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EUROPEAN PRESTANDARD prENV 1998-4PRNORME EUROPENNEEUROPISCHE VORNORM

English version

Eurocode 8: Design of structures for earthquake resistance

Part 4: Silos, tanks and pipelines

CEN

European Committee for StandardizationComit Europen de NormalisationEuropisches Komitee fr Normung

Central Secretariat: rue de Stassart 36, B1050 Brussels

CEN 1997 Copyright reserved to all CEN membersRef.No ENV 1998-4:1997


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Contents

Foreword

1 General

1.1 Scope 71.2 Safety Requirements 71.2.1 General 81.2.2 Serviceability limit state 81.2.3 Ultimate limit state 81.2.4 Reliability differentiation 91.2.5 System versus element reliability 91.2.6 Conceptual design 101.3 Seismic action 101.4 Analysis 10

1.4.1 General 101.4.2 Behaviour factors 111.4.3 Damping 111.4.4 Interaction with the soil 121.5. Safety verifications 121.5.1 General 121.5.2 Combinations of seismic action with other actions 12

2 Specific rules for silos2.1 Reliability differentiation 132.2 Combination of ground motion components 13

2.3 Analysis 142.4 Verifications 142.4.1 Serviceability limit state 142.4.2 Ultimate limit state 14

3 Specific rules for tanks3.1 Reliability differentiation 153.2 Compliance criteria 163.2.1 General 163.2.2 Serviceability limit state 163.2.3 Ultimate limit state 163.3 Combination of ground motion components 173.4 Methods of analysis 173.4.1 General 173.4.2 Behaviour factors 173.4.3 Hydrodynamic effects 183.5 Verifications 193.5.1 Serviceability limit state 193.5.2 Ultimate limit state 203.6 Complementary measures 203.6.1 Bunding 20

3.6.2 Sloshing 213.6.3 Piping interaction 21


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Foreword

Objectives of the Eurocodes

(1) The Structural Eurocodes comprise a group of standards for the structural

and geotechnical design of buildings and civil engineering works.

(2) They cover execution and control only to the extent that is necessary toindicate the quality of the construction products, and the standard of theworkmanship, needed to comply with the assumptions of the design rules.

(3) Until the necessary set of harmonized technical specifications for productsand for methods of testing their performance is available, some of the StructuralEurocodes cover some of these aspects in informative annexes.

Background to the Eurocode Programme

(4) The Commission of the European Communities (CEC) initiated the work ofestablishing a set of harmonized technical rules for the design of building and civilengineering works which would initially serve as an alternative to the different rules inforce in the various Member States and would ultimately replace them. Thesetechnical rules became known as the Structural Eurocodes.

(5) In 1990, after consulting their respective Member States, the CEC transferredthe work of further development, issue and updates of the Structural Eurocodes toCEN, and the EFTA Secretariat agreed to support the CEN work.

(6) CEN Technical Committee CEN/TC 250 is responsible for all StructuralEurocodes.

Eurocode Programme

(7) Work is in hand on the following Structural Eurocodes, each generallyconsisting of a number of parts:

EN 1991 Eurocode 1 - Basis of design and actions on structuresEN 1992 Eurocode 2 - Design of concrete structuresEN 1993 Eurocode 3 - Design of steel structures

EN 1994 Eurocode 4 - Design of composite steel and concrete structuresEN 1995 Eurocode 5 - Design of timber structuresEN 1996 Eurocode 6 - Design of masonry structuresEN 1997 Eurocode 7 - Geotechnical designEN 1998 Eurocode 8 - Design of structures for earthquake resistance of structuresEN 1999 Eurocode 9 - Design of aluminium alloy structures

(8) Separate subcommittees have been formed by CEN/TC 250 for the variousEurocodes listed above.

(9) This Prestandard is being published as an European Prestandard (ENV) with

an initial life of three years.


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(10) This Prestandard is intended for experimental application and for thesubmission of comments.

(11) After approximately two years CEN members will be invited to submit formalcomments to be taken into account in determining future actions.

(12) Meanwhile, feedback and comments on this Prestandard should be sent tothe Secretariat of CEN/TC250/SC8 at the following address:

IPQ c/o LNECAvenida do Brasil 101P1799 LISBOA CodexPORTUGAL

or to your national Standard Organization.

National Application Documents

(13) In view of the responsibilities of authorities in member countries for the safety,health and other matters covered by the essential requirements of the ConstructionProducts Directive (CPD), certain safety elements in this ENV have been assignedindicative values which are identified by (boxed values).The authorities in eachmember country are expected to assign definitive values to these safety elements.

(14) Some of the harmonized supporting standards may not be available by thetime this Prestandard is issued. It is therefore anticipated that a National ApplicationDocument (NAD) giving definitive values for safety elements, referencing compatible

supporting standards and providing guidance on the application of this Prestandard,will be issued by each member country or its Standards Organisation.

(15) It is intended that this Prestandard is used in conjunction with the NAD valid inthe country where the building or civil engineering works are located.

Matters specific to this Prestandard

(16) The scope of Eurocode 8 is defined in clause 1.1.1 of ENV 1998-1-1:1994 andthe scope of this Prestandard is defined in 1.1. Additional Parts of Eurocode 8 whichare planned are indicated in clause 1.1.3 of ENV 1998-1-1:1994.

(17) This Prestandard is divided into four sections. The first section presents thegeneral rules applicable to the design for earthquake resistance of silos, tanks andpipelines. The other sections deal with the specific rules for silos (section 2), tanks(section 3) and pipelines (section 4).

(18) Attention shall be paid to the fact that this Prestandard has to be used inconjunction with ENV 1998-1-1 and in addition to the provisions of the other relevantEurocodes.

(19) This Prestandard includes two informative annexes.

Intended future developments of this Prestandard


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(20) An objective of this Prestandard is to ensure the consistency between seismicdesign rules used for silos, tanks and pipelines and rules used for other constructionworks. It should be understood that this is a longterm objective which demands acontinuous progress and cannot be achieved in a single step.

(21) Parts in other Eurocodes dealing with the same structures as in thisPrestandard are still in preparation.

(22) A number of aspects of the seismic behaviour of silos, tanks and pipelines arenot yet well understood, and research on them is currently under way. It is expectedthat this Prestandard, and particular the design procedures and rules given in theAppendices will be updated in parallel with the advancement of the knowledge in thefield.


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1 General

1.1 Scope

(1) P This Prestandard aims at providing principles and application rules for the

seismic design of the structural aspects of integrated facilities composed of pipelinesystems and of storage tanks of different types and destinations, as well as forindependent items, such as for example single water towers serving a specificpurpose or groups of silos enclosing granular materials, etc. This Prestandard mayalso be used as a basis for evaluating the amount of strengthening needed byexisting facilities to bring them up to present standards.

(2) P This Prestandard includes the additional criteria and rules required for theseismic design of these structures without restrictions on their size, structural typesand other functional characteristics. For some types of tanks and silos, however, italso provides detailed methods of assessment and verification rules.

(3) P With reference to 1.1 of ENV 1998-1-1:1994, this Prestandard may not becomplete for those facilities associated with large risks to the population or theenvironment, for which additional requirements shall be established by thecompetent authorities. This Prestandard is also not complete for those constructionworks which have uncommon structural elements and which require specialmeasures to be taken and special studies are performed to ensure earthquakeprotection. In those two cases the present Prestandard gives general principles butnot detailed application rules.

(4) The nature of lifeline systems which often characterises the facilities covered

by this Prestandard requires concepts, models and methods that may differsubstantially from those in current use for more common structural types.Furthermore, the response and the stability of tanks subjected to strong seismicactions may involve rather complex phenomena of soil-structure-fluid interaction, noteasily amenable to simplified design procedures. Equally challenging may prove tobe the design of a pipeline system having to cross areas with poor and possiblyunstable soils. For the reasons given above, the organisation of this Prestandard isto some extent different from that of companion Parts of ENV 1998. ThisPrestandard is, in general, restricted to basic principles and methodologicalapproaches, while detailed analysis procedures are given in Annexes for a numberof typical situations.

(5) P For the formulation of the general requirements as well as for theirimplementation, a distinction is made among the facilities covered by the presentPart 4, i.e.: independent structures and redundant networks.

(6) P A structure can be considered as independent when its behaviour during andafter a seismic event is not influenced by that of other structures, and if theconsequences of its failure relate only to the functions demanded from it.


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1.2 Safety requirements

1.2.1 General

(1) P This Prestandard deals with structures which may differ widely in such basic

features as:

the nature and amount of stored product and associated potential dangerthe functional requirements during and after the seismic eventthe environmental conditions.

(2) Depending on the specific combination of the indicated features, differentformulations of the general requirements are appropriate. For the sake ofconsistency with the general framework of the Eurocodes, the two limit states formatis retained, with a suitably adjusted definition.

1.2.2 Serviceability limit state

(1) P Depending on the characteristics and the purposes of the structuresconsidered one or both of the two following serviceability limit states may need to besatisfied:

- full integrity;- minimum operating level.

(2) P The "full integrity" requirement implies that the considered system, including aspecified set of accessory elements integrated with it, remains fully serviceable andleak proof under a seismic event having an annual probability of exceedance whosevalue is to be established based on the consequences of its loss of function and/or ofthe leakage of the content.

(3) P The "minimum operating level" requirement implies that the consideredsystem may suffer a certain amount of damage to some of its components, to anextent, however, that after the damage control operations have been carried out, thecapacity of the system can be restored up to a predefined level of operation. Theseismic event for which this limit state must not be exceeded shall have an annualprobability of exceedance whose value is to be established based on the lossesrelated to the reduced capacity of the system and to the necessary repairs.

1.2.3Ultimate limit state

(1) P The ultimate limit state of a system is defined as that corresponding to theloss of operational capability of the system, with the possibility of partial recovery (inthe measure defined by the responsible authority) conditional to an acceptableamount of repairs.

(2) P For particular elements of the network, as well as for independent structureswhose complete collapse would entail high risks, the ultimate limit state is defined as

that of a state of damage that, although possibly severe, would exclude, however,brittle types of failures and would allow for a controlled release of the content. Whenthe failure of the afore mentioned elements does not involve appreciable risks to life


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and property, the ultimate limit state can be defined as corresponding to totalcollapse.

(3) P The reference seismic event for which the ultimate limit state must not beexceeded shall be established based on the direct and indirect losses caused by the

failure of the system.

1.2.4 Reliability differentiation

(1) P Pipeline networks and independent structures, either tanks or silos, shall beprovided with a level of protection proportioned to the number of people at risk and tothe economic and environmental losses associated with their performance levelbeing not achieved.

(2) P Reliability differentiation shall be achieved by appropriately adjusting the value

of the annual probability of exceedance of the design seismic action.(3) This adjustment should be implemented by applying to the reference seismicaction effects an importance factor I , as defined in 2.1(3) of ENV 1998-1-1:1994.Specific values of the factor I , necessary to modify the action effects so as tocorrespond to a seismic event of selected return period, are dependent on theseismicity of each region, and have therefore to be provided by the NationalApplication Document.

(4) P For the structures within the scope of this Prestandard it is appropriate toconsider 3 different levels of protection. Table 1.1 provides a framework for

establishing differential levels of protection. In the column at left there is aclassification of the more common uses of these structures, while the three columnsat right contain the appropriate levels of protection in terms of the values of theimportance factor I for three classes of reliability (see ENV 1991-1:1994).

Table 1.1 Importance factors

Use of the structure/facility Class1 2 3

Potable water supply

Non-toxic, non inflammable material [1,2] [1,0] [0,8]Fire fighting waterNon-volatile toxic materialLow flammability petrochemicals

[1,4] [1,2] [1,0]

Volatile toxic chemicalsExplosive and other high flammability liquids

[1,6] [1,4] [1,2]

(5) P Class 1 refers to situations with a high risk to life and large environmental,economic and social consequences.


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(6) P Situations with medium risk to life and considerable environmental, economicor social consequences belong to class 2.

(7) P Class 3 refers to situations where the risk to life is low and theenvironmental, economic and social consequences of failure are small or negligible.

(8) A more detailed definition of the classes, specific for pipeline systems, isgiven in 4.2.1

1.2.5 System versus element reliability

(1) P The reliability requirements set forth in 1.2.2 and 1.2.3 refer to the wholesystem under consideration, be it constituted by a single component or by a set ofcomponents variously connected to perform the functions required from it.

(2) P Although a formal approach to system reliability analysis is outside the scopeof this Prestandard, the designer shall give explicit consideration to the role playedby the various elements in ensuring the continued operation of the system, speciallywhen it is not redundant. In the case of very complex systems the design shall bebased on sensitivity analyses.

(3) P Elements of the network, or of a structure in the network, which are shown tobe critical, with respect to the failure of the system, shall be provided with anadequate extra margin of protection, commensurate with the consequences of thefailure. When there is no previous experience, those critical elements should beexperimentally investigated to verify the acceptability of the design assumptions.

(4) If more rigorous analyses are not undertaken, the extra margin of protectionfor critical elements can be achieved by assigning these elements to a class ofreliability one level higher than that proper to the system as whole.

(5) P The designer shall take into consideration that, in some cases, increasing thestrength of an element of a structure may decrease the global reliability of thestructure.

1.2.6Conceptual design

(1) P The design of a network or of an independent structure shall take intoconsideration the following general aspects for mitigation of earthquake effects:

- Quality control of the components;- Redundancy of the systems;- Easy access for inspection, maintenance and repair of damages;- Absence of interaction of the mechanical and electrical components with the

structural elements.

(2) P In redundant systems, in order to avoid spreading of damage due to

interconnection of components it shall be made possible to isolate parts of thesystem so as to take advantage of the redundancies.


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(3) In case of indispensable facilities vulnerable to earthquakes, of which damagerecovery is difficult or time consuming, or the damaged portions may be hard todetect, they should either be divided into independent parts or spare facilities shouldbe provided.

1.3 Seismic action

(1) P The seismic action to be used in the determination of the seismic actioneffects for the design of silos, tanks and pipelines shall be that defined in 4 of ENV1998-1-1:1994 in the various equivalent forms of elastic, site dependent responsespectra (4.2.2 of ENV 1998-1-1:1994), power spectrum (4.3.1 of ENV 1998-1-1:1994) and time-history representation (4.3.2 of ENV 1998-1-1:1994). In thosecases where a behaviour factor q larger than unity is acceptable (see 1.4.2), thedesign spectrum for linear analysis shall be used (4.2.2 of ENV 1998-1-1:1994).

(2) P The two seismic actions to be used for checking the serviceability limit stateand the ultimate limit state, respectively, shall be established by the competentNational Authority on the basis of the seismicity of the different seismic zones and ofthe level of the importance category of the specific facility.

(3) Possible reduction factors to take into account the lower return period of theseismic event associated with the serviceability limits state are given in 4.3 of ENV1998-1-2:1994.

1.4 Analysis

1.4.1 General

(1) P For the structures within the scope of this Prestandard the seismic actionseffects shall in general be determined on the basis of linear behaviour of thestructures and of the soil in their vicinity.

(2) P Nonlinear methods of analyses can be used to obtain the seismic actioneffects for those special cases where consideration of nonlinear behaviour ofstructure and surrounding soil is dictated by the nature of the problem, or where theelastic solution would be economically unfeasible. In those cases it shall be provedthat the design obtained possesses at least the same amount of reliability as the

structures explicitly covered by this Prestandard. The proof is deemed to beachieved if no failure is observed for realistically large variations of the mechanicalproperties adopted.


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1.4.2 Behaviour factors

(1) P The structures covered by this Prestandard are not expected to dissipateappreciable amounts of energy through their inelastic behaviour. Hence the value ofthe behaviour factor q shall in general be taken as q = 1. Use of q factors >1 is only

allowed provided the sources of energy dissipation are explicitly identified andquantified, and the capability of the structure to exploit them through appropriatedetailing is demonstrated.

(2) P For fully elastic design (q=1) the design seismic action is defined by the elasticspectrum. If values of q>1 are adopted, the design spectrum for linear analysis shallbe used.

(3) P Even if a value q = 1 is adopted for the overall response, structural elementsshall be designed with some local ductility and constructed from ductile materials.

1.4.3 Damping

1.4.3.1 Structural damping

(1) If the damping values are not obtained from specific information or by directmeans the following damping values should be used in linear analysis:

a) Serviceability limit state:reinforced concrete structures: 4%prestressed concrete structures: 2%

steel structures: 2%b) Ultimate limit state:

reinforced concrete structures: 7%prestressed concrete structures: 5%steel structures: 4%

1.4.3.2Contents damping

(1) The value = 0,5 % may be adopted for water and other fluids unlessotherwise determined.

(2) For granular materials an appropriate damping value should be used. In theabsence of more specific information a value of 10% may be used.

1.4.3.3Foundation damping

(1) Material damping varies with the nature of the soil and the intensity ofshaking. When more accurate determinations are not available, the values given inTable 4.1 of ENV 1998-5:1994 should be used.

(2) P Radiation damping depends on the direction of motion (horizontal translation,vertical translation, rocking, etc.), on the geometry of the foundation, on soil layeringand soil morphology. The values adopted in the analysis shall be compatible with


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actual site conditions and shall be justified with reference to acknowledgedtheoretical and/or experimental results. The values of the radiation damping used inthe analysis shall not exceed the value: = [20 %]. Guidance for the selection anduse of damping values associated with different foundation motions is given in AnnexB of ENV 1998-3:1996, and in Annex A of this Prestandard.

1.4.4 Interaction with the soil

(1) P Soil-structure interaction effects shall be addressed in accordance with 6 ofENV 1998-5:1994.

(2) Additional information on procedures for accounting for soil-structure interactionis given in Annex C of ENV 1998-3:1996, and Annex A of this Prestandard.

1.4.5 Weighted damping

(1) A procedure for accounting of the contributions of the differentmaterials/elements to the global average damping of the whole system is given inAnnex B of ENV 1998-3:1996.

1.5 Safety verifications

1.5.1 General

(1) P Safety verifications shall be carried out for the limit states defined in 1.2,following the specific provisions in 2.4, 3.5 and 4.5.

(2) In case plate thickness is increased to account for future corrosion effectsthe verifications shall be made for both the nonincreased and the increasedthickness.

1.5.2 Combinations of seismic action with other actions

(1) P Verifications shall be performed using the combination of seismic actioneffects with the other actions as prescribed in 4.4 (1) of ENV 1998-1-1:1994.

G A P Qkj I Ed k i ki" " " " " "+ + + 2 (1.1)

where: I importance factor as defined in 1.2.4

AEd seismic action effects as defined in 1.3Gkj permanent loads at their characteristics values. These will include

the weight of the structure and in case of partially backfilled orburied tanks, it includes earth cover and permanent externalpressures due to the water table

Pk characteristic value of the prestressing action

Qki variable loads at their characteristic values. Among these theeffects of the liquid should be considered for various levels of filling


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2i combination coefficient for quasi permanent value of variableaction i. The 2i values depend on the specific conditions of useand of functioning of the structure. Guidance on these values isgiven in ENV 1991-1:1994.

(2) P In the case of groups of silos and tanks, different likely distributions of full andempty reservoirs shall be considered according to the operation rules of the facility.At least, the cases where all reservoirs are either empty or full must be considered.

2 Specific rules for silos

2.1 Dynamic overpressure

(1) P Under dynamic conditions, the pressure exerted by the material on the walls,the hopper and the bottom, increases over the value relative to the condition at rest.This increased pressure must be considered concurrently with the effects of theinertia forces due to the seismic excitation.

(2) P Design pressures in combination with earthquake load shall be obtained bymultiplying the static pressure by the appropriate over-pressure correction factor Cd.Minimum required values of factors Cd are given in Table 2.1. (For values of H/dbetween 2 and 4 linear interpolation may be used).

Table 2.1 Minimum values of over-pressure factor Cd

H/d2 H/d40,75


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top of the material)

2.2 Combination of ground motion components

(1) P Silos shall be designed assuming the concurrent presence of one horizontal

component of the seismic motion, which acts along the worst direction in plan for theelement considered, and of the vertical component.

(2) When approximate methods are used, (for example, response spectrummodal analysis) the global maximum response can be obtained by combining theindividual peak contributions (separately obtained for the horizontal and the verticalexcitation) by means of the "square root of the sum of the squares" (SRSS) rule.

(3) P When accurate methods of analysis are used, the peak values of the totalresponse under the combined action of the horizontal and vertical excitation obtainedfrom the analysis shall be used in accordance with 4.3.2 of ENV 1998-1-1:1994 and3.3.4 of ENV 1998-1-2:1994.

2.3 Analysis

(1) P The model to be used for the determination of the seismic effects shallreproduce accurately the stiffness, mass and geometrical properties of thecontainment structure, shall account for the response of the contained material andfor the effects of interaction with the foundation soil.

(2) If more accurate evaluations are not undertaken, total mass of the granular

material inside the silos can be assumed as moving rigidly with the silos shell.(3) P Silos shall be analysed considering an elastic behaviour, unless properjustification is given.

2.4 Verifications


(1) P Under the seismic load combination given by expression 1.1 of 1.5.2 the silostructure shall be checked to satisfy the serviceability limit state verifications required

by ENV 1992-4 and ENV 1993-4.

(2) For steel silos, adequate reliability with respect to the occurrence of elastic orinelastic buckling phenomena is assured if the verifications regarding thesephenomena are satisfied under the seismic loading for the ultimate limit state.

2.4.2 Ultimate limit state

2.4.2.1 Global stability

(1) P Overturning and sliding shall not occur for the design seismic action. Theresisting shear force, which can be mobilized at the interface between the base ofthe silo and its foundation, shall be evaluated taking into account the effects of thevertical component of the seismic action.


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(2) P Uplift is acceptable if it is adequately taken into account in the analysis and inthe subsequent verifications of both the structure and of the foundation.

2.4.2.2 Shell

(1) P The maximum action effects (axial and membrane forces and bendingmoments) induced by the pertinent seismic load combination shall be less or equalto the ultimate strength capacity of the shell, evaluated as for non seismic situations.This includes all types of failure modes such as yielding, buckling, etc.

(2) Verifications are to be carried out in accordance with ENV 1992-4 and ENV1993-4.

2.4.2.3 Anchors

(1) P Anchoring systems shall be designed to remain elastic under the pertinentseismic load combination. They shall also be provided by an adequate amount ofductility, so as to avoid brittle failures.

2.4.2.4 Foundations

(1) P The forces transmitted to the soil by the silo acted upon by the pertinentseismic load combination shall not exceed the bearing capacity of the soil,evaluated in accordance with the procedures given in ENV 1998-5.

3 Specific rules for tanks

3.1 Compliance criteria

3.1.1 General

(1) P The general requirements set forth in 1.2. are deemed to be satisfied if, inaddition to the verifications specified in 3.4, the complementary measures indicatedin 3.5 are also satisfied.


(1) P It shall be ensured that under the relevant design seismic action and inrespect to the full integrity limit state or minimum operating level limit state:

- The tank system maintains its tightness against leakage of the content. Adequatefreeboard shall be provided, in order to prevent damage to the roof due to thepressures of the sloshing liquid or, if the tank has no rigid roof, to prevent theliquid from overstepping;


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- The hydraulic systems which are part of, or are connected to the tank, arecapable to accommodate stresses and distortions due to tank displacementsrelative to each other and to the soil, without impairment of their functions;

- Local buckling, if it occurs, does not initiate collapse and is reversible; forinstance, local buckling of struts due to stress concentration is acceptable.


(1) P It shall be ensured that under the relevant design seismic action:

- The overall stability of the tank is satisfied with respect to collapse. The overallstability refers to rigid body behaviour and may be impaired by sliding oroverturning;

- The spread of inelastic behaviour is restricted within limited portions of the tank,and the ultimate deformations of the materials are not exceeded;

- The nature and the extent of buckling phenomena in the shell are adequatelycontrolled;

- The hydraulic systems which are part of, or connected to the tank are designed soas to prevent loss of the tank content following the failure of some of itscomponents;

- The foundation shall not attain a failure mechanism before failure of the tank.

3.2 Combination of ground motion components

(1) P Tanks shall be designed assuming the concurrent presence of one horizontalcomponent and of the vertical component of the seismic motion.

(2) When the peak responses due to horizontal and vertical motions are determinedseparately, the most unfavourable combined effect can be obtained by means of thefollowing expression:(3)

p = pstphpv, (3.1)

where:

pstis the static pressure, andph, pvare the peak values of the horizontal and vertical pressure, respectively. The

signs of the terms in the combination should be selected so as to obtain the mostcritical effects in the various parts of the tank.

(3) P When accurate methods of analysis are used, the most unfavourable of thetotal response under the combined action of the horizontal and vertical excitationobtained from the analysis shall be used in accordance with 4.3.2 of ENV 1998-1-1:1994, and 3.3.4 of ENV 1998-1-2:1994.

3.3 Methods of analysis

3.3.1 General


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(1) P The model to be used for the determination of the seismic effects shallreproduce accurately the stiffness, mass and geometrical properties of thecontainment structure, shall account for the hydrodynamic response of the containedfluid and the effects of interaction with the foundation soil.

(2) P Tanks shall be analysed considering an elastic behaviour, unless properjustification is given for particular cases.

(3) P The localized non linear phenomena admitted under the ultimate limit statedesign seismic action (see 3.1.3) shall be restricted so as to not affect the globaldynamic response of the tank to any significant extent.

(4) Possible interaction between tanks due to connecting pipings shall beconsidered whenever appropriate.

(5) Methods for seismic analysis of tanks of usual shapes are given in Annex A.

3.3.2 Behaviour factors

(1) P Tanks of type and importance other than those mentioned below shall beeither designed for a fully elastic response (q=1), or, for properly justified cases, (see1.4.1(2)) the admissibility of their inelastic response shall be adequatelydemonstrated.

(2) P For elevated tanks, the supporting structure may be designed to respondbeyond the yield level under the ultimate limit state design earthquake.

(3) For simple support and simple geometry and for tanks belonging to class ofreliability 3, the values of q given in ENV 1998-1-3:1995 relative to invertedpendulum structures can be adopted.

(4) When the conditions above are not satisfied the energy dissipationcorresponding to the selected value of q shall be properly substantiated and thenecessary ductility provided through ductile design. The full elastic design action(i.e., q = 1), however, shall in all cases be used for the evaluation of the convectivepart of the fluid response.

3.3.3 Hydrodynamic effects

(1) P A rational method based on the solution of the hydrodynamic equations withthe appropriate boundary conditions shall be used for the evaluation of the responseof the tank system under the design seismic actions as defined in 1.3.

(2) P In particular, the analysis shall properly account for the following, whererelevant:

- the convective and the impulsive components of fluid motion;

- the deformation of the tank shell due to the hydrodynamic pressures, and theinteraction effects with the impulsive component;


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- the deformability of the foundation soil and the ensuing modification of theresponse.

(3) For the purpose of evaluating the dynamic response under seismic actions thefluid can be generally assumed as incompressible.

(4) Accurate evaluation of the maximum hydrodynamic pressures induced byhorizontal and vertical excitation requires the use of time-history analysis asindicated in 4.3.2 of ENV 1998-1-1:1994 or, equivalently, the adoption of harmonicanalysis and synthesis procedures with the power spectral densities indicated in4.3.1 of ENV 1998-1-1:1994 as input.

(5) Simplified methods based on mechanical analogues of the fluid behaviour andallowing for a direct application of the traditional response spectrum approach can beused, provided suitable conservative rules for the combination of the peak modal

contributions are adopted and provided the approximation introduced with thesemethods is shown to be adequate for the particular case considered. Acceptableprocedures accounting for the above mentioned effects are given in Annex A.

(6) P In order to provide adequate freeboard against liquid overstepping orimpacting with the roof, the maximum vertical displacement of the liquid surface shallbe calculated.

(7) Appropriate expressions are given in Annex A.

3.4 Verifications


(1) P Under the seismic load combination given by expression 1.1 of 1.5.2 the tankstructure shall be checked to satisfy the serviceability limit state verificationsrequired by ENV 1992-4 and ENV 1993-4.

3.4.1.1Shell

3.4.1.1.1Reinforced and prestressed concrete shells

(1) Calculated crack widths under the seismic load combination shall not exceedthe values specified in clause 4.4.2 of ENV 1992-1-1:1991 for the case of rareactions, taking into account the appropriate ambient conditions and sensitivity of thesteel to corrosion.

(2) In case of lined concrete tanks, transient concrete crack widths shall notexceed a value for which the local deformation of the liner reaches more than 50% ofthe rupture elongation.

3.4.1.1.2 Steel shells


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(1) Adequate reliability with respect to the occurrence of elastic or inelasticbuckling phenomena is assured if the verifications regarding these phenomena aresatisfied under the seismic loading for the ultimate limit state.

3.4.1.2 Piping

(1) P Relative displacements due to differential seismic soil movements shall beaccounted for when piping and tanks rest on distinct foundations.

(2) If reliable data are not available or accurate analyses are not made, aminimum value of the imposed relative displacement between the first anchoringpoint and the tank will be assumed as:

= Igxd

x500

( , and dgin m) (3.2)

where x is the distance between the anchoring point and the point of connection withthe tank, and dg is the maximum soil displacement as given in 4.2.3 of ENV 1998-1-1:1994.

(3) The design strengths for piping elements shall be taken equal to thoseapplicable for non seismic conditions.

(4) The zone of the tank where the piping is attached shall be designed to resistin the elastic range the forces transmitted by the piping amplified by a factor p =

1.3.


3.4.2.1 Stability

(1) P Overturning and sliding shall not occur for the design seismic action. Theresisting shear force which can be mobilized at the interface between the base of thetank and its foundation, shall be evaluated taking into account the effects of thevertical component of the seismic action.

(2) P Uplift is acceptable if it is adequately taken into account in the analysis and inthe subsequent verifications of both the structure and the foundation.

3.4.2.2 Shell

(1) P The maximum action effects (membrane forces and bending moments)induced by the pertinent seismic load combination shall be less or equal to theultimate strength capacity of the shell, evaluated as for non seismic situations. Thisincludes all types of failure modes such as yielding, buckling, etc.

3.4.2.3Piping

(1) P Under the combined effects of inertia and service loads, as well as under theimposed relative displacements quantified in 3.4.1.2, yielding of the piping shall be


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checked to occur in the piping and outside the connection with the tank. In order tocheck the integrity of the connection a possible overstrength of the piping ( p = 1,3)

shall be considered.

3.4.2.4 Anchorages

(1) P Anchoring systems shall be designed to remain elastic under the pertinentseismic load combination, they shall also be provided with an adequate amount ofductility, in order to avoid brittle failures.

3.4.2.5 Foundations

(1) P The forces transmitted to the soil by the tank acted upon by the pertinentseismic load combination shall not exceed the bearing capacity of the soil, evaluatedin accordance with the procedures given in ENV 1998-5.

3.5 Complementary measures

3.5.1 Bunding

(1) P Tanks, single or in groups, which are designed to control or avoid leakage inorder to prevent fire, explosions and release of toxic materials shall be bunded, i.e.must be surrounded by a ditch and/or an embankment.

(2) P If tanks are built in groups, the bunding shall be provided either to every single

tank or to the whole group, depending on the amount of risk associated with thefailure of the bund.

(3) P The bunding shall be designed to retain its full integrity (absence of leaks)under a seismic event at least as intense as the one considered for the ultimate limitstate of the enclosed system.

3.5.2 Sloshing

(1) P In the absence of explicit justifications, a freeboard shall be provided having aheight not less than the calculated height of the sloshing waves referred to in 3.3.3.

(6).

(2) P Damping devices as for ex. grillages can be used to reduce sloshing. To thesame effect, vertical partitions can also be introduced into the tanks. Theeffectiveness of these measures must however be demonstrated.

3.5.3 Piping interaction

(1) The piping shall be designed to minimize unfavourable effects of interactionbetween tanks and between tanks and other structures.

4 Specific rules for pipelines


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4.1 General

(1) P This Section aims at providing principles and application rules for the seismicdesign of the structural aspects of pipeline systems. This Section can also be usedas a basis for evaluating the amount of strengthening or increased redundancy

needed by existing facilities to bring them up to present standards.

(2) Pipeline systems usually comprise several associated facilities such aspumping stations, operation centers, maintenance stations, etc., each of themhousing different sorts of mechanical and electrical equipment. Since these facilitieshave a considerable influence on the continued operation of the system, it isnecessary to give them adequate consideration in the design process aimed atsatisfying the overall reliability requirements. Explicit treatment of these facilities,however, is not included within the scope of this Prestandard; in fact, some of thosefacilities are already covered in ENV 1998-1-1 and ENV 1998-1-2, while the seismicdesign of mechanical and electrical equipment requires additional specific criteria

that are beyond the scope of Eurocode 8.

(3) P Although large diameter pipelines are within the scope of this Prestandard, thecorresponding design criteria should not be used for apparently similar facilities likerailway tunnels and large underground gas reservoirs.

(4) P For the formulation of the general requirements to follow as well as for theirimplementation, a distinction needs to be made among the pipeline systems coveredby the present Prestandard i.e.: single lines and redundant networks.

(5) P For this purpose, a pipeline can be considered as a single line when itsbehaviour during and after a seismic event is not influenced by that of otherpipelines, and if the consequences of its failure relate only to the functionsdemanded from it.

(6) A pipeline network, examples of which are fuel, water, gas and sanitationnetworks, is a generally redundant system required to satisfy a set of demands, andwhose failure states correspond to the inability of the system to provide specifiedlevels of performance.

(7) Networks are often too vast and complex to be treated as a whole, and it is

both feasible and convenient to identify separate networks within a global one. Theidentification may result from the separation of the larger scale part of the system(eg. regional distribution) from the finer one (eg. urban distribution), or from thedistinction between separate functions accomplished by the same system.

(8) As an example of the latter situation, an urban water distribution system couldbe separated into a network serving street fire extinguishers and a second oneserving private users. The separation would facilitate providing different reliabilitylevels to the two systems. It is to be noted that the separation is related to functionsand it is therefore not necessarily physical: two distinct networks could have severalelements in common.

(9) The design of pipelines networks involves additional reliability requirementsand design approaches with respect to those provided in the present Prestandard.


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4.2Requirements

4.2.1 Reliability differentiation

(1) P A pipeline system traversing a large geographical region encounters a wide

variety of seismic hazards and soil conditions. In addition, a number of subsystemscan be located along a pipeline transmission system, which can be either associatedfacilities (tanks, storage reservoirs etc.), or pipeline facilities (valves, pumps, etc.).Under such circumstances, where seismic resistance is deemed to be important,critical components (pumps, compressors, control equipment, etc.) shall be designedunder criteria that provide for almost no damage in the event of a major severeearthquake. Other components, that are less essential and can sustain greateramounts of damage, need not be designed to such stringent criteria.

(2) P For reliability differentiation purposes the different components in a pipelinesystem shall be classified as follows.

Class 1: Structures and equipment performing vital functions that mustremain nearly elastic. Items that are essential for the safeoperation of the pipeline or any facility, or components that wouldcause extensive loss of life or a major impact on the environmentin case of damage. Other items, which are required to remainfunctional to avoid damage that would cause a lengthy shutdownof the facility (emergency communications systems, leak detection,fire control, etc.).

Class 2: Items that must remain operative after an earthquake, but need

not operate during the event; Structures that can deform slightly inthe inelastic range; Facilities that are vital, but whose service canbe interrupted until minor repairs are made. It is unlikely that failureof the component will cause extensive loss of life.

Class 3: Buildings, facilities and equipment that can deform inelastically to amoderate extent without unacceptable loss of function (noncriticalpiping support structures, buildings enclosing process operations,etc). It is unlikely that failure of the component will cause extensiveloss of life.

The values of the importance factors appropriate to each class and as functions ofthe use of the facility are given in Table 1.1 of 1.2.4 (4).

4.2.2 Serviceability requirements

(1) P Pipeline systems shall be constructed in such a way as to be able to maintaintheir supplying capability as a global servicing system as much as possible, evenunder considerable local damage due to high intensity earthquakes.

4.2.3Safety requirements

(1) P The principal safety hazard directly associated with the pipeline rupture undera seismic event is explosion and fire, particularly with regard to gas pipelines. The


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remoteness of the location and the size of the population that is exposed to theimpact of rupture shall be considered in establishing the level of protection .

(2) P For pipeline systems in environmentally sensitive areas, the damage to theenvironment due to pipeline ruptures shall also enter into the definition of acceptable

risk.

4.3 Seismic action

4.3.1 General

(1) P The following direct and indirect seismic hazard types are relevant for theseismic design of pipeline systems:

a) seismic waves propagation on firm ground and producing:

different ground shaking at distinct points on the surface;spatial soil deformation patterns within the soil medium;b) earthquake induced soil failures such as:

landslides;liquefaction;

c) permanent deformations; seismic fault displacements.

(2) P The two general requirements regarding the serviceability and the ultimatelimit states need, in principle, to be satisfied for all of the types of hazards listedabove. For hazards of type b) and c), however, it can generally be assumed thatsatisfaction of the ultimate limit state provides automatically the reliability level

required against the serviceability limit state so that one check only needs to beperformed.

(3) The fact that pipeline systems traverse or extend over large geographicalareas, and the necessity of connecting certain locations, does not always allow forthe best choices regarding the nature of the supporting soil. Furthermore, it may notbe feasible to avoid crossing potentially active faults, or to avoid laying the pipelinesin soils susceptible to liquefaction, as well as in areas that can be affected byseismically induced landslides and large differential permanent ground deformations.This situation is clearly at variance with that of other structures, for which a requisitefor the very possibility to build is that the probability of soil failures of any type be

negligible.

(4) It is recognized that the state of the art in geophysics (hazard type c) and ingeotechnics (hazard type b) is generally unable to provide quantitative predictions,either deterministic or probabilistic, of these hazards as functions of earthquakemagnitude and other characteristics.

(5) In most cases, the occurrence of hazards b) and c) simply cannot be ruledout. Based on available data and experience reasoned assumptions can be used todefine a model for the hazard.

4.3.2 Earthquake vibrations


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(1) P The quantification of one horizontal component of the earthquake vibrationsshall be carried out in terms of a response spectrum, or a power spectrum, or a timehistory representation (mutually consistent) as presented in 4 of ENV 1998-1-1:1994,which shall be referred to as containing the basic definitions.

(2) Only the three translational components of the seismic action may be taken intoaccount, (i.e., the rotational components can be neglected).

4.3.3 Modelling of seismic waves

(1) P A model for the seismic waves shall be established, from which soil strainsand curvatures affecting the pipeline shall be derived.

(2) Ground vibrations in earthquakes are caused by a mixture of shear, dilational,Love and Rayleigh waves, and wave velocities are a function of their travel paththrough lower and higher velocity material. Different particle motions associated withthese wave types make the strain and curvature also dependent upon the angle ofincidence of the waves. A general rule is to assume that sites located in the proximityof the epicenter of the earthquake are more affected by shear and dilational waves(body waves), while for sites at a larger distance, Love and Rayleigh waves (surfacewaves) tend to be more significant.

(3) P The selection of the waves to be considered and of the corresponding wavepropagation speeds shall be based as far as possible on geophysical considerations.

4.3.4 Permanent soil movements

(1) P The ground rupture patterns associated with earthquake induced groundmovements, either due to surface faulting or landslides, are likely to be complex,showing substancial variations in displacements as a function of the geologic setting,soil type and the magnitude and duration of the earthquake. The possibility of suchphenomena occurring at given sites shall be established, and appropriate modelsshall be defined.

4.4 Methods of analysis

4.4.1 Buried pipelines

(1) An acceptable analysis method for buried pipelines on stable soil, based onapproximate assumptions on the characteristics of ground motion, is given in AnnexB.

(2) P It is acceptable to take advantage of the postelastic deformation of pipelines.The deformation capacity of a pipeline shall be adequately evaluated.


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(2)P Buried pipelines crossing areas where soil failures or concentrated distortionscan occur, like lateral spreading, liquefaction, landslides and fault movements, shallbe checked to resist these phenomena.

4.5.1.1 Buried pipelines on stable soil (Ultimate limit state)

(1) The response quantities obtained from the analysis are the maximum valuesof axial strain and curvature and, for unwelded joints (reinforced concrete orprestressed pipes) the rotations and the axial deformations at the joints.

a) Steel pipelines

(2)P The combination of axial strain and curvature shall be compatible with theavailable ductility of the material in tension and with local and global buckling

resistance in compression.- allowable tensile strain 0,05- allowable compressive strain 0,4 t/R /> 0,05

where t and R are the thickness and radius of the pipe respectively.

(3)P Upward beam-type buckling of the pipeline shall be prevented by adequatesoil cover or by other restraining means.

b) Concrete pipelines

(4)P Under the most unfavourable combination of axial strain and curvature thesection of the pipe:

- shall not exceed the ultimate compressive strain of concrete- shall not exceed a tensile strain of steel such as to produce permanent cracks

incompatible with the specified requirements.

(5)P Under the most unfavourable combination of axial and rotationaldeformations, the joints shall not suffer damages incompatible with the specifiedrequirements.

4.5.1.2 Buried pipelines under differential ground movements (welded steelpipes) (Ultimate limit state)

(1) The segment of pipeline deformed by the displacement of the ground, eitherdue to fault movements, or caused by a landslide or by lateral spreading, should bechecked not to exceed the available ductility of the material in tension and not tobuckle locally or globally in compression. The limit strains are those in 4.5.1.1 a)

(2) In all areas of potential ground rupture pipelines should be provided withautomatic shutdown valves.


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4.5.1.3 Above-ground pipelines on stable soil

(1)P The load effects induced in the supporting elements (piers, frames, etc) by thedesign seismic action considered for the pipeline shall be less than or equal to theultimate strength capacity evaluated as for non-seismic conditions.

(2)P Under the most unfavourable combination of axial and rotationaldeformations, the joints shall not suffer damages incompatible with the specifiedserviceability requirements.

(3) For the pipeline itself the relevant provisions in 4.5.1.1 apply.

4.6 Design measures for fault crossings

(1) The decision to apply special fault crossing designs for pipelines where they

cross potentially active fault zones depends upon cost, fault activity, consequencesof rupture, environmental impact, and possible exposure to other hazards during thelife span of the pipeline.

(2) In the design of a pipeline for fault crossing, the following considerations willgenerally improve the capability of the pipeline to withstand differential movementsalong the fault:

a) Where practical, a pipeline crossing a strike-slip fault should be oriented in sucha way as to place the pipeline in tension.

b) Reverse faults should be intersected at an oblique angle, which should be assmall as possible, to minimize compression strains. If significant strikeslipdisplacements are also anticipated, the pipeline fault crossing angle should bechosen to promote tensile elongation of the line.

(3) The depth of pipeline burial should be minimized in fault zones in order toreduce soil restraint on the pipeline during fault movement.

(4) An increase in pipe wall thickness will increase the pipeline's capacity for faultdisplacement at a given level of maximum tensile strain. It would be appropriate touse relatively thickwalled pipe within [300 m] each side of the fault. It should be

recognized, however, that weld integrity may be reduced for large wall thicknesses.

(5) Reduction of the angle of interface friction between the pipeline and soil alsoincreases the pipeline's capacity for fault displacement at a given level of maximumstrain. One way to accomplish this is to use a hard, smooth coating such as anepoxy coating in the vicinity of the fault crossing.

(6) Close control should be exercised over the backfill surrounding the pipelineover a distance of [300 m]on each side of the fault. In general, a loose to mediumgranular soil without cobbles or boulders will be a suitable backfill material. If theexisting soil differs substantially from this, oversize trenches should be excavated fora distance of approximately [15 m]on each side of the fault.


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(7) For welded steel pipelines, the most common approach to accommodate faultmovement is to utilize the ability of the pipeline to deform well into the inelastic rangein tension in order to conform without rupture to the ground distortions. Whereverpossible, pipeline alignment at a fault crossing should be selected such that thepipeline will be subjected to tension plus a moderate amount of bending. Alignments

which would place the pipeline in compression are to be avoided to the extentpossible because the ability of the pipeline to withstand compressive strain withoutrupture is significantly less than that for tensile strain. When compressive strainsexists, they should be limited to that strain which would cause wrinkling or localbuckling of the pipeline.

(8) In all areas of potential ground rupture, pipelines should be laid in relativelystraight sections taking care to avoid sharp changes in direction and elevation. Tothe extent possible, pipelines should be constructed without field bends, elbows, andflanges that tend to anchor the pipeline to the ground.


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Annex A (informative)

Seismic analysis procedures for tanks

A.1 Introduction and scope

This Annex provides information on seismic analysis procedures for tanks subjectedto horizontal and vertical excitation and having the following characteristics:

a) cylindrical shape, with vertical axis and circular or rectangular cross-section;b) rigid or flexible foundation;c) fully or partially anchored to the foundation.

Extensions required for dealing with elevated tanks are briefly discussed, as it is thecase for cylindrical tanks with horizontal axis.

A rigorous analysis of the phenomenon of dynamic interaction between the motion ofthe contained fluid, the deformation of the tank walls and that of the underlyingfoundation soil, including possible uplift, is a problem of considerable analyticalcomplexity and requiring unusually high computational resources and efforts.Although solutions to the more simple cases of seismic response of tanks are knownfrom the early seventies, progress in the treatment of the more complex ones iscontinuing up to the present, and it is still incomplete.

Numerous studies are being published, offering new, more or less approximate,procedures valid for specific design situations. Since their accuracy is problem-dependent, a proper choice requires a certain amount of speciliazed knowledge fromthe designer. Attention is called to the importance of a uniform level of accuracyacross the design process: it would not be consistent, for ex., to select an accuratesolution for the determination of the hydrodynamic pressures, and then not to use acorrespondingly refined mechanical model of the tank (e.g., a F.E. model) forevaluating the stresses due to the pressures.

The necessary limitations in the scope and space of this Annex do not allow to gobeyond a detailed presentation of the seismic design procedure for the simplest of allcases: rigid circular tanks anchored to a rigid base. For all the situations which makethe problem more complex, as for ex. the flexibility of the tank, and/or that of the

foundation soil, and/or that of the anchoring system, since exact solutions are eithercomplicated and lengthy, or non existing, a brief explanation is given of the physicalphenomena distinguishing the particular situation from the reference case, andapproximate solutions are either summarized or reference is made to pertinentliterature.

At present, the most comprehensive documents giving guidelines for the seismicdesign of tanks are the ASCE volume: "Guidelines for the seismic design of oil andgas pipeline systems", 1984, ref. [5], and the Recommendations of a New ZealandStudy Group: "Seismic Design of Storage Tanks", 1986, ref. [10]. Although morethan ten years old they are still valuable in that they cover in detail a wide range of

cases. Both documents are used as sources for the present Annex.A.2 Vertical rigid circular tanks


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A.2.1 Horizontal earthquake excitation

The complete solution of the Laplace equation for the motion of the fluid contained ina rigid cylinder can be expressed as the sum of two separate contributions, called"rigid impulsive", and "convective", respectively. The "rigid impulsive" component of

the solution satisfies exactly the boundary conditions at the walls and at the bottomof the tank (compatibility between the velocities of the fluid and of the tank), but gives(incorrectly, due to the presence of the waves) zero pressure at the free surface ofthe fluid. A second term must therefore be added, which does not alter thoseboundary conditions that are already satisfied, and re-establishes the correctequilibrium condition at the top.

Use is made of a cylindrical coordinate system: r z, , , with origin at the center of thetank bottom, and the z axis vertical. The height and the radius of the tank aredenoted by H and R, respectively, is the mass density of the fluid, and

= =r

R

z

H, , are the adimensional coordinates.

A.2.1.1 Rigid impulsive pressure

The spatial-temporal variation of this component is given by the expression:

( ) ( ) ( )p t C H A ti i g , , , cos= , (A.1)where:

( ) ( )

( ) ( )C

I

Ii

n

n nn on

n

,

/

cos'

=

=

1

1

2 1 (A.2)

in which:

nn

H R= +

=2 1

2; /

( )I1 and ( )I1' denote the modified Bessel function of order 1 and its derivative1.

The time-dependence of the pressure pi in eq. (A.1) is given by the function ( )Ag t ,

which represents here the free-field motion of the ground (the peak value of ( )Ag t is

denoted by ag). The distribution along the height of pi in eq. (A.1) is given by thefunction Ci and is represented in Fig. A1(a) for = 1 (i.e. at the wall of the tank) and

cos = 1 (i.e. on the plane which contains the motion), normalized to R agand for

three values of =H

R.

The circumferential variation of pi follows the function cos Fig. A1(b) shows theradial variation of pi on the tank bottom as a function of the slenderness parameter

1The derivative can be expressed in terms of the modified Bessel functions of order 0 and 1 as:

( )( )

( )( )

I xdI x

dx I x

I x

x11

01' = = +


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. For increasing values of the pressure distribution on the bottom tends to becomelinear.

0.0 0.2 0.4 0.6 0.8 1.0

P Ra

0.0

0.2

0.4

0.6

0.8

1.0

=zH

= 0.5

= 1.0

= 3.0

0.0 0.2 0.4 0.6 0.8 1.0

=r/R

0.0

0.2

0.4

0.6

0.8

1.0

a b Fig. A1 - Variation of the impulsive pressure for three values of =H R/ .

1(a) variation along the height; 1(b) radial variation on the tank bottom.(Values normalized to R ag)

Pressure resultantsFor a number of purposes it is useful to evaluate the horizontal resultant of thepressure at the base of the wall: Qi , as well as the moment of the pressures withrespect to an axis orthogonal to the direction of the motion: Mi . The total momentMi immediately below the tank bottom includes the contributions of the pressures onthe walls and of those on the bottom.

By making use of eq. (A.1) and (A.2) and performing the appropriate integrals onegets:

- impulsive base shear: ( ) ( )Q t m A t i i g= (A.3)

where mi indicates the mass of the contained fluid which moves together with thewalls, is called impulsive mass,and has the expression:

( )( )

m m I

Ii

n

n nn

==

2 1310

/

/' (A.4)

with m R H= 2

total contained mass of the fluid.

- impulsive base moment: ( ) ( )M t m h A ti i i g = ' (A.5)


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with

( ) ( )( )

( )

( )

h H

I

I

I

I

i

n

n

n

n

n

n

n

n n

n

'

'

'

/

/

/

/

=

+ +

+

=

=

1

22

2 1

2

1

4

1

1

0

1

3

1

0

(A.6)

The two quantities mi and hi' are plotted in Fig. A2 as functions of the ratio

=H R/ .

0.0 1.0 2.0 3.0

=H/R

0.0

0.2

0.4

0.6

0.8

1.0

mi

/m

0.0 1.0 2.0 3.0

=H/R

0.0

0.5

1.0

1.5

2.0

2.5

3.0

h'i/H

(a) (b) Fig. A2 - Ratios m mi / and h Hi

' / as functions of the slenderness of the tank

It is noted from Fig. A2 that mi increases with , to become close to the total mass

for high values of this parameter, while hi' tends to stabilize at about mid height.

Values of hi' larger than Hfor squat tanks are due to the predominant contribution ofthe pressures on the bottom.

A.2.1.2 Convective pressure component

The spatial-temporal variation of this component is given by the expression:

( ) ( ) ( ) ( )p t J A tc n nn

n n , , , cosh cos==

1

1 (A.7)

with

( ) ( ) ( )

n n n nR

J=

2

12 1 cosh (A.8)


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1 2 31 8112 5 3314 8 5363= = =, , , J1= Bessel function of the first order

( )A tn = response acceleration of a single degree of freedom oscillator having a

frequency cn:( )

cn g

n

R n

2 = tanh (A.9)

and a damping factor value appropriate for the fluid.

Eq. (A.7) shows that the total pressure is the combination of an infinite number ofmodal terms, each one corresponding to a wave form of the oscillating liquid. Onlythe first oscillating, or sloshing, mode and frequency, needs in most cases to beconsidered for design purposes.

The vertical distribution of the sloshing pressures for the first two modes are shown

in Fig. A3(a), while Fig. A3(b) gives the values of the first two frequencies, asfunctions of the ratio H / R .

0.0 0.2 0.4 0.6 0.8 1.0

p/(R A(t))

0.0

0.2

0.4

0.6

0.8

1.0

=z/H

2nd

Mode

1st

Mode

= 0.5

= 1.0

= 3.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0

=H/R

0.5

1.0

1.5

2.0

2.5

(R/g)

1st

th Mode

2nd

Mode

(a) (b)

Fig. A3 - Variation of the first two modes sloshing pressures along the height(Fig. 3(a)), and values of the first two sloshing frequencies as functions of

One can observe from Fig. A3 that in squat tanks the sloshing pressures maintainrelatively high values down to the bottom, while in slender tanks the sloshing effect issuperficial.

For the same value of the response acceleration, the contribution of the secondmode is seen to be negligible. The other interesting result from Fig. A3.(b) is that thesloshing frequencies become almost independent of the parameter , when this islarger than about 1.

The value of c1 in this case is approximately given by the expression:

( ) c R R in metres1 4 2= , / (A.10)


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which, for the usual values of Rin petrochemical plants yields periods of oscillationof the order of few seconds (for instance, Tc1= 4,7 sec for R= 10 m).

Pressure resultants

In a way analogous to that followed for the impulsive component one may arrive atthe expressions for the base shear resultant and the total moment immediatelybelow the bottom plate of the tank.

The base shear is given by:

( ) ( )Q t m A t c cn nn

==

1

(A.11)

with the nth modal convective mass:

( )

( )m mcn

n

n n

=

2

12tanh

(A.12)

From eq. (A.11) one can note that the total shear force is given by the instantaneoussum of the forces contributed by the (infinite) oscillators having masses mcn ,

attached to the rigid tank by means of springs having stiffnesses: K mn n cn= 2 . The

tank is subjected to the ground acceleration ( )A tg and the masses respond with

accelerations ( )A tn .

From Fig. A3 (and the following, Fig. A4) one can verify that only the first of thesloshing masses needs to be considered.

The total moment can be expressed as:

( ) ( )( ) ( )M t m A t h Q t hc cn nn

cn cn cnn

= ==

=

1 1

(A.13)

where hcn is the level where the equivalent oscillator has to be applied in order to

give the correct value of Mcn :

( )( )

h Hcnn

n n

= +

1

2 cosh

sinh (A.14)

The values of mc1 and mc2 , and the corresponding values of hc1 and hc2 are shown

in Fig. A4, as functions of .


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0.0 0.5 1.0 1.5 2.0 2.5 3.0

=H/R

0.0

0.2

0.4

0.6

0.8

mc/

m

0.0 0.5 1.0 1.5 2.0 2.5 3.0

=H/R

0.0

1.0

2.0

3.0

4.0

hc

/H

1st

Mode

2nd

Mode

(a) (b)

Fig. A4 - First two sloshing modal masses (Fig. A4(a)), and corresponding heightshc1 and hc2 (Fig. A4(b)), as functions of

A.2.1.3 Height of the convective wave

The predominant contribution to the sloshing wave height is provided by the firstmode, and the expression of the peak at the edge is:

( )d R S T e cmax ,= 0 84 1 (A.15)

where Se ( ) is the appropriate elastic acceleration response spectrum, expressed ing (acceleration of gravity).

A.2.1.4 Combination of impulsive and convective pressures

The time-history of the total pressure is the sum of the two time-histories, theimpulsive one being driven by ( )A tg , the convective one by ( )A tc1 (neglectinghigher order components).

If, as it is customary in design practice, a response spectrum approach is preferred,

the problem of suitably combining the two maxima arises. Given the generally wideseparation between the central frequencies of the ground motion and the sloshingfrequency, the square root of the sum of squares rule may become unconservative,so that the alternative, upper bound, rule of adding the absolute values of the twomaxima is recommended for general use.

A.2.1.5 Effect of walls inertia

For steel tanks, the inertia forces acting on the shell due to its own mass are small incomparison with the hydrodynamic forces, and can normally be neglected. Forconcrete tanks however, the wall inertia forces may not be completely negligible. The

inertia forces are contained in the same vertical plane of the seismic excitation;considering their component normal to the surface of the shell one has for thepressure the following expression:


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( )p s A tw w g= cos (A.16)

with w = mass density of the wall materials = wall thickness

This pressure component, which is constant along the height, has to be added to theimpulsive component given by eq. (A.1). The total shear at the base is obtained bysimply considering the total mass of the tank multiplied by the acceleration of theground.

A.2.2 Vertical earthquake excitation

The hydrodynamic pressure on the walls of a rigid tank due to a vertical groundacceleration ( )A tv is given by:

( ) ( ) ( )p t H A tvr v , = 1 (A.17)

A.2.3 Combination of pressures due to horizontal and vertical excitation

The peak combined pressure due to horizontal and vertical excitation can beobtained by applying the rule given in 3.2.

A.3 Vertical deformable circular tanks

A.3.1 Horizontal earthquake excitation

When the tank cannot be considered as rigid (this is almost always the case for steeltanks) the complete solution of the Laplace equation is ordinarily sought in the formof the sum of three contributions, referred to as: "rigid impulsive", "sloshing" and"flexible".

The third contribution is new with respect to the case of rigid tanks: it satisfies thecondition that the radial velocity of the fluid along the wall equals the deformationvelocity of the tank wall, plus the conditions of zero vertical velocity at the tank

bottom and zero pressure at the free surface of the fluid.

Since the deformation of the wall is also due to the sloshing pressures, the sloshingand the flexible components of the solution are theoretically coupled, a fact whichmakes the determination of the solution quite involved. Fortunately, the dynamiccoupling is very weak, due to the separation which exists between the frequencies ofthe two motions, and this allows to determine the third component independently ofthe others with almost complete accuracy. The rigid impulsive and the sloshingcomponents examined in A.2 remain therefore unaffected.

No closed-form expression is possible for the flexible component, since the pressure

distribution depends on the modes of vibration of the tank-fluid system, and henceon the geometric and stiffness properties of the tank. These modes cannot beobtained directly from usual eigenvalue algorithms, since the participating mass of


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the fluid is not known a priori and also because only the modes of the type:( ) ( )f f , cos= are of interest (and these modes may be laborious to find among

all other modes of a tank).

Assuming the modes as known (only the fundamental one is normally sufficient, so

that in the following expressions both the mode index and the summation over allmodal contributions are dropped) the flexible pressure distribution has the form:

( ) ( ) ( )p t H d A tf n nn

f , , cos cos==

0

(A.18)

with:( ) ( )

( ) ( ) ( )

=

+

+

=

=

f s

Hb d

f s

H

f d d

sn nn

sn nn

' cos

cos

00

1

00

1

(A.19)

( ) ( )( )

b I

In

n

n

n

n

'

'

/

/=

2

12

1

1

(A.20)

( ) ( ) ( )( )

df d I

In

n

n

n

n

= 2 01

1

1

cos /

/' (A.21)

s is the mass density of the shell, s is its thickness and ( )A tf is the response

acceleration (relative to its base) of a simple oscillator having the fundamentalfrequency and damping factor of the first mode.

In most cases of flexible tanks, the pressure ( )pf in eq. (A.18) provides thepredominant contribution to the total pressure, due to the fact that, while the rigidimpulsive term (eq. (A.1)) varies with the ground acceleration ( )A tg , the flexible term(eq. (A.18)) varies with the response acceleration which, given the usual range ofperiods of the tank-fluid systems, is considerably amplified with respect to ( )A tg .

For the determination of the first mode shape of the tank, the following iterativeprocedure is suggested in ref. [2]. Starting from a trial shape ( )f and denoting

with ( )f i the one corresponding to the i-th iteration step, an "effective" mass of theshell is evaluated as:

( ) ( )

( ) ( )

i si

i s

p

g s f= +

2 (A.22)

where ( )psi is the amplitude of the pressure evaluated with eq. (A.18) at the i-th

step, and ( )s is the thickness of the shell, respectively.

The effective density from eq. (A.22) can then be used in a structural analysis of thetank to evaluate the (i+1)th mode shape, and so forth until convergence is achieved.


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The fundamental frequency of the tank-fluid system can be evaluated by means ofthe following approximate expression:

( )( ) ( )f E s H R g

s= / /

/1 22 (with = 1/3) (A.23)

with ( )g = +0 01675 0 15 0 462, , , (A.24)

Pressure resultantsStarting from eq. (A.18), the resultant base shear and total moment at the base canbe evaluated, arriving at expressions in the form:

- base shear ( ) ( ) ( )Q t m A t f f f= 1st mode only (A.25)

with ( )m m dfn

nnn=

=

1

0

(A.26)

-total moment ( ) ( )M t m h A tf f f f= (A.27)

with

( ) ( )

( )h H

dd I

d

f

n

n

n

n

n

n n

n

n

n

n

n

n

=

+

=

=

=

1 2

1

20

1

0

0

'

'

/

(A.28)

A.3.2 Combination of pressures terms due to horizontal excitation

The time-history of the total pressure is, in the case of flexible tanks, the sum ofthree time-histories: of the rigid impulsive one (eq. (A.1)), of the convective one (eq.(A.7)), and of the flexible one (eq. (A.18)) each of them differently distributed alongthe height and having a different variation with time.

Referring for simplicity to the base shears produced by these pressures (eqs. (A.3),(A.11) and (A.25)) one has:

( ) ( ) ( ) ( )Q t m A t m A t m A t i g cn nn

f f= + +=

1

(A.29)

where, it is recalled, ( )A tn is the total or absolute response acceleration of a simpleoscillator of frequency n (eq. (A.9)) subjected to a base acceleration ( )A tg ; while

( )A tf is the response acceleration, relative to the base, of a simple oscillator offrequency f (eq. (A.23)), and damping appropriate for the tank-fluid system, also

subjected to ( )A tg .

If the individual maxima of the terms in eq. (A.29) are known, which can be achievedby using a response spectrum of absolute and relative accelerations, the


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corresponding pressures on the tank needed for a detailed stress analysis can beobtained by spreading the resultant over the tank walls and floor according to therelevant distribution.

To expedite the design process, the masses mi , mcn and mf , the latter based on

assumed first mode shapes, have been calculated as functions of the ratio , and areavailable in tabular form or in diagrams, for ex. in ref. [5] and [10].

Use of eq. (A.29) in combination with response spectra, however, poses the problemof how to superimpose the maxima. Apart from the necessity of deriving a relativeacceleration response spectrum for ( )A tf , there is no accurate way of combining the

peak of ( )A tg with that of ( )A tf .

In fact, since the input and its response cannot be assumed as independent in therelatively high range of frequency under consideration, the square root of the sum ofsquares rule is unconservative. On the other hand, the simple addition of theindividual maxima can lead to overconservative estimates.

Given these difficulties, various approximate approaches based on the theorypreviously discussed have been proposed.

Two of these, presented as alternatives and illustrated in detail in ref. [5], are due toVeletsos-Yang (V.Y.) and Haroun-Housner (H.H.).

The V.Y. proposal consists essentially in replacing eq. (A.29) with the equation:

( ) ( ) ( )Q t m A t m A t i fa cn nn

= +=

1

(A.30)

i.e., in assuming the entire impulsive mass to respond with the amplified absolute

response acceleration of flexible tank system ( ) ( ) ( )( )A t A t A tfa f g= + . The maximumof ( )A tfa is obtained directly from the appropriate response spectrum.

The V.Y. procedure is an upper bound solution, whose approximation has beenproven to be acceptable for H R/ ratios not much larger than 1. Above this value,

corrections to decrease the conservativeness are suggested. In view of theconservative nature of the method, the effects of tank inertia may generally beneglected. If desired, the total base shear can be evaluated approximately by theexpression:

( ) ( ) ( )Q t m A t w o fa= (A.31)

where ( )A tfa is the pseudoacceleration response of the tank-fluid system, and

( )o m is the effective participating mass of the tank wall in the first mode, where m

is the total mass of the tank and the factor o may be determined approximatelyfrom:H R/ 0,5 1,0 3,0


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A.3.2.1 Simplified procedure for fixed base cylindrical tanks (Malhotra, 1997)8

ModelThe hydrodynamic effects in a tank are evaluated by the superposition of these twocomponents: (1) The impulsive component, which represents the action of the liquid

near the base of the tank that moves rigidly with the flexible wall of the tank; and (2)the convective component, which represents the action of the liquid that experiencessloshing motion near the free-surface. In this analysis, the tank-liquid system ismodeled by two single-degree-of-freedom systems, one corresponding to theimpulsive and the other corresponding to the convective action. The impulsive andconvective responses are combined by taking their numerical-sum rather than theirroot-mean-square value.

Natural periods:The natural periods of the impulsive and the convective responses,in seconds, are

T Cimp i= H

s / R E (A.35)

T C Rcon c= (A.36)

whereH= design liquid height,R = tanks radius, s= equivalent uniform thickness ofthe tank wall, = mass density of liquid, and E= Youngs modulus of elasticity oftank material. The coefficients Ciand Ccare obtained from Table A1. The coefficientCi is dimensionless, while Cc is expressed ins m/

/1 2 ; substituting R in meters in eq.

(A.36), therefore, gives the correct value of the convective period. For tanks withnonuniform wall thickness,smay be computed by taking a weighted average overthe wetted height of the tank wall, assigning highest weight to the thickness near thebase of the tank where the strain is maximum.

Impulsive and convective masses:The impulsive and convective masses mi andmcare given in Table A1 as fractions of the total liquid mass m.

Table A1

H/R C1 Cc mi/m mc/m hi/H hc/H hi/H h

c/H

0,30,50,71,01,52,02,53,0

9,287,746,976,366,066,216,567,03

2,091,741,601,521,481,481,481,48

0,1760,3000,4140,5480,6860,7630,8100,842

0,8240,7000,5860,4520,3140,2370,1900,158

0,4000,4000,4010,4190,4390,4480,4520,453

0,5210,5430,5710,6160,6900,7510,7940,825

2,6401,4601,0090,7210,5550,5000,4800,472

3,4141,5171,0110,7850,7340,7640,7960,825

Note: Ccis expressed in s m/ /1 2


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( ) ( ) ( )p t f H A tvf vf

, , cos=

0815

2 (A.40)

where:

( )f = 1,078 + 0,274 ln for 0,8 < < 4

( )f = 1,0 for < 0,8

( )A tvf is the acceleration response function of a simple oscillator having afrequency equal to the fundamental frequency of the axisymmetric interactionvibration of the tank and the fluid.

The fundamental frequency can be estimated by means of the expression:

( ) ( )

( ) ( )f

R

E I s

H Ivd

o

=

1

4

2

1

1 1

2 1

1 2

/

(with = 1/3) (A.41)

in which ( ) 1 2= / and where Eand are Young modulus and Poisson ratio ofthe tank material, respectively.

The maximum value of ( )p tvf is obtained from the vertical acceleration responsespectrum for the appropriate values of the period and the damping. If soil flexibility isneglected (see A.7) the applicable damping values are those of the material (steel,concrete) of the shell.

The maximum value of the pressure due to the combined effect of the rigid: ( )pvr and flexible: ( )pvf contributions can be obtained by applying the square root of thesum of squares rule to the individual maxima.

A.3.4 Combination of pressures due to horizontal and vertical excitation

The maximum value of the pressure due to the combined effect of horizontal andvertical excitation can be obtained by applying the square root of the sum ofsquares rule to the maximum pressures produced by each type of excitation.

A.4 Rectangular tanks

For tanks whose walls can be assumed as rigid, a solution of the Laplace equationfor horizontal excitation can be obtained in a form analogous to that described forcylindrical tanks, so that the total pressure is again given by the sum of an impulsiveand a convective contribution:

( ) ( ) ( )p z t p z t p z ti c, , ,= + (A.42)

The impulsive component has the expression:

( ) ( ) ( )p z t q z L A ti o g, = (A.43)


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where L is the half-width of the tank in the direction of the seismic action, and thefunction ( )q zo , which gives the variation of ( )pi along the height ( ( )pi is constant inthe direction orthogonal to the seismic action), is plotted in Fig. A5.

The trend and the numerical values of the function ( )q zo are quite close to those of acylindrical tank with radius R = L.The convective pressure component is given by a summation of modal terms(sloshing modes), each one having a different variation with time. As for cylindricaltanks, the dominant contribution is that of the fundamental mode, that is:

( ) ( ) ( )p z t q z L A tc c1 1 1, = (A.44)

where the function ( )q zc1 is shown in Fig. A6 together with the 2nd mode contribution( )q zc2 and ( )A t1 is the acceleration response function of a simple oscillator having

the frequency of the first mode, the appropriate value of the damping, and subjectedto an input acceleration ( )A tg .

The period of oscillation of the first sloshing mode is:

T L g

H

L

1

1 2

2

2 2

=

/

tanh

/

(A.45)

Pressure resultantsThe base shear and the moment on the foundation could be evaluated on the basisof expressions (A.43) and (A.44).

According to reference [10], for design purposes the values of the masses mi and

mc1 , as well as of the corresponding heights above the base: hi' and hc1 , calculated

for cylindrical tanks and given by the expressions (A.4), (A.12) and (A.6), (A.14),respectively, may be adopted for rectangular tanks as well (with Lreplacing R), witha margin of approximation not exceeding 15%.

Flexible wallsWall flexibility produces generally a significant increase of the impulsive pressures,while leaving the convec