Proceedings of the 9th Biennial ASME Conference on Engineering Systems Design and Analysis ESDA2008

July 7-9, 2008, Haifa, Israel

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rnational experience of seismic design.

ld be given to the checking reservoirs against ilure during the seismic event. The beginning of the cylindrical free supported on the base ected with a specific mode of deformation - rt of the bottom above the base. In this case, s in the connection joint between tank's

can lead to the structural failure. To prevent n the regions with high seismicity an anchor

Fh horizontal reaction; friction coefficient MXX overturning moment about X axis MYY overturning moment about Y axis dh pontoon horizontal movement dv pontoon vertical movement dr pontoon to reservoir wall relative movement w seismic wave height of the product p angle of plastic hinge rotation I moment of inertia for NOC Normal Operation Conditions DBE Design Basis Earthquake ZPA Zero Period Acceleration

1 Copyright 2008 by ASME SEISMIC ANALYSIS OF A LARGE

Alexander V. Kultsep CKTI-Vibroseism Co. Ltd., St. Pe

Phone: +7 812 3278599E-mail: akultsep

ABSTRACT Seismic qualification of the large oil tanks requires

consideration of a lot of specific failure modes. One of them is the failure induced by dynamic behaviour of the floating roofs or pontoons: a collision between floating steel roof and tank wall during an earthquake can lead to the post crash fire with severe system fault. Seismic behaviour of a 50000 m3 tank with floating pontoon has been investigated in a numeric study. Seismic safety limits of the considered tank including floating roof movement are presented. A validation study using numerical experiments of the tank with floating pontoon has been performed in order to verify the analytical approach. An influence of the tank anchorage on the tank seismic behaviour and specific failure modes connected with tank bottom uplift has been also investigated.

1 INTRODUCTION

Design of the big Oil Reservoirs in Russia is mostly regulated by the National Building Codes and Standards. Established several decades ago these Standards still provide a reliable and safe design of structures for Normal Operation Conditions. However, fast development of Russian Oil Industry in recent years has challenged new requirements for Seismic medigitalcollection.asme.org/ on 10/10/2013 Terms of Use: ht

ESDA2008-59272

IL TANK WITH FLOATING ROOF

Alexey M. Berkovsky rsburg, Russian Federation ax: +7 812 3278599 cvs.spb.su

fastenings of the reservoir wall to the basement are required by normative documents. Nevertheless, for conditions of moderate seismic loading, it proves to be possible to exclude the anchor fastenings, allowing the uplift of the bottom above the base. In this case it is possible to remove from the reservoir wall the anchor supports, that create stress concentration, and on the other hand somewhat reduce the overturning moment, transferred to the base of reservoir.

Another problem of the oil tanks is the seismic interaction of the floating roofs or pontoons with tank's inside structure. There are no clear requirements regarding floating roofs available in domestic or international rules. However, a collision between floating structure and reservoirs wall can produce sparks, followed by flammable vapor ignition resulting in severe tank fire damages as observed after the Kocaeli earthquake and other seismic events [1,2,3].

The presented positions and the proposed calculation procedure are demonstrated based on the example of a standard reservoir with the volume of 50000 m3.

NOMENCLATURE tp://asme.org/terms

Dow2 METHOD OF ANALYSIS

2.1 General information

The finite element method is used for calculation of reservoirs response. The tank structure and floating roof is modeled using shell and beam elements. The outer ring of reservoirs bottom is connected with basement using set of non-linear spring elements that simulate contact boundary conditions during bottom's uplift. For modeling of overall basement (soil) stiffness a conventional spring elements were also included in the model. Potential formulation is used for modeling of liquid sloshing effects [9]. Since the potential formulation has restricted possibilities to consider floating body dynamics, an elastic foundation layer was added to the pontoon elements in order to model floating body buoyancy. Assumption of the small structure displacements considered in the liquid potential formulation is obviously not valid in the gap between the pontoon and the reservoir wall because if the gap is going to close, the fluid pressure will be calculated for non-deformed model geometry. However, it is assumed that the calculated gap pressure is lower compared to the real pressures. Therefore the calculated movement of the floating roof should be larger, i.e. more conservative.

Because of the nonlinear nature of system (liquid with the free surface and the possibility of separation of bottom from base) dynamic calculation was carried out by the direct implicit integration method. Overall damping in system is taken into account with the use of Rayleigh dissipation matrix:

[C]= [M]+ [K], where [M] is the mass matrix; [K] is the stiffness matrix. The used coefficients and provide relative damping

about 2% for the main structural eigenfrequencies in the range from 3.5 Hz (tank breathing frequency) up to 10 Hz (horizontal and turnover vibration). Different damping coefficients were used for fluid elements in order to get 0.5% relative damping for the main sloshing mode (0.1 Hz).

Calculations were performed with finite element program SOLVIA developed by SOLVIA Engineering AB, Sweden [9].

2.2 Calculation method validation The most unclear point in the chosen calculation procedure

is the lack of the reliably fluid-structure interaction (FSI). In order to verify it and "feel" the margins of such approach a numerical test has been performed. Dynamic response of a benchmark tank (Figure 1) with the length of 2 m and the depth of 1 m with a floater was investigated using two different approaches: potential fluid formulation realized in the program SOLVIA and Arbitrary Lagrange Euler fluid formulation using the program LS-DYNA of Livermore Software Technology Corporation (LSTC), USA [10].

The tank was exposed to static gravity load and to the horizontal acceleration of 0.1 g applied step-wise after reaching

nloaded From: http://asmedigitalcollection.asme.org/ on 10/10/2013 Terms of Use: hof static equilibrium. The wave heights calculated with both methods have quite good correspondence (Figure 2). Similar results were obtained for the floater vertical motion.

Figure 1 Test tank with floater

However, for the horizontal floater motion the results

obtained with potential fluid formulation (SOLVIA) show significantly larger floater motions (Figure 3). Therefore it can be concluded that the using of potential fluid formulation for the tank with floating roof will produce more conservative results for the roof movement under seismic load compared to the methods with improved fluid-structure interaction procedure.

-0.2

-0.2

-0.1

-0.1

0.0

0.1

0.1

0.2

0.2

0 1 2 3 4 5 6 7

time (s)

wav

e he

ight

(m)

SOLVIALS-DYNA

Figure 2 Calculated wave heights (m)

-0.2

-0.2

-0.1

-0.1

0.0

0.1

0.1

0.2

0.2

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

time (s)

float

er m

ove

(m)

SOLVIA

LS-DYNA

Figure 3 Floater horizontal motions (m) 2 Copyright 2008 by ASME

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Down3 CALCULATION MODEL

Calculated reservoir has followed data:

Reservoir diameter 60.7 m Wall shell thickness (variable along height) from 26 to 13 mm Total liquid mass (density 900kg/m3) 44274 t Reservoir steel structure mass 765 t Mass of domical roof 66 t Pontoon mass 296 t

Figure 4. Calculation model of the reservoir

The whole calculation model contains outer shell and

bottom modeled with 7289 shell elements (Figure 4), pontoon modeled with 3934 solid elastic elements and naphtha (product) modeled with 91936 fluid elements (Figure 5). Nonlinear spring elements are also included in order to model contact conditions on the bottom outer ring. Linear springs simulate base soil response.

Figure 5 Calculation model details

The calculation of the ground base stiffness was carried out on the basis of the coefficient of the elastic uniform compression, determined according to the formula [8]:

wb=

f(tw

VSR

odea

p

Zp(fae 4

4

gaobr

cs

wda

Fluid elements

spings

Pontoon elements

loaded From: http://asmedigitalcollection.asme.org/ on 10/10/2013 Terms of Use: h)/1( 10 AAEbC oZ += [N/m3] here =5.00E+07 Pa is the ground elasticity module, is the ase area (A=200 m2 for the basement large than 200 m2), A10 10 m2, bo=1.5 (large-grained soil).

Coefficients, which characterize the stiffness of the

oundation for other base movements directions are C rocking), Cx (horizontal shift). They can be determined from he formulas: CX=0.7 CZ , C=2.0 CZ [8]. Stiffnesss of the hole soil base are presented in table 1.

Table 1 Basement stiffness

ertical stiffness KZ=ACZ KZ=2.66E+11 N/m hift stiffness KX=ACX KX=1.86E+11 N/m ocking stiffness K=IC K=1.22E+14 N/m

Seismic load was applied simultaneously in three

rthogonal directions using synthesis accelerograms. Two ifferent sets of accelerograms that represent different arthquake sources were used with relation between vertical nd horizontal components of 2/3 (table 2).

Table 2 Seismic load data (vertical direction)

arameter Seismic load 1

Seismic load 2

PA, g 0.2 0.2 eak acceleration in Z direction for 5% damping), g 0.64 0.66

requency range for peak cceleration, Hz 2.6-7.1 7.1-18

arthquake duration, s 8.5 3.5

CALCULATION RESULTS

.1 Basement reactions The maximum values of the dynamic base reactions are

iven in table 3. In the case if the anchoring of reservoir is bsent, fixation against the slippage on the base is achieved nly due to the friction between the reservoir bottom and the ase. Absence of the sliding motion is determined by the elationship:

hZ FF > For the reactions, given in table 3 and assuming friction

oefficient be equal =0.3, the condition indicated above is atisfied for whole duration of seismic simulation.

As shown in the table 3, basement reactions decrease if no all anchorage is installed. The reason for it is obviously lower ynamic stiffness of an unanchored tank compared to the nchored tank. 3 Copyright 2008 by ASME

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The bottom uplift can be accompanied by the appearance of a plastic hinge in the margin bottom plate, in the shell-to-bottom joint. In compliance with design practice the

DowTable 3 Extreme basement reactions Seismic load 1 Seismic load 2 Force component

without anchors

with anchors

without anchors

with anchors

MXX, MN*m 1772 2185 1133 1292 MYY, MN*m 1981 2504 1349 1453 (MYY2+MXX2), MN*m

2140 3264 1508 1604

max FZ, MN 508 507 539 533 min FZ, MN 347 351 359 333 max. FX, MN 90.6 115 61.7 67.3 max. FY , MN 78.8 100 63.0 68.1

4.2 Free surface motion and structure deflections As shown in table 4 the maximum dynamic deflections and

movements increase for the case of unanchored tank. Especially relative motion of the pontoon to the tank shell dr will arise up to 16% for an unanchored tank. The calculated free surface deflection (seismic wave height w) calculated for a tank without pontoon is up to 30% higher compared to the calculated maximum pontoon vertical motion, i.e. a pontoon can reduce the free surface waves up to 30%.

The maximum calculated bottom uplift 49 mm is connected with specific shell deformation due to seismic load (Figure 6). Because partial uplift of the bottom above the base is considered as possible, it is necessary to examine the permissibility of the stress state under these conditions.

Table 4 Extreme deflections and movements (mm)

Seismic load 1 Seismic load 2 without

anchors with anchors

without anchors

with anchors

dh, 82 80 24 21 dv, 230 196 71 70 wave height w

- 257 - 73

Bottom uplift u

49 0 15 0

Shell deflection

62 20 19 11

dr 116 100 26 23

Figure 6. Reservoirs shell deflection due to seismic

load (magnified).

Bottom uplift

nloaded From: http://asmedigitalcollection.asme.org/ on 10/10/2013 Terms of Use: hpermissible value of the angle of plastic hinge rotation in the joint is established. This angle can be calculated in accordance with [4] as follows:

bppp DpM //* = ;

tp ll ++= *3** 222

62710

pMll

p /)22(*

+=

where is the cylindrical stiffness of the bottom, E and are the Young modulus and the Poisson ratio of the reservoirs material, tb is the bottom thickness, Mp is the bottom plastic moment, l is the width of the bottom uplift zone which can be calculated from the following equations set in two unknown l and 0:

)1(12/ 23 vEtD bb =

012

26 202 =++ pll

DlD b

ub ;

012

46 2020 =+ pll

DlD

D bub

tt ;

where tt is the thickness of the reservoirs shell lower course, Dt is the cylindrical stiffness of this shell, u is the bottom uplift,

. 4/1222 )/)1(12( ttt Dt =A calculation performed according presented method

results for u = 49 mm in the value of p = 1.5, which is less than the permissible value of [p]=15 according [5]. 4.3 Shell stresses

Equivalent Tresca stresses in the middle surface of sheet are considered as deign stresses for the reservoirs shell. Absence of residual deformations of the shell after the seismic action is the criterion of strength. In this case the local plastic deformations due to bending moments in the shell are allowed for example in the zone of the shell-to-bottom joint. The performed calculations show that the greatest equivalent stresses appear in the middle of the shell height, in the zone where thickness decreases from 18 mm to 14 mm. High stresses in this region are connected with the large circumferential stretching stresses in the shell as a result of the hydrodynamic pressure action under seismic load (Figure 7).

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validate proposed computation scheme for the tanks with floating roofs.

The other finding from this evaluation is that tank's

anchorage required by the design rules in order to prevent tank overturning can be avoided based on analysis results performed in accordance with described scheme. It was shown that absence of tank's anchorage can simultaneously reduce basement moments and reservoirs shell stresses.

6 REFERENCES 1. Report on damage to industrial facilities in the 1999 KOCAELI earthquake, Turkey, K. Suzuki, Journal of Earthquake Engineering, Vol. 6, No. 2 (2002), 275-296 2. ZAMA SHINSAKU Damage and Failure of Oil Storage

Dow Figure 7 Distribution of maximum equivalent dynamic

stresses (Tresca) As shown in table 5 shell stresses are higher for an anchored tank.

Table 5 Maximum equivalent stress in the shell (MPa) Seismic load 1 Seismic load 2 Operation

condition without anchors

with anchors

without anchors

with anchors

NOC 173 173 173 173 NOC+DBE 358 443 314 313

Other criteria for the shell stresses are elastic and elastic-plastic buckling criteria (elephant-foot buckling). These criteria were checked according to the references [6, 7] and have met design requirements. 5 CONCLUSION REMARKS

The performed analyses demonstrate that potential fluid formulation can be successfully used for seismic evaluation of big oil tanks with floating roofs. However, use of this approach for solving of FSI problem leads to the conservative results for assessment of horizontal pontoon movement. At the same time, this conservatism could be considered as acceptable in case of low or moderate seismic input when even conservatively produced results give a positive answer for seismic qualification (criteria is possibility of collision between floating roof or pontoon and tank's inside wall). From the other hand, solution based on the potential formulation has significantly less computational costs. Let say, analysis of 80000 elements carried out with LS-DYNA (Arbitrary Lagrange Euler fluid formulation) takes ~ 70 hours. For comparison: same problem with use of "potential" algorithm can be solved on the same computer for 6 minutes only. It looks like a good engineering compromise between "complexity" of the problem and available tools and budget for its solving. However, additional computations for different tank dimensions and laboratory seismic tests on tank models should be performed in order to

nloaded From: http://asmedigitalcollection.asme.org/ on 10/10/2013 Terms of Use: hTanks due to the 1999 Kocaeli Earthquake in Turkey and Chi-Chi Earthquake in Taiwan - Journal of High Pressure Institute of Japan; vol: 41, issue: 2 , page: 79-86, 2003 3. Failure knowledge database: http://shippai.jst.go.jp/en/Detail?fn=0&id=CC1300013; http://shippai.jst.go.jp/en/Detail?fn=0&id=CC1200074, http://shippai.jst.go.jp/en/Detail?fn=0&id=CB1012035 4. K.Ishida, N.Kobayashi, An effective method of analyzing rocking motion for unanchored cylindrical tanks including uplift Fluid-Structure Dynamics PVP Vol. 9 5. BS EN 1998-4:2006 Eurocode 8, Part 4, Design of structures for earthquake resistance. Silos, tanks and pipelines, European Standard 1998 6. Welded steel tanks for oil storage API standard 650, tenth edition, Add. 1,2; Nov. 2001 7. Jp.Touret, Methods of seismic calculation for tanks 18tn European regional earthquake engineering seminar, Lyon, Sept. 1995 8. A.N. Birbraer, Seismic analysis of structures Sankt-Petersburg, Nauka, 1998 9. SOLVIA Finite element system. Users Manual, Report SE 03-1: SOLVIA Engineering AB, Vasteras, Sweden 10. LS-DYNA Users Manual, Version 970: Livermore Software Technology Corporation, Livermore, California, April 2003 5 Copyright 2008 by ASME

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