Seismic fragility analysis of an anchored vertical gas steel storage tank using tri-axial shaking table testing

Abstract

Hydrogen and gas storage tanks installed in facilities are typically vertical cylindrical structures made of steel. To allow for the discharge of stored materials, these tanks are anchored onto concrete blocks with sufficient height. However, this design results in a higher center of gravity, making the tanks more vulnerable to external forces such as earthquakes. This study fabricated a storage tank model and foundation concrete based on the results of the field investigation of the hydrogen storage tank. Then, an artificial earthquake was generated by referring to ICC-ES AC 156, a shaking table test method for non-structural elements. Experimenting on a full-scale structure is ideal; however, a storage tank model was fabricated and settled on the foundation concrete for tri-axial shaking table testing due to limited testing facilities and equipment performance. In the shaking table test, the presence or absence of water inside the storage tank was set as the condition for storing gases and liquids. The seismic behavior characteristics and failure mode of the storage tank model fixed in the foundation concrete were analyzed using the testing results. A seismic fragility curve was drawn up, and the high confidence and low probability of failure (HCLPF) was calculated.

Keywords

Earthquake vertical gas storage tank shaking table test seismic fragility analysis anchorage

Introduction

Various environmental problems are occurring worldwide due to extreme climate conditions caused by global warming. The direct and indirect damage caused by this is increasing, urging the need for greenhouse gas reduction methods and the development of alternative energy sources.¹ Therefore, hydrogen, which is considered eco-friendly and easily stored in the form of high-pressure gas, liquid hydrogen, and hydrogen storage alloys for various uses, is attracting attention as an alternative energy source.² Specifically, the global hydrogen storage and transportation system market is expected to generate an annual market value of $2.5 trillion by 2050. The capacity of electrolyzers is expected to grow from years 2020 to 2024 to six GW, which is approximately 1% of the global hydrogen market, to 40 GW by 2025 to 2030 and 500 GW by 2025.³ Consequently, the report predicts that six million tons of hydrogen will be annually produced by 2030 and 80 million tons by 2050. Hence, studies on hydrogen energy storage systems should be also emphasized.

To use hydrogen as an energy source, one of the important technologies are hydrogen storage technology and hydrogen production and utilization technology. Since hydrogen is very bulky and light in its gaseous state, it is generally not easy to store a large amount of hydrogen in a certain space. This requires gaseous hydrogen to be compressed and stored in a tank under high pressure. Accordingly, a storage tank that can withstand high pressure is required.⁴ Liquefaction, a method of turning hydrogen into a liquid form, is vital. The storage efficiency is more than four to five times higher than that of the compression method. Cryogenic storage tanks have been in the spotlight, along with the latest emergence of liquid hydrogen due to its convenience of storage and transportation.⁵

Cryogenic materials, such as hydrogen, nitrogen, and liquefied oxygen are often used in vertical storage tanks, and steel storage tanks are generally used in infrastructure facilities.⁶ Vertical storage tanks are mostly self-sustaining systems connected and fixed by wire-installed anchors that penetrate the foundation consisting of plain protrusion and reinforced concretes. In particular, leg-supported tanks are flexible structures, similar to towers, masts, chimneys, and bridges.

This method may cause various damages, applied with some factors, such as self-weight, height, sloshing, and fixation method of the facility elements when external factors, such as earthquakes are applied. External forces can lead to stress concentration at the anchorage, which may cause damage such as shear buckling of the legs, cracking of the support concrete, and anchor failure.^7–10 Figure 1 exhibits photographs of anchor failure of vertical storage tanks caused by an earthquake.^11–13

Figure 1.

Anchor failure of vertical storage tanks under seismic loading.

The hydrogen storage tank failure may lead to fatal accidents, such as loss of life and property, due to the unique characteristics of hydrogen. Thus, special attention should be paid to the handling of hydrogen storage tanks, and safety reviews should be also conducted. In Korea, safety management was introduced during the enactment of the Hydrogen Act as the need for safety management of hydrogen production and storage facilities was flagged from the hydrogen explosion accident at the Gangneung Science Complex in 2019. The Hydrogen Economy Promotion and Hydrogen Safety Management Act¹⁴ was enacted in 2024 to promote the systematic development of the hydrogen energy industry and determine safety management issues. Furthermore, the seismic design of hydrogen facilities should be confirmed in accordance with the detailed technical criteria for seismic design and performance verification of gas facilities and gas pipelines¹⁵ per the Enforcement Decree of the Hydrogen Economy Promotion and Hydrogen Safety Management Act.¹⁶ In Korea, storage tanks and pressure vessels with a storage capacity of more than 5 tons or 500 m³ should be earthquake-resistant in accordance with KGS GC 203.^17,18 Particularly, experiments confirmed that no functional problems occur under seismic loading. The reliability and safety criteria for hydrogen facilities are included in the criteria for high-pressure gas facilities. However, the methodology for demonstration and verification is insufficient because details are typically missing as general information is only presented.

Seismic design of gas storage tanks is crucial. The seismic performance of storage tanks can be evaluated through seismic fragility analysis, which indicates the probability of structural damage due to an earthquake and is used to assess seismic performance.¹⁹ However, most fragility analyses are conducted using analytical methods, and cases where seismic performance is evaluated through shaking table testing are limited. In seismic fragility analysis, failure criteria are essential. According to seismic response analysis from previous studies, the seismic fragility elements for leg-supported tanks are the connections between the concrete foundation and the protruding concrete, while the tank itself was structurally safe.²⁰ Therefore, this paper aims to verify seismic damage and evaluate the seismic fragility of an anchored vertical gas storage tank with leg supports on a concrete foundation through tri-axial shaking table testing.

In this study, the model storage tank was designed and fabricated based on field investigations. The input ground motion was generated based on the common application of the building’s seismic design criteria and the seismic design criteria. The shaking table test was conducted by referring to ICC-ES AC156,²¹ a shaking table testing method for non-structural elements. The dynamic behavior characteristics and the seismic fragility were analyzed using the testing results, and the analysis results were compared. The presence or absence of water inside the storage tank model was considered as a variable to examine gas and liquid storage conditions.

Test specimen

Field investigation

This study, among the various types of storage tanks, defined a vertical hydrogen storage tank installed on the concrete protrusion of the reinforced concrete slab top as a test specimen in terms of the support type and conducted a field investigation. During the field investigation, the study focused on the concrete strength at the lower part of the storage tank, the installation type, and the specifications of the anchor. Figure 2 details the examined fixture part shape and installed anchors of the specimen structure. The hydrogen storage tank was installed in the hydrogen production site, and the four columns for support were made of L-beam steel (75 mm × 75 mm × 9.5 mm). The anchors connecting the structure to the base were M20 cast-in-place anchors, and four anchors were installed one anchor for each fixture part.

Figure 2.

Vertical hydrogen storage tank in field investigation.

The foundation concrete strength was measured through the Schmidt Hammer testing in the field investigation. The Schmitter hammer testing was used to select the surface to be measured. The spacing between the strike points was 3 cm. The grid was drawn with five vertical lines and four horizontal lines, creating 20 intersections where measurements were taken. The minimum value of foundation concrete strength measured by the Schmidt hammer testing was 23 MPa.

Fabrication of storage tank model

The storage tank model was fabricated by referring to the hydrogen storage tank illustrated in Figure 2. The size and weight of the model storage tank were limited, as shown in Figure 3 and Table 1, based on the scale and capacity of the shake table equipment. However, the model storage tank did not take simulated law into consideration. The foundation concrete and fixture parts reflected the results of the field investigation as much as possible. They were also made of steel, considering the test equipment’s performance. The storage tank model was designed, taking the gas storage and liquid storage into account by referring to KGS FU671²² for the configuration of the four anchor fixture parts. Considering liquid storage and to control variables caused by sloshing, the model storage tank was completely filled with water to ensure no gaps were present inside. The weight of the storage tank model was approximately 282 kg, and when filled with water, it weighed 1056 kg. The 9.5 mm thick support column was made of L-shaped steel based on the field investigation results. The storage tank model was 6 mm thick.

Figure 3.

Design of test specimen and overview of shake table installation.

Table 1.

Specification of the test specimen.

			Size (mm)				Description
Type	Weight (kg)		L	W	H	t	Description
Tank	Empty	276	530	530	2,420	6	SS400
Tank	Water filled	1046	530	530	2,420	6	L-shape angle (75 × 75 × 9.5)
RC slab	908		1570	1570	290	150	$f_{ck}$ : 21 MPa
							Concrete protrusion
							(200 × 200 × 140)
Anchor bolt	–		250	–	–	–	ASTM A36, M20
Anchor bolt	–		250	–	–	–	Embedment depth: 200 mm

The anchor bolt was made of ASTM A36 material to M20 standard, cast-in-place with studs, and had an embedment depth of 200 mm.²³ Considering the minimum strength of the concrete protrusion and the conditions of concrete pouring, the design criteria for compressive strength ( $f_{ck}$ ) of the foundation concrete was determined as 21 MPa. The type of anchor parts and the fixed foundation concrete was plain concrete protrusion. The specifications of the concrete protrusion were prepared considering the field investigation results, design criteria for the concrete, and edge distance.²⁴ The shapes and specifications of the specimens fabricated are represented in Figure 3 and Table 1.

Shaking table testing

Test methods and procedures

The shaking table test was conducted using the six-degree-of-freedom shaking table of the Seismic Research and Test Center (SESTEC) at Pusan National University. The storage tank model made of foundation concrete and steel made by installing a cast-in-place anchor bolt was fixed with the same clamping force of 1400 kgf cm, referring to the fastening torque standard of the anchor bolt.²¹ A tri-axial strain gauge (FRAB-5-11-5LJB-F) was attached to the lower of the L-beam, as illustrated in Figure 4, to measure the stress and strain of the storage tank model fixture parts with respect to the input ground motion. A tri-axial accelerometer (PCB 3713B1130G) was attached to the top, bottom, and center of gravity height of the storage tank model to measure the acceleration response. A tri-axial accelerometer (8316A030D0TA00) was installed at the bottom of the shaking table to calculate the acceleration response transfer function of each location for the input acceleration location.

Figure 4.

Test set-up and sensor location.

The test methods and procedures are shown in Table 2. The shaking table testing was performed with the same procedure in the cases of an empty tank (SET-1) and a tank full of water (SET-2). Before the seismic simulation test, the anchor part and resonance search test were visually inspected. The resonance search test is a random wave test independently performed for each axis direction (X, Y, Z) for more than 60 s, with a frequency range of 0.5–50.0 Hz. Afterward, a seismic simulation test was carried out with the simultaneous excitation applied to the three axes by taking the created acceleration time history as input ground motion. After the seismic simulation test, a resonance search test and then a visual inspection were completed to check the change in the dynamic characteristics of the storage tank model and the anchor parts failure. The acceleration multiplier of the RRS calculated according to the Korea Design Standard (KDS) increased from 50% by 50% based on 100%, and the procedure was repeated until the test specimen failed.

Table 2.

Shaking table test procedures and methods.

SET no.	Test ID	Test no.	Test method	Remarks
SET-1 (empty tank)	RES-1	1–3	Broadband random wave (direction: X, Y, Z)	Amplitude: RMS 0.05 g
				Frequency: 05–50.0 Hz
				Duration: 60 s
	EQ 50%	4	Tri-axial (X, Y, Z) time history test	$S_{DS}$ : 0.275 g
				Duration: 30 s
	RES-2	5–7	Same as RES-1
	EQ 100%	8	Same as EQ 50%	$S_{DS}$ : 0.550 g
				Duration: 30 s
	RES-3	9–11	Same as RES-1
	EQ 150%	12	Same as EQ 50%	$S_{DS}$ : 0.825 g
				Duration: 30 s
	RES-4	13–15	Same as RES-1
	EQ 200%	16	Same as EQ 50%	$S_{DS}$ : 1.100 g
				Duration: 30 s
	RES-5	17–19	Same as RES-1
	EQ 250%	20	Same as EQ 50%	$S_{DS}$ : 1.375 g
				Duration: 30 s
	RES-6	21–23	Same as RES-1
	EQ 300%	24	Same as EQ 50%	$S_{DS}$ : 1.650 g
				Duration: 30 s
	RES-7	25–27	Same as RES-1
	EQ 400%	28	Same as EQ 50%	$S_{DS}$ : 2.200 g
				Duration: 30 s
	RES-8	29–31	Same as RES-1
SET-2 (water-filled tank)	RES-1	32–34	Broadband random wave (direction: X, Y, Z)	Amplitude: RMS 0.05 g
				Frequency: 05–50.0 Hz
				Duration: 60 s
	EQ 50%	35	Tri-axial (X, Y, Z) time history test	$S_{DS}$ : 0.275 g
				Duration: 30 s
	RES-2	36–38	Same as RES-1
	EQ 100%	39	Same as EQ 50%	$S_{DS}$ : 0.550 g
				Duration: 30 s
	RES-3	40–42	Same as RES-1
	EQ 150%	43	Same as EQ 50%	$S_{DS}$ : 0.825 g
				Duration: 30 s
	RES-4	44–46	Same as RES-1
	EQ 200%	47	Same as EQ 50%	$S_{DS}$ : 1.100 g
				Duration: 30 s
	RES-5	48–50	Same as RES-1
	EQ 250%	51	Same as EQ 50%	$S_{DS}$ : 1.375 g
				Duration: 30 s

Input ground motion

The required response spectrum (RRS) for shaking table testing was prepared, as portrayed in Figure 5, following ICC-ES AC156 based on the common application of KDS and seismic design standards.^25,26 The short-period design spectral acceleration (S_DS) for RRS preparation was calculated according to equations (1) and (2). The seismic zone factor (Z) for calculating the effective horizontal ground acceleration (S) was assumed to be 0.11g, covering most of Korea.

S = Z \times I

(1)

S_{DS} = S \times 2.5 f_{a} \times \frac{2}{3}

(2)

Figure 5.

Request response spectrum for ICC-ES AC 156.

The hydrogen storage tank as a test specimen was deemed appropriate to be classified as a special earthquake-resistant grade because of its potentially great impact on the society associated with major social disasters and functional paralysis in the event of an earthquake. Therefore, the risk factor (I) with a return period of 2400 years was assumed to be 2.0, leading to S = 0.22g.²⁷ The short-period ground amplification factor (F_a) was assumed to be 1.5, taking into account the soft ground (S₃) assumption and the effective horizontal ground acceleration. The RRS and seismic parameters created using the calculated S_DS in Figure 5 and Table 3. The damping ratio of the RRS was 5%.

Table 3.

Seismic parameters of AC 156 RRS.

Amplification (%)	Code	S_DS (g)	z/h	A_FLEX-H (g)	A_RIG-H (g)	A_FLEX-V (g)	A_RIG-V (g)
50	–	0.275	1	0.44	0.33	0.18	0.07
100	KDS	0.550	1	0.88	0.66	0.36	0.14
150	Common application of seismic design criteria	0.825	1	1.32	0.99	0.55	0.22
200	–	1.100	1	1.76	1.32	0.73	0.29
250	–	1.375	1	2.20	1.65	0.92	0.37
300	–	1.650	1	2.64	1.98	1.11	0.44
400	–	2.200	1	3.52	2.64	1.47	0.59

The acceleration time history for the seismic simulation test was prepared for two horizontal directions and one vertical direction. The correlation function value of the prepared acceleration time histories was less than 0.3. The duration of the strong earthquake was 20 s, while the duration of the shaking was 30 s.²⁸

Inspection results

Field investigation

The results of the visual inspection performed after the seismic simulation test according to the acceleration multiplier is described in Table 4 and Figure 6. In the case of SET-1, no failure occurred in EQ 50% to 250% of the input earthquake. After the excitation of EQ 300%, a crack of less than 0.03 mm occurred at the boundary of the concrete protrusion and foundation slab at anchor 1. After the excitation of EQ 400%, a crack expanded to 0.1 mm. In the case of SET-2, no failure occurred up to EQ 200%.

Table 4.

Comparison of visual inspection results after testing.

Test ID	SET-1 (empty tank)	SET-2 (water-filled tank)
EQ 50%	N/A	N/A
EQ 100%	N/A	N/A
EQ 150%	N/A	N/A
EQ 200%	N/A	N/A
EQ 250%	N/A	Failure of all concrete protrusion
EQ 300%	0.03 mm crack of anchor 1	–
EQ 400%	0.1 mm crack of anchor 1	–

Figure 6.

Failure modes in simulated earthquake tests based on the type of contents.

However, at EQ 250% excitation, concrete failure occurred along the boundary between the concrete protrusion and the foundation slab as illustrated in Figure 6, resulting in complete separation. Accordingly, the test was terminated. No structural damage to the model storage tank was found even after the completion of all tests.

Resonant frequency and failure mode

The resonant frequency was determined by calculating the transfer function (T_ab) of the response acceleration at each measurement location of the storage tank model for the acceleration location measured in the shaking table. The transfer function is the same as equation (3) here, P_aa is the power spectral density (PSD) of the input signal, and P_ba is the cross-power spectral density (CSD) of the input and output signals. The resonant frequency results for X and Y according to the test procedures are detailed in Table 5 and Figure 7.

T_{ab} (f) = \frac{P_{ab} (f)}{P_{aa} (f)}

(3)

Here, the vertical (Z) direction was excluded because no resonant frequency was found in the test frequency range of 0.5–50 Hz.

Table 5.

Comparison of resonance frequency results after testing.

SET no.	Test ID	Predominant resonant frequency (Hz)		Remarks
SET no.	Test ID	X	Y	Remarks
SET-1 (empty tank)	RES-1	26.00	23.75	–
	RES-2	26.00	23.75
	RES-3	26.00	23.75
	RES-4	25.75	23.50
	RES-5	25.75	23.25
	RES-6	25.50	23.00
	RES-7	25.00	22.50
	RES-8	24.75	22.25
SET-2 (water-filled tank)	RES-1	11.25	12.00	–
	RES-2	11.00	11.75
	RES-3	10.50	11.50
	RES-4	10.50	11.25
	RES-5	10.25	11.25

Figure 7.

Comparison of resonance frequency results for each set.

In the case of SET-1, the differences between the results of the resonance search test (RES-1) before the seismic simulation test and the results after the EQ 400% excitation with a 0.1 mm crack (RES-8) were 4.93% and 6.52% for X and Y directions, respectively. In the case of SET-2, the differences between the results of RES-1 and the results of RES-5 as the resonance search test before the foundation concrete failure were 9.30% and 6.45%, respectively. The differences between two different signals were calculated according to equation (4).

Percentage difference (%) = \frac{| V_{1} - V_{2} |}{0.5 (V_{1} + V_{2})}

(4)

Here, V₁ and V₂ are two different signals that were compared for calculating the percentage difference. IEEE 693 specifies that a change in the resonance point of over 20% can cause serious failure.²⁹ However, the results of this study confirmed that when facilities were installed with cast-in-place anchors on a concrete foundation, a change in the resonant frequency of over 5% was likely to cause serious failure on the foundation concrete. From the experimental results, it was found that a change in the resonant frequency by more than 5% could lead to significant damage to the concrete foundation, and cracks larger than 0.1 mm could cause such a change in resonant frequency. In previous studies and experiments considering cracks in concrete and anchor bolts, the crack size ranged from 0.1 to 1.0 mm. Therefore, in this study, cracks larger than 0.1 mm were defined as damage.

Stress response

Using the strain response measured from the tri-axial strain gauge attached to the fixture parts, the von Mises stress was calculated, as demonstrated in equations (5) and (6).

\begin{matrix} σ_{ps 1, 2} = \\ \frac{P_{ab} (f)}{2 (1 - ν^{2}) ((1 + ν) (ε_{1} + ε_{2}) \pm (1 - ν) \sqrt{2 {(ε_{1} - ε_{3})}^{2} + {(ε_{3} - ε_{2})}^{2}})} \end{matrix}

(5)

σ_{ν . M . s .} = \sqrt{σ_{ps 1}^{2} - σ_{ps 1} σ_{ps 2} + σ_{ps 2}^{2}}

(6)

Here, ε¹, ε², and ε³ represent the strain response of the axial, vertical, and diagonal directions of the tri-axial strain gauge, respectively. ν is the Poisson’s ratio of the model storage container material (SS400), and E is the modulus of elasticity. The maximum response force of each location according to the acceleration multiplier of the input earthquake is described in Table 6. At EQ 400% of SET-1, the maximum stress was 33.76 MPa. Meanwhile, the maximum stress was 75.68 MPa and 171.16 MPa at EQ 200% and EQ 250% of SET-2, respectively. Both specimens yielded stresses less than SS 400’s yield stress of 225 MPa. Therefore, no problem with the structural soundness and safety of the storage tank model was found under seismic loading according to this test procedure. It was also confirmed that the failure of the foundation anchor parts could occur before the failure of the storage tank model occurred. Figure 8 shows the stress response of EQ 200% of SET-2 before the foundation concrete failed. All yielded stress of 225 MPa or less.

Table 6.

Results of the maximum strain response for each SET.

SET no.	Test ID	Maximum von Mises stress responses (MPa)
SET no.	Test ID	SG1	SG2	SG3	SG4
SET-1 (empty tank)	EQ 50%	7.62	8.54	9.27	10.17
	EQ 100%	9.27	11.29	12.03	10.86
	EQ 150%	10.35	10.90	13.22	15.53
	EQ 200%	26.62	19.06	18.26	25.67
	EQ 250%	10.56	13.37	16.96	23.01
	EQ 300%	12.50	19.75	19.25	27.02
	EQ 400%	33.76	26.76	27.77	31.99
SET-2 (water-filled tank)	EQ 50%	19.11	19.33	11.69	24.55
	EQ 100%	34.79	28.47	16.45	42.53
	EQ 150%	47.17	105.37	30.29	57.79
	EQ 200%	45.45	75.68	41.66	74.76
	EQ 250%	85.91	176.11	116.27	109.44

Figure 8.

Comparison of stress results under conditions filled with water (SET-2, EQ 200%).

Acceleration response

In the event of foundation concrete failure, the difference in amplification to the acceleration response of A3 was observed as the largest among the total acceleration responses. Figure 9 depicts the time history of the acceleration response of A3 in SET-2 to EQ 100% of KDS, EQ 200% before concrete failure, and EQ 250% at the time of concrete failure. At EQ 250%, the concrete protrusion was observed to fail after 20 s of excitation, and the acceleration response signal was significantly amplified. In general, root mean square (RMS) was used to evaluate the acceleration response of major safety-related equipment. It is the square root value of the average of the squared of the measured time history and can represent the amplitude regardless of frequency. The amplification of the acceleration response may also be examined using the ratio of the acceleration response measured at the corresponding location of a specimen to the acceleration response measured at the bottom of the shaking table. The RMS and RMS ratio for the acceleration response of the storage tank model is exemplified in Figures 10 and 11. Here, RMS is calculated as shown in equation (7), and the RMS ratio is calculated using equation (8).

X_{RMS} = \sqrt{\frac{1}{N} \sum_{n = 1}^{N} X_{n}^{2}}

(7)

X_{RMS ratio} = \frac{X_{RMS (A_{i})}}{X_{RMS (Base)}}

(8)

Figure 9.

Comparison of acceleration response histories in each axial direction for A3 (SET-2).

Figure 10.

Comparison of RMS values for each artificial earthquake acceleration magnitude: (a) EQ 50%, (b) EQ 100%, (c) EQ 150%, (d) EQ 200%, (e) EQ 250%, (f) EQ 300%, and (g) EQ 400%.

Figure 11.

Comparison of RMS ratios for each artificial earthquake acceleration magnitude: (a) EQ 50%, (b) EQ 100%, (c) EQ 150%, (d) EQ 200%, (e) EQ 250%, (f) EQ 300%, and (g) EQ 400%.

In Figure 10, the results of both SET-1 and SET-2 illustrated a similar tendency to the RMS value of the acceleration response regardless of water filling at EQ 200% or lower, but the RMS value of SET-2 was greater than that of SET-1. This was especially true at A3, the center of gravity, and A4, the top point. Additionally, the acceleration amplification ratio to the horizontal direction was greater than the one to the vertical direction. The RMS ratio as the amplification tendency of the acceleration response was also not much different from the trend of SET-1 and SET-2. The percentage error for the horizontal two directions (X, Y), the RMS ratio of SET-1 and SET-2, was calculated using equation (8), as reflected in Table 7.

Table 7.

Percentage error of RMS ratio.

		Percentage error (%)
Location		EQ 50%	EQ 100%	EQ 150%	EQ 200%
A2	X	8.7	10.1	6.6	9.5
	Y	15.4	7.6	10.7	8.0
A3	X	8.6	4.3	2.7	8.3
	Y	1.9	19.7	21.7	20.5
A4	X	13.7	13.4	9.2	12.3
	Y	2.3	4.0	1.9	3.3

The percentage error difference between the RMS ratio of the acceleration response (A2) at the bottom and the acceleration response (A4) at the top of the storage tank model of SET-1 and SET-2 was 16% or lower. However, the percentage error of the acceleration response near the center of gravity (A3) differed by 19.7% at EQ 100% and exceeded 20% after EQ 150%. The tendency of the response at the center of gravity of SET-2 to be significantly amplified more than that of SET-1 is well illustrated in Figure 7. When EQ 100% was set in all locations (A2, A3, A4), a percentage error of 20% or lower was obtained.

Seismic fragility analysis

The fragility of equipment can be analyzed using the load mandated by the required design and the capabilities of the actual equipment. Specifically, the fragility of earthquakes is called seismic fragility. The typical fragility analysis methods are the deterministic fragility analysis and the probabilistic fragility analysis of these two methods, the probabilistic fragility analysis method was developed in line with nuclear energy in the 1980s.^30,31 In seismic fragility, the probability of equipment failure is assumed to have a log-normal distribution for the peak ground acceleration (PGA) of the earthquake. If the median value (A_m) of the PGA at the time of failure can be found, the probability of 5% failure can be expressed as high confidence and low probability of failure (HCLPF) in the probability of failure with 95% confidence. This can be obtained as presented in equation (9).³²

HCLPF = A_{m} \times e^{- 1.65 (β_{R} + β_{U})}

(9)

Here, β_R and β_U represent aleatoric and epistemic uncertainties, respectively. They can be determined as uncertainty factors of each aspect affecting the log-normal distribution.

On the other hand, A_m can be expressed as the ratio of TRS to RRS, the broad frequency input spectrum device capacity factor (F_D), the response factor for building for the installation of equipment (F_RS), and PGA as equation (10).

A_{m} = \frac{TR S_{C}}{RR S_{C}} \times F_{D} \times F_{RS} \times PGA

(10)

TRS_C and RRS_C signify the response spectrums correcting errors caused by the peak response to TRS and RRS and reflecting the modification factor, as shown in equations (11) and (12), each.

TR S_{C} = TRS \times C_{T} \times C_{I}

(11)

RR S_{C} = RRS \times C_{C} \times D_{R}

(12)

Here, C_T and C_R are the clipping factors for TRS and RRS, respectively. C_I is the capacity increase factor, and D_R is the demand reduction factor.

Figure 12 serves as an example of the fragility assessment process. Figure 12(a) shows the time history graph of the input seismic wave corresponding to 300% EQ of SET-1, and Figure 12(b) illustrates a comparison between the TRS of the time history in Figure 12(a) and the RRS corresponding to $S_{DS}$ = 0.55g. In Figure 13(b), the “Min ratio” represents the point where the TRS to RRS ratio is the lowest. This indicates the location of the most vulnerable frequency, which directly applies to the performance evaluation of the fragility device. Additionally, as can be observed in the same figure, there are no peaks in the TRS or RRS in this study.

Figure 12.

Example of acceleration time history of input motion and comparing TRS with RRS: (a) time history and (b) comparing TRS and RRS.

Figure 13.

Seismic fragility curves by axial direction under different conditions: (a) SET-1 and (b) SET-2.

This study applied a clipping factor of 1 since no peak existed for TRS and RRS. The capacity increase factor and the demand reduction factor were 1.1 and 0.92, respectively. F_D indicated the performance just before failure as the limit, and 1 was applied because the TRS assumed that the equipment had reached its limit. The uncertainties (β_R, β_U) for each factor were recommended in previous studies.³³ In the testing and research of anchor bolts considering cracks in concrete, the size of the cracks considered ranged from 0.1 to 1.0 mm.^34–36

Therefore, in this study, cracks larger than 0.1 mm were defined as the failure criterion. Based on the information summarized in Table 4, SET-1 can be defined as a failure at EQ 400% and SET-2 at EQ 250% in the shaking table testing. The study calculated seismic fragility using EQ 300% and EQ 200% for a conservative assessment. Figure 13(a) and (b) illustrate the seismic fragility curves of SET-1 and SET-2, respectively. Table 8 shows the parameters for creating a seismic fragility curve.

Table 8.

Parameters for seismic fragility curve.

Test ID	TRS	RRS	Frequency range
SET-1	Test 24 (EQ 300%)No clipping	Code: ICC-ES AC 156 (S_DS: 0.55 g,z/h = 1, PGA = 0.22 g)No clipping	2–33.3 Hz
SET-2	Test 47 (EQ 200%)No clipping

Table 9 shows the representative values of the seismic fragility curve. Both SET-1 and SET-2 exhibited lower seismic performance in the X-axis direction. The HCLPF for the X-axis direction in SET-1 is 0.263g, with a median value of 0.402g. For SET-2, the HCLPF and median values are 0.199 and 0.306g, respectively. An analysis of seismic waves observed at stations located 5.9–22 km from the epicenter of the 2016 Gyeongju earthquake revealed that the horizontal PGA (Peak Ground Acceleration) reached up to 0.404g.³⁷ The minimum HCLPF value for the horizontal direction in SET-1 is about 65% of the Gyeongju earthquake’s PGA, while the maximum horizontal PGA of the Gyeongju earthquake is approximately 2.03 times higher than the HCLPF in SET-2.

Table 9.

Representative values of seismic fragility curve.

Classification		SET-1	SET-2
HCLPF (g)	X	0.263	0.199
	Y	0.321	0.214
	Z	0.840	0.604
Median (g)	X	0.402	0.306
	Y	0.490	0.331
	Z	0.128	0.924

Conclusion

An experimental study was conducted to analyze the dynamic behavior characteristics and failure mode of hydrogen storage tanks in the event of an earthquake. The storage tank model and foundation concrete were designed and fabricated based on the field investigation and design criteria. A tri-axial shaking table testing was performed on the fabricated specimens, and a seismic fragility curve was drawn.

The RMS value of the acceleration response was similar for SET-1 and SET-2 regardless of water filling at EQ 200% or less. However, the RMS value of SET-2 was greater than that of SET-1. This tendency was especially apparent at A3, the center of gravity, and A4, the top point. In addition, the acceleration amplification ratio to the horizontal direction was greater than that to the vertical direction. Furthermore, the RMS ratio, which is the amplification tendency of the acceleration response, was not much different from the trend of SET-1 and SET-2.

The seismic fragility analysis reveals that the median values of SET-1 and SET-2 were 0.402 and 0.306g, each. The HCLPFs were 0.263 and 0.199g, respectively. For a seismic event with a PGA of 0.22g, which is the applied seismic design level in Korea, the probability of concrete cracking is greater than 5% at a 95% confidence level. However, this HCLPF is lower than the horizontal PGA value of 0.404g observed during the Gyeongju earthquake, indicating that seismic reinforcement of the anchorage for the hydrogen storage tank may be necessary.

At the end of all testing, no failure of the storage tank model was observed. The result of the seismic simulation test performed by increasing the acceleration multiplier demonstrated a small change in resonant frequency. However, it showed a gradually decreasing tendency. The testing exhibited that if the resonant frequency were lowered by 5% or over, a serious failure of the foundation concrete may occur. Therefore, the failure of the hydrogen storage tank installed with cast-in-place anchors assumed in this testing can be defined as cracking or separation of the foundation concrete and the concrete protrusion.

The failure mode of the storage tank model made based on the field investigation was the separation or cracking of the foundation concrete and the concrete protrusion. In the case of SET-1, where gas storage was assumed, a 0.1 mm crack occurred between the foundation concrete and the concrete protrusion. A crack size of 0.1 mm resulted in a resonant frequency shift of more than 5%. In SET-2, which assumed liquid storage, the support concrete detached from the foundation concrete after a resonant frequency change of more than 5%. Therefore, in this paper, cracks larger than 0.1 mm were defined as the failure criterion for seismic fragility analysis.

Based on the foregoing, this study will serve as data for the design of support parts not only for the hydrogen storage tank but also for the vertical storage tank that stores various types of gases.

Footnotes

Handling Editor: Vladimir Bratov

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was supported by the “Regional Innovation Strategy (RIS) and Basic Science Research Program” through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (MOE) (2022 RIS-005 and 2021R1A6A1A03044326).

ORCID iD

Sang-Moon Lee

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