On-Bottom Stability Design Of Submarine Pipelines – A .

Hadi Amlashi / IJCOE 2017, 1(3); p. 29-40This approach is very time consuming and requiresthe design data to be available, i.e. in later designphases (detail design) where optimization of thepipeline weight may be possible due to the availabilityof site-specific environmental data.Lateral StabilityFor the lateral stability, both Coulomb frictionresistance and the passive resistance from soil areaccounted for. A general design criterion is presentedas below:(5)A typical Displacement curve established based on dynamic simulationswhere 𝑌 is the non-dimensional lateral pipedisplacement (𝑌 𝑦/𝐷), the vector X contains maindesign parameters influencing the accumulateddisplacement (y) and 𝑌𝑎𝑙𝑙𝑜𝑤𝑎𝑏𝑙𝑒 is the allowed nondimensional lateral displacement (scaled to the pipediameter). The 𝑌𝑎𝑙𝑙𝑜𝑤𝑎𝑏𝑙𝑒 shall be defined based ondesign conditions, but generally the total accumulateddisplacement is limited to 10-pipe diameter.For the lateral on-bottom stability, three differentdesign methods are presented:1) A dynamic lateral stability analysis2) An absolute lateral static stability method.3) A generalized lateral stability method basedon database results from dynamic analysesThese methods are briefly addressed and theuncertainties involved are discussed subsequently.100Log(Dimentionless displacement Y)Downloaded from ijcoe.org at 23:31 0330 on Saturday November 13th 2021𝑌(𝑿) able)101Min. allowedsubmerged weight0,1110100Log (Dimensionless weight parameter)Figure 1 A typical Normalized Displacement versusNormalized Weight (typically shown for results from dynamicanalyses)Dynamic lateral stability analysisThe most complete approach for on-bottom lateralstability of a pipeline is to perform a dynamicsimulation.The dynamic response of a pipeline depends on waveto current ratio, wave period and soil type andpenetration (passive resistance). Due to highnonlinearities involved in the response of the pipeline,a complete sea state should be used. In lack of properfull sea state data, a 3-hours sea state data shall beused.Time-domain simulations are performed to calculatethe accumulated lateral displacement of a pipelinesubjected to hydrodynamic loads from waves, currentsand soil resistance forces.A typical result from the dynamic on-bottom stabilityanalyses is shown in Figure 1. An envelope curve istypically established based on many analysis cases tocalculate the maximum allowable displacement. Timeincrements should be small enough to capture theactual nonlinear behaviour of the pipe-soil interaction.Furthermore, the axial force (due to internal pressureand temperature) and end effects should properly beaccounted for. Also, the wave directionality togetherwith the maximum wave height and thesequence/number of waves must be accounted for.Hence, many analyses should be performed toestablish a representative envelope curve. Normally, aparametric study is performed to cover a displacementranges of zero to several diameters of the pipeline.It should be noted that the 𝑌𝑎𝑙𝑙𝑜𝑤𝑎𝑏𝑙𝑒 may further belimited due to the excessive bending of the pipelineand other constraints.However, in earlier phases of design, e.g. feasibilityand/or conceptual design stages, simpler yet reliabledesign approaches are required to ensure the onbottom stability of the pipeline accounting for theuncertainties in environmental loads and the soilbehaviour.Absolute lateral stability methodThe absolute lateral stability criteria, in DNV-RPF109 (2011), are defined in terms of UR (UtilisationRatio) as described below:𝜇𝐹 𝐹 𝑈𝑅𝐴𝑆,1 γ𝑆𝐶 𝜇𝑊𝑍 𝐹𝑌 1𝑠𝐹 𝑅𝑈𝑅𝐴𝑆,2 γ𝑆𝐶 𝑊𝑍 1𝑠(6)(7)where, γ𝑆𝐶 Safety factor for Safety Class and 𝜇 Friction coefficient. The design Peak load coefficients(𝐶𝑧 and 𝐶𝑦 ), ref. to Eqs. (13) and (14) and arecalculated from design tables in DNV-RP-F109(2011) by interpolations of design parametersKeulegan-Carpenter number (𝐾 𝑈 𝑇 𝐷) andsteady to oscillatory velocity ratio (𝑀 𝑉 𝑈 ) fora single design oscillation.The above criteria can be stated in terms of minimumrequired submerged weight (𝑊𝑠,𝑟𝑒𝑞. ). It means, thecriterion can read:𝑊𝑠𝑊𝑠,𝑟𝑒𝑞. 1(8)The relation between the Utilisation Ratio (𝑈𝑅) andthe minimum required submerged weight (𝑊𝑠,𝑟𝑒𝑞. ) for31

Hadi Amlashi / On-Bottom Stability Design of Submarine Pipelines – A Probabilistic Approachboth lateral and vertical stabilities, in Eqs. (6) and (7) ,can then be written as follow:𝑈𝑅𝐴𝑆,1 𝑈𝑅𝐴𝑆,2 𝜇𝑊𝑠,𝑙𝑎𝑡,𝑟𝑒𝑞. 𝐹𝑅𝜇𝑊𝑠 � 1 1Downloaded from ijcoe.org at 23:31 0330 on Saturday November 13th 2021𝑊𝑠,𝑣𝑒𝑟,𝑟𝑒𝑞. γ𝑆𝐶 𝐹𝑍 to(𝐹𝑍 )The peak vertical load(𝐹𝑌 ) are defined as: Spectrallyderivedoscillatoryvelocity (significant(11)amplitude)design(12)and peak horizontal load )2(13)𝐹𝑌 0.5𝑟𝑡𝑜𝑡,𝑦 𝜌𝑤 𝐷𝐶𝑦 (𝑈 𝑉 )2(14) 𝑉𝜇𝑟𝑡𝑜𝑡,𝑧 𝐶𝑍 𝐿 ] 𝑊𝑠 Significantweightparameter𝜏(15)oscillations in the𝑇 𝑇𝑢T Design duration of sea statesdesign(normally Numberofbottomderived mean zero𝑇𝑝 𝑔(𝑇𝑛 𝑇𝑝 )𝑔(𝑇𝑛 𝑇𝑝 ) , based on linear wave theory,up-crossing periodcan be graphically derived from Fig. 3-3 Spectrally)] e resistance factor which dependson several parameters such as: pipe penetration into soil (𝑧𝑝 ) clay strength parameter (𝐺𝑐 𝑠𝑢 𝐷𝛾𝑠 ) or sand density parameter (𝐺𝑠 𝛾𝑠𝑤 𝑔𝜌𝑤 ), etc.𝑊𝑠 0.5𝜌𝑤 𝐷𝑈𝑠2𝑓𝑝𝑎𝑠𝑠𝑖𝑣𝑒 can be calculated from Eqs. 3.233.29 in DNV-RP-F109 (2011). Significantwave height during𝑊𝑠 0.5𝜌𝑤 𝐷(𝑈 𝑉 )2a sea pipe-soil interaction𝑟𝑡𝑜𝑡,𝑦 Horizontalload reduction duetovelocityforDesignSpectralPeakcurrent velocity near 5)0.43 )(𝑧𝑡 𝐷)0.46𝛾𝑠 Dry unit soil 5)0.25 )(𝑧𝑡 𝐷)0.42weight for Clay𝑆𝑢Oscillatory Un-drainedoscillation,perpendicularDesign InputDesign Input𝛾𝑠𝑤 SubmergedamplitudedesignDesign Inputseabed(1 1.4𝑧𝑝 𝐷 )(1 0.18(𝜃𝑡clay shear strengthsingleDesign Input𝑈𝑟 Design Steady 0.14(𝜃𝑡pipe-soil Design InputPeriod0.7 (1 1.3(𝑧𝑝 𝐷 0.1)) (1interaction𝑈 is𝑇𝑢parameter related to𝑟𝑡𝑜𝑡,𝑧 Vertical loaddurationrecommended)𝐻𝑠Weight3-hourin DNV-RP-F109 (2011)pipe avelocity spectrumfor virtually stable𝐿 𝑑 𝑔ReferenceTable 1 Definition of Design ParametersCharacteristicValue in DNV-RP-F109 (2011)toThe parameters are as defined in Table 1.𝐿can be graphically derived from Fig. 3-2period𝑊𝑠,𝑙𝑎𝑡,𝑟𝑒𝑞. 𝑟𝑡𝑜𝑡,𝑦 𝐶 𝑌 𝜇𝑟𝑡𝑜𝑡,𝑧 𝐶 𝑍𝑟𝐶 𝑍)) 𝑓𝑝𝑎𝑠𝑠𝑖𝑣𝑒 (1 𝑡𝑜𝑡,𝑧𝐿 𝐿 spectrum,𝐻𝑠 𝑓(𝑇𝑛 𝑇𝑝 )𝑇𝑛𝑓(𝑇𝑛 𝑇𝑝 ), based on linear wave theory,pipelineBy introducing equations (13) and (14) into (11) and(12), the following criteria are derived:γ𝑆𝐶 (forperpendicular𝑇𝑛0.5𝑟𝑡𝑜𝑡,𝑧 𝜌𝑤 𝐷𝐶𝑧 (𝑈 𝑊𝑠,𝑣𝑒𝑟,𝑟𝑒𝑞. [γ𝑆𝐶 �𝑞. [current(1 𝑧0 𝐷)𝑙𝑛(1 𝐷 𝑧0 ) 1𝑈𝑟 () sin 𝜃𝑐𝑙𝑛(1 𝑧𝑟 𝑧0 )pipelineγ𝑆𝐶 (𝐹𝑌 𝜇𝐹𝑍 ) 𝐹𝑅𝜇 Steadyperpendicular(9)where 𝑊𝑠,𝑙𝑎𝑡,𝑟𝑒𝑞. and 𝑊𝑠,𝑣𝑒𝑟,𝑟𝑒𝑞. are:𝐹𝑍 𝑉 𝑉unit soil weight for0.5𝑈𝑠 ( 2𝑙𝑛𝜏 0.5772 2𝑙𝑛𝜏)Design InputSand𝜇 Soil frictiontofactorpipeline32Design Input

Downloaded from ijcoe.org at 23:31 0330 on Saturday November 13th 2021Hadi Amlashi / IJCOE 2017, 1(3); p. 29-40zt and θt are the trench depth and the trench angle,while zp is the soil penetration depth. For thedefinition of other parameters, reference is made toDNV-RP-F109 (2011).The characteristic load condition considered reflectsthe most probable extreme response during either atemporary phase (less than 12 months), i.e. aninstallation phase or a permanent operationalcondition (excess of 12 months), i.e. a productionphase.where 𝑊𝑠,𝑟𝑒𝑞. max(𝑊𝑠,𝑣𝑒𝑟,𝑟𝑒𝑞. , 𝑊𝑠,𝑙𝑎𝑡,𝑟𝑒𝑞. ) and𝑊𝑠,𝑎𝑙𝑙. is either 𝑊𝑠,𝑁𝐵𝑂,𝑎𝑙𝑙. or 𝑊𝑠,𝐴𝑐𝑐.,𝑎𝑙𝑙. , depending onthe allowed pipe displacement.Therefore, a certain level of interpretation should beapplied to determine what is deemed to be a stablepipeline with given viabilities in design parameters.This will be discussed subsequently in this paper.3. Reliability BasisGeneralThe adequate structural safety of offshore pipelines isensured by design, load/response monitoring andinspection during their design life.Reliability methods are now widely used to makeoptimal decisions regarding safety and life cycle costsof offshore structures, as mentioned e.g. in [10] and[11].Such methods can deal with uncertainties associatedwith the design, fabrication, installation and operationof e.g. pipeline systems, and may be classified asfollows:a) Structural Reliability Analysis (SRA), seee.g. [12]. The purpose of SRA is todeterminethefailureprobabilityconsidering fundamental variability, andnatural and man-made uncertainties dueto lack of knowledge.b) Quantitative Risk Analysis (QRA) whichdeals with the estimation of likelihood offatalities, environmental damage or lossof assets in the broad sense.The focus in the present paper is on the first one, i.e.Structural Reliability Analysis (SRA).For the considered failure mode, the possiblerealizations of 𝑿 (a vector of n random variables) canbe separated in two separate domains; namely the safedomain and the failure domain. The curved surfacebetween the safe and failure domains in the space ofbasic variables is denoted as the limit state surface,and the reliability problem is conveniently describedby a so-called limit state function 𝑔(𝑿).The probability of failure is the probability ofoccurrence in the failure domain:Generalized lateral stability methodThe generalized lateral stability criteria, in DNV-RPF109 (2011), can be defined in terms of UR as below:𝑈𝑅𝐺𝑆,𝑁𝐵𝑂 �,𝐴𝑐𝑐. �� 1 1(17)(18)The allowable weight for No-Break Out (𝑊𝑠,𝑁𝐵𝑂,𝑎𝑙𝑙. )and the allowable accumulated weight (𝑊𝑠,𝐴𝑐𝑐.,𝑎𝑙𝑙. ),corresponding to a displacement of 𝑦 𝑌 𝐷, arecalculated as below:𝑊𝑠,𝑁𝐵𝑂,𝑎𝑙𝑙. 0.5𝜌𝑤 𝐷𝑈𝑠 ���.,𝑎𝑙𝑙. 0.5𝜌𝑤 𝐷𝑈𝑠 𝐿𝑌(20)The significant weight parameter (𝐿), in general, isdefined as:𝐿 𝑊𝑠 0.5𝜌𝑤 𝐷𝑈𝑠2(21)𝐿𝑠𝑡𝑎𝑏𝑙𝑒 and 𝐿𝑌 are significant weight parameter forvirtually stable pipe (e.g. within 0.5𝐷) anddisplacement of up to 10-pipe diameter, respectively,and are determined by interpolation of design curvesgiven in DNV-RP-F109 (2011) using three nondimensional parameters, i.e. M (Steady to oscillatoryvelocity ratio for design spectrum), N (Spectralacceleration factor) and K (Significant KeuleganCarpenter number). The parameters are defined asfollows:𝑀 V 𝑈𝑠(22)𝑁 (𝑈𝑠 𝑇𝑢 ) 𝑔(23)𝐾 𝑈𝑠 𝑇𝑢 𝐷(24)𝑃𝑓 𝑃[𝑔(𝑿) 0] 𝑔(𝑿) 0 𝑓𝑿 (𝒙)𝑑𝒙The interpolation can be performed for both pipe onsoil and on clay, however with some limitations.Where 𝑓𝑿 (𝒙) represents the joint probability densityfunction for X and represent the uncertainty in thegoverning random variables. The integral of equationabove may be calculated by direct integration,simulation or FORM/SORM methods. In general, theaccuracy of the method should be validated beforeuse. Unless it is not done earlier for the problem inhand, crude Monte Carlo simulations should be usedto validate other approximate methods.The “tail sensitivity problem” causes the computedfailure probability to be of limited informative valueexcept for reliability comparisons made in the sameIt should, however, be noted that only one checkneeds to be passed to ensure that the pipeline islaterally stable, i.e. either the absolute stability or thegeneralized stability. However, in most cases ofdesigns against the on-bottom lateral stability, thefollowing relationship may exists:𝑊𝑠,𝑎𝑙𝑙. 𝑊𝑠,𝑟𝑒𝑞. 𝑊𝑠(26)(25)33

Downloaded from ijcoe.org at 23:31 0330 on Saturday November 13th 2021Hadi Amlashi / On-Bottom Stability Design of Submarine Pipelines – A Probabilistic Approachmodel space of probability distributions as mentionede.g. in [12]. The target level needs to be determinedbased on the same reliability methodology that will beapplied to demonstrate compliance with the targetlevel, see e.g. [10].The reliability index can be defined to express thesafety defined in the space of random variables, as𝛽 Φ 1 (𝑃𝑓 ), see [13].For the simple case, where 𝑿 consists of twovariables, i.e. the load L and the resistance R, the limitstate function can be specified as 𝑔(𝑿) 𝑅 𝐿 withthe distribution and the characteristic values as shownin Figure 2 (DNV-RP-C207, 2012) [14].Both the generalized and the absolute lateral stabilitymethods presented above are applied probabilisticallyaccounting for the random variables stated in theproceeding chapter.In reliability-based limit states design of pipelines, itis assumed that the loads and resistances follow someassumed distributions. However, it is important toaccurately model the on-bottom stability distributionand particularly its tail behaviour. Moreover, both thesystematic (bias) and random model uncertaintiesneed to be addressed. Monte Carlo Simulationtechniques can be applied for this purpose. Theadvantage of the MCS method is that it convergestowards exact results when enough simulations arecarried out. A drawback is that it is time-consumingespecially if small failure probabilities are to beestimated.Acomprehensiveoverviewofcomputational methods for the probability measurescan be found in Melchers (1999). In the present study,MCS method is used for comparison purpose.Monte Carlo Simulation (MCS) approach inExcel2013 is used for this matter. A VBA code iswritten to perform the simulations while assigning anynumber of random variables with their associateduncertainties.In the present work, the criteria for 𝑈𝑅𝐴𝑆 and 𝑈𝑅𝐺𝑆are used in probabilistic analyses. The suitability ofthe method is benchmarked against common designapproach, i.e. DNV-RP-F109 (2011).Uncertainty measuresUncertainties associated with random variables havemany sources, but in general, may be categorized astwo main types of uncertainty, see e.g. Madsen, H.O.et al. (1986): Aleatory, i.e. physical uncertainty Epistemic, i.e. uncertainty related to imperfectknowledge.Physical uncertainty (𝜒̂ 𝑝 ) is a natural randomness of aquantity which cannot be reduced, e.g. the randomvariability in the soil strength from a pointmeasurement within a soil sample.Uncertainty due to the imperfect knowledge, however,consists of statistical uncertainty, model uncertaintyand measurement uncertainty which can, in principle,be reduced by the collection of more data, byimproving engineering models and by employingmore accurate methods of measurement:a) The statistical uncertainty (𝜒̂ 𝑠𝑡 ) is caused bylimited number of observations of a randomquantity.b) Te model uncertainty (𝜒̂ 𝑚 ) is caused byidealized engineering models used for therepresentation and prediction of quantitiessuch as the passive soil resistance. The modeluncertainty involves two elements, viz. (1) abias (Bmod) if the model systematically leads toover-prediction or under-prediction of aquantity in question and (2) a randomnessFigure 2 A typical Reliability load and strength curvestogether with the corresponding characteristic valuesIn the partial safety factor method, the designresistance 𝑅𝑑 should be larger than the design loadeffect 𝐿𝑑 for the structural elements with which areverified for several different load combinations. Thedesign load and resistance are related to thecharacteristic values as follow:𝐿𝑑 𝛾𝐿 𝐿𝑐&𝑅𝑑 𝛾𝑅 𝑅𝑐(27)The characteristic values are defined as a quantityassociated with the probability distribution for loadsand resistance variables. This is further discussed inthe following section.Number all tables and figures according to theirappearance.4. Probabilistic on-bottom lateral stabilityMethodologyThe cumulative distribution function 𝐹𝑋 of a randomvariable 𝑋 is defined as the probability that 𝑋 fallsshort of x:𝐹𝑋 (𝑥) 𝑃[𝑋 𝑥](28)where P[.] denotes probability. The probability ofexceedance 𝑄𝑋 is defined as the complement of thecumulative distribution function:𝑄𝑋 (𝑥) 1 𝐹𝑋 (𝑥) 𝑃[𝑋 𝑥](29)The p quantile in the distribution of 𝑋 is the value of𝑋 whose cumulative distribution function value is p,as defined below:𝐹𝑋 (𝑥𝑝 ) 𝑝(30)34

Downloaded from ijcoe.org at 23:31 0330 on Saturday November 13th 2021Hadi Amlashi / IJCOE 2017, 1(3); p. 29-40(𝜒̂ 𝑟 ) associated with the variability in thepredictions from one prediction of thatquantity to another.c) The measurement uncertainty (𝜒̂ 𝑚𝑠 ) is causedby imperfect instruments and sampledisturbance when a quantity is observed. Likethe model uncertainty, the measurementuncertainty involves two separate elements,i.e. the systematic bias and the random error.2) A quantile in the probability distribution, e.g.the 5% (or 95%) quantile3) The mean value (plus) minus a factor ofstandard deviations, i.e. 𝜇 𝑘𝜎. For example,𝜇 2𝜎(for a normal distribution)corresponds to the 2.3% lower quantile.4) The most probable value, i.e. the value forwhich the probability density function ismaximum.It is noted that uncertainties due to the imperfectknowledge are statistically independent of physical(natural) uncertainties. The above stated uncertainties,are all represented by their generic distribution typesand associated distribution parameters.The measurement uncertainty can, conservatively, bedisregarded regardless of the accuracy of the methodof the measurement, as this is either unknown or isvery difficult to quantify. This is because the physicaluncertainty estimate (𝜒̂ 𝑝 ) implicitly account for themeasurement uncertainty with the given accuracy ofthe measurement. The net physical uncertaintyestimate (𝜒̂ 𝑝,𝑛𝑒𝑡 ) should then be represented as:The choice of the characteristic value usually dependson the design code, e.g. the choice of confidence andon the actual application, e.g. design constraints. Ingeneral, due to uncertainties involved in a randomvariable described by a probability distribution, theestimated characteristic value also becomesstatistically uncertain. To properly account for such astatistical variability, it is common to specify thecharacteristic value with a specified confidence level.An adequate confidence should, therefore, be used forthe estimation of the characteristic value from thedata. This is not explicitly defined in DNV-RP-F109(2011) and therefore is subject to the understanding ofthe user.In this paper, due to lack of proper statistical data, acharacteristic value of 𝜇 1.5𝜎 is assumed for loadsand resistance variables. This is equivalent toapproximately 6% (94%) lower (upper) quantile. It isemphasized that this assumption is also subject touncertainty, but used in this paper to benchmark theeffect of this definition on the probabilistic analysis.𝑉𝜒̂𝑝,𝑛𝑒𝑡 𝑉𝜒̂2𝑝 𝑉𝜒̂2𝑚𝑠(31)where 𝑉 denotes the coefficient of variation.Therefore, only physical, stochastic and modeluncertainties need to be accounted for. The totaluncertainty can then be formulated as, Ref. [12]:𝜒̂ 𝑡𝑜𝑡 𝜒̂ 𝑝 𝜒̂ 𝑠𝑡 𝐵𝑚𝑜𝑑 𝜒̂ 𝑟(32)Random variables and uncertaintiesTable 2 and Table 3, respectively, define the mainparameters for two hypothetical design cases, i.e. case(1) in water depth of 330m and clay soil type and case(2) in water depth of 135m with sand soil types.Due to lack of proper statistical data, normaldistribution (with a bias of 1.0) is assumed for allrandom variables. This is subject to uncertainty, but itis assumed here for the sake of simplicity and tobenchmark the effect of variables randomness on theresults.The CoV of 0.15 is used for all load variables. Forresistance variables, the CoV of soil unit weightvariables (dry and submerged) are assumed to be 0.1,while the two other variables, i.e. the undrained shearstrength and the friction coefficient are assumed tohave a CoV of 0.15. The choice of random uncertainty(CoV) is arbitrary in these examples. However, as ageneral practice, more uncertainties are given to loadvariables than resistance variables.The determination of uncertainties in randomvariables for hydrodynamic loads and the soilresistance is a cumbersome task to perform andrequires sufficient statistical data. Since the designmethods given in DNV-RP-F109 (2011) are usedhere, it is assumed that these uncertainties areproperly accounted for in the given design formats.However, definition of characteristic design valuese.g. parameters associated with hydrodynamic loadsand the soil resistance is subject to uncertainty andshould properly be accounted for.Due to lack of the readily available statistical data, theassumed random variables with associateduncertainties for the considered characteristic designvalues in case studies, are further discussed in theproceeding chapter.Characteristic valuesFor practical deterministic design by codes andstandards (such as DNV-RP-F109), a characteristicvalue is rather used instead of entire variabilityassociated with the specified probability distribution.This is usually defined as a (characteristic) quantityassociated with the assumed probability dist

DNV-OS-F101 (2013) [9]. If this displacement leads to significant strains and stresses in the pipe itself, these load effects should be dealt with in accordance with relevant codes, e.g. DNV-OS-F101 (2013). Generally, SLS criterion is a condition which, if exceeded,