Structural_design_of_buried_pipelines_under_various_conditions_of_...[1].pdf

Document type: Technical ReportDocument subtype: Document stage: Unique Acceptance ProcedureDocument language: ET:\NAW\KRO\165-wg12\tg 1\1295-2\EN_1295-2_(E).docSTD Version 2.1cCEN/TC 165Date:2004-08prCEN/TR 1295-2CEN/TC 165Secretariat: DINStructural design of buried pipelines under various conditions of loading Part 2: Summary of nationally established methods of designStatischeBerechnungvonerdverlegtenRohrleitungenunterverschiedenenBelastungsbedingungen Teil 2:Zusammenstellung national eingefhrter BerechnungsverfahrenCalcul de rsistance mcanique des canalisations enterres sous diverses conditions de charge Partie 2 : FffICS:Descriptors:Doc CEN/TC 165 N_1371Doc CEN/TC 164 N 1681prCEN/TR 1295-2:2004 (E)2ContentsForeword..................................................................................................................................................................... 4Introduction ................................................................................................................................................................ 41 Scope.............................................................................................................................................................. 42 Normative references ................................................................................................................................... 53 Definitions...................................................................................................................................................... 54 Additional details about established methods .......................................................................................... 5Annex A (informative)Summary of Methods of different countries...................................................................... 6A.1 Austria............................................................................................................................................................ 6A.1.1 General remarks............................................................................................................................................ 6A.1.2 Principles ....................................................................................................................................................... 6A.1.3 Technical data ............................................................................................................................................... 7A.1.4 Deformation ratio ..................................................................................................................................... 10A.1.5 Loads............................................................................................................................................................ 11A.1.6 Vertical loads............................................................................................................................................... 11A.1.7 Horizontal loads .......................................................................................................................................... 12A.1.8 Reaction pressure at the pipe invert ......................................................................................................... 13A.1.9 Additional load effect.................................................................................................................................. 13A.1.10 Pipe loading in the longitudinal direction ................................................................................................ 14A.1.11 Structural design of the pipe ..................................................................................................................... 14A.2 Belgium........................................................................................................................................................ 19A.2.1 Flowchart ..................................................................................................................................................... 19A.2.2 Design, formulae, tables and charts, symbols and abbreviations......................................................... 19A.3 Denmark....................................................................................................................................................... 31A.3.1 General ......................................................................................................................................................... 31A.3.2 Charges........................................................................................................................................................ 34A.3.3 Safety............................................................................................................................................................ 37A.3.4 Partial safety factors................................................................................................................................... 37A.3.5 Calculations................................................................................................................................................. 38A.4 France........................................................................................................................................................... 40A.4.1 Scope............................................................................................................................................................ 40A.4.2 Original features of the method................................................................................................................. 40A.4.3 Description................................................................................................................................................... 40A.4.4 Example of calculation ............................................................................................................................... 48A.5 Germany....................................................................................................................................................... 50A.5.1 Introduction ................................................................................................................................................. 50A.5.2 Types of soil ................................................................................................................................................ 50A.5.3 Live loads..................................................................................................................................................... 51A.5.4 Effects of the installation on the structural calculation.......................................................................... 55A.5.5 Loading ........................................................................................................................................................ 55A.5.6 Load distribution......................................................................................................................................... 56A.5.7 Pressure distribution at pipe circumference............................................................................................ 61A.5.8 Sectional forces, stresses, strains, deformations................................................................................... 62A.5.9 Dimensioning............................................................................................................................................... 63A.6 Netherlands.................................................................................................................................................. 67A.6.1 General ......................................................................................................................................................... 67A.6.2 Earth load..................................................................................................................................................... 67A.6.3 Evenly distributed surface load................................................................................................................. 68A.6.4 Traffic loads................................................................................................................................................. 68A.6.5 Heavy transport ........................................................................................................................................... 69A.6.6 Self weight of pipe ...................................................................................................................................... 69A.6.7 Water weight ................................................................................................................................................ 69A.6.8 Loads form external and internal water pressure.................................................................................... 69prCEN/TR 1295-2:2004 (E)3A.6.9 Thermal loading ...........................................................................................................................................70A.6.10 Moments and normal forces.......................................................................................................................71A.6.11 Calculation model for a concrete pipe.......................................................................................................73A.6.12 Recommended design values ....................................................................................................................80A.7 Norway ..........................................................................................................................................................85A.7.1 Types of loads..............................................................................................................................................85A.7.2 Soil loads ......................................................................................................................................................85A.7.3 Self weight of pipe .......................................................................................................................................85A.7.4 Weight of water ............................................................................................................................................85A.7.5 Traffic load....................................................................................................................................................86A.7.6 Load distribution and bedding reaction....................................................................................................86A.7.7 Safety analysis .............................................................................................................................................86A.7.8 Structural design..........................................................................................................................................86A.8 Sweden..........................................................................................................................................................87A.8.1 Design of buried plastic pipes....................................................................................................................87A.8.2 Calculation method for rigid pipes.............................................................................................................95A.9 United Kingdom...........................................................................................................................................98A.9.1 General description .....................................................................................................................................98A.9.2 Calculation procedures...............................................................................................................................98A.9.3 Rigid pipes....................................................................................................................................................99A.9.4 Semi-rigid pipes .........................................................................................................................................102A.9.5 Flexible pipes .............................................................................................................................................105prCEN/TR 1295-2:2004 (E)4ForewordThisdocumentprCEN/TR1295-2hasbeenpreparedbyTechnicalCommitteeCEN/TC 165Wastewaterengineering, the secretariat of which is held by DIN.This document is currently submitted to the Technical Committee Approval.This European Standard was prepared by a Joint Working Group (JWG 1) of Technical Committees TC 164, Watersupply, the secretariat of which is held by AFNOR, and TC 165, Waste water engineering, the secretariat of whichis held by DIN.Thisstandardisintendedforuseinconjunctionwiththeseriesofproductstandardscoveringpipesofvariousmaterials for the water industry.ThisstandardincludesaninformativeAnnexAinwhichareincludedadditionaldetailsaboutthenationallyestablishedmethodsofdesigndeclared,submittedbyandusedinmembercountries,andcollatedbytheJointWorking Group.IntroductionThestructuraldesignofburiedpipelinesconstitutesawiderangingandcomplexfieldofengineering,whichhasbeen the subject of extensive study and research, in many countries over a period of very many years.Whilst many common features exist between the design methodswhichhavebeendevelopedandestablishedinthe various member countries of CEN, there are also differences reflecting such matters as geological and climaticvariations, as well as different installation and working practices.In view of these differences, and of the time required to develop a common design method which would fully reflectthe various considerations identified in particular national methods, a two stage approach has been adopted for thedevelopment of this European Standard.Inaccordancewiththistwostageapproach,theJointWorkingGroup,atitsinitialmeeting,resolved"firsttoproduce an EN giving guidance on the application of nationally established methods of structural design of buriedpipelines under various conditions of loading, whilst working towards a common method of structural design". Thisstandard represents the full implementation of the first part of that resolution.1ScopeInadditiontoEN 1295-1,thisstandardgivesadditionalguidancewhencomparedwithEN 1295-1ontheapplication of the nationally established methods of design declared by and used in CEN member countries at thetime of preparation of this standard (see informative Annex A).This guidance is an important source of design expertise, but it cannot include all possible special cases, in whichextensions or restrictions to the basic design methods may apply.Sinceinpracticeprecisedetailsoftypesofsoilandinstallationconditionsarenotalwaysavailableatthedesignstage, the choice of design assumptions isleft to the judgement of the engineer. In this connectiontheguide canonly provide general indications and advice.prCEN/TR 1295-2:2004 (E)52ReferencesThisTechnicalReportincorporatesbydatedorundatedreference,provisionsfromotherpublications.Thesereferencesarecitedattheappropriateplacesinthetextandthepublicationsarelistedhereafter.Fordatedreferences, subsequent amendments to or revisions of any of these publications apply to this Technical Report onlywhenincorporatedinitbyamendmentorrevision.Forundatedreferencesthelatesteditionofthepublicationreferred to applies.EN 1295-1,Structuraldesignofburiedpipelinesundervariousconditionsofloading Part 1:Generalrequirements.3DefinitionsFor the purposes of this Technical Report, the definitions given in EN 1295-1 apply.4Additional details about established methodsAnnex Agivesforseveralcountriesdetailsabouttheestablishedmethodsofdesigndeclared,submittedbyandused in member countries.prCEN/TR 1295-2:2004 (E)6Annex A(informative)Summary of Methods of different countriesA.1AustriaA.1.1General remarksThe Austrian Standard B 5012 consists of two parts. Part one contains basic information regarding the definition oflaying and installation conditions, soil mechanics parameters and traffic loads.Part two deals with the fundamentals of the mechanical model used, load assumptions and load idealisations, themodelforthecalculationofstressconditions,strainconditionsandthedeformationofburiedpipesbasedonthepipe-soil interaction, and safety factors, calculated on the basis of the probabilistic theory of reliability.In the annex of part two, the formulae and a guidance for their use are given.TheNORMmodelpermitstheanalysisanddesignofallkindofburiedpipes,includingpressureandnonpressure applications of all pipe materials.A.1.2PrinciplesThecalculationsystemisbasedonthemodeloftheembeddedcircularornoncircularring.Thepipe-soilinteraction is taken into account by the following interpretations :theshear-stiffbeamabovethepipeforthecalculationoftheverticalloadingduetotheearthweightanduniformly distributed surcharge ;thecompatibilityofthehorizontalpipeandsoilmovementsforthecalculationofthehorizontalembedmentreaction pressures ;assumptionsforthedistributionoftheverticalreactionpressuredependentonthebeddingandlayingconditions and on the pipe-soil stiffness ratio (see figure A.1)The loading due to traffic loads is calculated by means of the Boussinesq theory.Figure A.1 Mechanical modelSoilmechanicsparametersareproposedinNORMB5012,part1,asafunctionofthesoilgroupandthecompaction. Other values may be used when they are measured in advance. The soil mechanics parameters usedprCEN/TR 1295-2:2004 (E)7arerealvalueswithoutanycorrectionsinrespectofindeterminedinfluencesandcanthusbemeasuredandcontrolled by means of standard soil mechanics tests.The stress dependence of the soil stiffness moduli is taken into account.The calculation of stress or strain in the pipe wall and pipe deformation has to be done using first order theory andalso, where appropriate, second order theory.InadditiontotheusuallayingconditionstheNORM-methoddealswithsomespecialcasessuchasadeformationlayerabovethecrownofrigidpipes,agapatthesidesofthepipeandaninitialdeformationofthepipe.For the calculation constant bedding and laying conditions in longitudinal direction are assumed. As a consequencethecalculationisrealisedasatwodimensionalorplanproblem.However,effectsoftheinternalpressureinlongitudinal direction are considered in the case of pressure pipes.A.1.3Technical dataThe following data describe the pipe, the installation conditions and the soil properties.A.1.3.1Pipe dataThe most important data are the geometrical properties like diameter and wall thickness and the material propertieslike modulus of elasticity, strength and specific weight.Height of upper bedding Hzw = 0,25 daDpr ! to that in the rest of the embedment ! 90 %a) Bedding type AF1 (with special compaction of upper bedding)Dpr = constant in the whole embedment according to the installation caseb) Bedding type AF2 (without any special compaction of upper bedding)prCEN/TR 1295-2:2004 (E)8c) Bedding type AF3 (with special compaction of upper bedding or special material with ES2u ! 2 ES2o)hb and hzw see NORM B2503 = Bwhb and hzw see NORM B2503 = Bwd) Bedding type AF4 (concrete bedding) e) Bedding type AF5 (concrete bedding)Figure A.2 Bedding typesA.1.3.2Installation dataThe following geometrical data have to be fixed:tsdepth of cover;bstrench width at the height of the pipe crown;trench wall angle measured from the horizontal line ;angleofverticalreactionpressure(dependingonbeddingtype,installationtypeandonthedeformationratio - see table 2 of NORM B 5012, part 2).bedding types: The NORM B 5012, part 1, distinguishes between five bedding types as shown in figure A.2. Thefirst three bedding types AF1, AF2, AF3 refer to pipe laying in soil material, the bedding types AF4 and AF5 relateto pipe laying in concrete support.installationtypes:Forthespecificationofthesoilmechanicscalculationparameterstheinstallationtypecorresponding to the type of construction is to be fixed. The NORM B 5012 part 1 defines three installation types.The installation type is to be specified for the backfilling zone and the pipe zone separately.EF1:InstallationtypeEF1includesallinstallationprocedureswhichinvolveaveryhighdensityofthebackfillingmaterial.EF2: Installation type EF2 includes procedures which involve a moderately high density of the backfilling material.Thosedensitiesareachievedwheninstallingandintensivelycompactinglayerbylayeragainstathinwalledsheeting, withdrawn after compacting, or when installing and moderately compacting against the natural soil.prCEN/TR 1295-2:2004 (E)9EF3: Installation type EF3 includes all the other installation procedures, which cannot be defined as EF1 and EF2and which involve a low or unpredictable density or allow a gap to form after withdrawing the trench support.TheProctordensitiesrequiredforeachinstallationtypeshallbeverified,exceptforinstallationtypeEF3,A.Thevalue of the Proctor density to be used in the static calculation is quoted in table A.1 for every installation type.A.1.3.3Soil dataIfthesoilcharacteristicsaremeasuredfortheparticularcase,thosevaluesmaybeusedforthecalculation.Incasesuchvaluesarenotavailable,theNORMproposesvalueswhichcanbeusedasmeanvaluesinthecalculation, as in table A.1 and table A.2.Table A.1 Specific weight, internal friction angle and degree of compaction related to soil groupsSpecific weight B 'BProctor density Dpr in % for the installation type Soil groupkN/mInternal frictionangle 1 to 2degreeEF1 EF2 EF3BG 1 20 12 35 97 90 85BG 2 20 12 30 97 90 85BG 3 20 12 25 95 90 85BG 4 20 12 20 95 90 85The following soil groups are defined in NORM B 5012, part 1, in accordance with Austrian Standard B 4400 :BG1 : Non-cohesive soils (GE, GW, GI, SE, SW, SI)BG2 : Weakly cohesive soils of mixed grained size with low fine grain fraction (GU, GT, SU, ST)BG3 : Cohesive soils of mixed grained size with a high fine grain fraction (Gr , Gq , Sr , Sq )BG4 : Fine grained cohesive soils (UL, UM, TL, TA, TM)The short-term stiffness moduli Eso for a low initial stress level (0 =10 kN/m2) and exponent b for the calculation ofthe stress-dependent stiffness modulus are given as in table A.2.Table A.2 Stiffness moduli Eso and exponent b related to the Proctor density Dpr in %Stiffness moduli Eso and exponent b related with the Proctor density Dpr in % Soil group85 90 92 95 97 100 102BG1 3,8 5,3 6,0 7,2 8,2 10,0 11,4BG2 2,1 2,9 3,3 4,0 4,5 5,5 6,3BG3 1,3 1,8 2,1 2,5 2,9 3,5 4,0BG4 0,9 1,2 1,4 1,7 1,9 2,3 2,6Exponent b 0,5For special conditions Dpr values can be interpolated.The stress-dependent stiffness modulus can be calculated as follows:prCEN/TR 1295-2:2004 (E)10bE E

=0so swhereis the existing vertical stress in kN/m2, ( = PSE + PSO) ; 0 = 10 kN/m2.The long term stiffness modulus shall be calculated by multiplying the short term modulus by the factor k50.Wall friction and earth pressure ratios K1 and K2 in the main backfill (WZ) and the embedment (RZ) are proposedin NORM B 5012 as in table A.3.Table A.3 Wall friction angle and earth pressure ratios K1 and K2Installation type K1K2EF11321 - sin 11 - sin 2EF213111sin 1sin 1+22sin 1sin 1+EF3 0 0 0index 1 : the value is valid for the main backfill (WZ) ;index 2 : the value is valid for the embedment (RZ).A.1.4Deformation ratio Thedeformationratioisdefinedastheratiooftheverticalpipedeflection(VR)tothesettlementofthesoiladjacenttothepipe(VB)undertheexpectedtotalloadandtakingintoaccountofthepipesupportreaction(bedding type), but excluding the horizontal embedment reaction.The deformation ratio is defined as :VBVR=For circular pipes a simple formula is given.The deformation ratio indicates the deformation class of the buried pipe as shown in table A.4.Table A.4 Deformation classesDeformation class Deformation ratio Deformation behaviour of the installed pipeS 0,00 to 0,1 rigidSF greater than 0,1 to 1,00 semi flexibleF greater than 1,00 flexibleThe characterisations of the deformation classes are as follows :prCEN/TR 1295-2:2004 (E)11deformationclassS(rigidpipes):Thepipedeformationsaresmallandcanbeneglected.Theverticalloadconcentration upon the pipe crown must be calculated, the horizontal embedment reactions are very small and sonegligible.deformation class SF (semiflexible pipes) : The vertical pipe deformation is still less than the soil settlement atthesideofthepipe.Sotheverticalloadconcentrationuponthepipecrownistobecalculated.Howeverthehorizontal pipe deformation is not negligible and therefore the horizontal embedment reactions are to be calculatedas well.deformation class F (flexible pipes) : The vertical pipe deformation is greater than the soil settlement at the sideofthepipe.Noloadconcentrationoccurs.Thehorizontalembedmentreactionsareessentialforthestabilityofthose pipes and thus shall be calculated exactly.A.1.5LoadsThe following loads are taken into account :Earth loads,Permanent uniformly distributed surcharge,Traffic loads,Surcharges of limited extent (e.g. building loads),Self-weight of the pipe,Water filling,Internal pressure,External water pressure.A.1.6Vertical loadsA.1.6.1Earth load and uniformly distributed surchargeThe reduction of thevertical pressure on pipe installedintrenchesaccordingtothesilotheorycanbetakenintoconsideration, when the friction forces at the trench walls can be relied upon for the whole lifetime of the pipe.An application of the silo theory is not allowed in the following circumstances :for a cover depth up to 1 m;for pipes below the water table;when further excavation work cannot be excluded in the vicinity of the original trench walls.The average vertical pressure at the pipe crown level results from the effect of the force of gravity on the soil PSE,and from the distributed surcharge PSO.The effective vertical pressure on the pipe qv is calculated byqv = R. (PSE + PSO)where R is the concentration factor;R ! 1,0 for deformation classes S and SF (rigid and semi flexible);prCEN/TR 1295-2:2004 (E)12R = 1,0 for deformation class F (flexible).Factor R is calculated using the shear-stiff beam theory.Forrigidandsemiflexiblepipestheinfluenceofthepipeflexibilitycanbetakenintoaccountforembankmentcondition by: ) 1 (max maxRD R = =For trench condition with trench widths bs less than 4 da, the effect of the trench walls on the load concentration canbe considered approximately with :34d 31as RD RDRb =A.1.6.2Traffic loadsThe vertical pressures caused by traffic loads are calculated using the theory the Boussinesq for the vehicle typesin accordance with NORM B 4002 and railways loads in accordance with NORM B 4003, using impact factors.Traffic loads are considered to have no influence on the horizontal pressure, nor on the soil stiffness modulus.A.1.6.3Other loadsAdditionalsourcesofverticalpressureareconsidered,suchassurchargesoflimitedextentandexternalwaterpressure.A.1.7Horizontal loadsThehorizontalloadiscausedbytheearthload,uniformlydistributedsurcharge,externalwaterpressure,theinfluence of thecompactioninthepipezoneinordertocreateinitialovalizationduringinstallation,self-weightofthe pipe and water filling.The total horizontal loading hqconsists of two parts :a lateral pressure qh, which exists without any horizontal pipe side movement ;the embedment reactions pressure qh*, which results from horizontal pipe side movement.Total horizontal pressure : *h h hq q q + =Lateral pressure qhThe component qh is influenced by the internal friction and the compaction of the soil and can be calculated byvK 2 hq K q = , with( )BaSO SERvK2 34 + +=dP P qwhereK2is the earth pressure ratio as in table A.3 ;qvKis the vertical pressure at the springline ;dais the vertical external diameter.prCEN/TR 1295-2:2004 (E)13Embedment reaction pressure qh*The calculation of embedment reaction pressure qh* is based on the theory of compatibility between the horizontalpipe and soil displacements at the pipe side. It can be interpreted as the intersection of the characteristic lines forsoil and pipe, assuming linear conditions for both in the considered range of displacements and stresses.NORMB5012part2employsadistributionofthehorizontalbeddingreactionpressurecorrespondingtoanangleh=180forstandardconditions.Howeveritcanbeappropriatetocalculatewithamoreconcentratedbedding reaction pressure in the pipe side area, corresponding to a smaller distribution angle in some cases.The calculation for variable bedding areas of flexible pipes is explained in1) .A.1.8Reaction pressure at the pipe invertReaction pressure at the pipe invert is assumed to act as follows:uniformly distributed in vertical direction for laying in soil material;uniformly distributed in radial direction for laying in concrete bedding.In case the bedding angle is not defined by the bedding, as it is for bedding type AF3 or concrete bedding, NORMB5012part1proposesthereactionpressureangletobeusedinthecalculation,whichisdependentontheinstallation type, the bedding type and the deformation ratio .A.1.9Additional load effectNORM B 5012 part 2 deals with the following additional load effects:ground water;horizontal earth pressure from compaction (causing initial deformation);self weight and water filling;influence of cushion layers;internal pressure.groundwater:Groundwaterinfluences the soil densityand the soil stiffness modulus. Thecalculationofstress,strain and pipe deformation, caused by external water pressure, is explained.horizontalearthpressurefromcompaction:Compactioninthepipezonecancauseextrahorizontalembedment pressure and initial deformation of pipe. Guidance for the calculation of the loading and the influenceon the initial deformation, on the total loading and the final deformation are given by NORM B 5012, part 2.selfweightofthepipe:NORMB5012part2advisestotakeintoaccounttheinfluenceofselfweightofthepipe, when the following condition is fulfilled:05 , 0vrd qgwheregris the pipe weight per unit length; 1) Netzer, W.: Oberguggenberger, M.: Pregl, O.: The horizontal bedding of flexible buried pipelines in variable bedding areas.3R international 32 (1993). Heft 2/3. Februar/Mrz. Further quotations of literature can be found in NORM B 5012.prCEN/TR 1295-2:2004 (E)14qvis the total vertical load per unit area.cushion layers: Cushion layers above the crown of rigid pipes are used to reduce the load concentration, when sixrequirements, mentioned in NORM B 5012, are fulfilled.internal pressure: Two critical load cases are to be examined.A.1.10 Pipe loading in the longitudinal directionNORMB5012part2dealswiththefollowingloadings,whichcausestresses,strainsordeformationsinthelongitudinal direction of the pipe:stresses resulting from discontinuous bedding;longitudinalforcesinpressurepipelineswithbends,branches,reducingpieces,valvesanddeadends(resistance to these forces by concrete thrust blocks or by friction between the pipe and the soil);longitudinal forces resulting from transverse contraction or expansion;longitudinal forces resulting from temperature change.The extreme fibre stresses at the external boundaries of the pipe wall are calculated by( )4i4aa L L L L4r rr Ms dFWMAF = =whereFLis the resulting longitudinal force;MLis the resulting longitudinal bending moment;d is the mean pipe diameter;rais the external pipe radius;riis the internal pipe radius;s is the wall thickness.A.1.11 Structural design of the pipeA.1.11.1GeneralPipe design is to be made by the following analyses:stress (or strain) design according to first order theory;deformation design according to first order theory;stress (or strain) design according to second order theory;deformation design according to second order theory.The design of the pipeline shall ensure that the stress (or strain) does not exceed the allowable value, defined astheultimatevaluedividedbythesafetyfactor(asintableA.6)and/orthatthedeformationdoesnotexceedtheallowable deformation. The NORM B 5012, part 2, gives advice as to which of the criteria a) to d) shall be takeninto consideration for the particular case.prCEN/TR 1295-2:2004 (E)15Separatedverificationofbucklingisnotrequired.Bucklingsafetyisprovedbythestress(strain)ordeformationdesign according to second order theory.A.1.11.2Calculation of the stress (or strain) according to first order theoryThe calculation of normal forces and bending moments due to:earth load;permanent, uniformly distributed surcharge;traffic loads;surcharges of limited extent;is described in NORM B 5012, part 2, for standardloadingandinstallation conditions and for the standard loaddistribution.Alltheotherloadcasestakenintoconsideration,suchasselfweightofthepipe,waterfilling,internalpressure,external water pressure and other possible loadings shall be superimposed in the manner as indicated in NORMB 5012, part 2.The formulas and coefficients for the calculation of the bending moments and normal forces are given in NORMB 5012, part 2, appendix.The stresses are calculated by using the normal forces and bending moments per unit length asK2I IKI II6 = =sMsNWMANin which K considers the influence of the wall curvature.The strains can be calculated byRIIE =whereERis the pipe elasticity modulus.A.1.11.3Calculation of the deformation according to first order theoryThe formulas and coefficients for the calculation of the deformation due to first order theory aregiven in NORMB 5012, part 2, appendix.A.1.11.4Calculation of the stress (or strain) and deformation according to second order theoryNormalforcesNII,bendingmomentsMIIanddeformationsVIIaccordingtosecondordertheoryarecalculatedfrom the first order results as follows:NII NIMII= emMIVII= evVIAmplification factors em and ev can be obtained from diagrams in NORM B 5012, part 2, appendix.prCEN/TR 1295-2:2004 (E)16StressesaccordingtosecondordertheoryarecalculatedaslaiddowninA.11.2forfirstordertheorybutusingsection forces NII and MII.A.1.11.5Design criteria for non pressure pipesTheNORMB5012,part2,adviseswhichoftheverificationinA.1.11.1shouldbeusedforthedesigninaparticular case.Forpipesforwhichalimitedbendingcompressivestressistobeconsidered,theverificationofthestressisadecisive design criterion, as for pressure pipes.A.1.11.6Design criteria for pressure pipesConcerningtheresultingstresses,causedbyinternalpressure(i)andbyallotherloadings(a),threetypesofpressure pipes can be distinguished as in table A.5.Table A.5 Design stress spN for the design of pressure pipesDeformation class Distinctive feature Design stress spNType of pressure pipeS " 0,1(rigid)i + a1SFor4 , 02Rzul

=srEZres2F4 , 02Rzul>

=srEZi or a3zulpermitted stress (requR as in A.1.11.7) ;resresultant tensile stress at the extreme fibre point (pipe crown or invert) resulting from superimposition ofinternalpressureandexternalloading,calculatedasinsecondordertheorytakingintoaccounttheso-called rerounding effect.Stress res is to be calculated by:res = ni (a + i)where ni is a reduction factor which is derived as a function of Z (as in table A.5) and of the stress ratio i/a fromdiagrams 17 to 28 in NORM B 5012, part 2, appendix.Characteristic features of the types of pressure pipes as in table A.5:Type 1: Rigid pipes with deformation ratio < 0,1, because of their low deformability, are always to be designed forthe full superimposition of the stresses a + i.Type2:Thedeformabilityofthesepipesishighenoughtoinduceareroundingeffectcausedbytheinternalpressure.Thiseffectreducesnotonlythepipedeformation,causedbytheexternalloads,butalsotheresultingstress i + a to res.Type 3: The deformability of these pipes increases to such an extent, that the resulting stress res becomes a lowerfigure that the stress i or a. This type is indicated by Z > 0,4 or > 8,0, or by ni found from the broken line sectorprCEN/TR 1295-2:2004 (E)17of the graphs in diagrams 17 to 28 in NORM B 5012, part 2. In this case, the pipe is to be designed for the highervalue of i or a.A.1.11.7Design procedureItshallbeverifiedthatthedesignstressorstrain(maximumstress- max-strain- max-orres)liesinthepermitted range, i.e. that a required minimum safety factor is provided with respect to the ultimate stress or strain.Design procedure:requ requresRrequRmaxult, ,max = = =whereis the achieved security factor,requis the required safety factor as in table A.6.If there is a biaxial state of stress (e.g. with stress 1 in the peripheral direction and 2 in the longitudinal direction),then the equivalent stress22 2 121 + =cis to be subject to the above mentioned design procedure.Table A.6 Required safety factors requRequired safety factor requMaterialsafety class 1 safety class 2Concrete 1,5 2,2Fibre-cement non pressure 1,0 1,8Fibre-cement pressure pipe 1,1 2,2PRV 1,5 2,0Ductile cast iron 1,0 1,4PE 1,2 1,4PVC 1,2 1,4Steel 1,4 1,7Steel reinforced concrete 1,4 1,7Steel fibre concrete 1,5 2,0Clay 1,6 2,2Safety class 1: This safety class applies to seldom occurring load cases (e.g. pressure testing, construction loads),orwhenintheeventoffailureitisexpectednohazardstohumanbeings,groundwater,buildingsofwhenimpairments of the use of the pipeline and no considerable economic consequences are not to be expected.Safetyclass2:Thissafetyclassappliesfornormaloperation,particularlyiftheabovementionedhazards,impairments of the use of the pipeline or considerable economic consequence are to be expected in case of failure.prCEN/TR 1295-2:2004 (E)18Therequiredsafetyfactorsrequarecalculatedaccordingtothetheoryofreliability,takingintoaccountalltheuncertainties and scattering of variables which have a significant effect on the load or on the resistance of the pipe.The following failure probabilities pf are laid down :for safety class 1: pf = 10-3for safety class 2: pf = 10-5,The failure probability is less than equal to the above mentioned values, when the achieved safety factor is greaterthan/equal to the safety factor requ of table A.6 for the actual pipe material.ThesafetyfactorsoftableA.6areapplicabletopipesmanufactured,testedandlaidinaccordancewiththerelevant Austrian pipe standards (B 5010 to B 5016, B 2503 and B 2538, part 2).ThesafetyfactorsstatedinTableA.6onlyapplytotheuseofthecalculationmodelproposedintheAustrianstandardB5012togetherwiththeloadassumptionsandtheotherrequirementsinthecalculation.Ifothercalculationmodels,loadassumptionsorrequirementsarespecifiedforthestaticcalculation,thenothersafetyfactors are to be used, which guarantee the compliance with the above mentioned failure probabilities pf.prCEN/TR 1295-2:2004 (E)19A.2BelgiumCalculation procedure of the ISO 2785: Directives for selection of asbestos-cement pipes subject to external loadswith or without internal pressure.A.2.1FlowchartA.2.2Design, formulae, tables and charts, symbols and abbreviationsA.2.2.1Symbols and abbreviationsA width of uniform surcharge of small extent, in metres;a distance between two wheels on a single axle of a truck, in metres;prCEN/TR 1295-2:2004 (E)20B width of trench at the crown of the pipe, in metres;B distance of the spring-line of a pipe from the wall of the trench in which it is buried, in metres;h distance between two wheels of two different axles of a truck, in metres;c diagonal distance between two wheels of two different axles of a truck, in metres;C.C90 earth-load coefficient for a trench with vertical walls;Ccload coefficient for superimposed concentrated moving loads;Cdload coefficient for uniform surcharges of small extent;Cnload coefficient for uniform surcharges of large extent;Cv, Cd1, Cv2, Cv3coefficients of vertical deformation of pipe;Ch2, Ch3coefficients of horizontal deformation of pipe;d nominal or internal diameter of pipe, in millimetres;Dexternal diameter of pipe, in metres;e base of natural logarithms;E modulus of elasticity, in Newtons per square millimetre;Epmodulus of elasticity of pipe, in Newtons per square millimetre;Esmodulus of compression of soil, in Newtons per square millimetre;Etmodulus of elasticity of road construction material, in Newtons per square millimetre;E1, E2, E3, E4moduliofcompressionofsoilandbackfillinvariouszonesofthetrench,inNewtonpersquaremillimetre;H, H1, H2heights of earth cover of a pipe, in metres;Heequivalent height of earth cover a pipe laid under a paved road, in metres;HT heavy truck;I modulus of inertia of the wall of the pipe per unit length, in cubic millimetres;k factor of ring-bending moment;kv1, kh1, khp, kwfactors of ring-bending moments due to vertical and horizontal loads, horizontal reaction pressureand water-load respectively;K1, K2coefficients of lateral earth pressure;L length of uniform surcharge of small extent, in metres;LT light truck;m, m0, m1, mmconcentration factors of vertical earth pressure over the pipe;prCEN/TR 1295-2:2004 (E)21Meultimatering-bendingmomentofpipewhentestedinaccordancewithISO881orISO160,inKilonewton metre per metre;Mmmaximum ring-bending moment in the wall of a buried, Kilonewton metre per metre;M1the ring-bending moment that will fracture the pipe when combined with an internal hydraulic pressurep1;M2the ultimate ring-bending moment when no internal pressure affects the pipe;n concentration factor of lateral earth pressure on the sides of the pipe;Pdintensity of distributed load, in kilonewtons per square metre;Pjpipe projection ratio;Pwhydraulic working pressure, in Megapascal;P1the internal hydraulic pressure that will fracture the pipe when combined with a ring-bending momentM1;P2the internal hydraulic pressure that will burst a pipe which is notexposed to any external load;PecrushingloadofapipewhentestedinaccordancewithISO881,inkilonewtonsper200or300millimetre lengths of pipe;Pvmaximum wheel load of a truck, in kilonewtons;Pvcvertical pressure on a pipe due to moving concentrated surcharge, in kilonewtons per square metre;Pvdvertical pressure on a pipe due to moving distributed surcharge, in kilonewtons per square metre;qv, qv1, qv2vertical earth pressure on the pipe, in kilonewtons per square metre;qvttotal vertical pressure due to earth and moving load on the pipe, in kilonewtons per square metre;qh, qh1, qh2horizontal earth pressure on the pipe, in kilonewtons per square metre;qhp, qhp1, qhp2horizontal soil reaction pressure on the pipe, in kilonewtons per square metre;r mean radius of pipe, in metres;s wall thickness of pipe, in metres;spstiffness of pipe, in Newtons per square metre;Sshhorizontal stiffness of soil backfill in the zone of the pipe, in Newtons per square millimetre;Ssvvertical stiffness of pipe bedding, in Newtons per square millimetre;t1, t2thickness of layers in a road structure, in metres;Vs, Vs1stiffness ratio;Vpspipe-soil system stiffness;prCEN/TR 1295-2:2004 (E)22w, w1, w2unit weight of backfill soil, in kilonewtons per cubic metre;W crushingloadperunitlengthofpipewhentestedinaccordancewithISO160,inkilonewtonspermetre;x1, x2 , x3auxiliary parameter defined in the text; half the bedding angle of pipe; slope of the wall of the trench; specific weight of water in kilonewtons per cubic metre; deformation coefficient; correction factor;dreduction factor of the resistance of the pipe to external load due to the action of internal pressure;zreduction factor of the resistance of the pipe to internal pressure due to the action of external load;dsafety factor against crushing of a pipe loaded externally without internal pressure;zsafety factor against bursting of a pipe when a ring-bending moment is applied together with a internalhydraulic pressure; angle of internal friction of backfill soil; angle of friction between the backfill soil and the wall of the trench; impact factor.A.2.2.2Required basic dataD, s, r, Eppipe parameters ;B, H trench/embankment conditions ;K1, K2coefficients of lateral earth pressure, out of table A.8 ; angle of internal friction, out of soil investigation or table A.7 ;pjprojection ratio ;E1 - E2 - E3 - E4soil conditions, out of soil investigation or table A.7.prCEN/TR 1295-2:2004 (E)23Table A.7 Properties of soils for calculating earth-loadModuli of compression Esb at followingProctor standard densities (%) achievedby self-consolidation compactionN/mm2Groupof soilTypes of soila Unit,weight, kN/m3degrees85 90 92 95 97 1001 Non-cohesive 20 35 2,5 6 9 16 23 402 Slightly cohesive 20 30 1,2 3 4 8 11 203 Mixed cohesive 20 25 0,8 2 3 5 8 144 Cohesive 20 20 0,6 1,5 2 4 6 10aThe four types of soil are:non-cohesive: gravel, sand;slightly cohesive: binding non-uniform sand or gravel;mixed cohesive: rock flour, weathered rock soils, clayey sand;cohesive: clay, silt, loam.bThemoduliofcompressionEsofthesoilsaremeasuredbyapplyingtheCBR(CaliforniaBearingRatio)method using a round plate of an area of 700 cm2.Table A.8 Coefficients of lateral earth pressuresGroup of soil K1K21 0,5 0,42 0,5 0,33 0,5 0,24 0,5 0,1K1 and K2 shall always be considered simultaneously.A.2.2.3Selection of type of pipe layingThree types of pipe laying are defined, see figures A.3, A.4 and A.5.key1 Narrow trenches2 Wide trench3 Embankment conditions: positive projectionNOTE Type 1 covers trenches, wide trenches and positive projection embankment conditions.Figure A.3 Type 1 of layingprCEN/TR 1295-2:2004 (E)24NOTE Type 2 covers negative projection conditions.Figure A.4 Type 2 of pipe layingNOTE Type 3, two or more pipelines in a single trench.Figure A.5 Type 3 of pipe layingA.2.2.4Determination of the pipe soil system parametersa)Stiffness of the pipe Sprs EpS3p) (12=with2s Dr=b)Vertical stiffness of the bedding Ssvj2svPES =c) Horizontal stiffness of the bedding Ssh2 sh0,6 E S =321 0,361 1,662 11 0,639 1,662withEEDBDBDB1]1

|

'| + |

'|

|

'| += d)Pipe-soil fitness Vps (see figure A.6)shSSVpps=The distribution of the vertical earth pressure and reaction.prCEN/TR 1295-2:2004 (E)25a soil bedding, Vps < 0,1 b soil bedding, Vps > 0,1 c concrete bedding, Vps < 0,1Figure A.6 Distribution of earth pressure and reactionsForthecalculationofring-bendingmomentsanddeflectionsofthepipe,theverticalearthpressureisalwaysassumed to be rectangularly distributed over its crown, as shown in Figure A.6.The distribution of the reaction depends on the pipe-soil system stiffness Vps:casen1:pipeonsoil-beddingandVps0,1,accordingtofigureA.6.b,i.e.verticallydirectedreaction,rectangularly distributed along the bedding angle 2 ;case n3: in the case of rigid bedding (for example a concrete cradle) and when Vps > 0,1, according to figureA.6.c, i.e. radially directed and evenly distributed reaction along the bedding angle 2 .e)Deformation3h psh1C VC= f)Deformation factors Cv + =vs v1 vC C CCv, Ch1, Cv3, Ch3 out of table A.9.Table A.9 Deformation factorsFactors corresponding to vertical soil pressure qvCase 1 Figure A.6.a Case 2 Figure A.6.b Case 3 Figure A.6.c Bedding angle2 degrees Cv1Ch1Cv1Ch1Cv1Ch160 - 0,0833 + 0,0833 - 0,1053 + 0,1026 - 0,1041 + 0,101790 - 0,0833 + 0,0833 - 0,0966 + 0,0956 - 0,0916 + 0,0916120 - 0,0833 + 0,0833 -0,0893 + 0,0891 - 0,0763 + 0,0777180 - 0,0833 + 0,0833 - 0,0833 + 0,0833 - 0,0417 + 0,0417prCEN/TR 1295-2:2004 (E)26Factors corresponding to horizontal soil pressures qh and qhpFactors for qhFactors for qhpCases 1 and 2Figures A.6.a and bCase 3Figure A.6.cCase 1Figure A.6.aBedding angle2 degreesCv2Ch2Cv2Ch2Cv3Ch360 + 0,0833 - 0,0833 + 0,0827 - 0,0829 + 0,0640 - 0,065890 + 0,0833 - 0,0833 + 0,0798 - 0,0805 + 0,0640 - 0,0658120 + 0,0833 - 0,0833 + 0,0721 - 0,0735 + 0,0640 - 0,0658180 + 0,0833 - 0,0833 + 0,0417 - 0,0417 + 0,0640 - 0,0658NOTE Factors Cv and Ch correspond to the following equations for calculating the deflection of the pipe:Dv = 2 Cv qr4/EIandDh = 2 Ch qr4/EIwhereCv = Cv1 or Cv2 or Cv3;Ch = Ch1 or Ch2 or Ch3;q = qhv or qh or qhpg)Stiffness ratio Vssv vpsS C SV.=with lateral earth pressure qhp;vs v1psS CSV =without lateral earth pressure qhp;h)Concentration factor of vertical earth pressure over the pipe mo22034KKm+=i)Concentration factor of vertical earth pressure over the pipe m1( )( )

+ +=0s1 1s0s1 0 ms m1111 1mV mVmV m mV mmj)Concentration factor of vertical earth pressure over the pipe mmprCEN/TR 1295-2:2004 (E)27( ) ( ) 0,2511,6p0,620,2512,23,511j 41j j 41jm+ ++ + =p EEDHp EEPDHmk)Concentration factor of vertical earth pressure over the pipe m341 3 11 1m B mm=+ for 4 1 < 0,1)60 CrownSpring lineBottom+ 0,286- 0,293+ 0,377- 0,250+ 0,250- 0,250---+ 0,229- 0,264+ 0,42090 CrownSpring lineBottom+ 0,273- 0,279+ 0,313- 0,250+ 0,250- 0,250---+ 0,210- 0,243+ 0,321120 CrownSpring lineBottom+ 0,261- 0,265+ 0,275- 0,250+ 0,250- 0,250---+ 1,190- 0,220+ 0,260Case 3 of load distribution (bedding types C, Vps > 0,1)90 CrownSpring lineBottom+ 0,266- 0,271+ 0,277- 0,245+ 0,244- 0,224---+ 0,189- 0,230+ 0,262120 CrownSpring lineBottom+ 0,240- 0,240+ 0,202- 0,232+ 0,228- 0,187---+ 0,157- 0,181+ 0,145180 CrownSpring lineBottom+ 0,163- 0,125+ 0,087- 0,163+ 0,125- 0,087---+ 0,0350,000+ 0,035A.2.2.10Calculation of the safety factormeMM =prCEN/TR 1295-2:2004 (E)3021medPpwMM = ( )

=e2m 2z1MMPwPwhere: is the safety factor against crushing of a pipe loaded externally without any internal pressure;dis the safety factor against crushing when an internal hydraulic pressure Pw is applied together with aring bending moment Mm;zisthesafetyfactoragainstburstingwhenaringbendingmomentMmisappliedtogetherwithaninternal hydraulic pressure Pw.A.2.2.11Are the safety factors acceptable ?The recommended minimum safety factor against crushing of non-pressure pipes is: = 1,5Therecommendedminimumsafetyfactorsforpressurepipesundercombinedloadsaccordingtothedifferentdiameters are:from 175 mm to 200 mm:d = 2,5 andz = 3,5;from 250 mm to 500 mm:d = 2,5 andz = 3,0;from 600 mm to 2500 mm:d = 2,5 andz = 2,5.NOTE When the maximum working pressure does not exceed 0,3 MPa, the two safety factors may be reduced to 2,0 each.prCEN/TR 1295-2:2004 (E)31A.3DenmarkA.3.1GeneralThe design method described below is a simplified method which can be used generally for rigid pipes. However, itwill always be acceptable to use more accurate methods if their quality is proved.The course of the calculations in accordance with the principle using the procedures and formulae described belowis illustrated on the flowchart below. In practice, routine design is usually carried out with the aid of tables of chartsbased on these principles.List of symbolsdiinternal diameter of pipe, m;dyexternal diameter of pipe, m;F crushing test load, kN/m;ftbending tensile strength, MN/m2;hddepth of cover, m;k factor;l length of pipe, m;P axle load, kN;p railway line load, kN/m;Q wheel load, kN;q uniformly distributed surface load, kN/m2;r bearing capacity, kN/m2;t pipe wall thickness, m;v loading per unit of area, kN/m2;vgequivalent addition of load for self-weight of pipe, kN/m2;vjvertical earth load, kN/m2;vqvertical pipe loading from uniformly distributed surface load, kN/m2;vtvertical pipe loading from traffic load, kN/m2;vwequivalent addition for water load, kN/m2; (without index) unit weight of backfill above water table, kN/m3; (with index) partial safety factor;prCEN/TR 1295-2:2004 (E)32 earth load coefficient (Marston coefficient);General indices:c concrete;d design;f load dependant;k characteristic;m material dependant;s steel.prCEN/TR 1295-2:2004 (E)33Assemble basic data1)Pipe dimension (diameter DN)2)Depth of cover (hd to top of pipe)3)Laying conditions (including laying class, see A.3.2.3)4)Level of controlSelect type of pipeChoosebetween:StandardisedpipesaccordingtoDS400orspecialpipesaccordingtocompany specifications ; circular pipes with or without a base.Choose load and bedding distributions1)Distribution of load (usually equal to external diameter of pipe)2)Distribution of bedding reaction (bedding class)The characteristic bearing capacity rk for the chosen pipe is then fixed.Identify partial safety factors1)Partial safety factors f for loads2)Partial safety factors m for materialsThe design bearing capacity rd of the chosen pipe can now be determined (rd = rk/m).Choose parameters for earth load1)Unit weight of backfill material , usually fixed to 21 kN/m32)Soil load coefficient (Marston) = 1,6 for normal laying class for:low and high laying classesjacking pipesupper pipe in a stepped trenchpipes placed on a piled foundationpipes under water, etc.prCEN/TR 1295-2:2004 (E)34Calculate external and internal loadsCharacteristicvaluesPermanentloadsEarth load vj = x y x hdSelf-weight of pipe vgA.3.2.3A.3.2.4Variable loadsUniformly distributed surface load vqTraffic loads vtExternal/internal water pressure vwA.3.2.5A.3.2.6-RoadA.3.2.7-RailwaysA..3.2.8Design value Total load vd =(yf x v) A.3.4.2No ControlIs the bearing capacity greater than or equal to the design load (rd ! vd)YesSELECTED TYPE OF PIPE IS ACCEPTABLEFigure A.8 Flowchart for pipeline designA.3.2ChargesA.3.2.1Types of loadsWhen designing a buried pipe the following types of loads shall be considered:Permanent loadsearth load;self-weight of pipe.Variable loadsdistributed surface load;traffic loads;loads from external and internal water pressure.A.3.2.2Distributed of load and bedding reactionThe vertical load is assumed uniformly distributed over a width equal to the external diameter of the pipe.The horizontal load is assumed uniformly distributed over a width equal to:the external diameter of the pipe when using circular pipes;the height to the pipe from its top to its axis when using pipes with base.prCEN/TR 1295-2:2004 (E)35The bedding reaction is assumed to be a vertical action uniformly distributed over a width equal to:0,5 times the external diameter circular pipes laid with normal bedding;0,7 times the external diameter of circular pipes laid with an improved bedding;the external width of circular jacking pipes;the width of the base when using pipes with a base.In the longitudinal direction of the pipe the bedding reaction is assumed to be uniformly distributed. If the length ofthe pipe is large in relation to its diameter due consideration shall be given as to the validity of this assumption.NOTE If no exact evaluation is carried out the bedding reaction can be assumed uniformly distributed if the useful length issmaller than or equal to :1,0 m for di " 0,15 m ;di /0,15 m for0,15 m< di " 0,40 m ;2,7 m for di > 0,40 m.A.3.2.3Earth loadThe characteristic vertical load on a pipe from the backfill is determined by:vj = hd kN/m2,with the relieving effect of the lateral pressure being included in .If a closer examination is not carried out and the laying conditions are not extreme, the following values for canbe used:for low laying class (with no requirements for the stiffness of the sidefill): 1,62 + 0,50 hd/dy + 0,54 dy/ hd ;for normal laying class (with the stiffness of the sidefill at least the same as the stiffness of the backfill): 1,6;for high laying class (with the stiffness of the sidefill at least five times the stiffness of the backfill): 1,4;for jacking pipes: 1,0;for the upper pipe in a stepped trench: 1,62 + 0,25 hd/dy + 0,27 dy/ hd ;for pipes supported on piles: 1,62 + 0,50 hd/dy + 0,54 dy/ hd ;for pipes laid under water: 1,62 + 0,50 hd/dy + 0,54 dy/ hd .Theunitweightofthebackfillmaybefixedat21kN/m3.Forunderwaterbackfill,mayhoweverbefixedat11 kN/m3.A.3.2.4Self-weight of pipesThe loading effect of the self-weight of the pipe shall be included, either as a deduction in the load bearing capacityof the pipe or as an equivalent addition to the vertical load.A.3.2.5Uniformly distributed surface loadThe action on a pipe from an uniformlydistributed characteristic surface loadq isgiven in kN/m2 and determinedprCEN/TR 1295-2:2004 (E)36by:vq = q.A.3.2.6Traffic load from roadsAthree-axlegroupisassumedinwhicheachaxleloadconsistsoftwowheelloadsQwithacentre-to-centredistance of 2,0 m and an axle-to-axle distance of 1,5 m. The contact surface of the wheel load is assumed to be arectangle with sides of 0,2 m in the direction of travel and 0,6 m across the same.ThecharacteristicvalueofQisassumedtobe65kNfornormalroadtrafficand100kNforheavyroadtraffic.These loads include an impact factor which is independent of the earth cover.The load vt from a wheel load Q is determined - in case of depth of cover of more than some 1,3 m - in accordancewith Boussinesqs theory.NOTE With a good approximation, the traffic loading can be determined on the basis of an assumption that the distributionof stress through the ground is 1:2. This leads to the following expression for the loading from the specific load group in kN/m2:( )( ) 2 3 6 2 6 , ,d d t+ + = h h Q At depths of cover hd < 1,34 m the loading is changed into the action from one wheel load:( )( ) 6 0 2 0 , ,d d t+ + = h h Q which value may be reduced as a function of the pipe diameter by using the following factor:( )( ) 18 1 3 10 75 0 1 1y y d, d d h k + =A.3.2.7Traffic load from railway tracksThe standard railway loading of the Danish State Railways shall be used as a basis for the calculation of the loadsfrom railways, i.e.:characteristic axle load inclusive impact factor: P= 410 kN ;evenly distributed line p = 80 kN/m.NOTE Ifastressdistributionof1:2inthegroundisassumedacrossthelineroad,theloadcanbedeterminedbythefollowing expression :The loading for one track in kN/m2:( )( ) 2 2,d d t+ + = h p h P The loading from two or more tracks :for hd < 2,3 m: as for one trackfor hd ! 2,3 m:( ) ( ) ( ) 7 6 2 4 6 8 , ,d d t+ + + = h p h P A.3.2.8Load from external and internal water pressureTheeffectonapipeduetoitswater-filledstateshallusuallybeincluded,eitherasadeductioninthebearingcapacity of the pipe or as an equivalent addition to the vertical load.Theeffectonapipeduetoaninternalpositiveornegativepressureshallbeincluded.Adimensioningpositivepressure shall include both the hydrostatic and the hydrodynamic pressure, as a possible surge in addition totheworking pressure.prCEN/TR 1295-2:2004 (E)37In principle, the effect on a pipe due to an external water pressure shall be included.A.3.3SafetyA.3.3.1Safety analysisThe safety shall be evaluated in accordance with the partial coefficient method. The load bearing capacity of a pipecan either be determined arithmetically alone or by a combination of calculation and testing.Safety analysis by calculation:Whensafetyisevaluatedarithmeticallyrequirementsaremadeonthematerials;thisincludestheirstrength,theexecution of calculations, execution of the work and control of pipe materials and execution of workmanship.Safety analysis by combining calculation and testing:When safety is evaluated through a combination of calculation and testing the same requirements shall be made asforarithmeticalevaluationalone;requirementsonpipematerialsshallbereplacedbyrequirementsonbearingcapacity of the pipes as established in a given test method.The control of the bearing capacity of thepipes canbe carried outin a destructive or a non-destructive test. Thetestmethodshallbeworkedoutsoastoachieveatestresultgovernedbythesamepropertiesasthosethatdetermine the bearing capacity under the existing load exerted upon the buried pipe.A.3.3.2Limit statesServiceability limit state:Theserviceabilitylimitstateisconsideredashavingbeenreachedwhenthefirstcrackformsinanunreinforcedpipe and when the cracks formed will affect the working life of a reinforced pipe.Ultimate limit state:For unreinforced pipes the ultimate limit state coincides with the serviceability state. For reinforced pipes this statehasbeenreachedwhenayieldmechanismhasbeenformedorwhenthebearingcapacityofthepipemayotherwise be considered exhausted.NOTE For reinforced pipes the splitting off of the cover on the inside of the pipe may create a possible ultimate limit state.Shear rupture in the pipe wall due to displacement may appear if the pipe is exerted to a line load.A.3.4Partial safety factorsA.3.4.1Action combinationsTwo action combinations shall be examined:action combination 1 for the serviceability state;action combination 2 for the ultimate limit state.A.3.4.2Design loadsThe designload vdis determined asthesumofthecharacteristicpermanentloadandthecharacteristicvariableload, both multiplied by the appropriated partial safety factor f:( ) =f dFor action combination1f=1,0forbothtypesofloadsandforactioncombination2f=1,0forthepermanentload and 1,3 for the variable load.prCEN/TR 1295-2:2004 (E)38A.3.4.3Design material parametersIf the load bearing capacity of the pipe is estimated on the basis of full scale tests the partial safety factor m = 1,5in the case of moderate control (factory production control), 1,4 in the case of normal control and 1,3 in the case ofextended control.For reinforced pipes which are structural analysed solely on the basis of calculations, partial safety factors for thereinforcement respectively the concrete shall be fixed as follows:s: 1,4 for normal control and 1,3 for extended control ;c: 1,8 for normal control and 1,7 for extended control.A.3.5CalculationsItshallbeprovedthatthedesignloadbearingcapacityofapipeisgreaterthatthedesigneffectofactionsconsidered.A.3.5.1Determination of effects of actionServiceability limit state:When determining the internal forces with a view to evaluating the serviceability limit state the elasticity theory shallbe used with the commonly accepted approximations.Ultimate limit state:When determining the internal forces with a view to evaluating the ultimate limit state the elasticity theory shall beappliedinthecaseofunreinforcedpipes,andeithertheelasticitytheoryortheplasticitytheoryinthecaseofreinforcedpipes.Iftheplasticitytheoryisapplied,itisanassumptionthattherequiredductilityispresentinthestructure.A.3.5.2Determination of the load bearing capacity of unreinforced pipesThe load bearing capacity of unreinforced pipes is determined by a calculation of their strength of the basis of theactual laying conditions as compared to the design strength determined on thebasisof the testload declared forthe pipe.NOTE The characteristic load bearing capacity for a pipe in kN/m2 may be determined by:y k kd F k r =wherek is the ration between the maximum stressed from a load 1 during the crushing test and in buried conditions;Fkis the declared crushing test load of the pipe, kN/m.The safest determination of k is achieved when the maximum tensile stress during the test is present in the samepoint,oratanyrateinsectionsofthesamewallthicknessandcurveofthegravitylineasintheundergroundconditions. The test arrangement should be selected so that the crack load and the rupture load are identical.Thecrushingtestloadandtheloadbearingcapacitycanbefixedonthebasisofabendingtensilestressdeterminedintheusualcalculationofthebasisoftheelasticitytheorywithplanestressdistributioninthecross-section of the pipe wall compared to a bending tensile strength ft by:( ) ( )25 02 0 1 6 4,i i t, , d t d f + =prCEN/TR 1295-2:2004 (E)39IftheeffectivelengthofthepipelnislargerthanthecriticallengthlnforwhichthebeddingreactioninthelongitudinaldirectionofthepipecanbetakenasevenlydistributedthebearingcapacityinkN/m2 shallbecalculated from:( )y k n c kd F l l k r2=A.3.5.3Determination of the load bearing capacity of reinforced pipesThe load bearing capacity may be determined on the basis of tests or calculations. If tests are used the testloadshall be arranged so as to come as close as possible to the distribution of the moment and shear force to be foundin the relevant soil load. If calculations are applied the rules of the standard for Design of Concrete Structures shallbe applied.A.3.5.4Determination of laying depthsThe maximum and possibly minimum acceptable laying depths for a pipe shall be determined by a load estimationof the basis of the actual design loads compared to the design load bearing capacity in kN/m2:m k d d r r = prCEN/TR 1295-2:2004 (E)40A.4FranceA.4.1ScopeThe pipes concerned are those:laid in traditional way on continuous bedding on the ground in trenches or beneath embankments;with depth of cover greater than 0,8 m, when laid under road;formingpartofagravitysystem,internalwaterheadbeingnotgreaterthan4metres(0,04MPa)(forpressurised pipelines - see Fascicule 71 of CCTG).A.4.2Original features of the methodOriginal features of the method are:this method applies to all types pipes without discontinuity for the full range of ring stiffness;ittakesintoaccountthespecificlayingconditions:soiltypes,compactionconditions,watertable,conditionsunder which trench sheeting is removed;thecalculationofbendingmomentsanddiametricaldeflectionusesthesecond-ordertheorywhichmakesitpossible to take buckling into account;the model takes into account soil/pipe interaction;the safety is verified at different limits-states;flow charts indicate the routing of calculation;give the values of the design parameters;a large number of tables and charts make the calculation easier.A.4.3DescriptionA.4.3.1Parameters usedThe pipe parameters are the following:Dmmid-thickness diameter;e thickness of the pipe wall;e0out of roundness before application of loads;ETishort-term modulus of elasticity;ETvlong-term modulus of elasticity;CR stiffness class for flexible pipes;rasishort-term ring stiffness;rasvlong-term ring stiffness;vTPoissons ratio.The soil and laying parameters, which depend on the soil type (5 groups typified) and the degree of compaction (3cases) are the following:prCEN/TR 1295-2:2004 (E)41Esmodulus of elasticity; density;k1shear coefficient;SPoissons ratio;k2horizontal earth pressure coefficient;2 conventional bedding reaction angle.The values of parameters Es, k2 and 2are given in tables.The presence of ground water is taken into account by reducing the value of Es.The conditions under which sheeting is removed (3 cases) are taken into account by reducing the values of Es, 2,k1 and k2.Stiffness criterion RIG:The stiffness criterion characterises the cross sectional behaviour of the pipe in the soil:Figure A.9 Cross-sectional behaviour of pipes in the soilA.4.3.2Calculation of actionsVertical pressure due to backfill, pr:Vertical pressure due to backfill is calculated with the following equation:H C p =rwithprvertical pressure; density of soil;H depth of cover;C concentration factor.in the case of flexible pipe: C = 1in the case of rigid pipe:laid under embankment: C = C 2laid in trench:narrow trench: C = C1wide trench:C = C2prCEN/TR 1295-2:2004 (E)42C1 and C2 are calculated using Marstons theory (C1 and C2 can be taken from charts).Vertical pressure due to live loads, per:Live loads are calculated using Frolichs theory, considering the standard convoy defined in the figure A.10.The load due to the wheels passing directly above the centreline of the pipe is increased by an impact factor of 1,6,and for the other wheels by a impact factor of 1.Figure A.10 Standard convoyNOTE A table gives the values of per for different DN and H for De " 1,2 Di .vertical pressure due to permanent surface loads, pep:For pipes laid in narrow trench, it is calculated with the following equation:B H ke p p1 2 =o epwherepopermanent surface pressure;H depth of cover;B trench width.Vertical pressure due to construction, pec:Theverticalpressureduetoconstructionshallbetakenintoaccountifitisgreaterthanthatduetotrafficandpermanent surface loads.Total vertical pressure, pv:Total vertical pressure is given by the following equation:prCEN/TR 1295-2:2004 (E)43( )ec ep er r vmax p p p p p p + + + =Horizontal pressure, ph:Horizontal pressure is given by the following equation:v hp k p =2External hydrostatic pressure, pwe:External hydrostatic pressure (due to the water table) is considered as uniform, and calculated at the springline ofthe pipe.Average external confining pressure,pTheaverageexternalconfiningpressureisthehydrostaticpressureequivalenttotheverticalandhorizontalpressures. It is used in particular to verify buckling.It is given by the following equation:

++ =212v wekp p pA.4.3.3Calculation of efforts and deflectionIn the model used, the pipe is considered an infinitely long cylindrical shell with elastic behaviour. The pipe is takento have a geometrical imperfection prior to the application of any loads, i.e. it does not have an ideal circular crosssection (production tolerances or deflection due to self weight).The soil is considered as elastic. It is modelled by a infinite number of elastic springs acting perpendicularly to thepipe wall (Winkler assumption).The model also assumes that there isno slippage between the soil and thepipe,andthat radial displacement ofthe pipe wall results in reception pressure of the soil proportional to the displacement.Mathematical analysis results in determination of:the critical buckling pressure (to be compared to the average confining pressure when verifying buckling);the maximum bending moment and deflection, taking account of second-order effects and soil/pipe interaction.A.4.3.4Verification of safetyUltimate limit state verification:In principle the following verifications are performed for rigid and flexible pipes:pipe with rigid behaviour: short-term strength (bearing capacity or stress or resisting moment);pipe with flexible behaviour: short- and long-term strength (bearing capacity or stress or resisting moment) andbuckling stability.The following safety factors shall be applied:on actions: 1,25;on materials: depending on the type of pipe and its man-entry capability.prCEN/TR 1295-2:2004 (E)44Table A.11 Safety factorsNon man-entry Man-entryReinforced concrete 1,4 1,4Non reinforced concrete 1,6 1,76Fibre cement 1,5 1,65Compact PVC 1,2 1,32Cast iron 1,2 1,2Vitrified clay 1,6 1,76The safety factor for buckling is 2,5.Serviceability limit state verification:In principle the following verification:pipe with rigid behaviour: for reinforced-concrete pipes, it is verified that under service loading any cracks arestable and of limited opening.pipewith flexible behaviour:itisverifiedthatunderserviceloadsshort-termandlong-termdeflectionremainlower that allowable values.Fatigue limit state verification:Thisverificationisgenerallyonlyapplicabletopipeswithflexiblebehaviourlaiddirectlybeneathheavy-traffickedpavements.Choice of parameters used in the design methodprCEN/TR 1295-2:2004 (E)45prCEN/TR 1295-2:2004 (E)46prCEN/TR 1295-2:2004 (E)47prCEN/TR 1295-2:2004 (E)48A.4.4Example of calculationA.4.4.1AssumptionsPipe parametersType : reinforced concreteNominal size, DN : 600Thickness of pipe wall, e (mm) : 75Short-term modulus of elasticity, ETi (MPa) : 40,000Long-term modulus of elasticity, ETv (MPa) : 14,000Poisson's ration of material : 0,2Out of roundness prior to application of loads, eo (mm) : 1,0Soil and laying parameters- Design assumptionsSoil group : 2Density (kN/m3) : 18Depth of cover, H (en m) : 3,50Laid in trench? : yesTrench width, B (en m) : 2,00Water table? : noQuality of compaction : controlled compactionTrench sheeting? : yesThickness of sheeting, b (m) : 0,10Conditions for removal of sheeting : layer by layer of fill after compaction- Values for the design parametersModulus of elasticity of soil, Es (MPa) : 0,88Poissons ration of soil : 0,30Shear coefficient, k1: 0,09Horizontal earth pressure coefficient, k2: 0,26Conventional bedding reaction angle, 2 () : 66External loadsLive loads : BC convoyprCEN/TR 1295-2:2004 (E)49Permanent surface loads, pep (en kN/m2) : 0Exceptional construction loads, pec (kN/m2) : 0A.4.4.2Verification of safetyUltimate limit stateSafety factor for actions : 1,25Vertical pressure backfill, pr (en kN/m2) : 123,53Pressure due to live loads, per (kN/m2) : 18,31Permanent surface loads, pep (kN/m2) : 0,00Exceptional construction loads, pec (kN/m2) : 0,00Total vertical pressure, pv (en kN/m2) : 141,83Average confining pressure,p(kN/m2) : 89,04Bending moment, Mu, per metre of pipe (kN.m/m) : 4,84Safety factor for material : 1,40Minimum failure load to be guaranteed, Fr (kN/m) : 63,02SUITABLE STRENGTH CLASS: 135 A WITHCORRESPONDING STRENGTH, RG (kN/m) : 81Serviceability limit stateSafety factor for actions : 1,00Vertical pressure of backfill, pr (kN/m2) : 98,82Pressure due to live loads, per (kN/m2) : 14,65Permanent surface loads, pep (kN/m2) : 0,00Exceptional construction loads, pec (kN/m2) : 0,00Total vertical pressure, pv (kN/m2) : 113,47Average confining pressure,p(kN/m2) : 71,23Bending moment, Ms, per metre of pipe (kNm/m) : 3,87Safety factor for material : 1,40Minimum stable crack-opening load to , Ff (kN/m) : 35,99SUITABLE STRENGTH CLASS: 135 A (ASSUMPTIONFG/RG = 0,67) WITH CRACKING RESISTANCE, Fg (kN/m) : 54,27MINIMUM STRENGTH CLASS TO BE USED: 135 AprCEN/TR 1295-2:2004 (E)50A.5GermanyThis annex is a summary of the ATV-A127 standard of the German Association for Water Pollution Control (ATV),Guideline for the Structural Calculation of Drains and Sewers, 3rd Edition, 1999.All figures, diagrams, equations and footnotes are taken from the ATV-A 127 standard. For jacking pipes, the ATV-A161standardisvalid.ForpipelinesindepositsunderveryhighloadsATV-M 127-1andforReliningandMounting ATV-M 127-2 is valid.A.5.1IntroductionThecalculationmethodappliesforthestructuralcalculationofundergroundpipesofallstandardisedpipematerials.The calculation method is applicable for rigid and flexible pipes of various stiffness and installation conditions, withacontinuoustransitionfromtrenchtoembankment,wherebytheloadingofthepipeisdependentonthedeformation characteristics of the pipe and their mutual interaction.The methodappliesforcircularpipes,itcanbeappliedanalogouslyforothercross-sections.Prerequisiteisthatthe initial assumptions taken for the structural calculation are in agreement with the construction method.A.5.2Types of soilThe types of soil mainly found in Germany are summarised into four groups:Group 1: Non-cohesive soils (GE, GW, GI, SE, SW, SI)Group 2: Slightly cohesive soils (GU, GT, SU, ST)Group 3: Cohesive mixed soils, (cohesive sand and gravel, cohesive stony weathered soil) silt ( U G ,T G ,U S ,T S , UL, UM)Group 4: Cohesive soils (e.g. clay) (TL, TM, TA, OU, OT, OH, OK, UA)The resulting calculationvalues of the soil deformation modulus for loading tensions up to 5 m covering (0 ... 0,1N/mm) are given in table A.12. For higher covering in embankments the deformation modul EB can be calculatedwith following equation:zEB ! B,100

=pE ETable A.12 Soil typesGroup Unit weight Unit weightunderbuoyancyAngle ofinternal wallDeformation modulus EB in N/mm2with degree of compaction DPr in %long-termdiminuationfactorBkN/m3'BkN/m3friction degree85 90 92 95 97 100 f1G1 20 11 35 22)6 9 16 23 40 1,0G2 20 11 30 1,2 3 4 8 11 20 1,0G3 20 10 25 0,8 2 3 5 8 13 0,8G4 20 10 20 0,6 1,5 2 4 6 10 0,5prCEN/TR 1295-2:2004 (E)51A.5.3Live loadsRoad traffic loads, railway loads and aircraft loads are considered separately.A.5.3.1Road traffic loadsFor load determination, standard vehicles are defined in DIN 1072 should be applied (Figure A.11).SLW 60, SLW 30 LKW 12Figure A.11 Standard vehiclesTable A.13 Loads and wheel contact areas for standard vehiclesWheel contact area StandardvehicleTotal loadkNWheel loadkN WidthmLengthmSLW 60 600 100 0,60 0,20SLW 30 300 50 0,40 0,20front 20 0,20 0,20 LKW 12 120rear 40 0,30 0,20Forheightofcoverfrom0,5mto2,0m,theeffectofasinglewheelloadiscalculatedgeometrically;theloaddistribution depends upon external pipe diameter and pipe length. Over 2,0 m height of cover the load distributioniscalculatedaccordingtotheBoussinesqFormula.Thedynamicinfluenceistakenintoaccountwiththeimpactcoefficients according to table A.14Table A.14 Impact coefficients for road traffic loadsStandard vehicle SLW 60 1,2SLW 30 1,4LKW 12 1,5prCEN/TR 1295-2:2004 (E)52a) Pressure p as result of SLW 60, h = 0,5 m to 2,0 m c) Pressure p as result of SLW 12, h = 0,5 m to 2,0 mb) Pressure p as result of SLW 30, h = 0,5 m to 2,0 m d) Pressure p as result of SLW 60, SLW 30, LKW 12,h = 2 m to 10 mFigure A.12 Soil stresses due to road traffic loadsThe horizontal component of the live load is not taken into account.A.5.3.2Railway traffic loadsForrailwaytrafficloadstheloadconfigurationinaccordancewithUIC71(figureA.13andfigureA.14)withaminimum height cover of h = 1,5 m or inside diameter of the pipe (the greater value is relevant). Impact coefficientsare in accordance with the following equation, h in m:( ) 0 1 60 0 10 0 40 1 , , , , = h prCEN/TR 1295-2:2004 (E)53Figure A.13 Load configuration UIC 71Figure A.14 Pressure p as result of railway traffic loadsA.5.3.3Aircraft traffic loadsFigures A.15 and A.16 apply for the design aircraft upwards from a minimum covering of 1,0 m. The effect of theimpact coefficient (= 1,5) is included in figure A.15 and A.16.prCEN/TR 1295-2:2004 (E)54Figure A.15 Load configuration of design aircraftFigure A.16 Pressure p as result of aircraft traffic loadsprCEN/TR 1295-2:2004 (E)55A.5.3.4Surface loads of limited extentSurface loads of limited extent are to be calculated with an evenly distributed spread of pressure using a ratio lessthan 1:1.A.5.4Effects of the installation on the structural calculationEffects of the installation of the pipe are taken into account in the structural calculation:installation of the pipe between vertical or sloped walls of a trench, in a stepped trench or in an embankment;method of trench construction (thickness of sheeting, extraction of sheeting);possible soil exchange;influence of groundwater;employment of compacting equipment;placing and compaction of soil in the embedment with/without control of soil compaction and pipe deformation;an even placement of the pipe is assumed in the longitudinal direction;theemploymentofmediumandheavycompactingequipmentispermittedonlyupwardsfromaheightofbackfill of at least 1,0 m.A.5.5LoadingA.5.5.1Load casesThe following load cases shall be taken into account:earth loads;live loads;surface loads;self weight;weight of filling water;internal and/or external pressure.Longitudinal bending, temperature differences and buoyancy shall be taken into account additionally as applicable.A.5.5.2Earth load taking into account the silo theoryThe reduction of the earth load pE = xB h may only be taken into account if it is ensured that the silo effect actspermanently. Additional conditions are E1 " E3 and DPr > 90 %.The wall friction angle to be applied is given for the backfill in table A.15, depending on the backfilling conditions A1to A4.prCEN/TR 1295-2:2004 (E)56Table A.15 Earth pressure ratio K1 and wall friction angle Surcharge conditionK1A1 0,5 2/3 A2 0,5 1/3 A3 0,5 0A4 0,5 Backfill conditions:A1: Backfill compacted in layers against existing natural soil (without control of the compaction grade);A2 : Verticaltrenchconstruction,trenchsheetingwithlightsheetpiles,whicharewithdrawnonlyafterbackfilling;Trench plates or shoring equipment which are removed progressively during backfilling;Uncompacted backfill;Jetting of backfill (soil group G1 only);A3 : Verticaltrenchconstructionusingheavyinterlockingsheetpiles,timberboards,trenchplatesorshoringequipment, which are only removed after completion of backfilling;A4 : Backfill compacted in layersagainstexistingnaturalsoilwithcontroloftherequiredgradeofcompaction(except for G4 soils).A.5.6Load distributionThe soil pressure resulting from earth load are redistributed depending on the pipe/soil stiffness ration (see figureA.21).A.5.6.1Embedment conditionsThe bedding conditions of the pipe in the embedment (zone up to 30 cm above the pipe crown) determine the loaddistribution.B1 : Embedmentcompactedinlayersagainsttheexistingnaturalsoilorinlayersinaembankment(withoutcontrol of the compaction grade);B2 : Vertical trench construction within the embedment with light sheet piles, which reach to the trench bottomand are withdrawn only after backfilling;Trenchplatesandshoringequipment,ontheassumptionthatcompactionofthesoilisassuredafterremoval of the plates or shoring equipment;B3 : Vertical trench construction within the pipeline zone using heavy interlocking sheet piles or light sheet piles,deeper than the trench bottom and compaction against them;B4 : Embedment compacted in layers against the existing soil or in layers in an embankment with control of therequired grade of compaction (expected for G4 soils).The deformation moduli E1 to E4 are shown in figure A.17 and table A.16. The effective deformation modulus E2 iscalculated taking into account the type of soil, the influence of a possibly existing groundwater (reduction factor f2)and the achievable soil compaction in the pipe trench, depending ontheworking spacebetweenpipeandtrenchwall or sheading (reduction factor B, see figure A.18 and the following equation).prCEN/TR 1295-2:2004 (E)5720 B 2 1 2E f f E = Table A.16 Calculation values for deformation moduls E1 and E20 independent from the initialcompactionBackfill condition A1 A2 and A3 A4Embedment condition B1 B2 and B3 B4Compaction degree Dpr in %,Deformation moduli E1 and E20in N/mm2DprE1, E20DprE1, E20DprE1, E20Soil groups G1 95 16 90 6 97 23G2 95 8 90 3 97 11G3 92 3 90 2 95 5G4 92 2 90 1,5 - -With equal compacting of the soil adjacent to and above the pipe E20 = E1 may be achieved. E20 may not beassumed to be greater than E1, except with exchange of soil in the embedment or for embedment conditionB4.Reduced compaction adjacent to the pipe in narrow trenches is taken into account in figure A.18 (take noteof minimum trench width according to DIN EN 1610).Settlements as a result of the influence of groundwater are taken into account through a reduction of the E20value with the factor f according to following equation:120 75pr2= DfThe value of Dpr shall be taken from the table for the respective embedment condition.Figure A.17 Designation of deformation moduli for the different soil zonesFigure A.18 Reduction factors B for E2prCEN/TR 1295-2:2004 (E)58A.5.6.2Relative pipe projectionThe relative pipe projection a is givenin figure A.19depending on pipe shape and pipeinstallation. The effectiverelative pipe projection a takes into account the different displacements of the soils above and adjacent to the pipe.26 , 0 '21 =EEa aA.5.6.3Concentration factorsThe calculation of the concentration factors takes place using the model of the shear resistant beam on an elasticbedding which is described by means of spring of different stiffness for of the pipe and for the laterally existing soil.A.5.6.3.1Maximum concentration factorForarigidpipeunderembankmentthemaximumconcentrationfactormaxiscalculatedusingthefollowingequation (see figure A.20).( ) ( )adhaEEaaEEadh

+ + ++ =25 , 0 '6 , 1'62 , 025 , 0 '2 , 2'3,51 max1414aFigure A.19 Relative pipe projectionprCEN/TR 1295-2:2004 (E)59Figure A.20 Concentration factor max for b/da = ! and E4 = 10 E1A.5.6.3.2Concentration factors R and BForpipeofanystiffnesstheconcentrationfactorRiscalculatedaccordingtothefollowingequation,takingintoaccount the horizontal stiffness of the embedment. For pipes of high stiffness (Vs > 100) is R = max .425 , 0 '1 max3' 3'25 , 0 '1 max3' 4' max2ss + + + =aK Ka VaK Ka VsRwith**'* qh v, qv v,* qh v,qv h,qh h,qh v,K c cK ccccK + + =Bv vRsS =cSVTheloadconcentrationabovethepipeleads,forreasonsofequilibrium,toachangeoftheverticalsoilstresslateral to the pipe (see figure A.21) with the concentration factor B according to the following equation.34RB=With B the transferred earthload on the soil lateraltothepipecanbecalculated,sothatadeterminationofthehorizontalearthpressureqhwithanearthpressurecoefficientK2accordingtotableA.17ispossible.Theconcentration factors are limited by the shear resistance of the soil (fu " RG " fo).prCEN/TR 1295-2:2004 (E)60Figure A.21 Redistribution of soil stressesTable A.17 Earth pressure ratio K21 2 3K2Soil groupVRB > 1,0 VRB " 1,0G1 0,5 0,4G2 0,5 0,3G3 0,5 0,2G4 0,5 0,1Bedding reaction pressure qh* = 0 qh* > 0A.5.6.3.3Stiffness ratioThe stiffness ratio VRB is defined as the quotient of the pipe stiffness SR and the horizontalbedding stiffness SBh.Due to mechanical similarity it is possible to make an assessment whether the pipe is rigid or flexible and to whatextentitisdependentonasupportofthehorizontalbeddingreactionpressure.Aminimumpipestiffnessofmin SR = 3.10-3 N/mm2.BhRRBS8SV =A.5.6.4Relative trench widthTheinfluenceofexistingtrenchwalls,withinatrenchwidth1"b/da "4,aretakenintoaccountwiththeconcentration factor RG.(see also figure A.22).343 1: 4 1RGPaPadbdb + = prCEN/TR 1295-2:2004 (E)61Figure A.22 Concentration factor RGA.5.6.5Total loading of the pipeA.5.6.5.1Vertical total loadThe vertical total load of the pipe is:v E RG vp p q + = A.5.6.5.2Horizontal total loadThe horizontal total load is: as a result of earth pressure:

+ =2B E B 2 hadp K q as a result of lateral bedding reaction:* qh h, RBh qh h, v qv h,h*c Vq c q cq + =A.5.7Pressure distribution at pipe circumferenceA.5.7.1Bedding reactionsBedding Case I (see figure A.23) for the stress and strain proof of rigid and flexible pipes.Bedding Case II (see figure A.24) for the stress and strain proof of rigid pipes.Bedding Case III (see figure A.25) for the deformation proof of flexible pipes.prCEN/TR 1295-2:2004 (E)62Figure A.23 Bedding case I Figure A.24 Bedding case IIFigure A.25 Bedding case IIIA.5.7.2Lateral pressureThe lateral earth pressure is assumed as shown in figure A.26.a) Bearing case II b) Bearing cases I and IIIFigure A.26 Lateral pressureA.5.8Sectional forces, stresses, strains, deformationsSectional forces, stresses, strains and deformations are calculated in general with the following equations:Section forces:2mmqr M=mnqr N =prCEN/TR 1295-2:2004 (E)63 with m, n initial values for bedding moments and axial forces.stresses:k WMAN =strains:

= = kR3m68 2MN SS rsEdeformations:( ) *8s2h * qh v, h qh v, v qv v,Rmvq c q c q crd + + = ( ) *8s2h * qh h, h qh h, v qv h,Rmvq c q c q crd + + = A.5.9DimensioningA.5.9.1Relevant proofsFor rigid pipes where the loading does not produce any appreciable deformation and therefore has no effect on thepressure distribution, the proof of stress, strain or load-bearing capacity is relevant.For flexible pipes where the loadingis significantlyinfluenced by the deformation, theproof of deformation, strain(UP-GF only) and stability shall be carried out.A.5.9.2Stress/strain proof= =R RA.5.9.3Proof of load bearing capacity (load class)EZN =totFFwithEZ bedding factors according to table A.18Table A.18 Bedding factorsBedding case Bearing angle2 Bedding factorEZI 60901201,591,912,18II 901201802,172,502,69Concrete pipes DIN 4032-KFW : EZ = 1,07 (s3/s2)2Concrete pipes DIN 4032-EF : EZ = 2,1prCEN/TR 1295-2:2004 (E)64A.5.9.4Deformation proofThe maximum calculated deformation shall not exceed 6 % (2 % under railway tracks). For higher deformation uptomax.9 %anonlinearproofhastobeperformed.Theshorttermvalueimmediatelyafterinstallationshallbeexecuted without traffic load.A.5.9.5Stability proofThe stability proof is carried out for the vertical total load, the external water pressure and for the superposition ofboth loadings, taking into account imperfections (a, av2).A.5.9.5.1Vertical total loadBh R v2 v 2 S S q krit = vvq q krit= A.5.9.5.2External water pressureR D a aS p krit = with:Dsnap-through coefficientw w ah p =aap p crit = A.5.9.5.3Simultaneously acting vertical total load and external water pressureaavv1p critpq critq+= A.5.9.6Additional proof for profiled pipesProof shall be carried out forProfile stability,Multiple axial tensions.A.5.9.7SafetyA.5.9.7.1PrinciplesThe safety factors are determined on the basis of the probabilistic reliability theory. Within this the dispersion of theload-bearingcapacityofthepipe(e.g.strength,dimensions)andtoloading(e.g;soilproperties,liveloads,installation conditions) are taken into consideration.A.5.9.7.2Safety factors against fracture and instabilityThe necessary safety factors are given in tables A.19, A.20 and A.21, dependent on the classes of safety.Safety class A (normal case):prCEN/TR 1295-2:2004 (E)65endangering of groundwater;prejudice of use;failure has significant economic consequences.Safety class B (special case):no endangering for groundwater;slight prejudice of use;failure has slight economic consequences.Table A.19 Safety factors, failure through fracture Pipe materialSafety class A(normal case)pf = 10-5Safety class B(special case)pf = 10-3Asbestos cementConcreteVitrified clay2,2 1,8Reinforced concrete 1,75 1,4High density polyethylene(PE-HD)Polyvinylchloride (PVC-U)2,5 2,0Steel (ZM)Cast iron (ZM)1,5 1,3Unsaturated polyester,glassfibre reinforced (UP-GF)2,0 1,75Table A.20 Safety factors, failure through instability Pipe materialSafety cl. A(normal case)pf = 10-5Safety cl. B(spec. case)pf = 10-3SteelCast iron (ZM)High density polyethylene(PE-HD)Polyvinylchloride (PVC-U)Unsaturated polyester,glassfibre reinforced (UP-GF)2,5 2,0prCEN/TR 1295-2:2004 (E)66A.5.9.7.3Safety against inadmissible large deformationsForthepermittedshort-andlong-termdeformationinA.3.9.4itisassumedthatthislimitvalueappliesas90%fractile.A.5.9.7.4Proof of fatigue strength under fluctuating stressesProof is to be carried out for pipes beneath railway loadsandunder aircraft traffic loads.Proof can be necessarybeneath road traffic loads with heights of cover " 1,50 m. The absorbable frequency range 2 A of the pipe materialshallbeverified.Thedifferentfrequencyofmaximumloadsshallbetakenintoconsideration,usingreductionfactors, with proof of fatigue strength under fluctuating loads (see table A.21).Adyn2pr Table A.21 Reduction factorsTraffic loadReduction factor SLW 60SLW 30HIC 71BFZ0,50,81,00,6prCEN/TR 1295-2:2004 (E)67A.6NetherlandsA.6.1GeneralLoads are in accordance with CUR report n 122.Loads depending on the width of the bedding reaction:Earth load;Evenly distributed load;Traffic load;Self weight of pipe;Internal load due to weight of water;Heavy transport loads (not named in CUR 122).Loads not depending on the width of the bedding reaction:Load from external and internal water pressure ;Temperature differences across pipe wall.The distribution of the load on the pipe in the ground is given in figures A.27 to A.32.herein 2k

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