applied sciences Article Experimental and Numerical Investigation for Seismic Performance of a Large-Scale LNG Storage Tank Structure Model Zengshun Chen , Zhengang Xu 1, *, Lingxiao Teng , Jun Fu 1,3,4 , Tao Xu 1,5 and Zhihang Zhao 1, * * Citation: Chen, Z.; Xu, Z.; Teng, L.; Fu, J.; Xu, T.; Zhao, Z Experimental and Numerical Investigation for Seismic Performance of a Large-Scale LNG Storage Tank Structure Model Appl Sci 2022, 12, 8390 https:// doi.org/10.3390/app12178390 Academic Editors: Panagiotis G Asteris, Nikola Grgi´c and School of Civil Engineering, Chongqing University, Chongqing 400045, China Science and Technology Quality Department, Chongqing Design Institute Co., Ltd., Chongqing 400015, China Key Laboratory of Icing and Anti/Deicing, China Aerodynamics Research and Development Center, Mianyang 621000, China Construction Management Department, Construction of Five Investment Management Company, Changsha 410116, China Management Department, Construction of Chongqing High-Tech Building Materials Company, Chongqing 401431, China Correspondence: zhengangxu@cqu.edu.cn (Z.X.); zhaozhihang@cqu.edu.cn (Z.Z.) Abstract: As special equipment for storing energy, the safety performance of liquified natural gas (LNG) storage tanks under earthquake action is extremely important To study the dynamic characteristics of the large-scale LNG storage tank structure and the dynamic response under earthquake action, the shaking table test and numerical simulation analysis of the LNG storage tank structure model are carried out The results of the shaking table test demonstrate that the natural vibration frequency of the tank model is significantly reduced after the isolation measures are taken The acceleration response of the seismic storage tank increases approximately linearly along the direction of height, and the seismic isolation bearing has a significant seismic isolation effect on the acceleration of the storage tank The numerical simulation results show that the seismic responses and their spectral characteristic curves of the numerical model and the shaking table test are the same, which verifies the feasibility and rationality of the numerical model After seismic isolation measures are taken, the seismic responses of large-scale LNG storage tanks, such as base shear force, overturning bending moment and acceleration, are reduced to varying degrees, but the displacement of the storage tank increases to some extent When carrying out the seismic isolation design of LNG storage tanks, it is necessary to focus on the displacement of the storage tank to prevent damage of the auxiliary pipeline led by excessive displacement Goran Baloevi´c Received: 18 July 2022 Accepted: 12 August 2022 Keywords: LNG storage tank; shaking table test; dynamic characteristics; dynamic response; seismic performance Published: 23 August 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations Copyright: © 2022 by the authors Licensee MDPI, Basel, Switzerland This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ Introduction The large liquified natural gas (LNG) storage tank is an important energy storage equipment, which is widely used in chemical raw material production and energy supply Typically, LNG storage tanks are built in coastal areas to receive LNG from maritime transport However, poor geological conditions in coastal areas, which are prone to suffer from foundation liquefaction [1], result in settlement and inclination of buildings The safety of large LNG storage tanks is always threatened by earthquakes Once a severe earthquake comes, large LNG storage tanks will suffer from a tremendous overturning bending moment and dynamic hydraulic pressure, which may lead to damage to the storage tank [2] and buckling failure of the inner tank [3,4] This can lead to leakage of LNG, which can result in fires and explosions [5–7] It is critical that large LNG storage tanks remain intact during the course of earthquakes Therefore, it is of great practical 4.0/) Appl Sci 2022, 12, 8390 https://doi.org/10.3390/app12178390 https://www.mdpi.com/journal/applsci Appl Sci 2022, 12, 8390 of 20 significance and engineering value to study the seismic performance of large-scale LNG storage tanks Liquid−solid interaction is the most obvious difference between storage tanks and conventional civil structures (such as houses and bridges) Under the external excitation, the liquid will slosh back and forth, which will generate tremendous dynamic hydraulic pressure on the tank wall, which in turn will affect the structure In order to study the liquid−solid interaction of the storage tank, Housner [8] first proposed a two-particle mass−spring model, which divided the liquid into a rigid component and a convection component Considering the elastic deformation of the tank wall under load, Haroun and Housne [9] proposed a simplified mechanical model, which takes into account the elastic deformation of the tank wall and the interaction between the liquid and the solid For the convenience of engineering application, Malhotra et al [3] proposed a simplified seismic design method, which takes into account the influence of liquid convection and pulsation on the tank wall Jadhav et al [10] studied the effect of different isolator parameters on the seismic response of the foundation isolation liquid storage tank In order to verify the correctness of the simplified model of the storage tank proposed by the above researchers, some researchers [11–13] used finite element software to analyze the seismic time history of the storage tank, and compared the calculation results of the finite element and the simplified model; it was found that the difference between the two is not large, which verifies the rationality of the simplified model Moslemi and Kianoush [14] used ANSYS finite element software to conduct a parametric study on the dynamic behavior of cylindrical storage tanks, and the study illustrated that the current liquid tank design codes of the dynamic hydraulic pressure is too conservative Saha et al [15] studied the seismic response of liquid storage tanks isolated by elastomeric bearings and sliding systems under near-fault seismic motion Kangda [16] reviewed the research status of the finite element method used in the barrier and barrier-free liquid storage tanks, and introduced the method of establishing the finite element model of the liquid storage tank in ANSYS software in detail However, as storage tanks are being built larger, it is difficult to control the seismic response of storage tanks with seismic measures In order to reduce the seismic response of the liquid storage tank, seismic isolation devices are introduced into the liquid storage tank structure, such as friction pendulum bearings, lead-core rubber bearings, etc In order to study the seismic response of the isolated storage tank under the excitation of near-fault ground motion, Panchal et al [17,18] selected different isolation bearings for analysis The research results show that the isolating affection of the variable frequency friction pendulum bearing is better than that of the friction pendulum bearing Zhang et al [19] derived the nonlinear restoring force expression of the multiple friction pendulum system, and studied the seismic response of the isolated storage tank on this basis Tang et al [20] conducted shaking table tests on storage tanks with different isolation devices The test results show that the horizontal displacement of the laminated rubber bearing isolated tank is the largest In comparison, both friction pendulum bearing and variable curvature friction pendulum bearing have good isolation over a wider frequency band Moeindarbari et al [21] investigated the multiple level performance of a seismically isolated elevated storage tank isolated with multi−phase friction pendulum bearing, and a mathematical formula involving complex time history analysis was presented for the analysis of a typical storage tank for a multiphase friction pendulum bearing Seleemah et al [22] studied the seismic response of liquid storage tanks isolated by elastomeric or plain bearings; it was found that base isolation is quite effective in reducing the earthquake response of liquid storage tanks The type of site has a significant effect on the seismic response of the storage tank The foundation of the storage tank was considered as a rigid foundation in previous studies In fact, the foundation frequently suffers from uneven settlement Ormeño et al [23] conducted shaking table tests on rigid-foundation storage tanks and flexible-foundation storage tanks, and the results showed that the axial stress of flexible-foundation storage tanks was reduced compared to rigid-foundation storage tanks Tsipianitis et al [24] proposed a detailed numerical Appl Sci 2022, 12, 8390 of 20 framework for seismic analysis of liquid storage tanks considering soil-structure interaction (SSI), and studied the effect of SSI on the seismic performance of storage tanks In summary, the current research has made great progress in the field of seismic resistance (seismic isolation) of storage tanks However, some researchers’ studies are based on simplified mechanical models or numerical simulation models, without conducting a shaking table test to verify their results A few researchers have carried out shaking table tests, but their studies lack the numerical simulation to prove it In view of this, this paper analyzes the seismic response of the storage tank model based on the shaking table test and numerical simulation, and studies the seismic isolation effect of the lead-core rubber bearing on the storage tank On this basis, the dynamic response of a large LNG storage tank of 200,000 cubic meters under earthquake action is analyzed, and the seismic isolation pattern of the storage tank is studied Shaking Table Test of LNG Storage Tank Model To reveal the dynamic response mechanism of large-scale LNG storage tanks under earthquake action, a shaking table test was carried out on the structural model of LNG storage tanks in this paper In the experiment, the dynamic response of a storage tank model was obtained by using the acceleration sensor and the displacement sensor, and the dynamic characteristics of a large LNG storage tank were studied 2.1 Test Model This paper takes an actual large-scale LNG storage tank as a reference Considering the complexity of its structure, a simplification was made when designing the structure model storage tank It is necessary to ensure that the prototype structure is similar to the experimental structure during the design, but it is difficult to meet this requirement in most cases Therefore, the storage tank structure model only retains the main structure of large LNG storage tank, such as the outer tank, pile foundation, dome and inner tank, ignoring the structures that not bear weight, such as the aluminum ceiling, steel dome and auxiliary pipelines The geometric dimensions and material parameters of the tank model are as follows The height of the outer tank wall is m, and the sagittal height of the dome is 0.2 m The inner diameter of the outer tank wall is 2.5 m, and the thickness of the outer tank wall is 0.2 m The distance between the outer tank and the inner tank is 0.35 m, the diameter of the inner tank is 0.9 m, the height of the inner tank is 1.5 m, and the wall thickness of the inner tank is mm There are 13 pile foundations in the model tank For the seismic storage tank, the pile foundation and the bearing platform of the storage tank are directly connected For the seismic storage tank, lead−core rubber bearings are arranged between the pile foundation and the bearing platform of the storage tank, as shown in Figure 1a,b The diameter of the pile is 0.4 m and the length of the pile is 0.3 m The plans of the seismic storage tank and isolation storage tank are shown in Figure The outer tank is made of C50 concrete with an elastic modulus, Poisson’s ratio and density of 34.5 GPa, 0.167 and 2500 kg/m3 , respectively The inner tank is made of steel with and elastic modulus, Poisson’s ratio and density of 210 GPa, 0.3 and 7800 kg/m3 , respectively Appl Sci 2022, 12, x FOR PEER REVIEW of 21 FOR PEER REVIEW Appl Sci 2022, 12, x8390 4of of 21 20 JSD-16 JSD-8 JSD-15 JSD-7 100 100 JSD-16 JSD-8 100 JSD-7 100 JSD-6 100 JSD-14 100 100 JSD-6 950 JSD-15 100 JSD-14 950 200 200 950 950 200 JSD-13 200 JSD-5 360 360 JSD-12 JSD-13 JSD-4 JSD-5 360 390 360 390 JSD-11 JSD-12 JSD-4 JSD-3 390 300 390 330 300 300 JSD-10 JSD-11 200 JSD-2 JSD-3 JSD-1 300 JSD-9 330 400 200 JSD-10 400 JSD-2 JSD-9 2900 330 JSD-1 400 2900 330 400 2900 (a) (b) 2900 Figure (a) The plans of the storage tank: (a) seismic storage tank; (b) (b) isolation storage tank (units: mm) Figure of the the storage storagetank: tank:(a) (a)seismic seismicstorage storagetank; tank;(b) (b) isolation storage tank (units: Figure 1 The The plans plans of isolation storage tank (units: mm) mm).The earthquake shaking table is a three-dimensional horizontal excitation hydraulic earthquake shaking table is aofthree-dimensional hydraulic drive The device The specific parameters this device are as horizontal follows: theexcitation size of the table is The earthquake shaking table is aof three-dimensional horizontal excitation hydraulic drive device The specific parameters this device are as follows: the size of the tableisis m × m; the maximum load capacity is 60 t; the maximum anti-overturning moment drive device The specific parameters ofisthis device are as follows: the size of the table is m × m; the maximum load capacity 60 t; the maximum anti-overturning moment 1800 kN·m; the limit displacement of the table is ± 250 mm The measurement point layout 61800 m ×kN m; load capacity 60 t;isthe maximum anti-overturning moment is ·m;the themaximum limit displacement of theistable ± 250 mm The measurement point layout of the storage tank model is shown in Figure Acceleration sensors and displacement of thekN· storage is shown sensors and displacement 1800 m; thetank limitmodel displacement of in theFigure table is1.± Acceleration 250 mm The measurement point layout sensors were arranged in the experiment According to the structural characteristics of the sensors were arranged in the experiment According to the structural characteristics of of the storage tank model is shown in Figure Acceleration sensors and displacement storage tank, acceleration sensors were arranged at the pile foundation, the bearing platthe storage tank, acceleration sensors were arranged at the pile foundation, the bearing sensors were arranged in the experiment According to the structural characteristics of the form, the height of the center of mass, and the dome, and the displacement sensor was platform, theacceleration height of the centerwere of mass, and the dome, the displacement storage tank, sensors arranged at the pile and foundation, the bearingsensor platarranged at the bottom of the dome Figure 2a is the test model of the storage tank, and was arranged at the bottom ofof the dome Figure 2a is the of the storage form, the height of the center mass, and the dome, andtest themodel displacement sensor tank, was Figure 2b is the actual layout of the acceleration sensor The acceleration sensor selected and Figure the actual the acceleration acceleration sensor arranged at 2b the isbottom of thelayout dome.ofFigure 2a is the testsensor model The of the storage tank, and for the test was Endevco 7290E (Endevco Corporation, Irvine, CA, USA); the acceleration selected2bfor the actual test was Endevco (Endevco Corporation, Irvine, sensor CA, USA); the Figure is the layout of the7290E acceleration sensor The acceleration selected range that can be tested was ± 10 g The Endevco 7290E is a rugged, variable capacitance acceleration range that can be tested was ± 10 g The Endevco 7290E is a rugged, variable for the test was Endevco 7290E (Endevco Corporation, Irvine, CA, USA); the acceleration accelerometer with integral electronics for voltage regulation, filtering, and signal amplicapacitance accelerometer with electronics for voltage regulation, and range that can be tested was ± 10integral g The Endevco 7290E is a rugged, variablefiltering, capacitance fication signal amplification accelerometer with integral electronics for voltage regulation, filtering, and signal amplification (a) (b) Figure (a)Test (b)sensor Figure2.2.(a) (a) Testmodel modelof ofthe thestorage storagetank; tank; (b) (b) layout layout of of the the acceleration acceleration sensor Figure (a) Test of the storage tank; (b) layout of the acceleration sensor 2.2 Seismic Wavemodel Selection In the shaking table test, the ground motion is input in the form of base acceleration In this paper, the prototype of test tank is located in a Class II site Based on seismic codes 2.2 Seismic Wave Selection Appl Sci 2022, 12, 8390 In the shaking table test, the ground motion is input in the form of base acceleration of 20 In this paper, the prototype of test tank is located in a Class II site Based on seismic codes for building structures [25] and design codes for large oil storage tanks [26], the selected seismic waves should be close to the natural period of the site where the structure is lofor building structures [25] and design codes large oilThree storage tanksseismic [26], thewaves selected cated to increase the seismic response of thefor structure natural and seismic waves should be close to the natural period of the site where the structure is located one artificial wave were selected for experiment, namely the El Centro wave, Taft wave, toWolong increase the and seismic response of which the structure Three natural seismic waves and wave Artificial wave, satisfies the wave selection requirements ofone seisartificial wave were selected for experiment, namely the El Centro wave, Taft wave, Wolong mic waves The time history curve of the seismic wave is shown in Figure During the wave and Artificial wave, which wave selection requirements of to seismic experiment, the peak values ofsatisfies seismicthe wave acceleration were adjusted 0.1 g,waves 0.25 g, The time history curve of the seismic wave is shown in Figure During the experiment, 0.5 g and 0.75 g, respectively Since the storage tank model is scaled from a large storage the peak values of seismic wave acceleration were adjusted to 0.1 g, 0.25 g, 0.5 g and tank, the time of the seismic wave needed to be scaled, and the time interval was com0.75 g, respectively Since the storage tank model is scaled from a large storage tank, the pressed to 1/5 of the original seismic record The test conditions were carried out accordtime of the seismic wave needed to be scaled, and the time interval was compressed to ing to the peak acceleration from minor to large To determine the changing pattern of the 1/5 of the original seismic record The test conditions were carried out according to the dynamic characteristics of the LNG storage tank, the natural vibration characteristics of peak acceleration from minor to large To determine the changing pattern of the dynamic the storage tank model were obtained by white noise scanning before the start of the shakcharacteristics of the LNG storage tank, the natural vibration characteristics of the storage ing table test and after the application of seismic waves at all levels The arrangement of tank model were obtained by white noise scanning before the start of the shaking table test test conditions is shown in Table and after the application of seismic waves at all levels The arrangement of test conditions is shown in Table (a) (b) (c) (d) Figure3.3.Time Timehistory historyofofseismic seismicwave waveacceleration: acceleration:(a) (a)ElElCentro Centrowave; wave;(b) (b)Taft Taftwave; wave;(c) (c)Wolong Wolong Figure wave; (d) Artificial wave wave; (d) Artificial wave Table Arrangement of test conditions Condition Number 2−5 Test Condition White noise Wolong, Artificial White noise Excitation Direction X, Y, Z X, Z; X, Y, Z X, Y, Z Peak Acceleration (g) 0.05 0.1 0.05 Appl Sci 2022, 12, 8390 of 20 Table Arrangement of test conditions Condition Number Test Condition Excitation Direction Peak Acceleration (g) 2–5 7–10 11 12–21 22 23–34 35 White noise Wolong, Artificial White noise Wolong, Artificial White noise El Centro, Taft, Wolong, Artificial White noise El Centro, Taft, Wolong, Artificial White noise X, Y, Z X, Z; X, Y, Z X, Y, Z X, Z; X, Y, Z X, Y, Z X; X, Z; X, Y, Z X, Y, Z X; X, Z; X, Y, Z X, Y, Z 0.05 0.1 0.05 0.25 0.05 0.50 0.05 0.75 0.05 2.3 Design of Lead-Core Rubber Bearing Using MATLAB software to analyze the frequency spectrum of the seismic wave after compression time, the predominant periods of the El Centro wave, Taft wave, Wolong wave and Artificial wave were 0.125 s, 0.134 s, 0.078 s and 0.067 s, respectively In order to avoid the resonance phenomenon of the test tank, the isolation period should be far from the seismic predominant period A lead-core rubber bearing is arranged between the test tank and the pile foundation, and the parameters of them are shown in Table Table Lead-core rubber bearing parameters Item Parameter Item Parameter type effective outer diameter outer diameter of bearing lead diameter side length of sealing plate sealing plate thickness rubber layers layers of sheet steel thickness of rubber layer thickness of steel plate total thickness of rubber total thickness of steel plate LRB300 300 mm 320 mm 60 mm 400 mm 11 mm 26 layer 25 layer mm mm 78 mm 50 mm height shear modulus rubber standard elastic modulus second shape factor effective area bearing area hardness correction coefficient vertical stiffness equivalent horizontal stiffness yield force post yield stiffness equivalent damping ratio 150 mm 0.392 MPa 1.5 MPa 5.77 70,685.8 mm2 160,000 mm2 0.9 887 kN/mm 821 kN/m 22.6 kN 469 kN/m 30.9% The calculation formula of the isolation period is as follows [27]: s Tiso = 2π Mi + M s Kiso (1) Total stiffness of horizontal isolation layer Kiso is: Kiso = nk iso Mi = tanh[0.866( D/hw )] Ml 0.866( D/hw ) (2) (3) where: Tiso is the isolation period; Kiso is the horizontal stiffness of the isolation layer; Mi is the mass of the liquid that moves with the tank; Ms is the mass of the tank; k iso is the equivalent stiffness of a single lead-core rubber bearing; D is the diameter of the inner tank; hw is the height liquid storage, its value is 0.75 m; and Ml is the total mass of the liquid Taking the equivalent stiffness of a single isolation bearing in Table into Equation (2), and then from Equation (1), the isolation period can be obtained as 0.967 s, which is distant from the predominant period of the input seismic wave This preliminarily indicates that it is reasonable to choose lead rubber bearing Appl Sci 2022, 12, 8390 of 20 Analysis of Test Results 3.1 Natural Vibration Characteristics The dynamic characteristics of the tank model will change somewhat after being excited by seismic waves subjected to different peak accelerations By processing the data in the condition of white noise, the natural vibration frequency of the tank model can be obtained, as shown in Table Table Natural vibration frequency of tank model under white noise excitation (Hz) Condition Number Explanation before test after 0.10 g earthquake after 0.25 g earthquake after 0.50 g earthquake after 0.75 g earthquake 11 22 35 Seismic Storage Tank Isolation Storage Tank X Y X Y 16.8 16.1 7.3 7.0 15.7 15.7 7.0 6.9 15.7 15.7 6.9 6.5 15.2 14.0 6.5 6.3 15.0 13.6 6.4 6.0 It can be seen from Table that: (1) (2) After seismic isolation measures are taken, the natural vibration frequency of the tank model is significantly reduced Before the seismic wave is applied, along the X-direction, the frequencies of the seismic storage tank and the seismic isolation tank are 16.8 Hz and 7.0 Hz After the seismic isolation, the frequency of the storage tank decreases by 9.5 Hz, with a decrease of 56.5% Along the Y-direction, the frequencies of the seismic storage tank and the isolation storage tank are 16.1 Hz and 7.0 Hz, and the frequency of the storage tank is reduced by 9.1 Hz after isolation, with a decrease of 56.5% This shows that the isolation bearing has the same effect on the natural vibration frequency of the tank in the X- and Y-directions With the increase of peak acceleration of the seismic wave, the natural vibration frequency of the seismic storage tank and the seismic isolation storage tank decreases gradually This indicates that the tank was damaged, and that the damage was progressive After the test, along the X-direction, the natural vibration frequencies of the seismic storage tank and the isolation storage tank decreased by 1.8 Hz and 0.9 Hz, respectively; along the Y-direction, the natural vibration frequencies of the seismic storage tank and the isolation storage tank decreased by 2.5 Hz and Hz, respectively This indicates that the damage degree of the isolation storage tank is smaller than that of the seismic storage tank 3.2 Acceleration Response In this paper, the data collected under the action of seismic waves with peak accelerations of 0.5 g and 0.75 g are selected to analyze acceleration responses and their differences between the seismic storage tank and the isolation storage tank By extracting the peak acceleration of the measurement points, and the results shown in Figures and can be obtained As can be seen from the figure: (1) The acceleration of the seismic storage tank approximately increases linearly along the direction of height, and the acceleration will change abruptly at the dome position, which indicates that the lateral stiffness of the dome position is much lower than that of the tank wall After the seismic isolation measures are taken, acceleration response of the storage tank is significantly reduced In the direction of seismic wave action, the isolation effect is particularly obvious Under the action of the Wolong wave (XYZ, Appl Sci 2022, 12, 8390 Appl Sci 2022, 12, x FOR PEER REVIEW (2) of 20 0.75 g), the maximum acceleration of the seismic storage tank and the isolation storage (2) With the increase of peak acceleration of the seismic wave, the acceleration o tank are 20.68 m/s2 and 8.92 m/s2 , respectively, and the isolation rate reaches 56.9% seismic storage tank and the isolation storage tank also increases Compared wi With the increase of peak acceleration of the seismic wave, the acceleration of the Taft wave (XZ direction) condition, when the PGA is 0.50 g, the maximum acc seismic storage tank and the isolation storage tank also increases Compared with tions of the seismic storage tank and the isolation storage tank are 13.62 m/s2 an the Taft wave (XZ2 direction) condition, when the PGA is 0.50 g, the maximum acm/s , respectively; when the PGA is 0.75 g, the maximum accelerations2 of the se celerations of the seismic storage tank and the isolation storage tank are 13.62 m/s storage tank and the isolation storage tank are 17.93 m/s2 and 4.21 m/s2, respect and 2.25 m/s , respectively; when the PGA is 0.75 g, the maximum accelerations of This istank because of the arrangement lead-core rubber the2 ,isolation the seismic storage and the isolation storageof tank are 17.93 m/s2bearings and 4.21in m/s so the increase of of the the arrangement acceleration of isolation storage tank is respectively This is because of the lead-core rubber bearings in not the as obvio that of the seismic tank isolation tank, so the increase of the acceleration of the isolation storage tank is not as obvious as that of the seismic tank (a) (b) (c) (d) Figureof4.peak Comparison of peak in the theseismic X-direction of tank: the seismic Figure Comparison acceleration in theacceleration X-direction of storage (a) Taft storage wave tank: (a wave (XZ direction, 0.50 g); (b) Artificial wave (XYZ direction, 0.50 g); (c) Wolong wave (XYZ (XZ direction, 0.50 g); (b) Artificial wave (XYZ direction, 0.50 g); (c) Wolong wave (XYZ direction, tion, 0.75 g); (d) Taft wave (XZ direction, 0.75 g) 0.75 g); (d) Taft wave (XZ direction, 0.75 g) The above only compares the peak accelerations of the seismic and the isolation storage tanks In order to visualize how their acceleration changes, the acceleration time history curves of measuring point and measuring point 17 are selected for comparative analysis in the time domain and frequency domain Figures and are the acceleration time history curve and the corresponding spectrum curve under the action of the Taft wave (XYZ direction, 0.75 g) and the Wolong wave (XYZ direction, 0.75 g), respectively It can be seen from the comparison of acceleration time history curves that the acceleration response of the isolation storage tank is smaller than that of the seismic storage tank, which indicates that the lead-core rubber bearing has a good seismic isolation effect Comparing Figure 6a with Figures 6c and 7a,c, it is also found that the seismic isolation effect of lead-core rubber bearing is related to the seismic wave Under the action of the Wolong wave (XYZ direction, 0.75 g), the isolation efficiency of lead-core rubber bearing is 74.8% (X-direction) Appl Sci 2022, 12, 8390 of 20 (Y-direction), Appl Sci 2022, 12, xand FOR 68.0% PEER REVIEW respectively; under the action of the Taft wave (XYZ direction, of 0.75 g), the isolation efficiency of the lead-core rubber bearing is 33.2% (X-direction) and 48.5% (Y-direction), respectively (a) (b) (c) (d) 21 Figure of Comparison of peak acceleration in the X direction of the isolation (a) Taft Figure Comparison peak acceleration in the X direction of the isolation storagestorage tank: tank: (a) Taft wave (XZ direction, 0.50 g); (b) Artificial wave (XYZ direction, 0.50 g); (c) Wolong wave (XYZ direcwave (XZ direction, 0.50 g); (b) Artificial wave (XYZ direction, 0.50 g); (c) Wolong wave (XYZ tion, 0.75 g); (d) Taft wave (XZ direction, 0.75 g) direction, 0.75 g); (d) Taft wave (XZ direction, 0.75 g) The above only compares the peak accelerations of the seismic and the isolation storage tanks In order to visualize how their acceleration changes, the acceleration time history curves of measuring point and measuring point 17 are selected for comparative analysis in the time domain and frequency domain Figures and are the acceleration time history curve and the corresponding spectrum curve under the action of the Taft wave (XYZ direction, 0.75 g) and the Wolong wave (XYZ direction, 0.75 g), respectively It can be seen from the comparison of acceleration time history curves that the acceleration response of the isolation storage tank is smaller than that of the seismic storage tank, which indicates that the lead-core rubber bearing has a good seismic isolation effect Comparing Figure 6a with Figures 6c and 7a,c, it is also found that the seismic isolation effect of lead-core rubber bearing is related to the seismic wave Under the action of the Wolong wave (XYZ direction, 0.75 g), the isolation efficiency of lead-core rubber bearing is 74.8% (X-direction) and 68.0% (Y-direction), respectively; under the action of the Taft wave (XYZ direction, 0.75 g), the isolation efficiency of the lead-core rubber bearing is 33.2% (X-direction) and 48.5% (Y-direction), respectively Appl Sci 2022, 12, x FOR PEER REVIEW Appl Sci 2022, 12, 8390 10 of 21 10 of 20 (a) (b) (c) (d) Figure Appl Sci 2022, 12, x FOR PEER REVIEW 11 of 21 Figure 6 Taft Taft wave wave (XYZ (XYZ direction, direction, 0.75 0.75 g): g): (a) (a) acceleration acceleration time time history history curves curves in in the the X-direction; X-direction; (b) characteristic curve (b) spectrum spectrum characteristic curve in in the the X-direction; X-direction; (c) (c) acceleration acceleration time time history historycurves curvesin inthe theYYdirection; (d) spectrum characteristic curve in the Y-direction direction; (d) spectrum characteristic curve in the Y-direction Comparing spectral characteristics of the acceleration response, it can be seen that the spectral curve of the seismic storage tank has two obvious peaks, while the spectral characteristic curve of the isolation storage tank has only one peak Under the action of the Taft wave (XYZ direction, 0.75 g), the two peaks of the seismic storage tank are located around 13 Hz and 32 Hz, respectively, and the peak value of the isolation tank is located around Hz Under the action of the Wolong wave (XYZ direction, 0.75 g), the two peaks of the seismic storage tank are located around 10 Hz and 35 Hz, respectively, and the peak value of the isolation tank is located around Hz This shows that the lead-core rubber bearing can significantly suppress the high-frequency components in seismic waves (a) (b) (c) (d) Figure wave (XYZ (XYZ direction, direction,0.75 0.75g): g):(a) (a)acceleration accelerationtime time history curves X-direcFigure 7 Wolong Wolong wave history curves in in thethe X-direction; tion; (b) spectrum characteristic curve in the X-direction; (c) acceleration time history curves in the (b) spectrum characteristic curve in the X-direction; (c) acceleration time history curves in the YY-direction; (d) spectrum characteristic curve in the Y-direction direction; (d) spectrum characteristic curve in the Y-direction 3.3 Numerical Simulation Experimental Tank Model Comparing spectralofcharacteristics of the acceleration response, it can be seen that ANSYS curve software wasseismic used tostorage simulate thehas experimental storage tank model, the the spectral of the tank two obvious peaks, while the and spectral differences between the numerical results and the experimental results are compared to verify the validity and reliability of the finite element model, paving the way for further study on seismic performance of large LNG storage tanks The bilinear kinematic hardening model was used for the concrete outer tank, dome and pile foundation The material parameters of the numerical model are based on those of the test tank, and the parameters Appl Sci 2022, 12, 8390 11 of 20 characteristic curve of the isolation storage tank has only one peak Under the action of the Taft wave (XYZ direction, 0.75 g), the two peaks of the seismic storage tank are located around 13 Hz and 32 Hz, respectively, and the peak value of the isolation tank is located around Hz Under the action of the Wolong wave (XYZ direction, 0.75 g), the two peaks of the seismic storage tank are located around 10 Hz and 35 Hz, respectively, and the peak value of the isolation tank is located around Hz This shows that the lead-core rubber bearing can significantly suppress the high-frequency components in seismic waves 3.3 Numerical Simulation of Experimental Tank Model ANSYS software was used to simulate the experimental storage tank model, and the differences between the numerical results and the experimental results are compared to verify the validity and reliability of the finite element model, paving the way for further study on seismic performance of large LNG storage tanks The bilinear kinematic hardening model was used for the concrete outer tank, dome and pile foundation The material parameters of the numerical model are based on those of the test tank, and the parameters of the lead-core rubber bearing are shown in Table The storage tank is simulated by the SOLID186 element The pile foundation is simulated by the BEAM188 element The contact element is used for connection between the pile foundation and the storage tank Zhang et al [12,28–30] have conducted in-depth research on the numerical simulation of LNG storage tanks Their article gives detailed information about the meshing method and mesh element selection The results show that by dividing two elements along the thickness direction and ensuring that the element shape is a cube as much as possible, the simulated results can have high computational accuracy Therefore, the finite element model of the LNG storage tank in this paper was divided into elements in the thickness direction, 64 elements in the hoop direction, and 21 elements in the height direction; the mapped meshing method was used for the mesh division The selected element is SOLID186 element, which is a high-order element with 20 nodes and three degrees of freedom, with a total of 10,169 elements In the element library of ANSYS, there is no element that can directly simulate the mechanical properties of lead-core rubber isolation bearings Therefore, it is necessary to simplify the mechanical properties of the isolation bearing and conduct a reasonable simulation according to mechanical behavior of the isolation bearing The lead-core rubber bearing has good hysteresis performance and can be simulated by a bilinear model The mechanical properties of the lead-core rubber bearing in the horizontal and vertical directions are very different The lead-core rubber bearing will yield in the horizontal direction, but will not yield in the vertical direction According to this characteristic, nonlinear spring (Combin40) and linear spring (Combin14) are used to simulate the horizontal and vertical performances of the lead-core rubber bearing, respectively The basic parameters of lead rubber bearings are: stiffness before yield K1, stiffness after yield K2, yield load Q, and damping ratio The main real constants of COMBIN40 element are: Ku (stiffness before yielding), C (damping coefficient), M (mass), GAP (gap size), FSLID (shear force at yield), and Kd (stiffness after yielding) COMBIN40 is a two-stage spring When the limit force (FSLID) is reached, K1 does not work, and the stiffness becomes K2 If there is no K2, it is equivalent to the spring being pulled off, so the COMBIN40 can simulate the bilinear model A lead-core rubber bearing consists of three spring elements, COMBIN40 (X-direction), COMBIN40 (Y-direction) and COMBIN40 (Z-direction), where the COMBIN40 element in the X- and Y-directions should consider the bilinear model When establishing three spring elements, the thickness of the lead-core rubber support can be ignored, and the node positions of the elements can be coincident Then, the direction of spring element can be specified by changing the key option of the spring element When the element is established, the nodes of spring element are coupled with the SOLID186 element simulating the bearing platform The other end nodes of the horizontal spring in X- and Y-directions constrain all the degrees of freedom, and the other end nodes of the Z-direction spring Appl Sci 2022, 12, 8390 the node positions of the elements can be coincident Then, the direction of spring eleme can be specified by changing the key option of the spring element When the element established, the nodes of spring element are coupled with the SOLID186 element simula ing the bearing platform The other end nodes of the horizontal spring in X- and Y-dire 12 of 20 tions constrain all the degrees of freedom, and the other end nodes of the Z-directio spring element couple the degrees of freedom with the upper node of the BEAM188 el ment that simulates pile foundation The established numerical model of the test storag element couple the degrees of freedom with the upper node of the BEAM188 element that tank issimulates shown in The established numerical model of the test storage tank is pileFigure foundation shown in Figure ELEMENTS Seismic Storage Tank ELEMENTS Seismic Storage Tank Figure Finite element model of the LNG storage tank Figure Finite element model of the LNG storage tank In order to make the seismic waves input by the numerical model consistent with the seismic waves input by the test, the acceleration time history record of the shaking Intable order to make the seismic waves input by the numerical model consistent with th is used as the seismic excitation of the numerical model Considering that there are seismic waves input byconditions, the test, some the acceleration time history record for of numerical the shaking tab many experimental experimental conditions are selected is used as the seismic excitation of the numerical model.calculation Considering that simulation to compare experimental results and numerical results Thisthere paperare man takes the El Centro wave as an example experimental conditions, some experimental conditions are selected for numerical sim We selected the measuring points located on the side wall of the outer tank to compare lation to compare experimental results and numerical calculation results This paper tak the results, namely measuring points 2~5 and measuring points 10~13 Figure shows the the Elcomparison Centro wave as an example of acceleration time history curve and spectral characteristics of the seismic We selected the measuring points located on the wall of the outer tank storage tank and the corresponding numerical model, andside the following conclusions can to com be drawn: pare the results, namely measuring points 2~5 and measuring points 10~13 Figure theof acceleration timetime history curve,curve it can be seen that thecharacteristics acceleration shows(1)the Comparing comparison acceleration history and spectral of th responses of them are very close As the height of the measuring point increases, the seismic storage tank and the corresponding numerical model, and the following concl amplitude difference among the results of them increases, but the changing trend of sions can be drawn: the acceleration response is consistent This shows that the calculation results of the numerical model can reflect time the acceleration responseitofcan the be seismic tank.acceleratio (1) Comparing the acceleration history curve, seenstorage that the (2) Comparing the spectral characteristic curves, it canofbethe seen that the spectral responses of them are very close As the height measuring pointcharacincreases, th teristic curves of the two are not much different, especially in the range of 0~30 Hz; amplitude difference among the results of them increases, but the changing trend indeed, the results of the two are almost the same The spectral characteristic curves of the seismic storage tank and the numerical model have two obvious peaks, and the peak points are located around Hz and 32 Hz, respectively The first peak corresponds exactly to the predominant frequency of the El Centro wave Furthermore, as the height of measuring point increases, the second peak becomes more pronounced From the comparison in the frequency domain, the calculation results of the numerical model can also reflect the spectral characteristics of the acceleration response of the seismic storage tank Figure 10 shows the comparison of acceleration time history and spectral characteristics of the isolation storage tank and the numerical model It is similar to the results of the seismic tank; however, there are some differences, mainly in the spectral characteristics There are still two obvious peaks in the acceleration spectrum characteristic curve of the seismically isolated storage tank Compared with the seismic storage tank, the amplitude of the second peak of the isolation storage tank is significantly reduced This may be due to Appl Sci 2022, 12, x FOR PEER REVIEW 13 of 21 Appl Sci 2022, 12, 8390 13 of 20 the acceleration response is consistent This shows that the calculation results of the numerical model can reflect the acceleration response of the seismic storage tank the introduction mountscurves, to the tank, reduces thespectral high-frequency (2) Comparing of thelead-core spectral rubber characteristic it canwhich be seen that the characvibration of the tank teristic curves of the two are not much different, especially in the range of 0~30 Hz; Based on the numerical analysis the test it can be confirmed that indeed, the results of thesimulation two are almost the of same The tank, spectral characteristic curves the seismic response of the numerical simulation results is close to that of the test results, of the , the second peak becomes more pronounced From the comparison in the freand the fitting degree of their spectral characteristic curves is also very good, which verifies quency domain, the calculation results of the numerical model can also reflect the the rationality and effectiveness of the numerical model The numerical model of this paper spectral characteristics of the acceleration response of the seismic storage tank can be used for seismic response analysis of large LNG storage tanks (a) (b) (c) (d) Figure g): (a) measuring Figure 9 Comparison Comparison results results of of the the seismic seismic storage storage tank tank under under El El Centro Centro (X, (X, 0.5 0.5 g): (a) measuring point 2; (b) measuring point 3; (c) measuring point 4; (d) measuring point point 2; (b) measuring point 3; (c) measuring point 4; (d) measuring point Appl Sci 2022, 12, 8390 the seismic tank; however, there are some differences, mainly in the spectral characteristics There are still two obvious peaks in the acceleration spectrum characteristic curve of the seismically isolated storage tank Compared with the seismic storage tank, the amplitude of the second peak of the isolation storage tank is significantly reduced This may be due to the introduction of lead-core rubber mounts to the tank, which reduces the14highof 20 frequency vibration of the tank (a) (b) (c) (d) Figure 10 Comparison results of the isolation storage tank under El Centro (X, 0.5 g): (a) measuring point 11; (b) measuring point 11; (c) measuring point 12; (d) measuring point 13 Numerical Simulation Analysis of Large LNG Storage Tank 4.1 Introduction of Large LNG Storage Tank ANSYS software was used to establish a numerical model of a large 200,000 cubic LNG storage tank in this paper The inner diameter of the outer tank is 86.4 m, the height of the outer tank wall is 42.68 m, the thickness of the bottom and top of the outer tank wall is 1.1 m, and the thickness of the middle part is 0.8 m The thickness of the dome is 0.5 m, and the arc radius is 86.4 m The concrete cap has a diameter of 93 m and a thickness of 1.5 m Numerical Simulation Analysis of Large LNG Storage Tank 4.1 Introduction of Large LNG Storage Tank Appl Sci 2022, 12, 8390 ANSYS software was used to establish a numerical model of a large 200,000 cubic LNG storage tank in this paper The inner diameter of the outer tank is 86.4 m, the height of the outer tank wall is 42.68 m, the thickness of the bottom and top of the outer tank wall 15 of 20 is 1.1 m, and the thickness of the middle part is 0.8 m The thickness of the dome is 0.5 m, and the arc radius is 86.4 m The concrete cap has a diameter of 93 m and a thickness of 1.5 m (The thickness in the middle is reduced to 1.2 m) The diameter of the inner tank is (The thickness in the middle is reduced to 1.2 m) The diameter of the inner tank is 84.2 m, 84.2 m, its height is 40.23 m, and the maximum design liquid level is 38.92 m The inner its height is 40.23 m, and the maximum design liquid level is 38.92 m The inner and outer and outer tanks are filled with thermal insulation material perlite, with a thickness of 1.1 tanks are filled with thermal insulation material perlite, with a thickness of 1.1 m The m The electric heat tracing low-cap pile foundation is adopted, with a radius of 0.7 m and electric heat tracing low-cap pile foundation is adopted, with a radius of 0.7 m and a total a total of 428 piles Since the foundation of the storage tank is regarded as a rigid foundaof 428 piles Since the foundation of the storage tank is regarded as a rigid foundation in tion this paper, the pile length calculated the to ground to theofbottom ofThe the length cap thisinpaper, the pile length calculated is from is thefrom ground the bottom the cap The length of the outer pile foundation is m, and the length of the inner pile foundation of the outer pile foundation is m, and the length of the inner pile foundation is 2.3 m is The 2.3 cross-sectional m The cross-sectional schematic of LNG the large LNG storage tank and of the schematic diagram diagram of the large storage tank and the layout the layout of the pile foundation are shown in Figures 11 and 12 LRB1100 is used for the pile foundation are shown in Figures 11 and 12 LRB1100 is used for the isolation bearing, isolation bearing, its vertical stiffness is kN/mm,horizontal the equivalent horizontal stiffness its vertical stiffness is 6374 kN/mm, the6374 equivalent stiffness is 3507 kN/m, the is stiffness 3507 kN/m, the stiffness after yield is 1892 kN/m, and the yield force is 316.7 kN The after yield is 1892 kN/m, and the yield force is 316.7 kN The material properties material properties oftanks the LNG storageintanks of the LNG storage are shown Tableare shown in Table Appl Sci 2022, 12, x FOR PEER REVIEW 16 of 21 Figure The cross-sectional schematic diagram the large LNG storage tank (units: mm) Figure 11.11 The cross-sectional schematic diagram ofof the large LNG storage tank (units: mm) Figure12 12.The Thelayout layoutofofthe thepile pilefoundation foundation(units: (units:mm) mm) Figure Table Material parameters of LNG storage tank Material C40 (outer tank) Elastic Modulus 34.5 GPa Poisson’s Ratio 0.167 Density 2500 kg/m3 Appl Sci 2022, 12, 8390 16 of 20 Table Material parameters of LNG storage tank Material Elastic Modulus Poisson’s Ratio Density C40 (outer tank) C50 (pile foundation) Prestressed steel strand Ordinary reinforced 9% Ni steel Expanded perlite Foam glass brick 34.5 GPa 32.5 GPa 195 GPa 200 GPa 206 GPa 0.9 GPa 0.011 GPa 0.167 0.167 0.3 0.3 0.3 0.2 0.2 2500 kg/m3 2500 kg/m3 7800 kg/m3 7850 kg/m3 7850 kg/m3 120 kg/m3 65 kg/m3 4.2 Dynamic Response of LNG Storage Tank The four seismic waves selected in Section 2.2 were used to analyze the one direction seismic response of the large LNG storage tank The peak ground acceleration (PGA) of the seismic wave was adjusted to 2.2 m/s In order to compare the effect of isolation bearings on the seismic response of large LNG storage tanks, numerical models of LNG storage tanks with and without isolation bearings were established, respectively By comparing the seismic responses of the LNG storage tank, such as acceleration, displacement, base shear force and overturning bending moment, the effect of the isolation bearing was analyzed The overturning moment is the sum of the bending moment acting on the bottom of each pile foundation The isolation rate in Table is defined as Equation (4): λ= Rnon−iso − Riso Rnon−iso (4) where Rnon−iso is the seismic response peak value of the seismic storage tank, and Riso is the seismic response peak value of the isolation storage tank Table Peak seismic response of 200,000 cubic meters of the LNG storage tank El Centro Taft Wolong Artificial Base shear force (108 N) seismic isolation isolation rate 1.32 0.61 53.8% 2.05 0.77 62.4% 1.71 0.31 81.9% 1.73 0.55 68.2% Overturning bending moment (108 N·m) seismic isolation isolation rate 2.18 1.92 11.9% 3.37 2.46 27.0% 2.82 1.01 64.2% 2.84 1.68 40.8% Acceleration of the outer tank wall (m/s2 ) seismic isolation isolation rate 4.92 2.47 49.8% 5.34 2.36 55.8% 5.35 2.88 46.0% 4.04 2.55 36.9% Displacement of the outer tank wall (m) seismic isolation isolation rate 0.0054 0.0380 −604% 0.0065 0.0322 −395% 0.0059 0.0494 −737% 0.0057 0.0174 −205% Effective dynamic stress of outer tank wall (MPa) seismic isolation isolation rate 0.86 0.16 81.4% 1.01 0.14 86.1% 1.09 0.21 80.7% 0.85 0.09 89.4% We then analyzed the base shear and overturning bending moment of large LNG storage tanks It can be seen from Figures 13 and 14 and Table that after installing the isolation bearing, the base shear force and overturning bending moment of the LNG storage tank are significantly reduced Under the action of the Wolong wave, the seismic isolation bearing has the best effect, the seismic isolation rate of base shear force is 81.9%, and the seismic isolation rate of overturning bending moment is 64.2% Under the action of four kinds of seismic waves, the average damping rate of base shear force is 66%, and the overturning moment is 36.0% This shows that the ability of isolation bearing to reduce the Appl Sci 2022, 12, 8390 17 of 20 Appl Sci 2022, 12, x FOR PEER REVIEW base Appl Sci 2022, 12, x FOR PEER REVIEW 18 of 21 shear force is significantly better than the ability to reduce the overturning bending 18 of 21 moment (a) (a) (b) (b) (c) (c) (d) (d) Figure (d) Artificial wave Figure 13 13 Base Base shear shear force: force: (a) (a)El ElCentro Centrowave; wave;(b) (b)Wolong Wolong wave; wave; (c) (c) Taft Taft wave; wave; Figure 13 Base shear force: (a) El Centro wave; (b) Wolong wave; (c) Taft wave; (d) (d) Artificial Artificial wave wave (a) (a) (b) (b) (c) (c) (d) (d) Figure 14 Overturning bending moment: (a) El Centro wave; (b) Wolong wave; (c) Taft wave; (d) Figure Overturning El El Centro wave; (b) (b) Wolong wave; (c) Taft wave; (d) Figure 14 14 Overturningbending bendingmoment: moment:(a)(a) Centro wave; Wolong wave; (c) Taft wave; Artificial wave Artificial wave (d) Artificial wave We then analyzed the seismic response of the outer wall of an LNG storage tank The We the response ofof the outer wall oftank an storage tank The We then then analyzed analyzed theseismic seismic response the outer wall of LNG an storage tank displacement and acceleration diagrams of the seismic storage andLNG the seismic isoladisplacement and acceleration diagrams of the seismic storage tank and the seismic isolaThe displacement and acceleration diagrams of the seismic storage tank and the seismic tion storage tank are compared, as shown in Figures 15 and 16 It can be seen from the tion storage tank are compared, as shown inofFigures 15 and 16 It16 can be seen from the isolation tank are compared, as shown in Figures 15 and It increase can be seen figure thatstorage the displacement and acceleration the seismic storage tank withfrom the figure that the displacement and acceleration of the seismic storage tank increase with the the figure the displacement accelerationare of the seismic storage increase increase ofthat height, and its changeand characteristics mainly realized as tank “shear type” with The increase of height, and its change characteristics are mainly realized as “shear type” the increase of height, and its change characteristics are mainly realized as “shear type” displacement and acceleration of the isolation storage tank hardly change with theThe indisplacement and acceleration of the the isolation storage tank hardly change with theThis increase of height, and the whole shows characteristics of “rigid body translation” crease of height, and the whole shows the characteristics of “rigid body translation” This is because the displacement mainly occurs in the isolation layer after the introduction of is becauserubber the displacement mainly occurs in the isolation layer after thethe introduction of lead-core bearings After the seismic isolation measures are taken, acceleration lead-core rubber bearings After the seismic isolation measures are taken, the acceleration Appl Sci 2022, 12, 8390 18 of 20 The displacement and acceleration of the isolation storage tank hardly change with the 19 of 21 increase of height, and the whole shows the characteristics of “rigid body translation” This is because the displacement mainly occurs in the isolation layer after the introduction of lead-core rubber bearings After the seismic isolation measures are taken, the19acceleration Appl Sci 2022, 12, x FOR PEER REVIEW of 21 response is significantly reduced It can seen that under response of ofthe thestorage storagetank tank is significantly reduced It be can be from seen Table from 5Table that the action the Taft wave, seismic effect of acceleration is the best, under the of action of the Taftthe wave, the isolation seismic isolation effect of acceleration isreaching the best, 55.8% Under theUnder actionthe of four kinds of seismic the average isolation rate of accelreaching 55.8% of four kinds ofwaves, seismic the average response of the storage tankaction is significantly reduced It can be waves, seen from Table thatisolation under rate eration is 47.1% However, due to the relatively weak horizontal direction of the isolation of the acceleration isTaft 47.1% However, due to theeffect relatively weak horizontal of the action of the wave, the seismic isolation of acceleration is the best,direction reaching layer, theUnder displacement of storagewaves, tank isthe much larger than that ofaccelthe seismic isolation layer, the action displacement of the storage tank is much larger that of the 55.8% the of the fourisolation kinds of isolation seismic average isolation ratethan of storage tank Under the action four of seismic waves, the displacement erationstorage is 47.1% However, due the relatively horizontal direction of thedisplacement isolation of the seismic tank Under thetoof action ofkinds fourweak kinds of seismic waves, the of the displacement the isolation storage tank is much largertank than that of the seismic seismic isolation tank isof5.8 times that of of thethe seismic storage Therefore, thelayer, seismic isolation tank is 5.8 times that seismic storage tankon onaverage average Therefore, storage tank Under the action of fourbearing kinds ofofseismic waves,tank, the displacement of to thepay when selecting the isolation storage it isit necessary atselecting theseismic seismic isolation bearing ofthe the storage tank, is necessary to pay seismic tank is 5.8 times that of the seismic storage tankthe on damage average tention toisolation the ofofthe tank prevent of attention to thedisplacement displacement thestorage storage tanktoto prevent the damageTherefore, of the the auxiliary auxiliary when selecting the the seismic isolation bearing of the tank, ittank is necessary to pay atpipeline caused by excessive displacement ofstorage the storage Appl Sci 2022, 12, x FOR PEER REVIEW tention to the displacement of the storage tank to prevent the damage of the auxiliary pipeline caused by the excessive displacement of the storage tank (a)(a) (b) (b) Figure Acceleration cloud cloud diagram tank: (a) seismic storage tank; tank; (b) isolation storagestorage Figure 15.15.Acceleration diagramofofstorage storage tank: (a) seismic storage (b) isolation Figure tank 15 Acceleration cloud diagram of storage tank: (a) seismic storage tank; (b) isolation storage tank tank (a) (b) Figure 16 Displacement cloud diagram of storage tank: (a) seismic storage tank; (b) isolation storage tank Figure (a) 16 Displacement cloud diagram of storage tank: (a) seismic (b) storage tank; (b) isolation storage tank Conclusions Figure 16 Displacement cloud diagram of storage tank: (a) seismic storage tank; (b) isolation storage Conclusions tank In this paper, we carried out a shaking table test and numerical simulation study of a In this paper, we carried out a shaking table test and numerical simulation study of scaled model of aoflarge LNG storage modelsof ofthe theseismic seismic storage tank and a scaled model a large LNG storagetank tank.Firstly, Firstly, the the models storage tank Conclusions theand seismic isolation tank tank werewere designed, andand thethe sensors were arranged the seismic isolation designed, sensors were arrangedon onthe thestorage stor- tank this paper,Secondly, welead-core carried a shaking table and simulation study of model Secondly, the rubber bearing wastest designed according to thetoparameters ageIntank model theout lead-core rubber bearing was numerical designed according the a scaled model large LNG tank.seismic Firstly, the models of the seismic storage tank parameters of of thea storage tank.storage Then, four waves were selected as the external and the seismic isolation tank were designed, and the sensors were arranged on the storage tank model Secondly, the lead-core rubber bearing was designed according to the parameters of the storage tank Then, four seismic waves were selected as the external Appl Sci 2022, 12, 8390 19 of 20 of the storage tank Then, four seismic waves were selected as the external excitation for the shaking table test, and the shaking table test was carried out The numerical model was used to simulate the dynamic response of the seismic storage tank and the isolation storage tank to verify the validity of the numerical model On this basis, an actual LNG storage tank of 200,000 cubic meters was selected to study its seismic dynamic response and the effect of isolation bearings The following conclusions are drawn: (1) (2) (3) (4) By processing the data in the condition of white noise, the natural vibration frequency of the tank model is obtained After analysis, it can be seen that the natural vibration frequency of the storage tank model is significantly reduced after the isolation measures are taken The isolation bearing has the same effect on the natural vibration frequency of the tank in the X- and Y-directions By analyzing the acceleration response of the seismic storage tank and the seismic isolation tank, it can be seen that the acceleration of the seismic storage tank shows an approximately linear increasing trend along the height direction After the seismic isolation measures are taken, the acceleration response of the storage tank is significantly reduced With the increase of peak acceleration of seismic waves, the seismic response of the storage tank model also increases, and the increase of the seismic storage tank is more obvious In this paper, the numerical model was used to simulate the dynamic response of the seismic storage tank and the isolation storage tank By comparing test results and numerical simulation results, it can be seen that the calculation results of the numerical model can reflect the acceleration response of the storage tank model and its corresponding spectral characteristics This verifies the feasibility and rationality of the numerical model When studying the seismic dynamic response of large LNG storage tanks, the numerical model in this paper can be used for analysis Based on the numerical analysis results of a 200,000 cubic meter LNG storage tank, the average seismic isolation rates of base shear force and overturning bending moment are 66% and 36%, respectively, and the average seismic isolation rate of acceleration reaches 47.1% The addition of seismic isolation bearings in the seismic design of LNG storage tanks is beneficial to reduce the construction cost of the storage tanks However, the displacement of the storage tank will increase significantly after isolation Therefore, the displacement of the LNG storage tank needs to be strictly controlled after the seismic isolation measures are taken Author Contributions: Writing—original draft preparation, Z.C.; writing—review and editing, Z.X.; methodology, L.T and Z.Z.; software, Z.X., J.F and T.X.; data curation, T.X.; visualization, Z.Z and T.X All authors have read and agreed to the published version of the manuscript Funding: The authors appreciate the testing facility, as well as the technical assistance provided by the CLP Power Wind/Wave Tunnel Facility at the Hong Kong University of Science and Technology The work is funded by the Key Laboratory of Icing and Anti/De-icing of CARDC (Grant No IADL 20200304), the National Natural Science Foundation of China (Grant No.: 51908090), the Fundamental Research Funds for the Central Universities (Project No.: 2021CDJQY-001, 2022CDJXY-016), the Natural Science Foundation of Chongqing, China (cstc2020jcyj-msxmX0921), the Key Project of Technological Innovation and Application Development in Chongqing (Grant No.: cstc2019jscxgksbX0017) and the Key Project of Science and Technology Research Program of Chongqing Municipal Education Commission (KJCXZD2020010) Institutional Review Board Statement: Not applicable Informed Consent Statement: Not applicable Data Availability Statement: No data were reported in this study Acknowledgments: The authors would like to thank the anonymous reviewers for their valuable comments on the manuscript Conflicts of Interest: The authors declare no conflict of interest Appl Sci 2022, 12, 8390 20 of 20 References 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Bertalot, D.; Brennan, A.J.; Villalobos, F.A Influence of Bearing Pressure on Liquefaction-Induced Settlement of Shallow Foundations Géotechnique 2013, 63, 391–399 [CrossRef] Parker, J In-Service Behaviour of Creep Strength Enhanced Ferritic Steels Grade 91 and Grade 92—Part Weld Issues Int J Press Vessel Pip 2014, 114–115, 76–87 [CrossRef] Malhotra, P Practical Nonlinear Seismic Analysis of Tanks Earthq Spectra 2000, 16, 473–492 [CrossRef] Niwa, A.; Clough, R.W Buckling of Cylindrical Liquid-Storage Tanks under Earthquake Loading Earthq Engng Struct Dyn 1982, 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