SeismicAnalysisofaLargeLNGTankconsideringtheEffectof ... · 26/5/2020 · sinusoidal excitation....

Research ArticleSeismic Analysis of a Large LNG Tank considering the Effect ofLiquid Volume

Yi Zhao 12 Hong-Nan Li13 Xing Fu1 Shuocheng Zhang2 and Oya Mercan2

1State Laboratory of Coastal and Offshore Engineering Dalian University of Technology Dalian 116023 China2Department of Civil and Mineral Engineering University of Toronto Toronto ON Canada M5S 1A43School of Civil Engineering Shenyang Jianzhu University Shenyang 110168 China

Correspondence should be addressed to Yi Zhao yzmaildluteducn

Received 26 May 2020 Revised 21 August 2020 Accepted 27 August 2020 Published 16 September 2020

Academic Editor Masoud Mirtaheri

Copyright copy 2020 Yi Zhao et alampis is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Large Liquefied Natural Gas (LNG) tanks are prone to damage during strong earthquakes and accurate seismic analysis must beperformed during the design phase to prevent secondary disasters However the seismic analysis of large LNG tanks is associatedwith high computational requirements which cannot be satisfied by the calculation efficiency of traditional analytical techniquessuch as the Coupled EulerianndashLagrangian (CEL) method ampus this paper aims to employ a less computationally demandingalgorithm the Smoothed Particle Hydrodynamics-Finite Element Method (SPH-FEM) algorithm to simulate large LNG tanksampe seismic response of a 160000m3 LNG prestressed storage tank is evaluated with different liquid depths using the SPH-FEMalgorithm and simulation results are obtained with excellent efficiency and accuracy In addition large vonMises stress at the baseof the tank indicates that strong earthquakes can severely jeopardize the structural integrity of large LNG tanks amperefore theSPH-FEM algorithm provides a feasible approach for the analysis of large liquid tanks in seismic engineering applications

1 Introduction

Natural gas is a reliable source of energy that is used globallyto meet growing energy demands With the increasingconsumption of natural gas over the past few years LiquefiedNatural Gas (LNG) tanks have become a major componentof urban infrastructure As a result the scale of tank con-struction has also increased but this change has been as-sociated with various safety risks LNG storage tanks havehigh seismic risks compared to traditional buildings becausethey can lead to secondary disasters such as explosions andenvironmental pollution that result in significant propertydamage or loss of life In addition LNG tanks are morevulnerable to earthquakes owing to their low redundancylow ductility and low energy-dissipating capacity comparedto conventional structures [1] For example the destructionof an LNG tank during the 1964 Japan earthquake causedfires and explosions that resulted in serious societal lossesand pollution Another example was the 1976 Tangshanearthquake in which the bottom ring of a storage tank

buckled and led to liquid leakage [2] ampus it is of para-mount importance to investigate the seismic performance ofLNG tanks to ensure their structural safety

To analyze the dynamic performance of large LNG tanksit is essential to understand fluidndashstructure interaction (FSI)and dynamic performance of the structure Different fromconventional structures seismic analysis of liquid storagetanks must account for fluidndashstructure interaction as a resultof inertial earthquake loading and hydrodynamic pressureampe seismic design of storage tanks was initially establishedon the rigid wall model proposed by Housner [3] in 1957and many subsequent models have improved on this theoryHowever many tanks designed according to this model havesuffered damage during earthquakes [2] ConsequentlyVeletsos and Yang [4 5] proposed a single-degree-of-free-dommodel for a flexible tank wall that assumed that the tankvibrated under a given bending mode In 1981 Haroun andHousner [6] developed a more realistic model that con-sidered the dynamic interaction of liquid and the tank wallampis method is known as the coupled vibration effect model

HindawiShock and VibrationVolume 2020 Article ID 8889055 18 pageshttpsdoiorg10115520208889055

and it divides the liquid into three components a convectioncomponent a flexible impulsive component and a rigidimpulsive component In addition Hu et al [7] presented amethod for mass addition using user subroutines to studythe seismic response of a large cylindrical thin-walledstorage tank based on the theories of Housner and VeletsosLiquid mass was added to the solid wall without consideringliquid sloshing Hariri-Ardebili et al [8] compared theendurance time analysis (ETA) method to the time-historyanalysis (THA) and incremental dynamic analysis (IDA)method to investigate the seismic performance of a high-risetelecommunication tower Hadj-Djelloul and Djermane [9]used the three-dimensional finite element technique to studythe seismic response of perfect and imperfect elevated watertanks ampey also investigated the effect of geometric im-perfection on the dynamic performance of elevated watertanks

Based on applicable theories regarding fluidndashstructureinteraction since the 1950s there have been several studieson the dynamic analysis of LNG storage tanks Hwang [10]investigated the dynamic response of an LNG tank using acombination of Boundary Element Method (BEM) andFinite Element Method (FEM) programs Wu [11] per-formed time-history analysis of LNG storage tanks withFEM software and found that deformation of the inner tankwas effectively prevented by adding a prestressed concretewall and an insulating layer Christovasilis and Whittaker[12] investigated the seismic response of a conventional andisolated vertical cylindrical LNG tank by applying finiteelement analysis to mechanical models ampe results obtainedfrom two numerical models were in good agreement anddemonstrated that a mechanical model could be used withconfidence for the preliminary analysis and design ofconventional and isolated LNG tanks Sun et al [13] derivedand calculated the dynamic response of base-isolated LNGstorage tanks considering soilndashstructure interaction theeffect of which was proven to be insignificant Chen et al[14] investigated the dynamic response of a typical160000m3 LNG prestressed concrete outer tank underimpact loading and types of impact damage were deter-mined based on dynamic response results including stressdisplacement energy and critical impact velocity Li et al[15] conducted numerical dynamic analysis of LNG storagetanks and concluded that filling the space between the outerand inner tank could improve seismic performance withlittle effect on the sloshing height Du [16] adopted theCoupled EulerianndashLagrangian (CEL) analysis technique inABAQUS to simulate fluidndashstructure interaction [17] inLNG tanks but the CELmethod exhibited liquid leakage andlow simulation efficiency

ampe aforementioned numerical simulation methods arevery computationally intensive due to the sheer size of largeLNG tanks Given the recent rise in large LNG tank con-struction it is essential to employ a fast analysis method thatcan simulate the seismic response of LNG tanks in practicalengineering applications ampus an efficient smoothed par-ticle hydrodynamics-finite element method (SPH-FEM)algorithm [18] which has not been previously appliedto large land-based LNG tanks is proposed in this paper

SPH-FEM methods retain the advantages of FEM in sim-ulating FSI problems while adopting the advantages of SPHin modeling fluid behaviour

SPH is suitable for modeling fluid behaviour because it isa mesh-free method that discretizes a liquid field intoparticles [19] A kernel function is used to approximatedifferential equations and the function value at any point isthen expressed by neighboring nodes based on a local ap-proximation ampe SPH algorithm can overcome the weak-ness in mesh-based methods regarding fluid simulation byeffectively addressing free surfaces and moving interfaces inaddition to large deformation of materials As a result afterits development by Lucy [20] and Gingold [21] in 1977 theSPH method has been successfully adopted for studies incontinuous solid mechanics and fluid mechanics to solveproblems related to structural failure large deformation andliquid sloshing [22] Huang et al [23] verified the feasibilityof liquid sloshing analysis using the SPH method byobtaining results that corresponded to theoretical analysisLiu et al [24] performed a three-dimensional numericalsimulation of free surface liquid sloshing in a prismatic tanksubjected to a sinusoidal excitation using the SPH algorithmand the numerical results exhibited good agreement withexperimental data Shao et al [25] also presented an im-proved SPH algorithm to model liquid sloshing dynamicsand the numerical results agreed well with the experimentalobservations ampe SPH algorithm has also been widely ap-plied to simulate embankment flow [26] wave breaking [27]and explosions [28] amperefore the SPH algorithm is aversatile analysis method that can be applied to a variety ofstructural problems including the fluid component of largeLNG tanks

Coupled with a FEM method for the solid componentan SPH-FEM algorithm greatly improves the calculationaccuracy and efficiency for fluidndashstructure impact problemsampe coupled SPH-FEM method was first proposed by Att-away et al [29] using a masterndashslave algorithm to accountfor the contact between FE elements and SPH particlesKalateh and Koosheh [30] used the SPH-FEM method tosimulate the interaction between a convergent-divergentnozzle and cavitating flow and the results showed that thebehaviour of liquid and vapor at the interface matched othernumerical and experimental methods Liang and Chen [31]applied the SPH-FEM method to soilndashstructure interactionproblems during the seismic analysis of a rectangular un-derground structure and results indicated that the distri-bution and magnitude of seismic earth pressure wereinfluenced by the magnitude of soil deformation Fragassaet al [32] analyzed the effect of air in FSI problems bycoupling FEM and SPH ampey concluded that air had littleeffect on stress prediction but it had a greater effect on thebehaviour of the structure after the initial fluid impact Inthis study the SPH-FEM algorithm provides an accurate andefficient method for the analysis of a large LNG tank underdynamic earthquake loading

Section 2 of this paper presents an overview of the SPH-FEM methodology Section 3 verifies the SPH-FEM algorithmby comparing it to the traditional Coupled EulerianndashLagrangian(CEL) method on the analysis of a cubic water tank under

2 Shock and Vibration

sinusoidal excitation Subsequently Section 4 analyzes thedynamic response of a 160000m3 LNG storage tank underthree earthquakes with the same site conditions Section 5concludes the study and reiterates the advantages of the SPH-FEM algorithm as an innovative accurate and efficient methodto simulate large LNG tanks

2 Methodology

21 SPH 0eory ampe formulation of the SPH method isoften divided into two parts the integral representation ofthe field function and the particle approximation [33] ampeintegral representation of the function f(x) in the SPHalgorithm begins with the following identity [18]

f(x) 1113946Ω

f xprime( 1113857δ x minus xprime( 1113857dxprime (1)

where f(x) is a function of the three-dimensional positionvector x and the Dirac delta function is given by the fol-lowing equation

δ x minus xprime( 1113857 1 x xprime( 1113857

0 xnexprime( 1113857

⎧⎨

⎩ (2)

If a smoothing function W(x minus xprime h) replaces the Deltafunction kernel δ(x minus xprime) the integral representation off(x) can be written as follows

f(x) asymp 1113946Ω

f xprime( 1113857W x minus xprime h( 1113857dxprime (3)

where W is the smoothing kernel function and h is thesmoothing length that defines the area of influence of thesmoothing kernel function W ampe smoothing kernelfunction W should satisfy the following conditions (seeequations (4)ndash(6))

(1) ampe normalization condition states that

1113946Ω

W x minus xprime h( 1113857dxprime 1 (4)

(2) ampe Delta function property is observed when thesmoothing length approaches zero

limh⟶0

W x minus xprime h( 1113857 δ x minus xprime( 1113857 (5)

(3) ampe compact condition implies that

W x minus xprime h( 1113857 0 when x minus xprime1113868111386811138681113868

1113868111386811138681113868gt κh (6)

where κ which is a constant related to the smoothingfunction of the point at x defines the effective (nonzero)area of the smoothing function

ampe basic governing fluid dynamics equations are basedon three fundamental laws of conservation conservation ofmass momentum and energy ampe governing equations fordynamic fluid flows can be written as a set of partial dif-ferential equations using the Lagrangianmethod this systemof partial differential equations is the famous NavierndashStokes

equations the governing equations of which are given asfollows (see equations (7)ndash(9))

(1) ampe continuity equation

dρdt

minusρzv

β

zxβ (7)

(2) ampe momentum equation

dvα

dt1ρ

zσαβ

zxβ (8)

(3) ampe energy equation

de

dtσαβ

ρzv

α

zxβ (9)

A continuous density particle approximation method isemployed to approximate the density ampis approximationmethod is obtained by applying the SPH approximationconcept to transform the continuity equation Differentforms of density approximation equations can be obtainedby applying different conversions and operations to (7) Onesuch approach is to apply the SPH approximation to thevelocity divergence then the particle density in (7) can beevaluated in the following form of a gradient

Dρi

Dt ρi 1113944

N

j1

mj

ρj

]βij middotzWij

zxβi

(10)

ampe particle approximation method for the momentumequation is similar to the abovementioned continuousdensity method and some transformations are requiredampemomentum equation approximation can be derived indifferential form based on different transformationsEquation (11) can be obtained using the SPH particle ap-proximation method to transform the gradient term of themomentum equation (equation (8))

D]αiDt

1113944N

j1mj

σαβi + σαβj

ρiρj

zWij

zxβi

(11)

ampere are several approximation expressions of the workperformed by pressure thus the internal energy calculationfor the work performed by pressure has many alternativeforms ampe following form (12) is the most commonly used

Dei

Dt12

1113944

N

j1mj

pi

ρ2i+

pj

ρ2j⎛⎝ ⎞⎠]βij

zWij

zxβi

+μi

2ρi

εαβi εαβj (12)

Time stepping in ABAQUS is explicit and is limited bythe Courant Condition as shown below (equation (13))

Δt mina

05l

cs + 2ξμalρa( 1113857( 11138571113896 1113897 (13)

where cs is the local speed of soundampe time step used in allsimulations is 10times10minus6 s and the convergence of thesimulation is guaranteed [34]

Shock and Vibration 3

22 Coupled SPH-FEM ampe main concept in SPH-FEMcoupling is centered around the relationship between thetwo algorithms In each time step the velocity and dis-placement of FEM nodes are transferred to particles Si-multaneously the coordinate and velocity of particles aretransferred to FEM nodes While particles supply boundaryconditions for FEM FEM maintains the continuity of theparticles by preventing the boundary effect [35] In this studyregarding fluidndashstructure interaction velocity and dis-placement fields on the solidndashfluid interface are exchangedin order to couple the interaction forces between SPH andFEM A schematic computation flowchart of the SPH-FEMcoupling method is displayed in Figure 1

3 Example Verification

Compared to the SPH-FEM method the coupled Euler-ianndashLagrangian (CEL)method developed byDu [16] is anotheranalysis technique that is suitable for most fluidndashstructureinteraction problems Qiu et al [36] applied the CELmethod tolarge deformation problems in geotechnical engineering suchas pile sinking and ship grounding to demonstrate its reli-ability Meng et al [37] used the CEL method to simulate theinfluence of pile-sinking construction on the soil around thepile under undrained conditions In this section a simpleexample is provided to compare the accuracy and efficiencybetween the SPH-FEM and the CEL method using ABAQUSsoftware [34]

31Descriptionof theProblem A cubic water tank is taken asa model and is designed according to the following geo-metric specifications the side length is 1m the wallthickness is 10mm and the liquid height is 08m ampe tankmodel is composed of concrete with the following materialproperties density ρ 2500 kgm3 Youngrsquos modulusE 325times109Nm2 and Poissonrsquos ratio U 03 ampe be-havior of a material experiencing liquid sloshing is extremelycomplex and an equation of state is used to describe thepressure volume and energy of thematerialampeNewtonianfluid constitutive material formulation is used for water inthis section and theMiendashGruneisen equation of state whichdescribes the volumetric strength and density of a materialis defined in Table 1 ampe isotropic pressure in theMiendashGruneisen equation of state is defined as follows

p(ρ e) 1 minus12Γ0η1113874 1113875PH + Γ0ρ0Em

pH ρ0c

2η(1 minus sη)

2

η ρρ0

minus 1

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(14)

where H is the Hugoniot curve Em is the internal energy perunit mass η is the volumetric compressibility and c is thesonic speed of the material ampe coefficients s and c can be

described by the linear relationship between shock velocityand particle velocity

Us c + sUp (15)

where Us is shock wave velocity and UP is particle velocityampis equation of state describes the fluid motion

ampe equation of state of Us minus Up provides a model forthe hydrodynamic material and the properties of water arelisted in Table 1

ampe water-filled models constructed based on the twoalgorithms are shown in Figures 2 and 3 ampe models bothuse 1600 C3D8R-type concrete elements and the SPH-FEMalgorithm model uses 22000 PC3D-type liquid elements Inthe SPH-FEM algorithm the ratio of liquid element size tothe side length of the container is 5270 ampe SPH methodalso uses a cubic spline as the interpolation polynomialSmoothing length is an important parameter and has sig-nificant influence on the accuracy of the prediction [38 39]By default ABAQUS calculates a smoothing length at thestart of the analysis so that an element is associated withapproximate 30 to 50 particles on average Since thesmoothing length remains constant throughout the analysisdepending on whether the behavior in the model is ex-pansive or compressive the average number of particles perelement can either decrease or increase [34] In the CELmodel a total of 80000 EC3D8R-type liquid elements areused including 20000 elements in the initial position ampeEulerian elements in the CEL method must be finely meshedover the entire tank trajectory and allow liquid to movefreely in the grid because the quantity and quality of themesh affects simulation accuracy Gravity is applied to theentire model (g 98ms2) and the tank is subjected to ahorizontal excitation given by v(t) sin(wt)

Setup structure fluid domain and boundary

Update velocity displacementand energy of the particle

Update velocity displacementand stress of the particle

Finite elementSPH particle

SPH boundaryparticle

Element interfacenode

Output results

Displacement

Velocity

Boundarycondition

Figure 1 Computation flowchart of the SPH-FEM couplingmethod


32 Comparison of Results between the SPH-FEM and CELMethod ampe results of the two algorithms during one pe-riod are compared based on three factors sloshing wavepattern stress distribution on container wall and compu-tational efficiency Both methods can accurately reflect thesloshing wave pattern (as shown in Figure 4) but the CELmethod exhibits liquid leakage especially at the bottom ofthe water tank ampe CEL method is also not applicable whenthe liquid volume fraction in the Eulerian element is lessthan 05 because some elements are no longer containedwithin the container wall [34]

Using the two algorithms the von Mises stress distri-bution on the container wall at 08 s and 16 s in one period isshown in Figure 5 ampe maximum von Mises stress and thevon Mises stress distribution on the walls calculated usingthe two methods are in good agreement ampus the liquidelement size in the SPH-FEMmethod can be scaled up basedon an optimal ratio of 5 270 and applied to a large LNG tankwhile maintaining calculation accuracy

As shown in Table 2 the simulation time for the CELmethod is twice that of the SPH-FEM method indicatingthat the SPH-FEM algorithm is muchmore efficient than theCEL method In summary both methods can accuratelysimulate stress on tank walls and the liquid sloshing pattern

but the CEL method exhibits liquid leakage Fluid leakage isa common problem in CEL method and has not been solvedso far amperefore the SPH-FEM method has a significantadvantage over CEL in the analysis of large liquid storagetanks

4 Seismic Analysis of a 160000m3 LNG Tank

41 Project Overview ampis study employed a 160000m3

LNG prestressed storage tank which was adapted from anLNG technical manual as shown in Figure 6 [40] ampe innerdiameter of the outer tank is 82m the wall height is 3855mthe wall thickness is 08m and the dome thickness is 04mampe tank also has components to secure the moisture-prooflinings and roof-bearing rings

ampe inner tank has a total of 10 layers as shown inFigure 6 each of which has a height of 355m For exampleLayer R1249 refers to the first layer from the bottom with athickness of 249mm ampese layers gradually thicken fromthe top to the bottom as given in Table 3

ampe LNG storage tank consists of four parts LNG aninner tank an insulation layer and an outer tank ampe innertank is composed of 9 Ni steel ampe tank exhibits excellentlow-temperature resistance [41 42] ampe tank is also char-acterized by good weldability and low susceptibility to coldcracks ampe insulation layer is composed of expanded perliteand resilient felt ampe expanded perlite clings to the innerwall of the outer tank and the outer wall of the inner tank isfitted with resilient felt which prevents the perlite fromsettling and provides elastic properties for the perlite ampiselasticity is necessary because the tank shrinks due totemperature changes ampe prestressed concrete externaltanks are constructed to increase the overall safety of thetank in the event of accidental LNG leakage Adapting to theadvice of Huang [43] the material of the outer tank is60MPa high-strength concrete ampe material characteristicsof the tank and LNG are listed in Tables 4 and 5 respectively

42 Finite Element Model ABAQUS software [44 45] isused to establish the finite element model (FEM) as shown inFigure 7 ampe tank model is relatively large and the asso-ciated interactions are extremely complex Rebar rods areembedded within the tank wall using the ldquoEmbeddedrdquooption in ABAQUS which allows the rebar elements to workin conjunction with each other ampe outer tank and theinsulation layer are composed of C3D8Rmesh elements andthe inner tank is composed of S4R shell elements Shellelements are selected because the thickness of the inner tankis much smaller than its radius of curvature ampe LNG isdiscretized into particles using the aforementioned Us minus Up

Table 1 Material properties of water

Material Density (kgm3) Sonic speed (ms) Dynamic viscosity (kg(mmiddots))

Coefficients ofthe equation of

states Γ0

Water 1000 1480 0001 0 0

Figure 2 Model for the SPH-FEM algorithm

Figure 3 Model for the CEL method


(a) (b)

(c) (d)

Figure 4 Comparison of the sloshing pattern between the two algorithms (a) At 08 s with the SPH-FEM algorithm (b) at 08 s with theCEL method (c) at 16 s with the SPH-FEM algorithm and (d) at 16 s with the CEL method

+1297e + 05+1193e + 05+1090e + 05+9869e + 04+8837e + 04+7804e + 04+6772e + 04+5739e + 04+4707e + 04+3674e + 04+2642e + 04+1609e + 04+5768e + 03

S Mises(Avg 75)

(a)

+1312e + 05+1210e + 05+1108e + 05+1006e + 05+9039e + 04+8018e + 04+6997e + 04+5975e + 04+4954e + 04+3933e + 04+2911e + 04+1890e + 04+8686e + 03

S Mises(Avg 75)

(b)

Figure 5 Continued


equation in Section 3 ampe element size is chosen based onthe small tank in Section 3 for which the sloshing frequencycan be accurately calculated ampe ratio of liquid element sizeto container size in the large LNG tank is identical to theparameters of the small tank in Section 3

19T15S steel cables with a tensile strength of 1860MPaare embedded in the protective cover of the tank A total of122 steel cables are vertically anchored at the bottom and topof the concrete wall and 220 circumferential steel cables areanchored in separate half-circles on four vertical supportingcolumns arranged at 90deg [40]

ampe basic principles of applying prestress in ABAQUS[44] include various approaches such as the model pre-dictive control (MPC) method falling temperature methodinitial stress method and single rebar element method ampisstudy adopts the commonly utilized falling temperature

+1121e + 05+1032e + 05+9436e + 04+8547e + 04+7659e + 04+6770e + 04+5882e + 04+4993e + 04+4105e + 04+3216e + 04+2328e + 04+1439e + 04+5509e + 03

S Mises(Avg 75)

(c)

+1139e + 05+1050e + 05+9610e + 04+8772e + 04+7833e + 04+6944e + 04+6056e + 04+5167e + 04+4279e + 04+3390e + 04+2501e + 04+1613e + 04+7242e + 03

S Mises(Avg 75)

(d)

Figure 5 Comparison of the vonMises stress on the walls between the two algorithms (a) At 08 s with the SPH-FEM algorithm (b) at 08 swith the CEL method (c) at 16 s with the SPH-FEM algorithm and (d) at 16 s with the CEL method

Table 2 Comparison of the computational efficiencies of the two algorithms

Analysis time (s) Algorithm Simulation time Stable time step (s)

10 SPH-FEM 4h 52min 13 s 00165CEL 8 h 58min 14 s 00274

Prestressed concrete outer tank diameter 83600

400

800

354

30

Prestressed concrete tank radius 41000

Inner tank radius 40000

Maximum design level 347606

86600

1200

113

7538

550

Insulating layer

R1012

R912

R812

R712

R6122

R5147

R4173

R3198

R2224

R1249

Figure 6 LNG storage tank cross section (unit mm)

Table 3 ampickness of each layer in the inner tank

Layer 1 2 3 4 5 6 7 8 9 10ampickness(mm) 249 224 198 173 147 122 12 12 12 12


method that applies prestress by decreasing temperatureampe initial temperature is obtained with the followingformula

ΔT N

λ times E times A (16)

where N is the tension control force of the prestressed rebarwhich should not exceed 75 of the standard value of thestrength λ denotes the thermal expansion coefficient ofprestressed rebar E represents the elastic modulus of pre-stressed rebar and A is the cross-sectional area of pre-stressed rebar

ampe bottom boundary of the model is fixed and theinteraction between soil and structure is not considered ampestatic condition of the LNG tank is primarily calculatedbased on self-weight to ensure that the LNG liquid reachessteady state Natural frequencies are important parametersin the design of LNG prestressed storage tanks ampere arethree primary ways to extract eigenvalues in ABAQUS theAMS eigensolver the subspace iteration method and theblock Lanczos algorithm Here the first five frequencies ofthe empty tank are calculated with the Lanczos algorithm as3753Hz 4902Hz 5088Hz 5097Hz and 5204Hz

43 Records Selection In China seismic codes for largeLNG storage tanks are based on the seismic codes ofbuilding structures [46] with specifications for the de-sign of large oil storage tanks ampe normative theoreticalmodel is developed from the Housner rigid two-particletheoretical model considering the influence of the elastictank wall In addition Chinese seismic codes classifydesign objectives into three tiers based on the degree ofdamage ampe design of large LNG tanks belongs to thesecond tier meaning repairable damage without col-lapse Furthermore the Chinese seismic code dividesseismic sites into four classes based on soil stabilityshear wave velocity and thickness of overburden Soilstrength ranges from strongest to weakest from Class I toClass IV with Class I having the strongest soil In thispaper the large LNG tank is located in a Class II siteBased on guidelines for seismic wave selection [46]three waves are selected and scaled to ensure compat-ibility with the design spectrum at the chosen site ampedetails for three ground motions are shown in Table 6and the acceleration response spectra for ground mo-tions as well as the code acceleration response spectraare shown in Figure 8

Table 4 Material characteristics of the LNG prestressed storage tank

Parametermaterial Density (kgm3) Modulus of elasticity (MPa) Poissonrsquos ratio Yield strength (MPa)Prestressed concrete 2500 36times1010 02 mdashExpanded perlite 56 1125 015 mdashResilient felt 300 800 012 mdashRebar HRB400 7800 2times1011 03 400Steel cable 7800 195times1011 03 18609 Ni steel 7850 206times1011 03 600

Table 5 Material properties of LNG


Coefficients ofthe equation

of states [0

LNG (liquid) 480 1500 000113 0 0

y

xz

(a)

y

xz

(b)

Figure 7 FEM of the LNG storage tank (a) ampe outer tank (b) ampe inner tank


44 Results ampe entire simulation using the SPH-FEM al-gorithm is conducted using an ordinary personal computerampe processor is an Intelreg Coretrade i7-8700 CPU 410GHzand the installation memory is 1600GB ampe von Misesstress distribution of the inner tank alone under hydrostaticconditions at different LNG liquid levels without the effectof insulation layer and outer tank is shown in Figure 9

Among the three seismic waves Taft produces thegreatest von Mises stress on the outer and inner tank atdifferent LNG liquid levels amperefore Taft is chosen as thecritical wave for this analysis ampe stress distribution on theouter tank exhibits a symmetrical trend about the x- and z-axes Figure 10 shows the respective maximum stress of theouter tanks with LNG levels of 25 50 75 and 100 atthe instant corresponding to peak displacement When thetank is 100 filled with LNG the maximum stress of theouter tank is 5135MPa which is less than the compressivestrength of concrete thus the structure is safe In additionthe maximum stress of the outer tank is located at the domefor liquid levels of 25 and 50 but it is located at thebottom of the tank for liquid levels of 75 and 100 ampisphenomenon occurs because gravity plays a more importantrole than pressure with LNG liquid levels of 25 and 50However as liquid level increases pressure at the bottom ofthe tank increases at a much faster rate relative to the domeFurthermore while the maximum stress of the outer tank isnearly identical at 25 50 and 75 it increases signifi-cantly from 75 to 100 liquid level In general close at-tention should be paid to the dome and the bottom of the

tank during the design of large LNG tanks to ensurestructural safety

ampe respective maximum stress of the inner tank withLNG liquid levels of 25 50 75 and 100 is shown inFigure 11 ampe fact that dynamic conditions generate muchgreater stress than static conditions deems dynamic analysiscritical for LNG tanks When the tank is 100 full themaximum stress of the inner tank exceeds 500MPa andjeopardizes the safety of the structure considering that theyield strength of 9 Ni steel is between 500MPa and600MPa [47] Due to the severity of consequences after largeLNG tank failure it is imperative to reduce the stress of theinner tank to ensure its safety At the same time an earlywarning system should be implemented to control themaximum liquid level Different from the outer tank thestress of the inner tank changes significantly with the liquidlevel When the liquid level is at 25 and 50 maximumstress of the inner tank is below 300MPa At a liquid level of75 and 100 maximum stress exceeds 300MPa and500MPa respectively With an increase in the amount ofLNG the stress at the base of the inner tank gradually in-creases to notable levelsamperefore more attention should bepaid to the control of liquid level in the dynamic analysis andseismic design of large LNG storage tanks

According to postprocessing results three representativepaths as shown in Figure 12 are selected to analyze thevariations of the vonMises stress with the height of the tankStress distributions on the outer and inner tanks with respectto height at different liquid levels are illustrated in Figures 13and 14 respectively It can be observed that the stressdistribution on the outer tank changes more graduallycompared to that of the inner tank

In addition stress values along different paths are dif-ferent for a given liquid depth but the overall trends are thesameWhen the liquid level is less than 50 the stress on theouter tank first increases and then decreases with an increasein height When the liquid level exceeds 50 the stress onthe outer tank initially decreases then increases and de-creases again Moreover stress in the lower portion of thetank is much larger than stress in the upper portion when theliquid level is greater than 50 In addition a greater LNGliquid volume leads to greater stored energy and greaterstress at the base of the tank as shown in Figures 13 and 14In reality the bottom of an LNG tank is prone to bucklingfailure during a strong earthquake which is consistent withthe stress analysis results

When comparing outer and inner tanks it is observedthat different liquid amounts can produce similar stresslevels at a height of approximately 10m For the outer tankthe height that correspond to this stress level graduallydecreases from Path A to Path C In contrast for the innertank the height that corresponds to this stress level is nearlyidentical across all paths

ampe displacements of the highest point on the outer wallof the tank filled with 25 50 75 and 100 LNG areshown in Figure 15 In a Class II site the displacements forall three seismic waves are within the same range For thesame seismic wave variations in displacement with respectto time are nearly identical for each liquid volume In

Table 6 Details of the 3 ground motions employed in this study

Event Station TimeImperial Valley-01 El Centro Array 9 1940518Northridge-01 Northridge-Saticoy 1994117Kern County California Taft Lincoln School Tunnel 1994117

030

025

020

015

010

005

000

Sa (g

)

Period (s)

Site class IIImperial valley-01

Northridge-01Kern County

0 1 2 3 4 5 6

Figure 8 Acceleration response spectra of selected ground mo-tions and of code specifications


+4275e + 07+3919e + 07+3562e + 07+3206e + 07+2850e + 07+2494e + 07+2137e + 07+1781e + 07+1425e + 07+1069e + 07+7125e + 06+3562e + 06+0000e + 00

S MisesSNEG (fraction = ndash10(Avg 75)

(a)

+1247e + 08+1143e + 08+1039e + 08+9349e + 07+8310e + 07+7272e + 07+6233e + 07+5194e + 07+4155e + 07+3116e + 07+2078e + 07+1039e + 07+0000e + 00


(b)

+1912e + 08+1753e + 08+1593e + 08+1434e + 08+1275e + 08+1115e + 08+9560e + 07+7966e + 07+6373e + 07+4780e + 07+3187e + 07+1593e + 07+0000e + 00


(c)

+2711e + 08+2485e + 08+2259e + 08+2033e + 08+1807e + 08+1581e + 08+1355e + 08+1130e + 08+9036e + 07+6777e + 07+4518e + 07+2259e + 07+0000e + 00


(d)

Figure 9 Distribution of von Mises stress distribution on the inner tank under static conditions at different LNG liquid levels (a) At 25full (b) at 50 full (c) at 75 full and (d) at 100 full

+3201e + 07+2953e + 07+2705e + 07+2457e + 07+2209e + 07+1961e + 07+1713e + 07+1464e + 07+1216e + 07+9682e + 06+7201e + 06+4720e + 06+2239e + 06

S Mises(Avg 75)

Earthquakemotion direction

y

xz

(a)

+3222e + 07+3066e + 07+2810e + 07+2554e + 07+2299e + 07+2043e + 07+1787e + 07+1531e + 07+1275e + 07+1019e + 06+7633e + 06+5074e + 06+2515e + 06

S Mises(Avg 75)


y

xz

(b)

Figure 10 Continued


+3763e + 07+3480e + 07+3198e + 07+2915e + 07+2632e + 07+2349e + 07+2067e + 07+1784e + 07+1501e + 07+1219e + 06+9358e + 06+6531e + 06+3704e + 06

S Mises(Avg 75)


y

xz

(c)

+5135e + 07+4745e + 07+4355e + 07+3965e + 07+3575e + 07+3186e + 07+2796e + 07+2406e + 07+2016e + 07+1626e + 06+1236e + 06+8456e + 06+4556e + 06

S Mises(Avg 75)


y

xz

(d)

Figure 10ampe maximum vonMises stress distribution of the outer tank at different LNG liquid levels (a) At 25 full (b) at 50 full (c) at75 full and (d) at 100 full

+2373e + 08+2185e + 08+1998e + 08+1810e + 08+1622e + 08+1434e + 08+1246e + 08+1059e + 08+8709e + 07+6831e + 07+4953e + 07+3075e + 07+1197e + 07

S MisesSNEG (fration = ndash10)(Avg 75)


y

xz

(a)

+2641e + 08+2424e + 08+2207e + 08+1990e + 08+1773e + 08+1556e + 08+1339e + 08+1122e + 08+9046e + 07+6876e + 07+4706e + 07+2536e + 07+3655e + 06



y

xz

(b)

+3743e + 08+3439e + 08+3134e + 08+2830e + 08+2525e + 08+2221e + 08+1916e + 08+1612e + 08+1307e + 08+1003e + 08+6980e + 07+3935e + 07+8901e + 06



y

xz

(c)

+5285e + 08+4855e + 08+4425e + 08+3996e + 08+3566e + 08+3136e + 08+2707e + 08+2277e + 08+1847e + 08+1418e + 08+9882e + 07+5585e + 07+1289e + 07



y

xz

(d)

Figure 11 ampe maximum von Mises stress distribution of the inner tank under different LNG liquid levels (a) At 25 full (b) at 50 full(c) at 75 full and (d) at 100 full


addition the location for peak displacement nearly coincideswith the peak seismic wave acceleration ampe maximumdisplacement only reaches 416mm when the tank is filledwith 100 LNG and the seismic performance of the LNGtank is satisfactory based on this displacement calculation

Figure 16 illustrates that the base shear values of the tankare in the same range under different seismic waves for eachliquid volume For the same seismic wave variations in base

shear with respect to time as well as peak base shear forcesfollow the same general trend for each liquid volume ampemaximum base shear reaches 799lowast104 kN when the tank isfilled with 100 LNG under the Taft wave the minimumbase shear is 528lowast104 kN when the tank is filled with 25LNG under the Taft wave ampese values demonstrate that thebase shear of a LNG storage tank is dependent on the liquidlevel in the tank

Path A Path BPath C


Figure 12 ampree representative paths selected to analyze the von Mises stress distribution along the tank wall A B and C

40

35

30

25

20

15

10

5

0

Hei

ght (

m)

0 5 10 15 20 25Stress (MPa)

30 35 40 45 50

25 LNG filled50 LNG filled


(a)

40

35

30

25

20

15

10

5

0

Hei

ght (

m)

0 5 10 15 20 25Stress (MPa)

30 35 40 45 50



(b)40

35

30

25

20

15

10

5

0

Hei

ght (

m)

0 5 10 15 20 25Stress (MPa)

30 35 40 45 50



(c)

Figure 13 Distribution of the von Mises stress on the outer tank with height along different paths (a) Path A (b) Path B (c) Path C


45 Validation To verify the SPH-FEM simulation resultsunder earthquake loading they are compared with CELsimulation results in terms of tip displacements and baseshear ampe maximum tip displacement and the maximum

base shear using the SPH-FEM and CEL method under ElCentro Taft and Northridge seismic waves are shown inFigures 17 and 18ampe tip displacement of the outer wall andthemaximum base shear calculated using the two algorithms

0 50 100 150 200 250 300 350 400 450 500Stress (MPa)



36

30

24

18

12

6

0

Hei

ght (

m)

(a)

0 50 100 150 200 250 300 350 400 450 500Stress (MPa)



36

30

24

18

12

6

0

Hei

ght (

m)

(b)

0 50 100 150 200 250 300 350 400 450 500Stress (MPa)



36

30

24

18

12

6

0

Hei

ght (

m)

(c)

Figure 14 Distribution of von Mises stress on inner tank with respect to height along different paths (a) Path A (b) Path B (c) Path C

43210

ndash1ndash2ndash3ndash4

Disp

lace

men

t (m

m)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

(a)

43210


Disp

lace

men

t (m

m)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

(b)

43210


Disp

lace

men

t (m

m)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

(c)

Figure 15 Tip displacement of the outer wall under different liquid volume (a) El Centro (b) Northridge and (c) Taft


0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

10

5

0

ndash5

ndash10

Basa

l she

ar (lowast

104 kN

)

(a)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

10

5

0

ndash5

ndash10

Basa

l she

ar (lowast

104 kN

)

(b)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

10

5

0

ndash5

ndash10

Basa

l she

ar (lowast

104 kN

)

(c)

Figure 16 Base shear of the tank under different liquid volume (a) El Centro (b) Northridge and (c) Taft

SPHCEL

25 LNG 50 LNG 75 LNG 100 LNG

309 308 31331

367 361

416436

0

1

2

3

4

5

Disp

lace

men

t (m

m)

(a)

SPHCEL


19 188 201 207246 258

311326

0

1

2

3

4

5

Disp

lace

men

t (m

m)

(b)

Figure 17 Continued


SPHCEL


226 228 243 24628 288

3133

0

1

2

3

4

5

Disp

lace

men

t (m

m)

(c)

Figure 17 Comparison of the maximum tip displacement of the outer wall under different liquid volume between the two algorithms (a) ElCentro (b) Northridge and (c) Taft

SPHCEL


533 532 549 556622 632 662 621

0123456789

101112

Basa

l she

ar (lowast

104 kN

)

(a)

SPHCEL


414 419493 486

665 699

855926

0123456789

101112

Basa

l she

ar (lowast

104 kN

)

(b)

Figure 18 Continued


are in good agreement amperefore the feasibility of using theSPH-FEM algorithm for the seismic analysis of large LNGtanks is verified

5 Summary and Conclusions

In this study the SPH-FEM method is compared with theCEL method to demonstrate the advantage of SPH-FEM interms of efficiency and accuracy ampen the SPH-FEM al-gorithm is used to analyze the dynamic response of a160000m3 LNG prestressed storage tank subjected to threeearthquake waves in a Class II site ampe main conclusionsdrawn from the numerical simulations can be summarizedas follows

(1) Under static conditions the von Mises stress in-creases at a linear rate with an increasing liquidvolume Under dynamic conditions the von Misesstress increases at a nonlinear rate

(2) ampe stresses produced on the outer and inner tanksunder earthquake loading are very similar at a heightof approximately 10m for each liquid volume ampemaximum tip displacement of the outer tank is416mm and the maximum base shear is799lowast104 kN

(3) ampe maximum stress of the inner tank with 100LNG liquid level exceeds 500MPa under the chosenseismic waves and raises concerns for its structuralsafety Development of an improved structuralsystem and a warning mechanism is of paramountimportance to the design of LNG tanks at high liquidlevels

(4) ampe SPH-FEM algorithm is accurate and more effi-cient than the CEL method Moreover the SPH-FEMalgorithm exhibits excellent capability for simulatinglarge storage tanks under a reasonable time to provide

a reference for the design and construction of largeLNG tanks

ampe largest LNG prestressed storage tank in China iscurrently 200000m3 ampe sheer size of the tank requires asignificant amount of meshing during seismic simulationwhich is almost impossible to accomplish on an ordinarycomputer using a mesh-based method ampe SPH-FEM al-gorithm provides a feasible method to simulate extremelylarge LNG tanks on a personal computer which can helpdesigners obtain its seismic performance in an acceptabletime range without significant reliance on hardware capa-bilities Ongoing work is being performed to optimize thedesign of large LNG tanks under different earthquakes usingthe SPH-FEM algorithm and will be reported at a later time

Nomenclature

Ω Domain of integrationW(x) Kernel functionh Smoothing lengthρ Density kg m3

∆t Time step sizeN Number of particlesg Gravitational accelerationm Mass of particlecs Local speed of soundEm Internal energy per unit massη Volumetric compressibilityσ Stress] Velocityα Direction of coordinatesβ Direction of coordinatesU Poissonrsquos ratioξ Small positive numberi ampe ith component of a vector

SPHCEL


528 538578 567

761 762 799852

0123456789

101112

Basa

l she

ar (lowast

104 kN

)

(c)

Figure 18 Comparison of the maximum base shear under different liquid volume between the two algorithms (a) El Centro (b)Northridge and (c) Taft


j ampe jth component of a vector

Data Availability

ampe data of ground motions used to support the findings ofthis study have been deposited in the PEER Ground MotionDatabase

Disclosure

Any opinions findings conclusions and recommendationsexpressed here are those of the authors and do not neces-sarily reflect the views of the sponsors

Conflicts of Interest

ampe authors declare that they have no conflicts of interestregarding the publication of this paper

Acknowledgments

ampis research was supported by the China ScholarshipCouncil the Natural Science Foundation of China (Grantno 51738007) and the Natural Sciences and EngineeringResearch Council of Canada (NSERC) Discovery(201606290) Program ampe authors would like express theirappreciation to Professor Ozden Turan and Professor ErenSemercigil for their input

References

[1] J Jia Modern Earthquake Engineering Offshore and Land-Based Structures Springer Berlin Germany 2016

[2] J G Sun Isolation of Large Vertical Storage Tanks 0eoryMethods and Test Science Press Beijing China 2009

[3] G W Housner ldquoDynamic pressures on accelerated fluidcontainersrdquo Bulletin of the Seismological Society of Americavol 47 no 1 1957

[4] A Veletsos ldquoSeismic effects in flexible liquid storage tanksrdquo inProceedings of the 5th World Conference on EarthquakeEngineering Rome Italy June 1974

[5] A Veletsos and J Yang ldquoDynamics of fixed-base liquidstorage tanksrdquo in Proceedings of the USndashJapan Seminar forEarthquake Engineering Research with Emphasis on LifelineSystems Tokyo Japan 1976

[6] M A Haroun and G W Housner ldquoDynamic interaction ofliquid storage tanks and foundation soilrdquo Dynamic Responseof Structures Experimentation Observation Prediction andControl American Society of Civil Engineers New York NYUSA 1981

[7] Y H Hu Z Zhuang and X C You ldquoAddedmass approach toa large-scale liquid storage tank under seismic excitationsrdquo inProceedings of the Beijing Society of 0eoretical and AppliedMechanics Annual Meeting Beijing China June 2010

[8] M A Hariri-Ardebili H Rahmani-Samani andMMirtaherildquoSeismic stability assessment of a high-rise concrete towerutilizing endurance time analysisrdquo International Journal ofStructural Stability and Dynamics vol 14 no 6 Article ID1450016 2014

[9] N D H Djelloul and M Djermane ldquoEffect of geometricimperfection on the dynamic of elevated water tanksrdquo CivilEngineering Journal vol 6 no 1 2020

[10] I-T Hwang and K Ting ldquoBoundary element method forfluid-structure interaction problems in liquid storage tanksrdquoJournal of Pressure Vessel Technology vol 111 no 4pp 435ndash440 1989

[11] L Wu Comparative Research Analysis of the Effect ofEarthquake on LNG Tank Harbin Engineering UniversityHarbin China 2013

[12] I P Christovasilis and A S Whittaker ldquoSeismic analysis ofconventional and isolated LNG tanks using mechanical an-alogsrdquo Earthquake Spectra vol 24 no 3 pp 599ndash616 2008

[13] J Sun L Cui X Li Z Wang W Liu and Y Lv ldquoDesigntheory and method of LNG isolationrdquo Earthquakes andStructures vol 16 no 1 pp 1ndash9 2019

[14] Y Chen X Zhai and Y Wang ldquoNumerical study on thedynamic response of a massive liquefied natural gas outer tankunder impact loadingrdquo Journal of Zhejiang University Sciencevol 20 no 11 pp 823ndash837 2019

[15] J Li J Sun L Cui X Wang and J Hao ldquoSeismic performancenumerical simulation analysis of LNG storage tank with filledwallrdquo Earthquake Engineering and Engineering Dynamics vol 1no 3 pp 157ndash164 2014

[16] X H Du and X P Shen ldquoNumerical simulation of fluid-structure interaction of LNG prestressed storage tank underseismic influencerdquo Computers Materials and Continuavol 20 no 3 pp 225ndash241 2010

[17] R C Ju Coupled Vibration 0eory of Elastic Structure andLiquid Geological Publishing Press Bath UK 1983

[18] G R Liu and M B Liu Smoothed Particle Hydrodynamics AMeshfree Particle Method World Scientific Singapore 2004

[19] M B Liu and G R Liu ldquoSmoothed particle hydrodynamics(SPH) an overview and recent developmentsrdquo Archives ofComputational Methods in Engineering vol 17 no 1pp 25ndash76 2010

[20] L B Lucy ldquoA numerical approach to the testing of the fissionhypothesisrdquo 0e Astronomical Journal vol 82 no 82pp 1013ndash1024 1977

[21] R A Gingold and J J Monaghan ldquoSmoothed particle hy-drodynamics theory and application to non-spherical starsrdquoMonthly Notices of the Royal Astronomical Society vol 181no 3 pp 375ndash389 1977

[22] L Wang Z Wang and Y Li ldquoA SPH simulation on large-amplitude sloshing for fluids in a two-dimensional tankrdquoEarthquake Engineering and Engineering Vibration vol 12no 1 pp 135ndash142 2013

[23] Y T Huang D U Faxi H Liu et al ldquoAnalysis on sloshingcharacteristics of liquid in elastomer tank based on SPHmethodrdquo Computer Aided Engineering vol 24 no 2pp 36ndash41 2015

[24] F Liu M B Tong and J P Chen ldquoNumerical simulation ofthree-dimensional liquid sloshing based on SPH methodrdquoJournal of Nanjing University of Aeronautics and Astronauticsvol 42 no 1 pp 122ndash126 2010

[25] J R Shao H Q Li G R Liu and M B Liu ldquoAn improvedSPH method for modeling liquid sloshing dynamicsrdquo Com-puters amp Structures vol 100-101 no 6 pp 18ndash26 2012

[26] D Violeau and R Issa ldquoNumerical modelling of complexturbulent free-surface flows with the SPH method an over-viewrdquo International Journal for Numerical Methods in Fluidsvol 53 no 2 pp 277ndash304 2007

[27] S Shao ldquoSimulation of breaking wave by SPH methodcoupled with k-ϵ modelrdquo Journal of Hydraulic Researchvol 44 no 3 pp 338ndash349 2006

[28] Z Zhang L Wang F Ming V V Silberschmidt andH Chen ldquoApplication of smoothed particle hydrodynamics


in analysis of shaped-charge jet penetration caused by un-derwater explosionrdquoOcean Engineering vol 145 pp 177ndash1872017

[29] S W Attaway M W Heinstein and J W Swegle ldquoCouplingof smooth particle hydrodynamics with the finite elementmethodrdquo Nuclear Engineering and Design vol 150 no 2-3pp 199ndash205 1994

[30] F Kalateh and A Koosheh ldquoSimulation of cavitating fluid-Structure interaction using SPH-FE methodrdquo Mathematicsand Computers in Simulation vol 173 pp 51ndash70 2020

[31] S Liang and Z Chen ldquoSPH-FEM coupled simulation of SSIfor conducting seismic analysis on a rectangular undergroundstructurerdquo Bulletin of Earthquake Engineering vol 17 no 1pp 159ndash180 2019

[32] C Fragassa M Topalovic A Pavlovic and S VulovicldquoDealing with the effect of air in fluid structure interaction bycoupled SPH-FEMmethodsrdquoMaterials vol 12 no 7 p 11622019

[33] J K Chen J E Beraun and C J Jih ldquoAn improvement fortensile instability in smoothed particle hydrodynamicsrdquoComputational Mechanics vol 23 no 4 pp 279ndash287 1999

[34] ABAQUS 613 Abaqus Analysis Userrsquos Manual DassaultSystemes Simulia Core Providence RI USA 2013

[35] Y Li Z Chen X Ren R Tao R Gao and D Fang ldquoEx-perimental and numerical study on damage mode of RC slabsunder combined blast and fragment loadingrdquo InternationalJournal of Impact Engineering vol 142 Article ID 1035792020

[36] G Qiu S Henke and J Grabe ldquoApplication of a coupledEulerian-Lagrangian approach on geomechanical problemsinvolving large deformationsrdquo Computers and Geotechnicsvol 38 no 1 pp 30ndash39 2011

[37] Z Meng J Chen and J Wang ldquoampe coupled Eulerian-La-grangian analysis of pile jacking process in saturated soft clayby using modified cam-clay modelrdquo Journal of ShanghaiJiaotong University vol 51 no 3 pp 263ndash268 2017

[38] F Salehi and R Shamsoddini ldquoSPH simulation of the pen-etrating object in the wet soilrdquo Geomechanics and Geo-engineering pp 1ndash11 2020

[39] T El-Gammal E E Khalil H Haridy and E Abo-SerieldquoInfluence of smoothing length and virtual particles on SPHaccuracyrdquo International Journal of Materials Mechanics andManufacturing vol 1 no 2 pp 166ndash170 2013

[40] A Z Gu Q G Jin Y L Ju and JWang Technical Manual forLiquefied Natural Gas Machine Press Beijing China 2010

[41] N N Lv J Xie and J J Yang ldquoReview on constructiontechnology of large LNG low temperature storage tankrdquoUnique Construction no 1 pp 115ndash118 2010

[42] H Fang H Wu D G Wang and X G Chen ldquoReview ofresearch on seismic safety of liquid storage tanksrdquo EarthquakeDisaster Prevention Technology vol 7 no 2 pp 144ndash151 2012

[43] S N Huang and Z Q Wang ldquoampe first 160000 m3 fullcapacity LNG storage tank in Chinardquo Petroleum EngineeringConstruction vol 35 no 4 pp 15ndash17 2009

[44] Y Z Wang and C G Fu Structural Engineering Analysis ofAbaqus and Detailed Explanation of Examples China BuildingIndustry Press Beijing China 2010

[45] Y P Shi and Y R Zhou Example and Analysis of FiniteElement Software ABAQUS Machine Press Beijing China2006

[46] Ministry of Housing andUrban-Rural Development of ChinaCode for seismic design of buildings GB 50011-2010 Ministryof Housing and Urban-Rural Development of China BeijingChina 2010

[47] Standardization Administration Committee of the PeoplersquosRepublic of China 9 Nickel Steel Plates for Pressure Vesselswith Specified Low Temperature Properties StandardizationAdministration Committee of the Peoplersquos Republic of ChinaBeijing China 2010


and it divides the liquid into three components a convectioncomponent a flexible impulsive component and a rigidimpulsive component In addition Hu et al [7] presented amethod for mass addition using user subroutines to studythe seismic response of a large cylindrical thin-walledstorage tank based on the theories of Housner and VeletsosLiquid mass was added to the solid wall without consideringliquid sloshing Hariri-Ardebili et al [8] compared theendurance time analysis (ETA) method to the time-historyanalysis (THA) and incremental dynamic analysis (IDA)method to investigate the seismic performance of a high-risetelecommunication tower Hadj-Djelloul and Djermane [9]used the three-dimensional finite element technique to studythe seismic response of perfect and imperfect elevated watertanks ampey also investigated the effect of geometric im-perfection on the dynamic performance of elevated watertanks

Based on applicable theories regarding fluidndashstructureinteraction since the 1950s there have been several studieson the dynamic analysis of LNG storage tanks Hwang [10]investigated the dynamic response of an LNG tank using acombination of Boundary Element Method (BEM) andFinite Element Method (FEM) programs Wu [11] per-formed time-history analysis of LNG storage tanks withFEM software and found that deformation of the inner tankwas effectively prevented by adding a prestressed concretewall and an insulating layer Christovasilis and Whittaker[12] investigated the seismic response of a conventional andisolated vertical cylindrical LNG tank by applying finiteelement analysis to mechanical models ampe results obtainedfrom two numerical models were in good agreement anddemonstrated that a mechanical model could be used withconfidence for the preliminary analysis and design ofconventional and isolated LNG tanks Sun et al [13] derivedand calculated the dynamic response of base-isolated LNGstorage tanks considering soilndashstructure interaction theeffect of which was proven to be insignificant Chen et al[14] investigated the dynamic response of a typical160000m3 LNG prestressed concrete outer tank underimpact loading and types of impact damage were deter-mined based on dynamic response results including stressdisplacement energy and critical impact velocity Li et al[15] conducted numerical dynamic analysis of LNG storagetanks and concluded that filling the space between the outerand inner tank could improve seismic performance withlittle effect on the sloshing height Du [16] adopted theCoupled EulerianndashLagrangian (CEL) analysis technique inABAQUS to simulate fluidndashstructure interaction [17] inLNG tanks but the CELmethod exhibited liquid leakage andlow simulation efficiency

ampe aforementioned numerical simulation methods arevery computationally intensive due to the sheer size of largeLNG tanks Given the recent rise in large LNG tank con-struction it is essential to employ a fast analysis method thatcan simulate the seismic response of LNG tanks in practicalengineering applications ampus an efficient smoothed par-ticle hydrodynamics-finite element method (SPH-FEM)algorithm [18] which has not been previously appliedto large land-based LNG tanks is proposed in this paper

SPH-FEM methods retain the advantages of FEM in sim-ulating FSI problems while adopting the advantages of SPHin modeling fluid behaviour

SPH is suitable for modeling fluid behaviour because it isa mesh-free method that discretizes a liquid field intoparticles [19] A kernel function is used to approximatedifferential equations and the function value at any point isthen expressed by neighboring nodes based on a local ap-proximation ampe SPH algorithm can overcome the weak-ness in mesh-based methods regarding fluid simulation byeffectively addressing free surfaces and moving interfaces inaddition to large deformation of materials As a result afterits development by Lucy [20] and Gingold [21] in 1977 theSPH method has been successfully adopted for studies incontinuous solid mechanics and fluid mechanics to solveproblems related to structural failure large deformation andliquid sloshing [22] Huang et al [23] verified the feasibilityof liquid sloshing analysis using the SPH method byobtaining results that corresponded to theoretical analysisLiu et al [24] performed a three-dimensional numericalsimulation of free surface liquid sloshing in a prismatic tanksubjected to a sinusoidal excitation using the SPH algorithmand the numerical results exhibited good agreement withexperimental data Shao et al [25] also presented an im-proved SPH algorithm to model liquid sloshing dynamicsand the numerical results agreed well with the experimentalobservations ampe SPH algorithm has also been widely ap-plied to simulate embankment flow [26] wave breaking [27]and explosions [28] amperefore the SPH algorithm is aversatile analysis method that can be applied to a variety ofstructural problems including the fluid component of largeLNG tanks

Coupled with a FEM method for the solid componentan SPH-FEM algorithm greatly improves the calculationaccuracy and efficiency for fluidndashstructure impact problemsampe coupled SPH-FEM method was first proposed by Att-away et al [29] using a masterndashslave algorithm to accountfor the contact between FE elements and SPH particlesKalateh and Koosheh [30] used the SPH-FEM method tosimulate the interaction between a convergent-divergentnozzle and cavitating flow and the results showed that thebehaviour of liquid and vapor at the interface matched othernumerical and experimental methods Liang and Chen [31]applied the SPH-FEM method to soilndashstructure interactionproblems during the seismic analysis of a rectangular un-derground structure and results indicated that the distri-bution and magnitude of seismic earth pressure wereinfluenced by the magnitude of soil deformation Fragassaet al [32] analyzed the effect of air in FSI problems bycoupling FEM and SPH ampey concluded that air had littleeffect on stress prediction but it had a greater effect on thebehaviour of the structure after the initial fluid impact Inthis study the SPH-FEM algorithm provides an accurate andefficient method for the analysis of a large LNG tank underdynamic earthquake loading

Section 2 of this paper presents an overview of the SPH-FEM methodology Section 3 verifies the SPH-FEM algorithmby comparing it to the traditional Coupled EulerianndashLagrangian(CEL) method on the analysis of a cubic water tank under



2 Methodology


f(x) 1113946Ω





⎧⎨

⎩ (2)






1113946Ω



limh⟶0




1113868111386811138681113868gt κh (6)





dρdt

minusρzv

β

zxβ (7)


dvα

dt1ρ

zσαβ

zxβ (8)


de

dtσαβ

ρzv

α

zxβ (9)


Dρi

Dt ρi 1113944

N

j1

mj

ρj

]βij middotzWij

zxβi

(10)


D]αiDt

1113944N

j1mj

σαβi + σαβj

ρiρj

zWij

zxβi

(11)


Dei

Dt12

1113944

N

j1mj

pi

ρ2i+

pj


zWij

zxβi

+μi

2ρi



Δt mina

05l

cs + 2ξμalρa( 1113857( 11138571113896 1113897 (13)








pH ρ0c

2η(1 minus sη)

2

η ρρ0

minus 1

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(14)



Us c + sUp (15)










Output results

Displacement

Velocity

Boundarycondition
















states Γ0

Water 1000 1480 0001 0 0




(a) (b)

(c) (d)


+1297e + 05+1193e + 05+1090e + 05+9869e + 04+8837e + 04+7804e + 04+6772e + 04+5739e + 04+4707e + 04+3674e + 04+2642e + 04+1609e + 04+5768e + 03

S Mises(Avg 75)

(a)

+1312e + 05+1210e + 05+1108e + 05+1006e + 05+9039e + 04+8018e + 04+6997e + 04+5975e + 04+4954e + 04+3933e + 04+2911e + 04+1890e + 04+8686e + 03

S Mises(Avg 75)

(b)

Figure 5 Continued





+1121e + 05+1032e + 05+9436e + 04+8547e + 04+7659e + 04+6770e + 04+5882e + 04+4993e + 04+4105e + 04+3216e + 04+2328e + 04+1439e + 04+5509e + 03

S Mises(Avg 75)

(c)

+1139e + 05+1050e + 05+9610e + 04+8772e + 04+7833e + 04+6944e + 04+6056e + 04+5167e + 04+4279e + 04+3390e + 04+2501e + 04+1613e + 04+7242e + 03

S Mises(Avg 75)

(d)






400

800

354

30




86600

1200

113

7538

550

Insulating layer

R1012

R912

R812

R712

R6122

R5147

R4173

R3198

R2224

R1249






ΔT N










of states [0

LNG (liquid) 480 1500 000113 0 0

y

xz

(a)

y

xz

(b)













030

025

020

015

010

005

000

Sa (g

)

Period (s)



0 1 2 3 4 5 6



+4275e + 07+3919e + 07+3562e + 07+3206e + 07+2850e + 07+2494e + 07+2137e + 07+1781e + 07+1425e + 07+1069e + 07+7125e + 06+3562e + 06+0000e + 00


(a)

+1247e + 08+1143e + 08+1039e + 08+9349e + 07+8310e + 07+7272e + 07+6233e + 07+5194e + 07+4155e + 07+3116e + 07+2078e + 07+1039e + 07+0000e + 00


(b)

+1912e + 08+1753e + 08+1593e + 08+1434e + 08+1275e + 08+1115e + 08+9560e + 07+7966e + 07+6373e + 07+4780e + 07+3187e + 07+1593e + 07+0000e + 00


(c)

+2711e + 08+2485e + 08+2259e + 08+2033e + 08+1807e + 08+1581e + 08+1355e + 08+1130e + 08+9036e + 07+6777e + 07+4518e + 07+2259e + 07+0000e + 00


(d)


+3201e + 07+2953e + 07+2705e + 07+2457e + 07+2209e + 07+1961e + 07+1713e + 07+1464e + 07+1216e + 07+9682e + 06+7201e + 06+4720e + 06+2239e + 06

S Mises(Avg 75)


y

xz

(a)

+3222e + 07+3066e + 07+2810e + 07+2554e + 07+2299e + 07+2043e + 07+1787e + 07+1531e + 07+1275e + 07+1019e + 06+7633e + 06+5074e + 06+2515e + 06

S Mises(Avg 75)


y

xz

(b)

Figure 10 Continued


+3763e + 07+3480e + 07+3198e + 07+2915e + 07+2632e + 07+2349e + 07+2067e + 07+1784e + 07+1501e + 07+1219e + 06+9358e + 06+6531e + 06+3704e + 06

S Mises(Avg 75)


y

xz

(c)

+5135e + 07+4745e + 07+4355e + 07+3965e + 07+3575e + 07+3186e + 07+2796e + 07+2406e + 07+2016e + 07+1626e + 06+1236e + 06+8456e + 06+4556e + 06

S Mises(Avg 75)


y

xz

(d)


+2373e + 08+2185e + 08+1998e + 08+1810e + 08+1622e + 08+1434e + 08+1246e + 08+1059e + 08+8709e + 07+6831e + 07+4953e + 07+3075e + 07+1197e + 07



y

xz

(a)

+2641e + 08+2424e + 08+2207e + 08+1990e + 08+1773e + 08+1556e + 08+1339e + 08+1122e + 08+9046e + 07+6876e + 07+4706e + 07+2536e + 07+3655e + 06



y

xz

(b)

+3743e + 08+3439e + 08+3134e + 08+2830e + 08+2525e + 08+2221e + 08+1916e + 08+1612e + 08+1307e + 08+1003e + 08+6980e + 07+3935e + 07+8901e + 06



y

xz

(c)

+5285e + 08+4855e + 08+4425e + 08+3996e + 08+3566e + 08+3136e + 08+2707e + 08+2277e + 08+1847e + 08+1418e + 08+9882e + 07+5585e + 07+1289e + 07



y

xz

(d)






Path A Path BPath C



40

35

30

25

20

15

10

5

0

Hei

ght (

m)

0 5 10 15 20 25Stress (MPa)

30 35 40 45 50



(a)

40

35

30

25

20

15

10

5

0

Hei

ght (

m)

0 5 10 15 20 25Stress (MPa)

30 35 40 45 50



(b)40

35

30

25

20

15

10

5

0

Hei

ght (

m)

0 5 10 15 20 25Stress (MPa)

30 35 40 45 50



(c)





0 50 100 150 200 250 300 350 400 450 500Stress (MPa)



36

30

24

18

12

6

0

Hei

ght (

m)

(a)

0 50 100 150 200 250 300 350 400 450 500Stress (MPa)



36

30

24

18

12

6

0

Hei

ght (

m)

(b)

0 50 100 150 200 250 300 350 400 450 500Stress (MPa)



36

30

24

18

12

6

0

Hei

ght (

m)

(c)


43210


Disp

lace

men

t (m

m)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

(a)

43210


Disp

lace

men

t (m

m)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

(b)

43210


Disp

lace

men

t (m

m)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

(c)



0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

10

5

0

ndash5

ndash10

Basa

l she

ar (lowast

104 kN

)

(a)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

10

5

0

ndash5

ndash10

Basa

l she

ar (lowast

104 kN

)

(b)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

10

5

0

ndash5

ndash10

Basa

l she

ar (lowast

104 kN

)

(c)


SPHCEL


309 308 31331

367 361

416436

0

1

2

3

4

5

Disp

lace

men

t (m

m)

(a)

SPHCEL


19 188 201 207246 258

311326

0

1

2

3

4

5

Disp

lace

men

t (m

m)

(b)

Figure 17 Continued


SPHCEL


226 228 243 24628 288

3133

0

1

2

3

4

5

Disp

lace

men

t (m

m)

(c)


SPHCEL


533 532 549 556622 632 662 621

0123456789

101112

Basa

l she

ar (lowast

104 kN

)

(a)

SPHCEL


414 419493 486

665 699

855926

0123456789

101112

Basa

l she

ar (lowast

104 kN

)

(b)

Figure 18 Continued











Nomenclature



SPHCEL


528 538578 567

761 762 799852

0123456789

101112

Basa

l she

ar (lowast

104 kN

)

(c)




Data Availability


Disclosure




Acknowledgments


References




















































2 Methodology


f(x) 1113946Ω





⎧⎨

⎩ (2)






1113946Ω



limh⟶0




1113868111386811138681113868gt κh (6)





dρdt

minusρzv

β

zxβ (7)


dvα

dt1ρ

zσαβ

zxβ (8)


de

dtσαβ

ρzv

α

zxβ (9)


Dρi

Dt ρi 1113944

N

j1

mj

ρj

]βij middotzWij

zxβi

(10)


D]αiDt

1113944N

j1mj

σαβi + σαβj

ρiρj

zWij

zxβi

(11)


Dei

Dt12

1113944

N

j1mj

pi

ρ2i+

pj


zWij

zxβi

+μi

2ρi



Δt mina

05l

cs + 2ξμalρa( 1113857( 11138571113896 1113897 (13)








pH ρ0c

2η(1 minus sη)

2

η ρρ0

minus 1

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(14)



Us c + sUp (15)










Output results

Displacement

Velocity

Boundarycondition
















states Γ0

Water 1000 1480 0001 0 0




(a) (b)

(c) (d)


+1297e + 05+1193e + 05+1090e + 05+9869e + 04+8837e + 04+7804e + 04+6772e + 04+5739e + 04+4707e + 04+3674e + 04+2642e + 04+1609e + 04+5768e + 03

S Mises(Avg 75)

(a)

+1312e + 05+1210e + 05+1108e + 05+1006e + 05+9039e + 04+8018e + 04+6997e + 04+5975e + 04+4954e + 04+3933e + 04+2911e + 04+1890e + 04+8686e + 03

S Mises(Avg 75)

(b)

Figure 5 Continued





+1121e + 05+1032e + 05+9436e + 04+8547e + 04+7659e + 04+6770e + 04+5882e + 04+4993e + 04+4105e + 04+3216e + 04+2328e + 04+1439e + 04+5509e + 03

S Mises(Avg 75)

(c)

+1139e + 05+1050e + 05+9610e + 04+8772e + 04+7833e + 04+6944e + 04+6056e + 04+5167e + 04+4279e + 04+3390e + 04+2501e + 04+1613e + 04+7242e + 03

S Mises(Avg 75)

(d)






400

800

354

30




86600

1200

113

7538

550

Insulating layer

R1012

R912

R812

R712

R6122

R5147

R4173

R3198

R2224

R1249






ΔT N










of states [0

LNG (liquid) 480 1500 000113 0 0

y

xz

(a)

y

xz

(b)













030

025

020

015

010

005

000

Sa (g

)

Period (s)



0 1 2 3 4 5 6



+4275e + 07+3919e + 07+3562e + 07+3206e + 07+2850e + 07+2494e + 07+2137e + 07+1781e + 07+1425e + 07+1069e + 07+7125e + 06+3562e + 06+0000e + 00


(a)

+1247e + 08+1143e + 08+1039e + 08+9349e + 07+8310e + 07+7272e + 07+6233e + 07+5194e + 07+4155e + 07+3116e + 07+2078e + 07+1039e + 07+0000e + 00


(b)

+1912e + 08+1753e + 08+1593e + 08+1434e + 08+1275e + 08+1115e + 08+9560e + 07+7966e + 07+6373e + 07+4780e + 07+3187e + 07+1593e + 07+0000e + 00


(c)

+2711e + 08+2485e + 08+2259e + 08+2033e + 08+1807e + 08+1581e + 08+1355e + 08+1130e + 08+9036e + 07+6777e + 07+4518e + 07+2259e + 07+0000e + 00


(d)


+3201e + 07+2953e + 07+2705e + 07+2457e + 07+2209e + 07+1961e + 07+1713e + 07+1464e + 07+1216e + 07+9682e + 06+7201e + 06+4720e + 06+2239e + 06

S Mises(Avg 75)


y

xz

(a)

+3222e + 07+3066e + 07+2810e + 07+2554e + 07+2299e + 07+2043e + 07+1787e + 07+1531e + 07+1275e + 07+1019e + 06+7633e + 06+5074e + 06+2515e + 06

S Mises(Avg 75)


y

xz

(b)

Figure 10 Continued


+3763e + 07+3480e + 07+3198e + 07+2915e + 07+2632e + 07+2349e + 07+2067e + 07+1784e + 07+1501e + 07+1219e + 06+9358e + 06+6531e + 06+3704e + 06

S Mises(Avg 75)


y

xz

(c)

+5135e + 07+4745e + 07+4355e + 07+3965e + 07+3575e + 07+3186e + 07+2796e + 07+2406e + 07+2016e + 07+1626e + 06+1236e + 06+8456e + 06+4556e + 06

S Mises(Avg 75)


y

xz

(d)


+2373e + 08+2185e + 08+1998e + 08+1810e + 08+1622e + 08+1434e + 08+1246e + 08+1059e + 08+8709e + 07+6831e + 07+4953e + 07+3075e + 07+1197e + 07



y

xz

(a)

+2641e + 08+2424e + 08+2207e + 08+1990e + 08+1773e + 08+1556e + 08+1339e + 08+1122e + 08+9046e + 07+6876e + 07+4706e + 07+2536e + 07+3655e + 06



y

xz

(b)

+3743e + 08+3439e + 08+3134e + 08+2830e + 08+2525e + 08+2221e + 08+1916e + 08+1612e + 08+1307e + 08+1003e + 08+6980e + 07+3935e + 07+8901e + 06



y

xz

(c)

+5285e + 08+4855e + 08+4425e + 08+3996e + 08+3566e + 08+3136e + 08+2707e + 08+2277e + 08+1847e + 08+1418e + 08+9882e + 07+5585e + 07+1289e + 07



y

xz

(d)






Path A Path BPath C



40

35

30

25

20

15

10

5

0

Hei

ght (

m)

0 5 10 15 20 25Stress (MPa)

30 35 40 45 50



(a)

40

35

30

25

20

15

10

5

0

Hei

ght (

m)

0 5 10 15 20 25Stress (MPa)

30 35 40 45 50



(b)40

35

30

25

20

15

10

5

0

Hei

ght (

m)

0 5 10 15 20 25Stress (MPa)

30 35 40 45 50



(c)





0 50 100 150 200 250 300 350 400 450 500Stress (MPa)



36

30

24

18

12

6

0

Hei

ght (

m)

(a)

0 50 100 150 200 250 300 350 400 450 500Stress (MPa)



36

30

24

18

12

6

0

Hei

ght (

m)

(b)

0 50 100 150 200 250 300 350 400 450 500Stress (MPa)



36

30

24

18

12

6

0

Hei

ght (

m)

(c)


43210


Disp

lace

men

t (m

m)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

(a)

43210


Disp

lace

men

t (m

m)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

(b)

43210


Disp

lace

men

t (m

m)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

(c)



0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

10

5

0

ndash5

ndash10

Basa

l she

ar (lowast

104 kN

)

(a)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

10

5

0

ndash5

ndash10

Basa

l she

ar (lowast

104 kN

)

(b)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

10

5

0

ndash5

ndash10

Basa

l she

ar (lowast

104 kN

)

(c)


SPHCEL


309 308 31331

367 361

416436

0

1

2

3

4

5

Disp

lace

men

t (m

m)

(a)

SPHCEL


19 188 201 207246 258

311326

0

1

2

3

4

5

Disp

lace

men

t (m

m)

(b)

Figure 17 Continued


SPHCEL


226 228 243 24628 288

3133

0

1

2

3

4

5

Disp

lace

men

t (m

m)

(c)


SPHCEL


533 532 549 556622 632 662 621

0123456789

101112

Basa

l she

ar (lowast

104 kN

)

(a)

SPHCEL


414 419493 486

665 699

855926

0123456789

101112

Basa

l she

ar (lowast

104 kN

)

(b)

Figure 18 Continued











Nomenclature



SPHCEL


528 538578 567

761 762 799852

0123456789

101112

Basa

l she

ar (lowast

104 kN

)

(c)




Data Availability


Disclosure




Acknowledgments


References
























































pH ρ0c

2η(1 minus sη)

2

η ρρ0

minus 1

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(14)



Us c + sUp (15)










Output results

Displacement

Velocity

Boundarycondition
















states Γ0

Water 1000 1480 0001 0 0




(a) (b)

(c) (d)


+1297e + 05+1193e + 05+1090e + 05+9869e + 04+8837e + 04+7804e + 04+6772e + 04+5739e + 04+4707e + 04+3674e + 04+2642e + 04+1609e + 04+5768e + 03

S Mises(Avg 75)

(a)

+1312e + 05+1210e + 05+1108e + 05+1006e + 05+9039e + 04+8018e + 04+6997e + 04+5975e + 04+4954e + 04+3933e + 04+2911e + 04+1890e + 04+8686e + 03

S Mises(Avg 75)

(b)

Figure 5 Continued





+1121e + 05+1032e + 05+9436e + 04+8547e + 04+7659e + 04+6770e + 04+5882e + 04+4993e + 04+4105e + 04+3216e + 04+2328e + 04+1439e + 04+5509e + 03

S Mises(Avg 75)

(c)

+1139e + 05+1050e + 05+9610e + 04+8772e + 04+7833e + 04+6944e + 04+6056e + 04+5167e + 04+4279e + 04+3390e + 04+2501e + 04+1613e + 04+7242e + 03

S Mises(Avg 75)

(d)






400

800

354

30




86600

1200

113

7538

550

Insulating layer

R1012

R912

R812

R712

R6122

R5147

R4173

R3198

R2224

R1249






ΔT N










of states [0

LNG (liquid) 480 1500 000113 0 0

y

xz

(a)

y

xz

(b)













030

025

020

015

010

005

000

Sa (g

)

Period (s)



0 1 2 3 4 5 6



+4275e + 07+3919e + 07+3562e + 07+3206e + 07+2850e + 07+2494e + 07+2137e + 07+1781e + 07+1425e + 07+1069e + 07+7125e + 06+3562e + 06+0000e + 00


(a)

+1247e + 08+1143e + 08+1039e + 08+9349e + 07+8310e + 07+7272e + 07+6233e + 07+5194e + 07+4155e + 07+3116e + 07+2078e + 07+1039e + 07+0000e + 00


(b)

+1912e + 08+1753e + 08+1593e + 08+1434e + 08+1275e + 08+1115e + 08+9560e + 07+7966e + 07+6373e + 07+4780e + 07+3187e + 07+1593e + 07+0000e + 00


(c)

+2711e + 08+2485e + 08+2259e + 08+2033e + 08+1807e + 08+1581e + 08+1355e + 08+1130e + 08+9036e + 07+6777e + 07+4518e + 07+2259e + 07+0000e + 00


(d)


+3201e + 07+2953e + 07+2705e + 07+2457e + 07+2209e + 07+1961e + 07+1713e + 07+1464e + 07+1216e + 07+9682e + 06+7201e + 06+4720e + 06+2239e + 06

S Mises(Avg 75)


y

xz

(a)

+3222e + 07+3066e + 07+2810e + 07+2554e + 07+2299e + 07+2043e + 07+1787e + 07+1531e + 07+1275e + 07+1019e + 06+7633e + 06+5074e + 06+2515e + 06

S Mises(Avg 75)


y

xz

(b)

Figure 10 Continued


+3763e + 07+3480e + 07+3198e + 07+2915e + 07+2632e + 07+2349e + 07+2067e + 07+1784e + 07+1501e + 07+1219e + 06+9358e + 06+6531e + 06+3704e + 06

S Mises(Avg 75)


y

xz

(c)

+5135e + 07+4745e + 07+4355e + 07+3965e + 07+3575e + 07+3186e + 07+2796e + 07+2406e + 07+2016e + 07+1626e + 06+1236e + 06+8456e + 06+4556e + 06

S Mises(Avg 75)


y

xz

(d)


+2373e + 08+2185e + 08+1998e + 08+1810e + 08+1622e + 08+1434e + 08+1246e + 08+1059e + 08+8709e + 07+6831e + 07+4953e + 07+3075e + 07+1197e + 07



y

xz

(a)

+2641e + 08+2424e + 08+2207e + 08+1990e + 08+1773e + 08+1556e + 08+1339e + 08+1122e + 08+9046e + 07+6876e + 07+4706e + 07+2536e + 07+3655e + 06



y

xz

(b)

+3743e + 08+3439e + 08+3134e + 08+2830e + 08+2525e + 08+2221e + 08+1916e + 08+1612e + 08+1307e + 08+1003e + 08+6980e + 07+3935e + 07+8901e + 06



y

xz

(c)

+5285e + 08+4855e + 08+4425e + 08+3996e + 08+3566e + 08+3136e + 08+2707e + 08+2277e + 08+1847e + 08+1418e + 08+9882e + 07+5585e + 07+1289e + 07



y

xz

(d)






Path A Path BPath C



40

35

30

25

20

15

10

5

0

Hei

ght (

m)

0 5 10 15 20 25Stress (MPa)

30 35 40 45 50



(a)

40

35

30

25

20

15

10

5

0

Hei

ght (

m)

0 5 10 15 20 25Stress (MPa)

30 35 40 45 50



(b)40

35

30

25

20

15

10

5

0

Hei

ght (

m)

0 5 10 15 20 25Stress (MPa)

30 35 40 45 50



(c)





0 50 100 150 200 250 300 350 400 450 500Stress (MPa)



36

30

24

18

12

6

0

Hei

ght (

m)

(a)

0 50 100 150 200 250 300 350 400 450 500Stress (MPa)



36

30

24

18

12

6

0

Hei

ght (

m)

(b)

0 50 100 150 200 250 300 350 400 450 500Stress (MPa)



36

30

24

18

12

6

0

Hei

ght (

m)

(c)


43210


Disp

lace

men

t (m

m)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

(a)

43210


Disp

lace

men

t (m

m)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

(b)

43210


Disp

lace

men

t (m

m)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

(c)



0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

10

5

0

ndash5

ndash10

Basa

l she

ar (lowast

104 kN

)

(a)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

10

5

0

ndash5

ndash10

Basa

l she

ar (lowast

104 kN

)

(b)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

10

5

0

ndash5

ndash10

Basa

l she

ar (lowast

104 kN

)

(c)


SPHCEL


309 308 31331

367 361

416436

0

1

2

3

4

5

Disp

lace

men

t (m

m)

(a)

SPHCEL


19 188 201 207246 258

311326

0

1

2

3

4

5

Disp

lace

men

t (m

m)

(b)

Figure 17 Continued


SPHCEL


226 228 243 24628 288

3133

0

1

2

3

4

5

Disp

lace

men

t (m

m)

(c)


SPHCEL


533 532 549 556622 632 662 621

0123456789

101112

Basa

l she

ar (lowast

104 kN

)

(a)

SPHCEL


414 419493 486

665 699

855926

0123456789

101112

Basa

l she

ar (lowast

104 kN

)

(b)

Figure 18 Continued











Nomenclature



SPHCEL


528 538578 567

761 762 799852

0123456789

101112

Basa

l she

ar (lowast

104 kN

)

(c)




Data Availability


Disclosure




Acknowledgments


References
































































states Γ0

Water 1000 1480 0001 0 0




(a) (b)

(c) (d)


+1297e + 05+1193e + 05+1090e + 05+9869e + 04+8837e + 04+7804e + 04+6772e + 04+5739e + 04+4707e + 04+3674e + 04+2642e + 04+1609e + 04+5768e + 03

S Mises(Avg 75)

(a)

+1312e + 05+1210e + 05+1108e + 05+1006e + 05+9039e + 04+8018e + 04+6997e + 04+5975e + 04+4954e + 04+3933e + 04+2911e + 04+1890e + 04+8686e + 03

S Mises(Avg 75)

(b)

Figure 5 Continued





+1121e + 05+1032e + 05+9436e + 04+8547e + 04+7659e + 04+6770e + 04+5882e + 04+4993e + 04+4105e + 04+3216e + 04+2328e + 04+1439e + 04+5509e + 03

S Mises(Avg 75)

(c)

+1139e + 05+1050e + 05+9610e + 04+8772e + 04+7833e + 04+6944e + 04+6056e + 04+5167e + 04+4279e + 04+3390e + 04+2501e + 04+1613e + 04+7242e + 03

S Mises(Avg 75)

(d)






400

800

354

30




86600

1200

113

7538

550

Insulating layer

R1012

R912

R812

R712

R6122

R5147

R4173

R3198

R2224

R1249






ΔT N










of states [0

LNG (liquid) 480 1500 000113 0 0

y

xz

(a)

y

xz

(b)













030

025

020

015

010

005

000

Sa (g

)

Period (s)



0 1 2 3 4 5 6



+4275e + 07+3919e + 07+3562e + 07+3206e + 07+2850e + 07+2494e + 07+2137e + 07+1781e + 07+1425e + 07+1069e + 07+7125e + 06+3562e + 06+0000e + 00


(a)

+1247e + 08+1143e + 08+1039e + 08+9349e + 07+8310e + 07+7272e + 07+6233e + 07+5194e + 07+4155e + 07+3116e + 07+2078e + 07+1039e + 07+0000e + 00


(b)

+1912e + 08+1753e + 08+1593e + 08+1434e + 08+1275e + 08+1115e + 08+9560e + 07+7966e + 07+6373e + 07+4780e + 07+3187e + 07+1593e + 07+0000e + 00


(c)

+2711e + 08+2485e + 08+2259e + 08+2033e + 08+1807e + 08+1581e + 08+1355e + 08+1130e + 08+9036e + 07+6777e + 07+4518e + 07+2259e + 07+0000e + 00


(d)


+3201e + 07+2953e + 07+2705e + 07+2457e + 07+2209e + 07+1961e + 07+1713e + 07+1464e + 07+1216e + 07+9682e + 06+7201e + 06+4720e + 06+2239e + 06

S Mises(Avg 75)


y

xz

(a)

+3222e + 07+3066e + 07+2810e + 07+2554e + 07+2299e + 07+2043e + 07+1787e + 07+1531e + 07+1275e + 07+1019e + 06+7633e + 06+5074e + 06+2515e + 06

S Mises(Avg 75)


y

xz

(b)

Figure 10 Continued


+3763e + 07+3480e + 07+3198e + 07+2915e + 07+2632e + 07+2349e + 07+2067e + 07+1784e + 07+1501e + 07+1219e + 06+9358e + 06+6531e + 06+3704e + 06

S Mises(Avg 75)


y

xz

(c)

+5135e + 07+4745e + 07+4355e + 07+3965e + 07+3575e + 07+3186e + 07+2796e + 07+2406e + 07+2016e + 07+1626e + 06+1236e + 06+8456e + 06+4556e + 06

S Mises(Avg 75)


y

xz

(d)


+2373e + 08+2185e + 08+1998e + 08+1810e + 08+1622e + 08+1434e + 08+1246e + 08+1059e + 08+8709e + 07+6831e + 07+4953e + 07+3075e + 07+1197e + 07



y

xz

(a)

+2641e + 08+2424e + 08+2207e + 08+1990e + 08+1773e + 08+1556e + 08+1339e + 08+1122e + 08+9046e + 07+6876e + 07+4706e + 07+2536e + 07+3655e + 06



y

xz

(b)

+3743e + 08+3439e + 08+3134e + 08+2830e + 08+2525e + 08+2221e + 08+1916e + 08+1612e + 08+1307e + 08+1003e + 08+6980e + 07+3935e + 07+8901e + 06



y

xz

(c)

+5285e + 08+4855e + 08+4425e + 08+3996e + 08+3566e + 08+3136e + 08+2707e + 08+2277e + 08+1847e + 08+1418e + 08+9882e + 07+5585e + 07+1289e + 07



y

xz

(d)






Path A Path BPath C



40

35

30

25

20

15

10

5

0

Hei

ght (

m)

0 5 10 15 20 25Stress (MPa)

30 35 40 45 50



(a)

40

35

30

25

20

15

10

5

0

Hei

ght (

m)

0 5 10 15 20 25Stress (MPa)

30 35 40 45 50



(b)40

35

30

25

20

15

10

5

0

Hei

ght (

m)

0 5 10 15 20 25Stress (MPa)

30 35 40 45 50



(c)





0 50 100 150 200 250 300 350 400 450 500Stress (MPa)



36

30

24

18

12

6

0

Hei

ght (

m)

(a)

0 50 100 150 200 250 300 350 400 450 500Stress (MPa)



36

30

24

18

12

6

0

Hei

ght (

m)

(b)

0 50 100 150 200 250 300 350 400 450 500Stress (MPa)



36

30

24

18

12

6

0

Hei

ght (

m)

(c)


43210


Disp

lace

men

t (m

m)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

(a)

43210


Disp

lace

men

t (m

m)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

(b)

43210


Disp

lace

men

t (m

m)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

(c)



0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

10

5

0

ndash5

ndash10

Basa

l she

ar (lowast

104 kN

)

(a)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

10

5

0

ndash5

ndash10

Basa

l she

ar (lowast

104 kN

)

(b)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

10

5

0

ndash5

ndash10

Basa

l she

ar (lowast

104 kN

)

(c)


SPHCEL


309 308 31331

367 361

416436

0

1

2

3

4

5

Disp

lace

men

t (m

m)

(a)

SPHCEL


19 188 201 207246 258

311326

0

1

2

3

4

5

Disp

lace

men

t (m

m)

(b)

Figure 17 Continued


SPHCEL


226 228 243 24628 288

3133

0

1

2

3

4

5

Disp

lace

men

t (m

m)

(c)


SPHCEL


533 532 549 556622 632 662 621

0123456789

101112

Basa

l she

ar (lowast

104 kN

)

(a)

SPHCEL


414 419493 486

665 699

855926

0123456789

101112

Basa

l she

ar (lowast

104 kN

)

(b)

Figure 18 Continued











Nomenclature



SPHCEL


528 538578 567

761 762 799852

0123456789

101112

Basa

l she

ar (lowast

104 kN

)

(c)




Data Availability


Disclosure




Acknowledgments


References



















































(a) (b)

(c) (d)


+1297e + 05+1193e + 05+1090e + 05+9869e + 04+8837e + 04+7804e + 04+6772e + 04+5739e + 04+4707e + 04+3674e + 04+2642e + 04+1609e + 04+5768e + 03

S Mises(Avg 75)

(a)

+1312e + 05+1210e + 05+1108e + 05+1006e + 05+9039e + 04+8018e + 04+6997e + 04+5975e + 04+4954e + 04+3933e + 04+2911e + 04+1890e + 04+8686e + 03

S Mises(Avg 75)

(b)

Figure 5 Continued





+1121e + 05+1032e + 05+9436e + 04+8547e + 04+7659e + 04+6770e + 04+5882e + 04+4993e + 04+4105e + 04+3216e + 04+2328e + 04+1439e + 04+5509e + 03

S Mises(Avg 75)

(c)

+1139e + 05+1050e + 05+9610e + 04+8772e + 04+7833e + 04+6944e + 04+6056e + 04+5167e + 04+4279e + 04+3390e + 04+2501e + 04+1613e + 04+7242e + 03

S Mises(Avg 75)

(d)






400

800

354

30




86600

1200

113

7538

550

Insulating layer

R1012

R912

R812

R712

R6122

R5147

R4173

R3198

R2224

R1249






ΔT N










of states [0

LNG (liquid) 480 1500 000113 0 0

y

xz

(a)

y

xz

(b)













030

025

020

015

010

005

000

Sa (g

)

Period (s)



0 1 2 3 4 5 6



+4275e + 07+3919e + 07+3562e + 07+3206e + 07+2850e + 07+2494e + 07+2137e + 07+1781e + 07+1425e + 07+1069e + 07+7125e + 06+3562e + 06+0000e + 00


(a)

+1247e + 08+1143e + 08+1039e + 08+9349e + 07+8310e + 07+7272e + 07+6233e + 07+5194e + 07+4155e + 07+3116e + 07+2078e + 07+1039e + 07+0000e + 00


(b)

+1912e + 08+1753e + 08+1593e + 08+1434e + 08+1275e + 08+1115e + 08+9560e + 07+7966e + 07+6373e + 07+4780e + 07+3187e + 07+1593e + 07+0000e + 00


(c)

+2711e + 08+2485e + 08+2259e + 08+2033e + 08+1807e + 08+1581e + 08+1355e + 08+1130e + 08+9036e + 07+6777e + 07+4518e + 07+2259e + 07+0000e + 00


(d)


+3201e + 07+2953e + 07+2705e + 07+2457e + 07+2209e + 07+1961e + 07+1713e + 07+1464e + 07+1216e + 07+9682e + 06+7201e + 06+4720e + 06+2239e + 06

S Mises(Avg 75)


y

xz

(a)

+3222e + 07+3066e + 07+2810e + 07+2554e + 07+2299e + 07+2043e + 07+1787e + 07+1531e + 07+1275e + 07+1019e + 06+7633e + 06+5074e + 06+2515e + 06

S Mises(Avg 75)


y

xz

(b)

Figure 10 Continued


+3763e + 07+3480e + 07+3198e + 07+2915e + 07+2632e + 07+2349e + 07+2067e + 07+1784e + 07+1501e + 07+1219e + 06+9358e + 06+6531e + 06+3704e + 06

S Mises(Avg 75)


y

xz

(c)

+5135e + 07+4745e + 07+4355e + 07+3965e + 07+3575e + 07+3186e + 07+2796e + 07+2406e + 07+2016e + 07+1626e + 06+1236e + 06+8456e + 06+4556e + 06

S Mises(Avg 75)


y

xz

(d)


+2373e + 08+2185e + 08+1998e + 08+1810e + 08+1622e + 08+1434e + 08+1246e + 08+1059e + 08+8709e + 07+6831e + 07+4953e + 07+3075e + 07+1197e + 07



y

xz

(a)

+2641e + 08+2424e + 08+2207e + 08+1990e + 08+1773e + 08+1556e + 08+1339e + 08+1122e + 08+9046e + 07+6876e + 07+4706e + 07+2536e + 07+3655e + 06



y

xz

(b)

+3743e + 08+3439e + 08+3134e + 08+2830e + 08+2525e + 08+2221e + 08+1916e + 08+1612e + 08+1307e + 08+1003e + 08+6980e + 07+3935e + 07+8901e + 06



y

xz

(c)

+5285e + 08+4855e + 08+4425e + 08+3996e + 08+3566e + 08+3136e + 08+2707e + 08+2277e + 08+1847e + 08+1418e + 08+9882e + 07+5585e + 07+1289e + 07



y

xz

(d)






Path A Path BPath C



40

35

30

25

20

15

10

5

0

Hei

ght (

m)

0 5 10 15 20 25Stress (MPa)

30 35 40 45 50



(a)

40

35

30

25

20

15

10

5

0

Hei

ght (

m)

0 5 10 15 20 25Stress (MPa)

30 35 40 45 50



(b)40

35

30

25

20

15

10

5

0

Hei

ght (

m)

0 5 10 15 20 25Stress (MPa)

30 35 40 45 50



(c)





0 50 100 150 200 250 300 350 400 450 500Stress (MPa)



36

30

24

18

12

6

0

Hei

ght (

m)

(a)

0 50 100 150 200 250 300 350 400 450 500Stress (MPa)



36

30

24

18

12

6

0

Hei

ght (

m)

(b)

0 50 100 150 200 250 300 350 400 450 500Stress (MPa)



36

30

24

18

12

6

0

Hei

ght (

m)

(c)


43210


Disp

lace

men

t (m

m)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

(a)

43210


Disp

lace

men

t (m

m)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

(b)

43210


Disp

lace

men

t (m

m)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

(c)



0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

10

5

0

ndash5

ndash10

Basa

l she

ar (lowast

104 kN

)

(a)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

10

5

0

ndash5

ndash10

Basa

l she

ar (lowast

104 kN

)

(b)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

10

5

0

ndash5

ndash10

Basa

l she

ar (lowast

104 kN

)

(c)


SPHCEL


309 308 31331

367 361

416436

0

1

2

3

4

5

Disp

lace

men

t (m

m)

(a)

SPHCEL


19 188 201 207246 258

311326

0

1

2

3

4

5

Disp

lace

men

t (m

m)

(b)

Figure 17 Continued


SPHCEL


226 228 243 24628 288

3133

0

1

2

3

4

5

Disp

lace

men

t (m

m)

(c)


SPHCEL


533 532 549 556622 632 662 621

0123456789

101112

Basa

l she

ar (lowast

104 kN

)

(a)

SPHCEL


414 419493 486

665 699

855926

0123456789

101112

Basa

l she

ar (lowast

104 kN

)

(b)

Figure 18 Continued











Nomenclature



SPHCEL


528 538578 567

761 762 799852

0123456789

101112

Basa

l she

ar (lowast

104 kN

)

(c)




Data Availability


Disclosure




Acknowledgments


References






















































+1121e + 05+1032e + 05+9436e + 04+8547e + 04+7659e + 04+6770e + 04+5882e + 04+4993e + 04+4105e + 04+3216e + 04+2328e + 04+1439e + 04+5509e + 03

S Mises(Avg 75)

(c)

+1139e + 05+1050e + 05+9610e + 04+8772e + 04+7833e + 04+6944e + 04+6056e + 04+5167e + 04+4279e + 04+3390e + 04+2501e + 04+1613e + 04+7242e + 03

S Mises(Avg 75)

(d)






400

800

354

30




86600

1200

113

7538

550

Insulating layer

R1012

R912

R812

R712

R6122

R5147

R4173

R3198

R2224

R1249






ΔT N










of states [0

LNG (liquid) 480 1500 000113 0 0

y

xz

(a)

y

xz

(b)













030

025

020

015

010

005

000

Sa (g

)

Period (s)



0 1 2 3 4 5 6



+4275e + 07+3919e + 07+3562e + 07+3206e + 07+2850e + 07+2494e + 07+2137e + 07+1781e + 07+1425e + 07+1069e + 07+7125e + 06+3562e + 06+0000e + 00


(a)

+1247e + 08+1143e + 08+1039e + 08+9349e + 07+8310e + 07+7272e + 07+6233e + 07+5194e + 07+4155e + 07+3116e + 07+2078e + 07+1039e + 07+0000e + 00


(b)

+1912e + 08+1753e + 08+1593e + 08+1434e + 08+1275e + 08+1115e + 08+9560e + 07+7966e + 07+6373e + 07+4780e + 07+3187e + 07+1593e + 07+0000e + 00


(c)

+2711e + 08+2485e + 08+2259e + 08+2033e + 08+1807e + 08+1581e + 08+1355e + 08+1130e + 08+9036e + 07+6777e + 07+4518e + 07+2259e + 07+0000e + 00


(d)


+3201e + 07+2953e + 07+2705e + 07+2457e + 07+2209e + 07+1961e + 07+1713e + 07+1464e + 07+1216e + 07+9682e + 06+7201e + 06+4720e + 06+2239e + 06

S Mises(Avg 75)


y

xz

(a)

+3222e + 07+3066e + 07+2810e + 07+2554e + 07+2299e + 07+2043e + 07+1787e + 07+1531e + 07+1275e + 07+1019e + 06+7633e + 06+5074e + 06+2515e + 06

S Mises(Avg 75)


y

xz

(b)

Figure 10 Continued


+3763e + 07+3480e + 07+3198e + 07+2915e + 07+2632e + 07+2349e + 07+2067e + 07+1784e + 07+1501e + 07+1219e + 06+9358e + 06+6531e + 06+3704e + 06

S Mises(Avg 75)


y

xz

(c)

+5135e + 07+4745e + 07+4355e + 07+3965e + 07+3575e + 07+3186e + 07+2796e + 07+2406e + 07+2016e + 07+1626e + 06+1236e + 06+8456e + 06+4556e + 06

S Mises(Avg 75)


y

xz

(d)


+2373e + 08+2185e + 08+1998e + 08+1810e + 08+1622e + 08+1434e + 08+1246e + 08+1059e + 08+8709e + 07+6831e + 07+4953e + 07+3075e + 07+1197e + 07



y

xz

(a)

+2641e + 08+2424e + 08+2207e + 08+1990e + 08+1773e + 08+1556e + 08+1339e + 08+1122e + 08+9046e + 07+6876e + 07+4706e + 07+2536e + 07+3655e + 06



y

xz

(b)

+3743e + 08+3439e + 08+3134e + 08+2830e + 08+2525e + 08+2221e + 08+1916e + 08+1612e + 08+1307e + 08+1003e + 08+6980e + 07+3935e + 07+8901e + 06



y

xz

(c)

+5285e + 08+4855e + 08+4425e + 08+3996e + 08+3566e + 08+3136e + 08+2707e + 08+2277e + 08+1847e + 08+1418e + 08+9882e + 07+5585e + 07+1289e + 07



y

xz

(d)






Path A Path BPath C



40

35

30

25

20

15

10

5

0

Hei

ght (

m)

0 5 10 15 20 25Stress (MPa)

30 35 40 45 50



(a)

40

35

30

25

20

15

10

5

0

Hei

ght (

m)

0 5 10 15 20 25Stress (MPa)

30 35 40 45 50



(b)40

35

30

25

20

15

10

5

0

Hei

ght (

m)

0 5 10 15 20 25Stress (MPa)

30 35 40 45 50



(c)





0 50 100 150 200 250 300 350 400 450 500Stress (MPa)



36

30

24

18

12

6

0

Hei

ght (

m)

(a)

0 50 100 150 200 250 300 350 400 450 500Stress (MPa)



36

30

24

18

12

6

0

Hei

ght (

m)

(b)

0 50 100 150 200 250 300 350 400 450 500Stress (MPa)



36

30

24

18

12

6

0

Hei

ght (

m)

(c)


43210


Disp

lace

men

t (m

m)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

(a)

43210


Disp

lace

men

t (m

m)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

(b)

43210


Disp

lace

men

t (m

m)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

(c)



0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

10

5

0

ndash5

ndash10

Basa

l she

ar (lowast

104 kN

)

(a)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

10

5

0

ndash5

ndash10

Basa

l she

ar (lowast

104 kN

)

(b)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

10

5

0

ndash5

ndash10

Basa

l she

ar (lowast

104 kN

)

(c)


SPHCEL


309 308 31331

367 361

416436

0

1

2

3

4

5

Disp

lace

men

t (m

m)

(a)

SPHCEL


19 188 201 207246 258

311326

0

1

2

3

4

5

Disp

lace

men

t (m

m)

(b)

Figure 17 Continued


SPHCEL


226 228 243 24628 288

3133

0

1

2

3

4

5

Disp

lace

men

t (m

m)

(c)


SPHCEL


533 532 549 556622 632 662 621

0123456789

101112

Basa

l she

ar (lowast

104 kN

)

(a)

SPHCEL


414 419493 486

665 699

855926

0123456789

101112

Basa

l she

ar (lowast

104 kN

)

(b)

Figure 18 Continued











Nomenclature



SPHCEL


528 538578 567

761 762 799852

0123456789

101112

Basa

l she

ar (lowast

104 kN

)

(c)




Data Availability


Disclosure




Acknowledgments


References




















































ΔT N










of states [0

LNG (liquid) 480 1500 000113 0 0

y

xz

(a)

y

xz

(b)













030

025

020

015

010

005

000

Sa (g

)

Period (s)



0 1 2 3 4 5 6



+4275e + 07+3919e + 07+3562e + 07+3206e + 07+2850e + 07+2494e + 07+2137e + 07+1781e + 07+1425e + 07+1069e + 07+7125e + 06+3562e + 06+0000e + 00


(a)

+1247e + 08+1143e + 08+1039e + 08+9349e + 07+8310e + 07+7272e + 07+6233e + 07+5194e + 07+4155e + 07+3116e + 07+2078e + 07+1039e + 07+0000e + 00


(b)

+1912e + 08+1753e + 08+1593e + 08+1434e + 08+1275e + 08+1115e + 08+9560e + 07+7966e + 07+6373e + 07+4780e + 07+3187e + 07+1593e + 07+0000e + 00


(c)

+2711e + 08+2485e + 08+2259e + 08+2033e + 08+1807e + 08+1581e + 08+1355e + 08+1130e + 08+9036e + 07+6777e + 07+4518e + 07+2259e + 07+0000e + 00


(d)


+3201e + 07+2953e + 07+2705e + 07+2457e + 07+2209e + 07+1961e + 07+1713e + 07+1464e + 07+1216e + 07+9682e + 06+7201e + 06+4720e + 06+2239e + 06

S Mises(Avg 75)


y

xz

(a)

+3222e + 07+3066e + 07+2810e + 07+2554e + 07+2299e + 07+2043e + 07+1787e + 07+1531e + 07+1275e + 07+1019e + 06+7633e + 06+5074e + 06+2515e + 06

S Mises(Avg 75)


y

xz

(b)

Figure 10 Continued


+3763e + 07+3480e + 07+3198e + 07+2915e + 07+2632e + 07+2349e + 07+2067e + 07+1784e + 07+1501e + 07+1219e + 06+9358e + 06+6531e + 06+3704e + 06

S Mises(Avg 75)


y

xz

(c)

+5135e + 07+4745e + 07+4355e + 07+3965e + 07+3575e + 07+3186e + 07+2796e + 07+2406e + 07+2016e + 07+1626e + 06+1236e + 06+8456e + 06+4556e + 06

S Mises(Avg 75)


y

xz

(d)


+2373e + 08+2185e + 08+1998e + 08+1810e + 08+1622e + 08+1434e + 08+1246e + 08+1059e + 08+8709e + 07+6831e + 07+4953e + 07+3075e + 07+1197e + 07



y

xz

(a)

+2641e + 08+2424e + 08+2207e + 08+1990e + 08+1773e + 08+1556e + 08+1339e + 08+1122e + 08+9046e + 07+6876e + 07+4706e + 07+2536e + 07+3655e + 06



y

xz

(b)

+3743e + 08+3439e + 08+3134e + 08+2830e + 08+2525e + 08+2221e + 08+1916e + 08+1612e + 08+1307e + 08+1003e + 08+6980e + 07+3935e + 07+8901e + 06



y

xz

(c)

+5285e + 08+4855e + 08+4425e + 08+3996e + 08+3566e + 08+3136e + 08+2707e + 08+2277e + 08+1847e + 08+1418e + 08+9882e + 07+5585e + 07+1289e + 07



y

xz

(d)






Path A Path BPath C



40

35

30

25

20

15

10

5

0

Hei

ght (

m)

0 5 10 15 20 25Stress (MPa)

30 35 40 45 50



(a)

40

35

30

25

20

15

10

5

0

Hei

ght (

m)

0 5 10 15 20 25Stress (MPa)

30 35 40 45 50



(b)40

35

30

25

20

15

10

5

0

Hei

ght (

m)

0 5 10 15 20 25Stress (MPa)

30 35 40 45 50



(c)





0 50 100 150 200 250 300 350 400 450 500Stress (MPa)



36

30

24

18

12

6

0

Hei

ght (

m)

(a)

0 50 100 150 200 250 300 350 400 450 500Stress (MPa)



36

30

24

18

12

6

0

Hei

ght (

m)

(b)

0 50 100 150 200 250 300 350 400 450 500Stress (MPa)



36

30

24

18

12

6

0

Hei

ght (

m)

(c)


43210


Disp

lace

men

t (m

m)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

(a)

43210


Disp

lace

men

t (m

m)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

(b)

43210


Disp

lace

men

t (m

m)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

(c)



0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

10

5

0

ndash5

ndash10

Basa

l she

ar (lowast

104 kN

)

(a)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

10

5

0

ndash5

ndash10

Basa

l she

ar (lowast

104 kN

)

(b)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

10

5

0

ndash5

ndash10

Basa

l she

ar (lowast

104 kN

)

(c)


SPHCEL


309 308 31331

367 361

416436

0

1

2

3

4

5

Disp

lace

men

t (m

m)

(a)

SPHCEL


19 188 201 207246 258

311326

0

1

2

3

4

5

Disp

lace

men

t (m

m)

(b)

Figure 17 Continued


SPHCEL


226 228 243 24628 288

3133

0

1

2

3

4

5

Disp

lace

men

t (m

m)

(c)


SPHCEL


533 532 549 556622 632 662 621

0123456789

101112

Basa

l she

ar (lowast

104 kN

)

(a)

SPHCEL


414 419493 486

665 699

855926

0123456789

101112

Basa

l she

ar (lowast

104 kN

)

(b)

Figure 18 Continued











Nomenclature



SPHCEL


528 538578 567

761 762 799852

0123456789

101112

Basa

l she

ar (lowast

104 kN

)

(c)




Data Availability


Disclosure




Acknowledgments


References





























































030

025

020

015

010

005

000

Sa (g

)

Period (s)



0 1 2 3 4 5 6



+4275e + 07+3919e + 07+3562e + 07+3206e + 07+2850e + 07+2494e + 07+2137e + 07+1781e + 07+1425e + 07+1069e + 07+7125e + 06+3562e + 06+0000e + 00


(a)

+1247e + 08+1143e + 08+1039e + 08+9349e + 07+8310e + 07+7272e + 07+6233e + 07+5194e + 07+4155e + 07+3116e + 07+2078e + 07+1039e + 07+0000e + 00


(b)

+1912e + 08+1753e + 08+1593e + 08+1434e + 08+1275e + 08+1115e + 08+9560e + 07+7966e + 07+6373e + 07+4780e + 07+3187e + 07+1593e + 07+0000e + 00


(c)

+2711e + 08+2485e + 08+2259e + 08+2033e + 08+1807e + 08+1581e + 08+1355e + 08+1130e + 08+9036e + 07+6777e + 07+4518e + 07+2259e + 07+0000e + 00


(d)


+3201e + 07+2953e + 07+2705e + 07+2457e + 07+2209e + 07+1961e + 07+1713e + 07+1464e + 07+1216e + 07+9682e + 06+7201e + 06+4720e + 06+2239e + 06

S Mises(Avg 75)


y

xz

(a)

+3222e + 07+3066e + 07+2810e + 07+2554e + 07+2299e + 07+2043e + 07+1787e + 07+1531e + 07+1275e + 07+1019e + 06+7633e + 06+5074e + 06+2515e + 06

S Mises(Avg 75)


y

xz

(b)

Figure 10 Continued


+3763e + 07+3480e + 07+3198e + 07+2915e + 07+2632e + 07+2349e + 07+2067e + 07+1784e + 07+1501e + 07+1219e + 06+9358e + 06+6531e + 06+3704e + 06

S Mises(Avg 75)


y

xz

(c)

+5135e + 07+4745e + 07+4355e + 07+3965e + 07+3575e + 07+3186e + 07+2796e + 07+2406e + 07+2016e + 07+1626e + 06+1236e + 06+8456e + 06+4556e + 06

S Mises(Avg 75)


y

xz

(d)


+2373e + 08+2185e + 08+1998e + 08+1810e + 08+1622e + 08+1434e + 08+1246e + 08+1059e + 08+8709e + 07+6831e + 07+4953e + 07+3075e + 07+1197e + 07



y

xz

(a)

+2641e + 08+2424e + 08+2207e + 08+1990e + 08+1773e + 08+1556e + 08+1339e + 08+1122e + 08+9046e + 07+6876e + 07+4706e + 07+2536e + 07+3655e + 06



y

xz

(b)

+3743e + 08+3439e + 08+3134e + 08+2830e + 08+2525e + 08+2221e + 08+1916e + 08+1612e + 08+1307e + 08+1003e + 08+6980e + 07+3935e + 07+8901e + 06



y

xz

(c)

+5285e + 08+4855e + 08+4425e + 08+3996e + 08+3566e + 08+3136e + 08+2707e + 08+2277e + 08+1847e + 08+1418e + 08+9882e + 07+5585e + 07+1289e + 07



y

xz

(d)






Path A Path BPath C



40

35

30

25

20

15

10

5

0

Hei

ght (

m)

0 5 10 15 20 25Stress (MPa)

30 35 40 45 50



(a)

40

35

30

25

20

15

10

5

0

Hei

ght (

m)

0 5 10 15 20 25Stress (MPa)

30 35 40 45 50



(b)40

35

30

25

20

15

10

5

0

Hei

ght (

m)

0 5 10 15 20 25Stress (MPa)

30 35 40 45 50



(c)





0 50 100 150 200 250 300 350 400 450 500Stress (MPa)



36

30

24

18

12

6

0

Hei

ght (

m)

(a)

0 50 100 150 200 250 300 350 400 450 500Stress (MPa)



36

30

24

18

12

6

0

Hei

ght (

m)

(b)

0 50 100 150 200 250 300 350 400 450 500Stress (MPa)



36

30

24

18

12

6

0

Hei

ght (

m)

(c)


43210


Disp

lace

men

t (m

m)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

(a)

43210


Disp

lace

men

t (m

m)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

(b)

43210


Disp

lace

men

t (m

m)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

(c)



0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

10

5

0

ndash5

ndash10

Basa

l she

ar (lowast

104 kN

)

(a)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

10

5

0

ndash5

ndash10

Basa

l she

ar (lowast

104 kN

)

(b)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

10

5

0

ndash5

ndash10

Basa

l she

ar (lowast

104 kN

)

(c)


SPHCEL


309 308 31331

367 361

416436

0

1

2

3

4

5

Disp

lace

men

t (m

m)

(a)

SPHCEL


19 188 201 207246 258

311326

0

1

2

3

4

5

Disp

lace

men

t (m

m)

(b)

Figure 17 Continued


SPHCEL


226 228 243 24628 288

3133

0

1

2

3

4

5

Disp

lace

men

t (m

m)

(c)


SPHCEL


533 532 549 556622 632 662 621

0123456789

101112

Basa

l she

ar (lowast

104 kN

)

(a)

SPHCEL


414 419493 486

665 699

855926

0123456789

101112

Basa

l she

ar (lowast

104 kN

)

(b)

Figure 18 Continued











Nomenclature



SPHCEL


528 538578 567

761 762 799852

0123456789

101112

Basa

l she

ar (lowast

104 kN

)

(c)




Data Availability


Disclosure




Acknowledgments


References



















































+4275e + 07+3919e + 07+3562e + 07+3206e + 07+2850e + 07+2494e + 07+2137e + 07+1781e + 07+1425e + 07+1069e + 07+7125e + 06+3562e + 06+0000e + 00


(a)

+1247e + 08+1143e + 08+1039e + 08+9349e + 07+8310e + 07+7272e + 07+6233e + 07+5194e + 07+4155e + 07+3116e + 07+2078e + 07+1039e + 07+0000e + 00


(b)

+1912e + 08+1753e + 08+1593e + 08+1434e + 08+1275e + 08+1115e + 08+9560e + 07+7966e + 07+6373e + 07+4780e + 07+3187e + 07+1593e + 07+0000e + 00


(c)

+2711e + 08+2485e + 08+2259e + 08+2033e + 08+1807e + 08+1581e + 08+1355e + 08+1130e + 08+9036e + 07+6777e + 07+4518e + 07+2259e + 07+0000e + 00


(d)


+3201e + 07+2953e + 07+2705e + 07+2457e + 07+2209e + 07+1961e + 07+1713e + 07+1464e + 07+1216e + 07+9682e + 06+7201e + 06+4720e + 06+2239e + 06

S Mises(Avg 75)


y

xz

(a)

+3222e + 07+3066e + 07+2810e + 07+2554e + 07+2299e + 07+2043e + 07+1787e + 07+1531e + 07+1275e + 07+1019e + 06+7633e + 06+5074e + 06+2515e + 06

S Mises(Avg 75)


y

xz

(b)

Figure 10 Continued


+3763e + 07+3480e + 07+3198e + 07+2915e + 07+2632e + 07+2349e + 07+2067e + 07+1784e + 07+1501e + 07+1219e + 06+9358e + 06+6531e + 06+3704e + 06

S Mises(Avg 75)


y

xz

(c)

+5135e + 07+4745e + 07+4355e + 07+3965e + 07+3575e + 07+3186e + 07+2796e + 07+2406e + 07+2016e + 07+1626e + 06+1236e + 06+8456e + 06+4556e + 06

S Mises(Avg 75)


y

xz

(d)


+2373e + 08+2185e + 08+1998e + 08+1810e + 08+1622e + 08+1434e + 08+1246e + 08+1059e + 08+8709e + 07+6831e + 07+4953e + 07+3075e + 07+1197e + 07



y

xz

(a)

+2641e + 08+2424e + 08+2207e + 08+1990e + 08+1773e + 08+1556e + 08+1339e + 08+1122e + 08+9046e + 07+6876e + 07+4706e + 07+2536e + 07+3655e + 06



y

xz

(b)

+3743e + 08+3439e + 08+3134e + 08+2830e + 08+2525e + 08+2221e + 08+1916e + 08+1612e + 08+1307e + 08+1003e + 08+6980e + 07+3935e + 07+8901e + 06



y

xz

(c)

+5285e + 08+4855e + 08+4425e + 08+3996e + 08+3566e + 08+3136e + 08+2707e + 08+2277e + 08+1847e + 08+1418e + 08+9882e + 07+5585e + 07+1289e + 07



y

xz

(d)






Path A Path BPath C



40

35

30

25

20

15

10

5

0

Hei

ght (

m)

0 5 10 15 20 25Stress (MPa)

30 35 40 45 50



(a)

40

35

30

25

20

15

10

5

0

Hei

ght (

m)

0 5 10 15 20 25Stress (MPa)

30 35 40 45 50



(b)40

35

30

25

20

15

10

5

0

Hei

ght (

m)

0 5 10 15 20 25Stress (MPa)

30 35 40 45 50



(c)





0 50 100 150 200 250 300 350 400 450 500Stress (MPa)



36

30

24

18

12

6

0

Hei

ght (

m)

(a)

0 50 100 150 200 250 300 350 400 450 500Stress (MPa)



36

30

24

18

12

6

0

Hei

ght (

m)

(b)

0 50 100 150 200 250 300 350 400 450 500Stress (MPa)



36

30

24

18

12

6

0

Hei

ght (

m)

(c)


43210


Disp

lace

men

t (m

m)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

(a)

43210


Disp

lace

men

t (m

m)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

(b)

43210


Disp

lace

men

t (m

m)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

(c)



0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

10

5

0

ndash5

ndash10

Basa

l she

ar (lowast

104 kN

)

(a)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

10

5

0

ndash5

ndash10

Basa

l she

ar (lowast

104 kN

)

(b)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

10

5

0

ndash5

ndash10

Basa

l she

ar (lowast

104 kN

)

(c)


SPHCEL


309 308 31331

367 361

416436

0

1

2

3

4

5

Disp

lace

men

t (m

m)

(a)

SPHCEL


19 188 201 207246 258

311326

0

1

2

3

4

5

Disp

lace

men

t (m

m)

(b)

Figure 17 Continued


SPHCEL


226 228 243 24628 288

3133

0

1

2

3

4

5

Disp

lace

men

t (m

m)

(c)


SPHCEL


533 532 549 556622 632 662 621

0123456789

101112

Basa

l she

ar (lowast

104 kN

)

(a)

SPHCEL


414 419493 486

665 699

855926

0123456789

101112

Basa

l she

ar (lowast

104 kN

)

(b)

Figure 18 Continued











Nomenclature



SPHCEL


528 538578 567

761 762 799852

0123456789

101112

Basa

l she

ar (lowast

104 kN

)

(c)




Data Availability


Disclosure




Acknowledgments


References



















































+3763e + 07+3480e + 07+3198e + 07+2915e + 07+2632e + 07+2349e + 07+2067e + 07+1784e + 07+1501e + 07+1219e + 06+9358e + 06+6531e + 06+3704e + 06

S Mises(Avg 75)


y

xz

(c)

+5135e + 07+4745e + 07+4355e + 07+3965e + 07+3575e + 07+3186e + 07+2796e + 07+2406e + 07+2016e + 07+1626e + 06+1236e + 06+8456e + 06+4556e + 06

S Mises(Avg 75)


y

xz

(d)


+2373e + 08+2185e + 08+1998e + 08+1810e + 08+1622e + 08+1434e + 08+1246e + 08+1059e + 08+8709e + 07+6831e + 07+4953e + 07+3075e + 07+1197e + 07



y

xz

(a)

+2641e + 08+2424e + 08+2207e + 08+1990e + 08+1773e + 08+1556e + 08+1339e + 08+1122e + 08+9046e + 07+6876e + 07+4706e + 07+2536e + 07+3655e + 06



y

xz

(b)

+3743e + 08+3439e + 08+3134e + 08+2830e + 08+2525e + 08+2221e + 08+1916e + 08+1612e + 08+1307e + 08+1003e + 08+6980e + 07+3935e + 07+8901e + 06



y

xz

(c)

+5285e + 08+4855e + 08+4425e + 08+3996e + 08+3566e + 08+3136e + 08+2707e + 08+2277e + 08+1847e + 08+1418e + 08+9882e + 07+5585e + 07+1289e + 07



y

xz

(d)






Path A Path BPath C



40

35

30

25

20

15

10

5

0

Hei

ght (

m)

0 5 10 15 20 25Stress (MPa)

30 35 40 45 50



(a)

40

35

30

25

20

15

10

5

0

Hei

ght (

m)

0 5 10 15 20 25Stress (MPa)

30 35 40 45 50



(b)40

35

30

25

20

15

10

5

0

Hei

ght (

m)

0 5 10 15 20 25Stress (MPa)

30 35 40 45 50



(c)





0 50 100 150 200 250 300 350 400 450 500Stress (MPa)



36

30

24

18

12

6

0

Hei

ght (

m)

(a)

0 50 100 150 200 250 300 350 400 450 500Stress (MPa)



36

30

24

18

12

6

0

Hei

ght (

m)

(b)

0 50 100 150 200 250 300 350 400 450 500Stress (MPa)



36

30

24

18

12

6

0

Hei

ght (

m)

(c)


43210


Disp

lace

men

t (m

m)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

(a)

43210


Disp

lace

men

t (m

m)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

(b)

43210


Disp

lace

men

t (m

m)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

(c)



0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

10

5

0

ndash5

ndash10

Basa

l she

ar (lowast

104 kN

)

(a)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

10

5

0

ndash5

ndash10

Basa

l she

ar (lowast

104 kN

)

(b)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

10

5

0

ndash5

ndash10

Basa

l she

ar (lowast

104 kN

)

(c)


SPHCEL


309 308 31331

367 361

416436

0

1

2

3

4

5

Disp

lace

men

t (m

m)

(a)

SPHCEL


19 188 201 207246 258

311326

0

1

2

3

4

5

Disp

lace

men

t (m

m)

(b)

Figure 17 Continued


SPHCEL


226 228 243 24628 288

3133

0

1

2

3

4

5

Disp

lace

men

t (m

m)

(c)


SPHCEL


533 532 549 556622 632 662 621

0123456789

101112

Basa

l she

ar (lowast

104 kN

)

(a)

SPHCEL


414 419493 486

665 699

855926

0123456789

101112

Basa

l she

ar (lowast

104 kN

)

(b)

Figure 18 Continued











Nomenclature



SPHCEL


528 538578 567

761 762 799852

0123456789

101112

Basa

l she

ar (lowast

104 kN

)

(c)




Data Availability


Disclosure




Acknowledgments


References






















































Path A Path BPath C



40

35

30

25

20

15

10

5

0

Hei

ght (

m)

0 5 10 15 20 25Stress (MPa)

30 35 40 45 50



(a)

40

35

30

25

20

15

10

5

0

Hei

ght (

m)

0 5 10 15 20 25Stress (MPa)

30 35 40 45 50



(b)40

35

30

25

20

15

10

5

0

Hei

ght (

m)

0 5 10 15 20 25Stress (MPa)

30 35 40 45 50



(c)





0 50 100 150 200 250 300 350 400 450 500Stress (MPa)



36

30

24

18

12

6

0

Hei

ght (

m)

(a)

0 50 100 150 200 250 300 350 400 450 500Stress (MPa)



36

30

24

18

12

6

0

Hei

ght (

m)

(b)

0 50 100 150 200 250 300 350 400 450 500Stress (MPa)



36

30

24

18

12

6

0

Hei

ght (

m)

(c)


43210


Disp

lace

men

t (m

m)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

(a)

43210


Disp

lace

men

t (m

m)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

(b)

43210


Disp

lace

men

t (m

m)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

(c)



0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

10

5

0

ndash5

ndash10

Basa

l she

ar (lowast

104 kN

)

(a)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

10

5

0

ndash5

ndash10

Basa

l she

ar (lowast

104 kN

)

(b)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

10

5

0

ndash5

ndash10

Basa

l she

ar (lowast

104 kN

)

(c)


SPHCEL


309 308 31331

367 361

416436

0

1

2

3

4

5

Disp

lace

men

t (m

m)

(a)

SPHCEL


19 188 201 207246 258

311326

0

1

2

3

4

5

Disp

lace

men

t (m

m)

(b)

Figure 17 Continued


SPHCEL


226 228 243 24628 288

3133

0

1

2

3

4

5

Disp

lace

men

t (m

m)

(c)


SPHCEL


533 532 549 556622 632 662 621

0123456789

101112

Basa

l she

ar (lowast

104 kN

)

(a)

SPHCEL


414 419493 486

665 699

855926

0123456789

101112

Basa

l she

ar (lowast

104 kN

)

(b)

Figure 18 Continued











Nomenclature



SPHCEL


528 538578 567

761 762 799852

0123456789

101112

Basa

l she

ar (lowast

104 kN

)

(c)




Data Availability


Disclosure




Acknowledgments


References





















































0 50 100 150 200 250 300 350 400 450 500Stress (MPa)



36

30

24

18

12

6

0

Hei

ght (

m)

(a)

0 50 100 150 200 250 300 350 400 450 500Stress (MPa)



36

30

24

18

12

6

0

Hei

ght (

m)

(b)

0 50 100 150 200 250 300 350 400 450 500Stress (MPa)



36

30

24

18

12

6

0

Hei

ght (

m)

(c)


43210


Disp

lace

men

t (m

m)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

(a)

43210


Disp

lace

men

t (m

m)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

(b)

43210


Disp

lace

men

t (m

m)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

(c)



0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

10

5

0

ndash5

ndash10

Basa

l she

ar (lowast

104 kN

)

(a)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

10

5

0

ndash5

ndash10

Basa

l she

ar (lowast

104 kN

)

(b)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

10

5

0

ndash5

ndash10

Basa

l she

ar (lowast

104 kN

)

(c)


SPHCEL


309 308 31331

367 361

416436

0

1

2

3

4

5

Disp

lace

men

t (m

m)

(a)

SPHCEL


19 188 201 207246 258

311326

0

1

2

3

4

5

Disp

lace

men

t (m

m)

(b)

Figure 17 Continued


SPHCEL


226 228 243 24628 288

3133

0

1

2

3

4

5

Disp

lace

men

t (m

m)

(c)


SPHCEL


533 532 549 556622 632 662 621

0123456789

101112

Basa

l she

ar (lowast

104 kN

)

(a)

SPHCEL


414 419493 486

665 699

855926

0123456789

101112

Basa

l she

ar (lowast

104 kN

)

(b)

Figure 18 Continued











Nomenclature



SPHCEL


528 538578 567

761 762 799852

0123456789

101112

Basa

l she

ar (lowast

104 kN

)

(c)




Data Availability


Disclosure




Acknowledgments


References



















































0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

10

5

0

ndash5

ndash10

Basa

l she

ar (lowast

104 kN

)

(a)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

10

5

0

ndash5

ndash10

Basa

l she

ar (lowast

104 kN

)

(b)

0 5 10Time (s)

15 20

25 LNG50 LNG

75 LNG100 LNG

10

5

0

ndash5

ndash10

Basa

l she

ar (lowast

104 kN

)

(c)


SPHCEL


309 308 31331

367 361

416436

0

1

2

3

4

5

Disp

lace

men

t (m

m)

(a)

SPHCEL


19 188 201 207246 258

311326

0

1

2

3

4

5

Disp

lace

men

t (m

m)

(b)

Figure 17 Continued


SPHCEL


226 228 243 24628 288

3133

0

1

2

3

4

5

Disp

lace

men

t (m

m)

(c)


SPHCEL


533 532 549 556622 632 662 621

0123456789

101112

Basa

l she

ar (lowast

104 kN

)

(a)

SPHCEL


414 419493 486

665 699

855926

0123456789

101112

Basa

l she

ar (lowast

104 kN

)

(b)

Figure 18 Continued











Nomenclature



SPHCEL


528 538578 567

761 762 799852

0123456789

101112

Basa

l she

ar (lowast

104 kN

)

(c)




Data Availability


Disclosure




Acknowledgments


References



















































SPHCEL


226 228 243 24628 288

3133

0

1

2

3

4

5

Disp

lace

men

t (m

m)

(c)


SPHCEL


533 532 549 556622 632 662 621

0123456789

101112

Basa

l she

ar (lowast

104 kN

)

(a)

SPHCEL


414 419493 486

665 699

855926

0123456789

101112

Basa

l she

ar (lowast

104 kN

)

(b)

Figure 18 Continued











Nomenclature



SPHCEL


528 538578 567

761 762 799852

0123456789

101112

Basa

l she

ar (lowast

104 kN

)

(c)




Data Availability


Disclosure




Acknowledgments


References




























































Nomenclature



SPHCEL


528 538578 567

761 762 799852

0123456789

101112

Basa

l she

ar (lowast

104 kN

)

(c)




Data Availability


Disclosure




Acknowledgments


References




















































Data Availability


Disclosure




Acknowledgments


References



















































SeismicAnalysisofaLargeLNGTankconsideringtheEffectof ... · 26/5/2020 · sinusoidal excitation....

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Transcript of SeismicAnalysisofaLargeLNGTankconsideringtheEffectof ... · 26/5/2020 · sinusoidal excitation....