mathrm{ply}}=25.107N_f^{-0.131} {\mathrm{R}}^2=0.9820$$

(7)

Table 6. Comparison of leakage points for bending test.

Specimen Type		2-Ply Bellows		3-Ply Bellows
Unit		Minimum Leakage Displacement (mm)	Minimum Leakage Angle (Degree)	Minimum Leakage Displacement (mm)	Minimum Leakage Angle (Degree)
Leakage point	Monotonic [M]	237.1	37.5	237	37.5
	Amplitude 50% of constant amplitude cyclic loading [Amp. 50%]	55.0	10.1	61	11.2
Ratio of failure	Amp. 50%/M	0.23	0.27	0.26	0.30

compares the leakage points of the monotonic test with those of the constant amplitude cyclic loading test with an input amplitude of 50%. The minimum leakage displacement ratio between the constant amplitude cyclic loading test and the monotonic test is 0.23 for 2-ply and 0.26 for 3-ply, respectively. These changed to 0.2 and 0.3 when rounded to the first decimal place. In other words, they are smaller than 0.3. The minimum leakage angle ratio is 0.27 and 0.30 for 2-ply and 3-ply, respectively. These become 0.3 when rounded to the first decimal place. Therefore, for the multi-ply bellows used in this study, the leakage point ratio between the constant amplitude cyclic loading test with an input amplitude of 50% and the monotonic test is 0.3 or less.

5. Conclusions

In this study, the seismic performance of multi-ply metal bellows type expansion joints was evaluated through monotonic loading tests and multi-step increasing amplitude cyclic loading tests. The influence of low-cycle fatigue was also analyzed through constant amplitude cyclic loading tests.

The leakage point of the monotonic loading tests was observed at the location of the weld area between the bellows and the pipe. The leakage location in the increasing amplitude and constant amplitude cyclic loading tests, however, is the convolution of the bellows, indicating that damage locations differ between monotonic loading and cyclic loading.

There is no significant difference in the minimum leakage points of the monotonic loading tests between 2-ply bellows and 3-ply bellows. The leakage points of the multi-step increasing amplitude cyclic loading tests, however, are more than 9% higher for 3-ply bellows compared to 2-ply bellows. This indicates that the low-cycle fatigue performance becomes higher as the number of layers in bellows increases. In this study, it was assumed that low-cycle fatigue occurred when the number of cycles to failure ($N_f$) exceeded 500 cycles. Therefore, a low-cycle fatigue curve was designed for an input amplitude of 50% or higher in the constant amplitude cyclic loading test. Consequently, it was found that 3-ply bellows have higher low-cycle fatigue performance than 2-ply bellows. Therefore, it is estimated that the seismic performance of 3-ply bellows could better than 2-ply bellows.

For both 2-ply bellows and 3-ply bellows, the minimum leakage displacement of the multi-step increasing amplitude cyclic loading tests is less than 53% of that of monotonic loading tests. Low-cycle fatigue occurs at less than 26% of the minimum leakage displacement of the monotonic loading tests. In addition, the minimum leakage angle of the multi-step increasing amplitude cyclic loading tests is less than 60% of that of monotonic loading tests. The magnitude of the deformation angle at which low-cycle fatigue is observed is also smaller than 30% of the minimum leakage angle of the monotonic loading tests.

In the multi-step increasing amplitude cyclic loading tests conducted in this study, 15 cycles by the initial amplitude indicate one seismic event. Therefore, the cumulative plastic deformation attributed to low-cycle fatigue must be minimized at this stage. In addition, when seismic performance is evaluated using the cyclic loading history used in this study, the appropriate magnitude of the initial amplitude of the multi-step increasing amplitude cyclic loading test is less than 25% of the leakage displacement of the monotonic loading test or less than 30% of the leakage angle.

The results of this study can be used as data for the seismic design of bellows-type expansion joints. They can also be used as basic data to consider relative seismic displacement when performance verification and experimental research are conducted for the application of bellows-type expansion joints.