Dynamic responses of oil storage tank considering wind interference effect

Engineering Failure Analysis 104 (2019) 1053–1063

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Engineering Failure Analysis journal homepage: www.elsevier.com/locate/engfailanal

Dynamic responses of oil storage tank considering wind interference effect

T

⁎

Wei Jinga,b, , Jingxuan Wanga,b, Xuansheng Chenga,b a Key Laboratory of Disaster Prevention and Mitigation in Civil Engineering of Gansu Province, Lanzhou University of Technology, Lanzhou 730050, PR China b Western Engineering Research Center of Disaster Mitigation in Civil Engineering of Ministry of Education, Lanzhou University of Technology, Lanzhou 730050, PR China

A R T IC LE I N F O

ABS TRA CT

Keywords: Oil storage tank Wind interference effect Earthquake Fluid-structure interaction Dynamic responses

Oil storage tanks play a very important role in economic and social development; however, there are numerous cases of damage caused by wind and earthquake. Considering fluid-structure interaction, wind interference and material nonlinearity, firstly, wind fields are S^#simulated by computational fluid dynamics and solved by SIMPLEC method under the conditions of single tank and double tanks; second, the wind pressures in the two cases are obtained and applied to the oil storage tanks, 3-D numerical calculation model is established. Wind disturbance effect on dynamic responses is discussed, and influence of storage ratio and seismic wave type on dynamic responses under wind-earthquake action is further investigated. Results show that wind disturbance effect has a great influence on the dynamic responses of liquid storage tank, especially in the empty state. When the liquid storage ratio is large, traditional oil storage tank is easy to be damaged under the action of wind-strong earthquake. Wind interference effect should be considered in the design and application of oil storage tanks, at the same time, shock absorption and strengthening measures should be taken for oil storage tanks under wind-strong earthquake.

1. Introduction Oil prices fluctuate greatly under the influence of political and economic factors, at present, the United States, Japan and other developed countries have established a complete petroleum reserve system, but most countries have not yet completed the strategic reserve inventory, so it is urgent to improve the strategic petroleum reserve base. These practical problems are bound to continue to develop towards large-scale and large-amount oil storage tanks, at the same time, oil storage tanks will be seriously threatened and the losses will be greater under earthquake action. Oil storage tanks in special environments are not only threatened by earthquakes, but also often affected by strong winds during operation. Traditional non-isolation oil storage tanks often have inadequate seismic capacity, which makes them vulnerable to damage under the earthquake. Once the damage occurs, it will cause great losses to the economy; moreover, the leakage of special liquids will further lead to secondary disasters such as environmental pollution and fire; and the most serious case is that people life safety will be threatened. The remarkable characteristics of large oil storage tanks are large diameter-thickness ratio and small heightdiameter ratio, which makes oil storage tanks belong to wind-sensitive structure [1]. Oil storage tanks damaged by earthquake and

⁎ Corresponding author at: Key Laboratory of Disaster Prevention and Mitigation in Civil Engineering of Gansu Province, Lanzhou University of Technology, Lanzhou 730050, PR China. E-mail address: [email protected] (W. Jing).

https://doi.org/10.1016/j.engfailanal.2019.06.040 Received 10 December 2018; Received in revised form 8 May 2019; Accepted 20 June 2019 Available online 26 June 2019 1350-6307/ © 2019 Elsevier Ltd. All rights reserved.

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Fig. 1. Failure cases of liquid storage tanks.

wind load are as shown in Fig. 1. At present, a large number of researchers have carried out research on liquid storage tanks, Dogangun et al. [2] studied dynamic responses of rectangular liquid storage structure by three-dimensional finite element method. Livaoglu [3] used Housner simplified model to simulate FSI, studied seismic performance of rectangular liquid storage structure considering foundation effect in frequency domain it is found that the base shear force decreases with the decrease of foundation stiffness. Considering sloshing mechanism, liquid viscous and wall elasticity Shahverdiani et al. [4] studied dynamic responses of concrete liquid storage structure under resonant excitation by finite element method based on FSI. Ozdemir et al. [5] pointed out that the particularity of liquid storage structure relative to traditional structure is manifested in hydrodynamic pressure, large-amplitude non-linear liquid sloshing, in order to evaluate the anti-seismic ability of this kind of structure, numerical method is an indispensable and effective tool, because it can accurately consider some non-linear characteristic of liquid storage structure under earthquake action. Chen and Kianoush [6] proposed a simplified method for seismic analysis and design of liquid storage structures based on generalized single degree of freedom theory, and the hydrodynamic pressure and the main parameters affecting the liquid storage structure were analyzed considering the wall elasticity. Trebuňa et al. [7] studied failure of water storage tank by analytical, numerical and experimental analysis, the results of analysis were help to assess the failure reason and to express the recommendations for further analysis of the non-damaged tank. Rebouillat and Liksonov [8] summarized the FSI numerical methods and pointed out that the current methods used to predict the sloshing of liquid storage structure mainly include finite element method, finite difference method and smooth particle method. Li et al. [9] proposed a simplified mechanical model for sloshing of liquid storage structure with arbitrary cross section, and verified the rationality of the simplified model. Richter [10] proposed a complete Euler method for FSI problems, which used one-way implicit variational equation to solve the coupling problems. Hashemi et al. [11] proposed an analytical method for evaluating the impulse pressure of liquid storage structure under horizontal earthquake action considering FSI and wall elasticity. Nicolici and Bilegan [12] simulated FSI based on complete one-way coupling, it was found that impulse pressure of liquid would be amplified considering the elasticity of the wall. Liu and Lam [13] used the equivalent hydrostatics method to simulate the lateral pressure load of liquid storage structure, and obtained that the high-order modes had a great influence on non-linear stress state of the wall plate. Gilmanov and Le [14] proposed a numerical method to simulate the FSI of elastic thin plate under arbitrary deformation in incompressible fluid. Cheng et al. [15–17] studied dynamic responses of liquid storage structure based on potential flow theory and simplified method, respectively. Miladi and Razzaghi [18] performed Numerical analysis of un-anchored steel oil tank using ABAQUS, carried out a parametric study to evaluate the effect of amount of stored liquid on seismic behavior and performance of the studied tank, and obtained the critical PGA of the dynamic buckling of the considered tank. At present, the research on liquid storage tanks is mostly aimed at the situation of earthquake or wind action alone. The dynamic responses and failure modes of liquid storage tanks under wind and earthquake are quite different; besides, there are numerous cases of damage of liquid storage tanks under wind and earthquake; however, researches on liquid storage tanks are very deficient considering the combined effect of wind and earthquake. FSI, free surface liquid sloshing and tank material nonlinearity are considered. Wind field is simulated by computational fluid dynamics (CFD), pressure-velocity coupling is solved by using SIMPLEC method. In order to consider wind disturbance effect,wind fields with single tank and double tanks are calculated, respectively, then the flow field distribution and surface wind pressure around the tank are obtained. In order to better describe the mathematical problem, two Descartes coordinate system are defined, one of which is assumed to be fixed in space, and the other is moved with the liquid, 3-D numerical calculation model of oil storage tank is established, Newmark-β method is used to solve the dynamic problem, and Automatic Time Stepping scheme is used to control the size of time step to improve convergence. Near-field Northridge wave and farfield long-period Tianjin wave are selected as seismic input, and the wind disturbance effect on dynamic responses of liquid storage tank is studied. 2. Boundary conditions 2.1. Wind field boundary conditions For steady incompressible flows with high Reynolds number, there are four kinds of boundary conditions, as shown in Fig. 2. 1054

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Symmetry

Velocity-inlet

Pressure-outlet

Wall

Symmetry

Fig. 2. Boundary conditions for wind field simulation.

2.2. FSI boundary conditions On the FSI interface, the following conditions need to be satisfied:

{us = uf ,

(Displacement condition) σs⋅ns = σf ⋅nf ,

(Stress condition)

(1)

where uf and us are displacement vectors of liquid and structure on the FSI interface; σf and σs are stresses of liquid and structure on the FSI interface; nf and ns are outer normal vectors on the FSI interface. 2.3. Free surface boundary conditions In order to better describe the mathematical problem, two Descartes coordinate system are defined, as shown in Fig. 3, one of which is assumed to be fixed in space, and the other is moved with the liquid [19]. For any quantity q to be solved can be expressed in any one of the coordinate system, namely, q(x, y, z, t) = q(x', y', z', t). Free surface Γf is the interface between the liquid and the atmosphere, the interface will be affected by the surrounding pressure and surface tension. In the fixed Descartes coordinate system, the kinetic and dynamic boundary conditions on the free surface are:

∂ϕ ∂ϕ ∂η ∂η =0 − + ∂z ∂x ∂x ∂t

(2)

∂ϕ 1 + ∇ϕ⋅∇ϕ + gη = 0 2 ∂t

(3)

where η(x, y, t) is vertical coordinate of free surface in z(x, y, t); ϕ is velocity potential; g is gravity acceleration. Because liquid sloshing displacement is large, the moving coordinate for solving the problem will bring greater convenience; free surface boundary conditions Eqs. (2) and (3) in the fixed coordinate system can be expressed as Eqs. (4) and (5) in the moving coordinate system.

∂η′ ∂ϕ ∂η′ ∂ϕ +⎛ − us ⎞ =0 − ∂t ∂z ⎝ ∂x ′ ⎠ ∂x ′

(4)

∂ϕ 1 − us⋅∇ϕ + ∇ϕ⋅∇ϕ + gη = 0 2 ∂t

(5)

y

z y

z

x

x

Free surface at t+ t

y x

Free surface at t

Fig. 3. Schematic diagram of movement of liquid free surface. 1055

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where us is tank displacement under the action of earthquake. In the moving coordinate system, the potential function ϕ is composed of two parts: ϕ1 and ϕ2, which are caused by the motion of the structure and the interior liquid sloshing.

a ϕ = ϕ1 + ϕ2 , ϕ1 = −⎛ − x ′⎞ us′ ⎝2 ⎠

(6)

where a is the tank length Parallel to the direction of earthquake action. Taking Eq. (6) into Eqs. (4) and (5):

∂ϕ2 ∂η′ ∂ϕ2 ∂η′ + − =0 ∂t ∂x ′ ∂x ′ ∂z ′

(7)

∂ϕ2 du ′ 1 1 + ∇ϕ2⋅∇ϕ2 + gη′ + x ′ s = |us′ |2 ∂t 2 dt 2

(8)

Then the initial boundary value problems of free surface liquid sloshing in the moving coordinate system can be obtained:

⎧ ∂η′ = − ∂ϕ2 ∂η′ + ∂ϕ2 = 0, ⎪ ∂t ∂x ′ ∂x ′ ∂z′ ⎨ ∂ϕ2 du ′ 1 = − ∇ϕ2⋅∇ϕ2 − gη′ − x s , ⎪ t 2 dt ∂ ⎩

Γf Γf

(9)

3. Control equations 3.1. Wind field Modified k-ε model is used, two additional equations are used to calculate the turbulent kinetic energy k and the dissipation rate ε:

∂ (uj ρk ) ∂ (ρk ) ∂ ⎡⎛ ν ∂k ⎤ ⎡ 2 ∂u = ν + T⎞ ρkδij i − Pk⎤ − ρε + Sk = 0 + − ⎥ ⎢3 ⎥ ∂x j ∂x j ⎢ σ ∂ x ∂t ∂x j k j ⎝ ⎠ ⎣ ⎦ ⎣ ⎦

(10)

∂ (ρεuj ) ∂ (ρε ) ∂ ⎡⎛ ν ∂ε ⎤ ε 2 ε2 ∂u = + ν + T⎞ − C1ε ⎛⎜ ρkδij i − Pk ⎞⎟ − C2ε ρ + Sε ⎥ ∂x j ∂x j ⎢ 3 σ ∂ x k x k ∂t ∂ ε j j ⎠ ⎣⎝ ⎦ ⎝ ⎠

(11)

⎜

⎜

where Pk = νT

(

∂ui ∂xj

+

∂uj ∂xi

)

∂ui ∂xj

⎟

⎟

is generation term of turbulent kinetic energy k due to mean velocity gradient; δij is the Kronecker delta;

νT is Turbulence viscosity; Sk and Sε are custom source items; C1ε, and C2ε are empirical constants; the model constants are C1ε = 1.44, C2ε = 1.92, Cμ = 0.09 and σk = 1.0, which are the same as those used in the standard k-ε model [20]. For Sk and Sε, the model proposed by Enoki and Ishihara [21,22] is adopted and can be expressed as:

Sk =

1 1 β ρCf a |u |3 − βd ρCf a |u | k 2 p 2

(12)

Sε =

1 1 ε Cp1ε βp ρ Cf a |u |3 − Cp2ε βd ρCf a |u | ε 2 2 k

(13)

where βp and Cp1ε are model constants, which are equal to 1.0 and 1.5, respectively; βd and Cp2ε are modelled as the functions of the packing density γ0.

⎤ ⎛ 1 − γ0 ⎞ βd = min ⎡ ⎢4.0, αk1 exp ⎜ γ ⎟ + αk 2⎥ ⎝ 0 ⎠ ⎦ ⎣

Cp2ε

(14)

, γ0 ≤ γc ⎧ 0.7 ⎪ = γ − γc ⎞ ⎨ α1ε sin ⎜⎛π 0 ⎟ + α2ε , γ0 > γc 2(1 − γc ) ⎠ ⎪ ⎝ ⎩

(15)

where the coefficients are identified to be αk1 is 0.5, αk2 is 0.5, α1ε is 0.8, α2ε is 0.7 and γc is 0.312 [23]. 3.2. Fluid-structure interaction Based on the theory of liquid sloshing, the equation of liquid motion can be obtained from hydrodynamics:

¨ + ρf Br¨ + q 0 = 0 HP + AṖ + EP

(16)

Structure equation is: 1056

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Ms u ¨ s + Cs u̇ s + Ks us − BT P = −Ms u ¨ g + Pw

(17)

FSI is achieved by pressure vector p and coefficient matrix B in Eqs. 16 and 17, and the coupling motion equation of the system can be obtained:

¨ g + Pw ⎤ ⎡ Ms 0 ⎤ ⎡ r¨ ⎤ + ⎡ Cs 0 ⎤ ⎡ ṙ ⎤ + ⎡ Ks − BT ⎤ ⎡ r ⎤ = ⎡− Ms u P⎦ ⎢ ¨ ⎦ ⎣ 0 A ⎦ ⎣ Ṗ ⎦ ⎣ 0 ⎢ ρf B E ⎥ ⎣ P − q0 ⎥ ⎣ H ⎦ ⎣ ⎦ ⎣ ⎦

(18)

¨ g is earthquake acceleration vector; ρf is where Ms, Cs and Ks are mass, damping and stiffness matrices; us is displacement vector; u liquid density; P is liquid pressure vector; q0 is input excitation vector acting on liquid from structure; H, A, E and B are coefficient matrices. In this paper, Newmark-β method is adopted to solve the matrix differential equation: 1 ¨ s, t + γ Δt 2 u ¨ s, t + Δt us, t + Δt = us, t + Δt u̇ s, t + ⎛ − γ ⎞ Δt 2 u ⎝2 ⎠

(19)

u̇ s, t + Δt = u̇ s, t + (1 − β )Δt u ¨ s, t + β Δt u ¨ s, t + Δt

(20)

where βand γ are constants. Transforming Eq. (17) into the following incremental form:

Ms u ¨ s, t + Δt + Cs u̇ s, t + Δt + Ks us, t + Δt = −Ms u ¨ g (t + Δt ) + Pw + BT P With regards to the basic parameters of Newmark-β, it is absolutely stable to choose β = 0.5, γ = 0.25 and Δt ≤ maximum natural vibration period), and the result reaches the required accuracy. Substituting Eqs. (19) and (20) into Eq. (21):

Δt Δt ⎛Ms + ¨ s, t ⎞ + Ks us, t + Δt = −Ms u ¨ g (t + Δt ) + Pw + BT P Cs ⎞ u ¨ s, t + Δt + Cs ⎛u̇ s, t + u 2 2 ⎠ ⎝ ⎝ ⎠

(21) Tmax 100

(Tmax is the

(22)

From Eq. (20), the following equation can be obtained:

u ¨ s, t + Δt =

4 4 (us, t + Δt − us, t ) − u̇ s, t − u ¨ s, t Δt 2 Δt

(23)

Substituting Eq. (23) into Eq. (22):

2 4 2 ⎛Ks + Cs + Ms ⎞ us, t + Δt = Cs ⎛ us, t + u̇ s, t ⎞+ Δt Δt 2 ⎠ ⎝ ⎝ Δt ⎠ 4 4 Ms ⎛ 2 us, t + u̇ s, t + u̇ s, t ⎞ − Ms u ¨ g (t + Δt ) + Pw + BT P Δt ⎝ Δt ⎠

(24)

¨ s, t + Δt and u̇ s, t + Δt can be obtained from Eq. (23) and Eq. (20), respectively. us, t+Δt can be obtained from Eq. (24), u The model includes material nonlinearity, FSI and complex stress state, displacement is taken as convergence condition, and Automatic Time Stepping scheme is used to control the size of time step to improve convergence. ‖usk + 1 − usk‖ ≤ εd max {‖usk + 1 ‖, ε0 }

(25)

where εd is displacement tolerance; ε0 is predefined small constants. 4. Numerical example 4.1. Calculation model A chemical plant in Gansu Province, PRC is used as engineering case study, the tank diameter is 21 m, the tank height is 16 m, the tank wall thickness from the bottom to the top is as follows: 0-2 m is 14 mm; 2-4 m is 12 mm; 4-6 m is 10 mm; 6-10 m is 8 mm; and 1016 m is 6 mm. Plastic-Bilinear material model is used for the tank, its elastic modulus is 2.06 × 1011 Pa, Poisson's ratio is 0.30, density is 7800 kg/m3, strain hardening modulus is 2.06 × 109P, initial yield stress is 235 MPa, and Shell element is used for the tank. Potential-based fluid material and 3-D Fluid element are used to simulate the liquid, its density is 1000 kg/m3, and the bulk modulus is 2.3 × 109 Pa. The edge length of the mesh along the height is 1 m, number of divisions along the circumferential direction is 60. the calculation model established by ADINA is shown in Fig. 4. Near-field Northridge and far-field long-period Tianjin waves are chosen to conduct time history analysis, as shown in Fig. 5. Air fluid material is used to simulate wind field in Fluent, the density is 1.225 kg/m3, the viscosity coefficient is 1.7894 × 10−5 kg/mˑs. Solution method based on pressure as basic variable is used, Simple method for coupled iteration of pressure and velocity is used, first order discrete scheme is adopted for both momentum equation and turbulent energy dissipation rate equation. A single tank and double tanks are established, respectively, for the case of double tanks, the direction of wind load action is perpendicular to the line of the tank core. The distribution of wind pressure on the surface of liquid storage tank is obtained in Fluent, 1057

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Fig. 4. Calculation model.

1.6

0.4 0.35

Northridge

1.2

Fourier amplitude

Response acceleration/g

1.4

Tianjin

1

Northridge

0.3

Tianjin

0.25

0.8 0.6

0.2

0.15

0.4 0.2

0.1

0.05

0

0

0

1

2

3

4

5

6

0

Period/s

5

10

15

20

25

30

35

40

Period/s Fig. 5. Earthquake waves.

and the results of wind field are shown in Fig. 6. Then the wind pressure calculation results are extracted, as shown in Fig. 7, and acted on the calculation model as shown in Fig. 4. 4.2. Wind interference effect on dynamic responses Oil storage tanks are usually arranged in a certain form in actual oil depots, which will lead to disturbance and interference effect of wind field between oil storage tanks. In order to ensure the safety of oil storage tanks, it is necessary to study the influence of wind interference effect on dynamic responses of oil storage tanks. In order to study the effect of wind disturbance on the dynamic responses of oil storage tanks, the flow field distributions of single tank and double tank are solved by Fluent. Far-field long-period Tianjin wave is chosen, its peak ground acceleration (PGA) is adjusted to 0.40 g, and the dynamic responses of oil storage tanks under two kinds of wind fields are comparatively studied by ADINA. The comparisons of effective stress and displacement are shown in Fig. 8. As shown in Fig. 8, when the disturbance effect of wind between oil storage tanks is taken into account, the effective stress and displacement of the wall are significantly greater than those without considering the effect of wind disturbance. Therefore, in order to ensure the safety of oil storage tanks, it is necessary to consider the effect of wind interference in actual design. 4.3. Dynamic responses under different liquid storage ratio The change of liquid storage ratio is an important characteristic of liquid storage tank, and the wind load and earthquake action 1058

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6.33e+02

8.10e+02

5.08e+02

6.23e+02

3.84e+02

4.36e+02

2.80e+02

2.49e+02

1.35e+02

6.19e+01

1.07e+02

-1.25e+02

-1.14e+02

-3.12e+02

-2.38e+02

-4.99e+02

-3.63e+02

-6.86e+02

-4.78e+02

-8.74e+02

-6.12e+02

-1.06e+03

-7.36e+02

-1.25e+03

-8.60e+02

-1.43e+03

-9.85e+02

-1.62e+03

-1.11e+03

-1.81e+03

-1.23e+03

-2.00e+03

-1.36e+03

-2.18e+03

-1.48e+03

-2.37e+03

-1.61e+03

-2.58e+03

-1.73e+03

-2.74e+03

-1.86e+03

-2.93e+03

Fig. 6. Wind pressure cloud chart (unit: Pa).

Fig. 7. Wind pressure.

have different effects on oil storage tanks with different liquid storage ratio, that is, in empty state, the wind load will bring more adverse effects, but in the case of large liquid storage ratio, the earthquake action will lead to more adverse results. In order to study the dynamic responses of oil storage tanks under wind-earthquake action with different liquid storage ratios, liquid storage ratios 0% and 75% are compared, and Tianjin wave with PGA 0.40 g are used to conduct time history analysis. Besides, in order to investigate the wind interference effect, the influence coefficient is proposed, as shown in Eq. (14), in which, the denominator is the dynamic 1059

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12

18

Single tank

10

16

Double tank

8

Displacement/mm

Effective stress/MPa

20

14 12 10 8 6 4 2

Single tank Double tank

6 4 2 0 -2 -4 -6

0

-8 0

1

2

3

4

5

6

7

8

9

0

10

1

2

3

Time/s

4

5

6

7

8

9

10

Time/s

(a) Effective stress

(b) Wall displacement

Fig. 8. Wind interference effect on dynamic responses.

response without considering the effect of wind disturbance, while the numerator is difference value between dynamic responses corresponding to single tank and double tanks. By doing this, the effect of wind disturbance can be quantitatively assessed. The specific results are shown in Table 1.

R=

Dtwo − Done % Done

(26)

where R is influence coefficient of wind interference effect; Dtwo is dynamic response considering wind disturbance, Done is dynamic response without considering wind disturbance. As shown in Table 1, under the empty condition, the wall effective stresses without considering and considering wind disturbance are 11.572 MPa and 17.331 MPa, respectively, and the difference ratio is 49.77%; when the liquid storage ratio is 75%, the wall effective stresses without considering and considering wind disturbance are 194.702 MPa and 202.545 MPa, respectively, and the difference ratio is 4.03%. Under the empty condition, the wall displacement without considering and considering wind disturbance are 4.549 mm and 10.128 mm, respectively, and the difference ratio is 122.64; when the liquid storage ratio is 75%, the wall displacement without considering and considering wind disturbance are 238.233 mm and 256.576 mm, respectively, and the difference ratio is 7.70%. Under the empty condition, the Base shear force without considering and considering wind disturbance are 43.212kN and 63.356kN, respectively, and the difference ratio is 46.62%; when the liquid storage ratio is 75%, the wall effective stresses without considering and considering wind disturbance are 723.722kN and 785.997kN, respectively, the difference ratio is 8.57%. Thus, in the empty state, the wind disturbance effect on dynamic responses of oil storage tank is very large. When the liquid storage ratio is 75%, the effect of wind disturbance on the dynamic responses is basically reduced to less than 10%. The main reason is that liquid pressure can offset part of wind load. Therefore, when the liquid storage ratio is small, the wind disturbance effect will be great. When the liquid storage ratio is large, the earthquake will play a controlling role, and the influence of wind disturbance will be weakened. 4.4. Dynamic responses under different type earthquake action The near-field Northridge wave is chosen, which was recorded extensively in the immediate source region by strong groundmotion accelerometers, which is near-field earthquake. Besides, far-field long-period Tianjin wave is chosen. The calculation results Table 1 Effect of wind disturbance on dynamic responses under different liquid storage ratios. Dynamic responses

Effective stress/MPa

Wall displacement/mm

Base shear force/kN

Type

Liquid storage ratios

Single tank Double tank R (%) Single tank Double tank R (%) Single tank Double tank R (%)

1060

0%

75%

11.572 17.331 49.77 4.549 10.128 122.64 43.212 63.356 46.62

194.702 202.545 4.03 238.233 256.576 7.70 723.722 785.997 8.57

Engineering Failure Analysis 104 (2019) 1053–1063

W. Jing, et al. MAXIMUM 2.209E+8 EG 1, EL 1867, IPT 122 (2.051E+08) MINIMUM * 0.000 EG 1, EL 2266, IPT 222

MAXIMUM 2.224E+8 EG 1, EL 2237, IPT 222 (2.184E+08) MINIMUM * 0.000 EG 1, EL 2266, IPT 222

EFFECTIVE STRESS RSI CALC SHELL T=1.00 TIME 4.42

EFFECTIVE STRESS RSI CALC SHELL T=1.00 TIME 4.75

2.080E+08

2.080E+08

1.760E+08

1.760E+08

1.440E+08

1.440E+08

1.120E+08

1.120E+08

8.000E+07

6.000E+07

4.800E+07

4.800E+07

1.600E+07

1.600E+07

Fig. 9. Effective stress under near-field Northridge wave action.

of effective stress, displacement and base shear force under Northridge wave action are shown in Figs. 9–10, and under Tianjin wave action are shown in Figs. 11-12. From Figs. 9 and 11, under the action of Northridge wave, it can be seen that the effective stresses corresponding to considering and without considering wind interference effect are 218.422 MPa and 205.183 MPa, respectively; under the action of Tianjin wave, it can be seen that the effective stresses corresponding to considering and without considering wind interference effect are 202.545 MPa and 194.702 MPa, respectively. From Figs. 10 and 12, under the action of Northridge wave, it can be seen that the wall displacements corresponding to considering and without considering wind interference effect are 287.916 mm and 259.048, respectively; under the action of Tianjin wave, it can be seen that the wall displacements corresponding to considering and without considering wind interference effect are 256.576 mm and 238.233 mm, respectively. Besides, base shear forces under the two conditions are also discussed. Results show that the base shear force corresponding to considering and without considering wind interference effect are 882.787kN and 783.570kN, respectively; under the action of Tianjin wave, it can be seen that the base shear forces corresponding to considering and without considering wind interference effect are 785.9976kN and 723.722kN, respectively. It can be seen that the dynamic responses of oil storage tank under near-field earthquake is obviously greater than that under farfield long-period earthquake. Under strong earthquake, the force of liquid storage tank is close to the ultimate strength of material, and it is easy to fail. Therefore, in order to resist strong earthquakes, the traditional oil storage tank must adopt measures such as isolation under strong earthquake.

MAXIMUM 0.09462 NODE1, 1075 MINIMUM * -0.2590 NODE 1078

MAXIMUM 0.09534 NODE1, 1327 MINIMUM * -0.2879 NODE 1075

2-DISPLACEMENT TIME 5.2800

2-DISPLACEMENT TIME 3.6900

0.0750

0.0750

0.0250

0.0250

-0.0250

-0.0250

-0.0750

-0.0750

-0.1250

-0.1450

-0.1750

-0.1950

-0.2250

-0.2850

Fig. 10. Wall displacement under near-field Northridge wave action. 1061

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MAXIMUM 2.175E+8 EG 1, EL 1257, IPT 222 (1.947E+08) MINIMUM * 0.000 EG 1, EL 2266, IPT 222

MAXIMUM 3.362E+8 EG 1, EL 2069, IPT 122 (2.025E+08) MINIMUM * 0.000 EG 1, EL 2266, IPT 222

EFFECTIVE STRESS RSI CALC SHELL T=1.00 TIME 5.47

EFFECTIVE STRESS RSI CALC SHELL T=1.00 TIME 4.35

2.080E+08

3.250E+08

1.760E+08

2.750E+08

1.440E+08

2.250E+08

1.120E+08

1.750E+08

8.000E+07

1.250E+08

4.800E+07

7.500E+07

1.600E+07

2.500E+07

Fig. 11. Effective stress under far-field long-period Tianjin wave action.

MAXIMUM 0.06619 NODE1, 1078 MINIMUM * -0.2382 NODE 1075

MAXIMUM 0.1169 NODE1, 1075 MINIMUM * -0.2566 NODE 1078

2-DISPLACEMENT TIME 3.6900

2-DISPLACEMENT TIME 5.4400

0.0600

0.0800

0.0300

0.0267

0.0000

-0.0267

-0.0300

-0.0800

-0.0600

-0.1333

-0.0900

-0.1867

-0.1200

-0.2400

Fig. 12. Wall displacement under far-field long-period Tianjin wave action.

5. Conclusions (1) Because of wind interference effect, the wind pressure acting on the double tank surface is significantly larger than that of the single tank surface, and the wind pressure amplitude corresponding to double tank situation is nearly twice that of the single tank situation. (2) Under conbined action of earthquake and wind, tank dynamic responses are great, and tank stress is close to yield strength 235 Mpa of steel. Dynamic responses of oil storage tank corresponding to double tanks are obviously larger than that of single tank, it can be seen that if wind disturbance effect is not considered, the responses will be underestimate. (3) Effect of wind disturbance on empty oil storage tank is very great, with the increase of oil storage ratio, wind disturbance effect is weakened. (4) After wind disturbance effect being considered, the stress and deformation of oil storage tank under near-field earthquake are obviously larger than that under far-field long-period earthquake.

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Conflict of interests The authors declare that they have no conflict of interest. Acknowledgments This paper is a part of the China Postdoctoral Science Foundation (2018M633652XB), a part of the National Natural Science Foundation of China (Grant number: 51368039, 51708270), a part of the Hongliu Outstanding Young Talents Support Program of Lanzhou University of Technology (04-061807) and a part of the Plan Project of Science and Technology in Gansu Province (Grant number: 144GKCA032). References [1] Y. Lin, Wind Load and Wind-Induced Buckling of Large Steel Tanks, Zhejiang University, Hanzhou, 2014. [2] A. Doğangün, R. Livaoğlu, Hydrodynamic pressures acting on the walls of rectangular fluid containers, Struct. Eng. Mech. 17 (2) (2014) 203–214. [3] R. Livaoglu, Investigation of seismic behavior of fluid-rectangular tank-soil/foundation systems in frequency domain, Soil Dyn. Earthq. Eng. 28 (2) (2008) 132–146. [4] K. Shahverdiani, A.R. Rahai, F. Khoshnoudian, Fluid-structure interaction in concrete cylindrical tanks under harmonic excitations, Int. J. Civil Eng. 6 (2) (2008) 132–141. [5] Z. Ozdemir, M. Souli, Y.M. Fahjan, Application of nonlinear fluid-structure interaction methods to seismic analysis of anchored and unanchored tanks, Eng. Struct. 32 (2) (2010) 409–423. [6] J.Z. Chen, M.R. Kianoush, Generalized SDOF system for seismic analysis of concrete rectangular liquid storage tanks, Eng. Struct. 31 (2) (2009) 2426–2435. [7] F. Trebuňa, F. Šimčák, J. Bocko, Failure analysis of storage tank, Eng. Fail. Anal. 16 (1) (2009) 26–38. [8] S. Rebouillat, D. Liksonov, Fluid-structure interaction in partially filled liquid containers: a comparative review of numerical approaches, Comput. Fluids 39 (5) (2010) 739–746. [9] Y.C. Li, Q.S. Di, Y.Q. Gong, Equivalent mechanical models of sloshing fluid in arbitrary-section aqueducts, Earthq. Eng. Struct. Dyn. 41 (6) (2012) 1069–1087. [10] T. Richter, A fully Eulerian formulation for fluid-structure-interaction problems, J. Comput. Phys. 233 (2) (2013) 227–240. [11] S. Hashemi, M.M. Saadatpour, M.R. Kianoush, Dynamic analysis of flexible rectangular fluid containers subjected to horizontal ground motion, Earthq. Eng. Struct. Dyn. 42 (11) (2013) 1637–1656. [12] S. Nicolici, R.M. Bilegan, Fluid structure interaction modeling of liquid sloshing phenomena in flexible tanks, Nucl. Eng. Des. 258 (2) (2013) 51–56. [13] W.K. Liu, D. Lam, Nonlinear analysis of liquid-filled tank, J. Eng. Mech. 109 (6) (2014) 1344–1357. [14] A. Gilmanov, T.B. Le, F. Sotiropoulos, A numerical approach for simulating fluid structure interaction of flexible thin shells undergoing arbitrarily large deformations in complex domains, J. Comput. Phys. 300 (2015) 814–843. [15] X.S. Cheng, W. Jing, L.J. Gong, Simplified model and energy dissipation characteristics of a rectangular liquid storage structure controlled with sliding base isolation and displacement-limiting devices, J. Perform. Constr. Facil. 31 (5) (2017) 1–11. ASCE. [16] X.S. Cheng, W. Jing, L.J. Gong, Dynamic responses of a sliding base-isolated RLSS considering free surface liquid sloshing, KSCE J. Civ. Eng. 22 (12) (2018) 4964–4976. [17] W. Jing, X.S. Cheng, W. Shi, Dynamic responses of sliding isolation concrete rectangular liquid storage structure with limiting-devices under bidirectional earthquake actions, Arab. J. Sci. Eng. 43 (4) (2018) 1911–1924. [18] S. Miladi, M. S. Razzaghi, Failure analysis of an un-anchored steel oil tank damaged during the Silakhor earthquake of 2006 in Iran, Eng. Fail. Anal. 96 (2019) 31–43. [19] J.R. Cho, H.W. Lee, Non-linear finite element analysis of large amplitude sloshing flow in two-dimensional tank, Int. J. Numer. Methods Eng. 61 (4) (2004) 514–531. [20] B.E. Launder, D.B. Spalding, Mathematical Models of Turbulence, Academic Press, New York, 1972. [21] K. Enoki, T. Ishihara, A. Yamaguchi, A generalized canopy model for the wind prediction in the forest and the urban area, Proc. Eur. Wind Energy Conf. (2009) 16–19. [22] K. Enoki, T. Ishihara, A generalized canopy model and its application to the prediction of urban wind climate, J. Jpn Soc. Civil Eng. Ser. A1 Struct. Eng. Earthq. Eng. (SE/EE) 68 (1) (2012) 28–47. [23] Y. Qi, T. Ishihara, Numerical study of turbulent flow fields around of a row of trees and an isolated building by using modified k-ε model and LES model, J. Wind Eng. Ind. Aerodyn. 177 (2018) 293–305.

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