OTC-27727-MS

On-Bottom Stability Analysis of Submarine Pipelines, Umbilicals and CablesUsing 3D Dynamic Modelling

Bassem Youssef and Dermot O'Brien, Atteris Pty Ltd

Copyright 2017, Offshore Technology Conference

This paper was prepared for presentation at the Offshore Technology Conference held in Houston, Texas, USA, 1–4 May 2017.

This paper was selected for presentation by an OTC program committee following review of information contained in an abstract submitted by the author(s). Contents ofthe paper have not been reviewed by the Offshore Technology Conference and are subject to correction by the author(s). The material does not necessarily reflect anyposition of the Offshore Technology Conference, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the writtenconsent of the Offshore Technology Conference is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations maynot be copied. The abstract must contain conspicuous acknowledgment of OTC copyright.

AbstractSubmarine pipelines and umbilicals are essential elements of many offshore hydrocarbon developments. Ingeneral, the most economical approach is to lay the pipelines and umbilicals directly on the seafloor withadequate self-weight to avoid any requirement to perform secondary stabilisation work such as trenching.A fundamental design requirement for this scenario is to ensure adequate pipeline stability under extremeenvironmental loading conditions, as excessive lateral displacements may result in pipeline or umbilicaldamage.

The commonly used and widely accepted recommended practice DNV-RP-F109 (Ref. 3) provides threedesign approaches with increasing levels of complexity to perform on-bottom stability design. These threedesign approaches are: Absolute Lateral Static Stability, Generalised Lateral Stability and Dynamic LateralStability Analysis. The first method is based on two dimensional (2D) force balance equilibrium equationswhile the second method is based on extensive dynamic modelling results of 2D pipeline models. Thesefirst two methods are intended to provide conservative on-bottom stability designs for rigid pipelines. Thethird method involves detailed finite element modelling of the pipeline under a time domain hydrodynamicloading.

This paper highlights the DNV-RP-F109 recommended practice limitations with respect to the on-bottomstability design of flexible pipelines, umbilicals and cables. The paper presents a dynamic simulationmethodology, in accordance with the recommended practice DNV-RP-F109, for on-bottom stability designof rigid pipelines, flexible pipelines, umbilicals and cables, together with specific sensitivity analyses andcomparisons with the Absolute Stability method.

The dynamic modelling results and comparisons presented in this paper highlight some limitations of theAbsolute and Generalised methods for flexible pipelines, umbilicals and cables and illustrate the benefits ofusing the three dimensional (3D) dynamic stability analyses. The results of the sensitivity analyses clearlyidentify important parameters for the dynamic simulation, such as the hydrodynamic load correction due tothe pipeline movements, the pipeline axial stiffness and the seabed passive soil resistance, that significantlyaffect the on-bottom stability behaviour. Refining the identified parameters input values will lead to moreaccurate and cost effective on-bottom stability design.

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IntroductionPipeline on-bottom stability is a complicated interaction between the hydrodynamic loads, the pipelinestructure and the supporting soil. The pipeline length can vary from a few hundred meters to hundreds ofkilometers. For a long pipeline route it is more likely that one or more of the water depth, the pipelineheading, the metocean conditions or the soil conditions will vary. A 2D model will not take into account thefact that the hydrodynamic loads and soil resistance are shared along the pipeline route due to the effect of thepipeline stiffness. For the Soliton current case, which is usually high in velocity, short in period and localizedin distance, the 2D on-bottom stability methods of the recommended practice DNV-RP-F109 would resultin a too conservative pipeline weight requirement. In contrast with a 3D model, high hydrodynamic loadevents at any particular location along the pipeline route will be distributed and shared over a length of thepipeline, leading to a more realistic prediction of pipeline lateral movement.

The Generalised Lateral Stability method of the recommended practice DNV-RP-F109 is calibratedfor rigid pipeline regardless of the pipeline axial stiffness and bending stiffness. Therefore, the effect ofchanging the bending stiffness and axial stiffness values, as applicable for flexible pipe or umbilical, is notaccounted for. Other important parameters such as the operational internal pressure and temperature are notconsidered in the 2D on-bottom stability methods calibration. As a result, the 2D stability methods maypotentially under estimate the pipeline displacements.

An important factor in the on-bottom stability analysis is that the hydrodynamic loads are generated fora pipeline sitting on the seabed in stationary position. The generated hydrodynamic loads are much higherthan the hydrodynamic loads for a pipeline partially buried in the seabed or for a pipeline that experiencesa lateral velocity. For accurate and economical on-bottom stability design, in the 3D dynamic modellingthe hydrodynamic loads are corrected during the simulation to account for the pipeline lateral and verticalmovements.

For most of the pipeline cases, the pipeline route includes multiple changes in the heading direction andsometimes structure crossings. These changes in the pipeline route will affect the hydrodynamic loadingangles and may change the behaviour of the pipeline-hydrodynamic loads interaction. For some casesdifferent pipeline route headings could provide more stability for the pipeline if the hydrodynamic loads actparallel to the pipeline heading. An additional benefit of the 3D dynamic stability analysis is that accuratecalculation of the pipeline tension load, bending moments and tie-in loads at the tie-in connection can beachieved. Considering 3D modelling, the pipeline designer can include the tie-in connection details, theactual pipe route heading, the pipe bending stiffness and axial stiffness and any bending restrictors in themodel. The stability design in the vicinity of tie-in points can then be optimized compared to what can beachieved if 2D stability methods are relied upon.

For small diameter pipelines, less than 10 cm for example, or for cables; a significant limitation in thecurrent recommend practice is that the wave velocity correction due to the seabed boundary layer effect isnot accounted for. The specific gravity calculated by the Absolute stability method of the recommendedpractice DNV-RP-F109 to achieve the on-bottom stability requirements is un-realistic. For most of theseabed materials, the boundary layer height would be in a range of few centimeters. The effect of a fewcentimeters boundary layer height on the correction of the wave velocity on a small diameter pipeline orcable can be significant.

Using the 3D dynamic modelling the pipeline designer can overcome the limitations of the 2D stabilitymethods of the recommended practice DNV-RP-F109 and achieve more reliable and economic on-bottomstability designs (see Refs. 11 and 12 for 3D dynamic modelling discussions and examples).

OTC-27727-MS 3

DNV-RP-F109 On-bottom stability design methods

Absolute stability methodThe Absolute Stability method is calibrated to provide the minimum pipe submerged weight such that nolateral displacement occurs during the design storm return period. The method uses the maximum wavevelocity expected during the entire storm period. Therefore the pipeline submerged weight estimated tendsto be very conservative.

Remarks and limitations of the method:

• The method is based on the extreme wave velocity which may occur for a few seconds during thethree hours storm period at one particular location along the entire pipeline route.

• The method does not account for the pipe operational temperature and pressure.

Generalised stability methodThe generalized stability method is based on PONDUS dynamic stability simulations of 2D pipeline models.PONDUS is a computer program that computes the dynamic lateral response of offshore pipelines subjectedto wave and current action on a horizontal seabed (Ref. 3). The method is calibrated considering thesignificant wave velocity during the storm to provide the pipeline submerged weights corresponding topipeline lateral displacement between 0.5 outer diameter (D) and 10 D under the design storm return periodloading conditions.

Remarks and limitations of the method:

• This method is based on 2D section of the pipeline, ignoring the benefits of the 3D effect on thepipeline bending and axial stiffness and soil resistance on the pipeline stability.

• Unlike the Absolute stability method, this method uses the significant wave velocity to estimatethe pipe submerged weight values corresponding to pipeline lateral displacement of 0.5 OD and10 OD.

• Similar to the Absolute stability method, the method does not account for the pipe operationaltemperature and pressure.

• The method is applicable for silica sand soil and clay soil only and cannot be used for other soiltypes, such as calcareous or carbonate sand soil.

Dynamic stability methodThe dynamic stability method is considered the most sophisticated stability method as it requires a numericalmodelling tool and a level of expertise to perform the modelling and interpret the results. Using the numericalmodelling, the pipeline designer can overcome the limitations of the 2D methods mentioned above. Benefitsof using the 3D dynamic stability modelling have been discussed extensively in the literature (see forexample, Youssef et al., Ref. 10). As recommend by DNV-RP-F109, the following considerations arerequired for the dynamic stability modelling:

• Full sea-state time series using the wave spectrum should be utilized in the model; if no informationis available regarding the storm duration, a typical storm period of three hours should be used.

• Storm hydrodynamic loads of irregular wave on the pipeline should be calculated using advancedhydrodynamic force model that accounts for the wave wake effect.

• During the simulation, the hydrodynamic loads should be corrected to account for the pipelinedisplacement and penetration experienced during the simulation time history.

• Soil resistance should include two parts, a pure friction term and a passive resistance term,accounting for the pipe penetration in the soil and build-up of the soil berm.

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• Full pipeline length should be modelled including the actual route and the actual pipeline endsboundary conditions. For long pipeline routes, the middle section of the pipeline could be modelledwith special considerations for the model boundary conditions.

• The operating temperature and pressure should be included in the model.

Remarks and limitations of the method:

• The actual pipeline properties conditions can be modelled including axial stiffness and bendingstiffness, nonlinear cross section properties, any bending stiffeners, any change in the pipe crosssection or in the pipe weight along the pipeline route.

• For small diameter pipelines or cables, DNV-RP-F109 does not provide any considerationsregarding the wave velocity and hydrodynamic load corrections. Therefore, the results of the2D stability methods of the recommended practice DNV-RP-F109 and the dynamic stabilitymodelling are usually unrealistic for small diameter pipelines or cables if the wave velocity andthe hydrodynamic loads are not corrected. More discussion regarding this point will be presentedin numerical modelling section.

Figure 1 presents a diagrammatic sketch of the hydrodynamic-pipeline-soil model elements.

Figure 1—a- Diagrammatic Sketch of Hydrodynamic-Pipeline-Soil Model, b- Force Balance Diagram on the Pipeline Section

Dynamic stability modelling considerationThe on-bottom stability simulations presented in this paper are performed using the CORUS-3D software.The software code is written in FORTRAN programming language and introduced to the finite elementsoftware ABAQUS through the DLOAD subroutine to perform the hydrodynamic-pipe-soil interactioncalculations.

Hydrodynamic loadsThe Morison equation is an industry recognized and simply established method used to estimate thehydrodynamic loads around a cylinder. When applied to a pipeline on the seabed, lift (FL), drag (FD) andinertia (FM) loads under combined wave and steady current can be calculated as:

(1)

(2)

(3)

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where ρ is the density of the fluid, Uw the wave velocity, Uc the current velocity, the wave acceleration,D the pipe diameter and CL, CD and CM the lift, drag and inertia coefficients, respectively.

The value of the Morison equation coefficients are reported in many references (for example, Refs. 7,8 and 9) as a function of steady current to oscillatory wave velocity ratio, pipe roughness and Keulegan-Carpenter number (KC) which takes the form (KC=UwT/D). However, the Morison equation yields poorload prediction especially for the lift load component and for the irregular wave conditions (DNV-RP-F109,Ref. 3). More advanced hydrodynamic load model, Fourier load model, was presented by Sorenson et al.(Ref. 8) and based on intensive full-scale laboratory tests. This model takes into account the wave wakeeffect and the model is applicable to both regular and irregular waves, a wave only or wave and current.The Fourier transformation method has been used to fit the non-dimensional hydrodynamic loads and toestimate the Fourier coefficients. This hydrodynamic load model is recommended by DNV-RP-F109 (Ref.3) to estimate the hydrodynamic loads on the pipeline. Moreover, the Fourier load model is implementedin one of the widely accepted and used commercial pipeline simulation package of AGA Level 3 software(Ref. 1).

The basis for the Fourier method is that any quantity that has a periodic variation with a certain period Tcan be reproduced by superposition of a number of sine waves with periods equal to T and smaller, so thatthe ith sinusoidal wave or harmonic has a period Ti = T/i, where i = 1, 2, 3,…‥, N. The general expressionof the periodic quantity F(t) is:

(4)

where ao,ai and bi are the Fourier coefficients derived from experimental measured loads and is

the wave angular frequency.In order to obtain the non-dimensional load coefficient from the Fourier analysis, the measured physical

experimental loads have been normalized by . Before that, for the horizontal load case, the dragload was calculated by subtracting the inertia component from the measured horizontal load:

(5)

where Ca is the added mass coefficient with a value of 2.29 as determined from potential flow theory (Refs.1 and 8).

The decomposition of the non-dimensional horizontal (CH) and vertical (CV) loads have the expressions:

(6)

(7)

The total in-line load is found by adding the inertia term.

(8)

where CM = Ca + 1 and takes the value of 3.29 (Refs. 5 and 8).For full details of the Fourier hydrodynamic load model and the hydrodynamic loads coefficients,

reference should be made to Sorenson et al. (Ref. 8) and AGA (Ref. 1).

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Hydrodynamic load corrections. The hydrodynamic load calculations presented in the previous sectionassume a pipe fixed in position with its apex just touching the soil surface. In real field scenario, the pipelineon the seabed may move both horizontally and vertically under the effect of the applied hydrodynamic loadsand pipe self-weight load. Movements of the pipeline will change the relative velocity of the pipeline tothe flowing water. Pipeline vertical penetration also reduces the exposure of the pipeline and therefore thehydrodynamic loads acting on it. Moreover, if the pipeline is elevated from the seabed the hydrodynamicloads will also change. These effects must be taken into account to accurately predict the hydrodynamicloads on the pipeline.Pipeline horizontal movementThe hydrodynamic loads acting on the pipeline are calculated as a function of the water particle velocity andacceleration. For the case of a horizontally moving pipeline, the relative velocity and acceleration betweenthe pipeline and flowing water will change and consequently affect the hydrodynamic load. As explained bySorenson et al. (Ref. 8), the hydrodynamic loads on moving pipeline can be estimated by adding correctionterms to the pre-estimated hydrodynamic loads on a pipeline fixed in position.

(9)

(10)

(11)

where is the pipe acceleration, Ue the effective near pipe water velocity and CD,Corr and CL,Corr the dragand lift load correction coefficient, respectively. Values CD,Corr and CL,Corr are provided in AGA (Ref. 1). TheUe value can be calculated using the form:

(12)

Pipeline PenetrationA pipeline may become partially buried during the pipe laying process and can further penetrate into theseabed due to pipeline dynamic cyclic movements under small oscillatory wave action. With penetration,the pipeline becomes less exposed to the flowing water, which leads to a reduction in the hydrodynamicloads. DNV-RP-F109 (Ref. 3) recommended reducing the lateral and vertical loads as per the followingreduction factors equations:

(13)

(14)

where Rlateral is the reduction factor for lateral loads, Rvertical the reduction factor for vertical load and ZP isthe pipe vertical penetration.Wave boundary layer effectThe seabed material roughness influences the wave velocity at the vicinity of the seabed level. The waveboundary layer height defined as the minimum distance from the seabed to a point where the wave velocityin the x-direction equals the free-stream wave velocity amplitude (Ref. 6). In general, for pipeline on-bottomstability applications the wave boundary layer will only be a few centimeters in height. The recommended

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practice DNV-RP-F109 recommends ignoring the effect of wave boundary layer on the wave velocity. Thisis justified for large diameter pipelines where the influence of the boundary layer on the wave velocity overthe pipeline diameter is minor. However, for small pipelines or cables of 10 centimeter diameter or less,the effect of the wave boundary layer can be significant. Detailed modelling of the wave boundary layerincluding the eddy viscosity models, one-equation models (k-model) and two equations models is discussedand presented in Fredsoe and Deigaard (Ref. 4).

A schematic sketch of the wave boundary layer is presented in Figure 2-a. The wave velocity profilesin the boundary layer at different phases predicted by eddy viscosity models as discussed by Fredsoe andDeigaard (Ref. 4) is presented in Figure 2-b with the full line presents a steady eddy viscosity and the dashedline presents a time-varying eddy viscosity.

Figure 2—a- Wave Boundary Layer, b- Wave Velocity Profile within the Boundary Layer at Different Phase (Ref. 4)

The wave boundary layer thickness for a pipeline on smooth or rough seabed soils can be estimated basedon the methods introduced by Fredsoe and Deigaard (Ref. 4). For smooth seabed soil, the height of waveboundary layer (δ) can be approximated as:

(15)

where Re = Uw a/v is the amplitude Reynolds number defined by water particle excursion distance a, waveorbital velocity Uw and the kinematic viscosity of water ν. The water particle excursion distance a is definedas a = UwT/2π where T is the wave period.

On a rough seabed soil, δ is related to surface roughness and can be estimated as:

(16)

where kN is the Nikuradse roughness height and is dependent on seabed conditions. Under hydrodynamicallyrough flow conditions, the Nikuradse roughness height can be estimated as kN = 30z0 where z0 is the seabedroughness height.

The average wave velocity profile in a wave boundary layer considering a logarithmic form is presentedin Cheng et al. (Ref. 2). Considering a simplified linear profile of the wave velocity within the boundarylayer height, the average wave velocity over the pipe diameter can be calculated as follows:

(17)

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(18)

Soil ModelsOne of the most important parts of the on-bottom stability dynamic model is to model the full soilresistance which consists of a pure Coulomb friction part and a passive resistance part. The Coulombfriction value provides the lateral soil resistance capacity as a ratio of the pipe vertical weight. DNV-RP-F109 recommended for a concrete coated pipe a Coulomb friction value of 0.6 for sand or rock soils and aCoulomb friction value of 0.2 for clay soil. The passive soil resistance part accounts for the soil resistancecapacity due to pipeline penetration in the soil.

Considering a pure Coulomb friction only and ignoring the passive soil resistance term in the on-bottomstability modelling may lead to larger predicted pipeline horizontal displacements. The modified Coulombfriction model or the tri-linear Coulomb friction model (see Figure 3) accounts for the passive soil resistanceand requires much less efforts to be implemented in the finite element model. The model simply providesmodified Coulomb friction values equivalent to combined pure Coulomb resistance and passive soilresistance at different pipe lateral displacement levels. However, the tri-linear model requires geotechnicallaboratory testing of the soil sample to provide the tri-linear Coulomb friction model parameters.

Figure 3—Diagrammatic Sketch of Pipe-Soil Interaction Models Used in this Paper

The Verley and Sotberg (Ref. 14) soil resistance model is calibrated to model the passive resistance termof silica sand soil. DNV-RP-F109 recommended the use of Verley and Sotberg soil model to predict thepassive soil resistance of the silica sand soil. Full details of the model can be found in Verley and Sotberg(Ref 14) and DNV-RP-F109 (Ref. 3). Similar passive soil resistance models for clay soil and calcareoussoil are presented in Verley and Lund (Ref. 15) and Youssef and Cassidy (Ref. 13), respectively.

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Flowchart of the CORUS-3D code and the main procedure of the software are presented in Figure 4.

Figure 4—Flowchart and Procedure of the Dynamic Stability Software

Dynamic stability simulationsThe effects of the various parameters discussed above have been evaluated through performing a series of3D dynamic stability simulations with various sensitivity cases to gauge the effect of each parameter on thepredicted behaviour of a sample pipeline. Details of the performed analyses inputs including the sensitivitycases details are presented in Table 1.

Table 1—Dynamic Simulations Input Data and Details

Sensitivity Cases*Item Base Case

Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7

Outer Diameter 220 mm 25.4 mm

Wall thickness 11.5 mm 12.7 mm

Submerged weight 200 kN/m 11 kN/m

Specific gravity 1.52 3.14

Significant Waveheight

7.5 m

Peak period 10 sec

Steady current 0.5 m/s

Water depth 50 m

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Sensitivity Cases*Item Base Case

Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7

Wave spreading factor 2

Hydrodynamic loadcorrection

Yes No

Soil Model Pure Coulombfriction

Various

Pressure/ Temperature No Yes

Ends BoundaryConditions

Axially fixedLaterally free

Axial andlateral fixity

Routing Straight Dogleg

Bending and axialrigidity (EI and EA)

8.2E6 N.m2

1.5E9 N1E4 to 1E81E7 to 1E10

1E2 2.2E5

Wave Boundary layer No Yes

* The blank cells values are as per the Base Case values

Base CaseThe base case of the dynamic stability simulation examples is a 2,500 m long rigid pipeline in a 50 m waterdepth. The pipeline is modelled using 500 hybrid linear pipe element (PIPE31H) each 5 m length. Thesimulation is performed for a 30 minute storm loading and considered the hydrodynamic load correctiondue to the pipeline movements. In this example, the soil type considered is silica soil and the soil resistanceconsidered is a pure Coulomb friction with a value of 0.6. The contribution of the passive soil resistancehas not been included in this example and will be presented in the following examples. The pipeline endsboundary conditions are set to prevent the axial pipeline displacement and pipeline rolling. This exampleassumes the 2,500 m section of the pipeline is part of a longer pipeline route.

The wave velocity and hydrodynamic loads along the pipeline route are generated using the AGA (Ref.1) software assuming the wave heading direction is perpendicular to the pipeline route and consideringthe pipeline initial location, i.e. before any pipeline lateral or vertical displacements. The sea surface wasgenerated using the JONSWAP wave spectrum. It should be noted that the wave velocity and hydrodynamicloads at each pipeline node are different due to the wave spreading and the random numbers used duringgenerating the irregular wave. As recommend by DNV-RP-F109 to account for the random seed effect onthe pipeline lateral displacement, at least seven analyses with randomly chosen seeds should be performed.

For this example, ten pipeline simulation cases are performed using ten full generated sea-states withrandomly selected seeds. The final pipeline lateral displacements of the ten simulation cases are presented inFigure 5. As shown in the Figure, the average, minimum and maximum displacement values varies betweenthe ten simulation cases because of the change of the random seeds and random numbers used in generatingthe irregular sea-states. The average lateral displacement for the ten simulation cases varies between 10.23m and 14.06 m with an average value across all ten simulation cases of 12.48 m.

Figure 5—Pipeline Final Displacement – Ten Simulation Cases

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Detailed time history of the lateral displacements at three points along the pipeline route, at 500 m, 1250m and 2000 m, for the Seed 3 simulation case is presented in Figure 6. The detailed displacement timehistory presented in Figure 6 illustrates how the lateral displacement of different points along the pipelineroute varies with time as the hydrodynamic load changes. It is also shown in the graph that the lateraldisplacement of pipe node 251, at 1250 m, increased from about 8.20 m to about 12.10 m within a fewseconds around the 1550 s time period. To investigate this displacement further, the applied wave velocityand hydrodynamic loads are presented in Figure 7 to Figure 10 in blue lines. The actual pipe velocity andthe calculated hydrodynamic load corrections are also shown in Figure 7 to Figure 10 in red lines.

Figure 6—Pipeline Displacement Time History – Seed 3

Figure 7—Wave Velocity Time History

Figure 8—Drag Load Time History

Figure 9—Inertia Load Time History

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Figure 10—Lift Load Time History

As shown in the Figure 7, a peak wave velocity of about 1.1 m/s is formed around the 1550 s time period,which is almost double the value of the second highest wave velocity. Corresponding to this high wavevelocity value, high drag, inertia and lift loads are generated. During the dynamic simulation at the buildupof the wave velocity, the pipeline displaces laterally causing the pipe to gain velocity as shown by the red linein Figure 7 and as a result of this pipeline velocity, hydrodynamic load corrections are calculated and appliedduring the simulation (see the red lines in Figures 8 to 10). Correcting the pre-generated hydrodynamicloads by applying the hydrodynamic load corrections prevents the pipeline from experiencing larger un-realistic lateral displacement. It should be noted that every single pipe node during the dynamic simulationwill experience different time history of wave velocity, pipe velocity and hydrodynamic load corrections.

Sensitivity Simulation CasesThe base case simulation considering Seed 3 hydrodynamic loads is selected for the comparison purpose inthis section and to measure the sensitivity of the 3D simulation to the model input parameters.

Case 1 – Hydrodynamic load correction. To highlight the effect of the hydrodynamic load correction onthe final pipeline displacement, the base case example considering Seed 3 hydrodynamic loads is repeated,deactivating the hydrodynamic load correction due to pipeline displacement. Figure 11 shows the finallateral displacement results with and without the hydrodynamic load correction.

Figure 11—Pipeline Final Displacement W/WO Load Correction

As shown in Figure 11 the final pipeline displacement for the Seed 3 simulation without hydrodynamicload correction due to the pipeline displacement is almost four times the final pipeline displacement forthe same case with hydrodynamic load correction considered. The time history of node number 251 lateraldisplacement is shown in Figure 12. It is clear from Figure 12 that the points in time where the effect ofnot considering hydrodynamic load correction are most significant coincide with the points in time wherethe pipe velocity is significant in the base case, i.e. around the times 160, 420, 650, 1080 and 1550 s (seeFigures 7 to 10).

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Figure 12—Time History of Displacement W/WO Load Correction

Case 2 – Soil resistance modelling. The soil resistance in the base case simulations is modelled consideringpure Coulomb friction soil resistance term only appropriate for silica sand soil. To highlight the effect of thesoil resistance modelling on the on-bottom stability simulation results, the base case example consideringSeed 3 hydrodynamic loads is repeated three times to simulate the following soil resistance conditions: silicasand soil using Coulomb friction term and passive resistance term, calcareous sand soil using equivalent tri-linear Coulomb friction model and calcareous sand soil using Coulomb friction term and passive resistanceterm. Table 2 presents the soil models input data used in each of the simulation cases. It should be notedthat the soil model data for the last two cases are for the same calcareous soil sample.

Table 2—Soil Models Input Data

Item Silica SandCoulomb friction

Silica Sand Coulombfriction + Passive term

Calcareous Sand Tri-linear Coulomb friction

Calcareous Sand Coulombfriction + Passive term

Initial distance, passive term – 0.02D – 0.01D

Breakout friction – – 0.75 –

Breakout distance 0.50D 0.25D 0.25D

Residual friction 0.60 0.60 0.45 0.45

Residual distance – 1.00D 1.00D 0.75D

Results of the four simulations are presented in Figure 13. The results highlight the effect of the soilresistance model on the final pipeline displacement. For the silica sand soil cases, addition of the passiveterm reduces the maximum lateral displacement by approximately 30% relative to the base case. While forthe calcareous soil cases, the final lateral displacement is higher than the cases for silica sand soil. This resulthighlights the fact that the calcareous soil has less lateral resistance capacity than the silica sand soil. Thefinal lateral displacement of the tri-linear model is almost 10% higher than the final lateral displacement ofthe case with Coulomb friction term and passive resistance term. The vertical pipeline penetration at the endof the simulations is presented in Figure 14. As shown in the figure, the vertical penetration varies alongthe pipeline route due to the change in the hydrodynamic lift load distribution along the pipeline. Moreover,the vertical penetration for the calcareous sand soil cases is higher than the vertical penetration of the silicasand soil. While there is no record of the vertical penetration for the silica sand case with soil modelledusing pure Coulomb friction term.

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Figure 13—Pipeline Final Displacement – Soil Models

Figure 14—Pipeline Vertical Penetration – Soil Models

Case 3 – Operational pressure and temperature. Pipelines are more susceptible to displace laterallywhen the operational pressure and temperature are accounted for in the model. The base case exampleconsidering Seed 3 hydrodynamic loads is repeated including an operational pressure of 50 bar andoperational temperature of 70 C at start of the pipeline, length 0.0 m, and linearly reduced to 25 C at the endof the pipeline, length 2500 m. The ambient temperature used is 20 C. The final displacement of the base caseSeed 3 and the case considering the pressure and temperature is shown in Figure 15. It is clear from Figure15 that the final lateral displacement for the case with operational pressure and temperature is in generalhigher by approximately 25% than the case without operational pressure and temperature. The maximumtension force recorded during the simulation along the pipeline for both cases is presented in Figure 16. Asexpected the maximum tension values of the case with the operational pressure and temperature is higherthan the case without the operational pressure and temperature.

Figure 15—Pipeline Final Displacement W/WO Operational P&T

Figure 16—Pipeline Maximum Tension W/WO Operational P&T

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It should be noted that the axial forces, bending moments and section stresses can be extracted from thedynamic simulation program; however for the paper space limitation, the results of the axial forces onlywill be presented.

Case 4 – Pipeline end boundary conditions. To highlight the effect of the pipeline end boundarycondition effect on the pipeline displacement and tension loads, the base case example considering Seed3 hydrodynamic loads is repeated considering the pipeline is fixed at both ends. The final pipelinedisplacement and maximum tension loads are presented in Figure 17 and Figure 18. As shown in the figuresthe lateral displacement at the middle section of the pipeline has not been changed much. While the tensionload along the pipeline has increased by about 40% for the case with fixed pipeline end. Therefore, it isimportant to account for the pipeline's actual end constraints in the dynamic simulation to correctly estimatethe tension load and the pipeline stresses.

Figure 17—Pipeline Final Displacement

Figure 18—Pipeline Maximum Tension Loads

Case 5 – Pipeline route. One of the important aspects of modelling the pipeline in a 3D domain is toconsider the actual pipeline route rather than a simple straight route. To highlight the effect of considering thepipeline route on the on-bottom stability analysis, the base case example considering Seed 3 hydrodynamicloads is repeated considering a lateral offset of 350 m at the middle point of Seed 3 alignment and consideringa bend radius of 750 m as presented in Figure 19. For comparison purposes, the hydrodynamic loadsestimated for Seed 3 is used for the route 1 and route 2 simulations ignoring any hydrodynamic loadscorrection due to the change in the wave heading angle. The final pipeline displacements of the three casesare presented in Figure 20.

Figure 19—Pipeline Routes

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Figure 20—Pipeline Final Displacement

As shown from the results, the final pipeline lateral displacement changed significantly at the middlesection of the pipeline route. The effect at the pipeline's end location, 100 m or 200 m from each end, couldbe influenced by the pipeline end boundary conditions.

Case 6 – Flexible and rigid pipeline. To demonstrate the effect of pipeline axial stiffness and bendingstiffness on the pipeline on-bottom stability, the base case example considering Seed 3 hydrodynamic loadsis repeated with replacing the rigid pipe axial stiffness of (1.51E9 N) and bending stiffness of (8.21E6 N.m2)with a flexible pipeline axial stiffness value of (3.30E8 N) and bending stiffness value of (5.89E4 N.m2).The pipe self-weight, outer diameter and hydrodynamic loads are kept unchanged as per the base case data.The final lateral displacement results of the rigid and flexible pipeline cases are presented in Figure 21. Themaximum tension loads recorded during the simulation time is presented in Figure 22.

Figure 21—Pipeline Final Displacement

Figure 22—Pipeline Maximum Tension Loads

As shown in Figure 21, the predicted final displacement of the flexible pipeline case is higher than thefinal displacement of the rigid pipeline case by about 17% while the maximum tension force recordedfor the flexible pipeline is about 50% of the tension loads recorded for the rigid pipeline case. Therefore,disregarding the flexible pipeline properties in the on-bottom stability simulation may lead to conservativetension loads prediction and unconservative lateral displacements.

To further explore the effect of changing the pipeline axial stiffness and bending stiffness on the pipelinefinal displacement and tension load prediction, a test matrix of 20 simulation cases is performed consideringthe axial stiffness and bending stiffness combinations presented in Figure 23. The actual axial and bendingstiffness of the rigid and flexible pipeline cases are also shown in Figure 23. It should be noted that notall the test matrix cases represent real pipeline conditions; however, the test matrix cases are considered

OTC-27727-MS 17

acceptable for the purpose of this study to investigate the effect of the axial stiffness and bending stiffnesson the dynamic simulations. An example of the pipeline final lateral displacement for the cases with axialstiffness of 1.0E9 N is presented in Figure 24 while varying the pipeline bending stiffness.

Figure 23—Test Matrix Pipeline Stiffness

Figure 24—Pipeline Final Displacement – Varying EI Values

As shown in Figure 24 the change in the pipeline bending stiffness has a minor effect on the final pipelinedisplacement for all the cases except for the case with the highest bending stiffness of 1.0E8 N.m2. Thisbehaviour is expected to be a result of the bending stiffness being sufficiently high to redistribute thehydrodynamic loads along a sufficient axial length of the pipeline leading to a more stable pipeline. Asshown in the figure, the maximum lateral displacement of the case with bending stiffness of 1.0E8 N.m2

is 13.55 m which is about 84% of the maximum displacement value of the case with the bending stiffnessof 1.0E4 N.m2.

Figure 25 presents the maximum lateral displacements of all the test matrix cases. While Figure 26presents the maximum tension forces recorded along the pipeline route during the simulation.

Figure 25—Pipeline Maximum Displacement

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Figure 26—Pipeline Maximum Tension Loads

As shown in Figure 25 the maximum lateral displacement along the pipeline at the end of the simulationdecreases with the increase of the pipeline bending stiffness and axial stiffness. However, the effect of theincreasing the axial stiffness is much higher than the effect of increasing the pipeline bending stiffness onthe final pipeline displacement. For example the cases with pipeline bending stiffness of 1.0e8 N.m2, themaximum lateral displacement for the case with axial stiffness 1.0E7 N is about 21 m which is almost doublethe maximum lateral displacement of the case with axial stiffness 1.0E10 N. As shown in Figure 26, themaximum tension loads along the pipeline are much higher for the cases with high axial stiffness values.

Case 7 – Wave boundary layer. For small diameter pipelines, 10 cm diameter or less, or cables the2D stability method of DNV-RP-F109 (Ref. 3) provides unrealistic pipe specific gravity requirement. Asdiscussed in Cheng et al. (Ref. 2) it has been speculated that the exclusion of the wave boundary layer effectis attributing to the unrealistic prediction of the required pipeline specific gravity. Considering the waveboundary layer Equations 15 to 18, the wave velocity acting on the pipeline can be estimated accountingfor the seabed material roughness height. To highlight the effect of the wave boundary layer, the reducedwave velocity is calculated for a wave velocity of 0.5 m/s and wave period of 10 s. The example consideredfour different seabed materials and considered pipe outer diameter values of 2.54, 5, 10, 20 and 40 cm. Asshown from the reduced wave velocity results presented in Figure 27, the boundary layer has significanteffect for the cases with small diameter pipelines and for the cases of rough seabed material.

Figure 27—Wave Velocity Considering Boundary Layer

Figure 28 presented an example of the required pipeline specific gravity to achieve the DNV-RP-F109Absolute stability requirement for different pipeline outer diameters under peak wave velocity of 0.5 m/s and wave period of 10 sec without considering the wave boundary effect. The figure also presents therequired specific gravity requirement for the same pipeline case considering the wave boundary effect forthe four different seabed materials.

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Figure 28—Pipeline Specific Gravity for Absolute Stability

To highlight the effect of the wave boundary layer on the dynamic stability simulation, the hydrodynamicloads are generated for a 2.54 cm outer diameter cable in 50 m water depth. A submerged weight of 11 N/m and tension capacity 220 kN are considered. The specific gravity of the cable is 3.14. The metocean dataare as per the base case data (Table 1). Two cases have been simulated with and without considering thewave boundary layer effect. The final cable displacement and maximum tension load results from the twosimulation cases are presented in Figure 29 and Figure 30, respectively.

Figure 29—Cable Displacement W/WO Boundary Layer

Figure 30—Cable Maximum Tension Loads W/WO Boundary Layer

As shown in the figure, the cable is predicted to experience significant lateral displacement of about61.0 m for the case ignoring the wave boundary layer effect. When the wave boundary effect is taken intoaccount, the maximum predicted cable displacement along the cable route is about 1.2 m.

As DNV-RP-F109 (Ref. 3) states "It is not recommended to consider any boundary layer effect on thewave induced velocity", consideration of this effect should be used with caution.

ConclusionThis paper discusses the on-bottom stability analysis of submarine rigid and flexible pipelines, umbilicalsand cables in the light of recommended practice DNV-RP-F109. The limitations of the current recommendedpractice 2D design methods are first addressed before presenting the 3D dynamic analysis modelling tool.

Using 3D modelling, the pipeline designer can perform more reliable and cost effective on-bottomstability design. The pipeline designer can define the important analysis parameters such as the pipelineaxial stiffness, bending stiffness, material nonlinearity, the actual pipeline route, the pipeline end conditions,

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the operational pressure and temperature and the soil resistance models etc. The limitations of the 2D on-bottom stability design methods of DNV-RP-F109 and the advantages of performing the 3D dynamic on-bottom stability modelling are highlighted with the results of the dynamic stability simulation examples.

Based on the results of the simulation analyses presented in the paper, the following conclusions canbe drawn:

• The dynamic stability simulation should account for the effect of the random seed and randomnumbers used in generating the sea-states. As presented in the simulation section, the finalpipeline displacement will vary along the pipeline route due to the change in the random seed. Asrecommended by DNV-RP-F109, at least seven analyses with randomly chosen seeds should beperformed.

• The hydrodynamic loads acting on the pipeline should be corrected during the simulation to accountfor the experienced pipe velocity and or vertical penetration. Uncorrected hydrodynamic loads willlead to overly conservative predictions of pipeline lateral displacement.

• The soil resistance including the pure Coulomb friction term and passive resistance term shouldbe modelled in the on-bottom stability analysis. Moreover, the soil resistance model used inthe analysis should correctly represent the soil conditions in the field. The pipeline is shown tohave different lateral displacement behaviour under the same metocean loads with changing soilresistance model.

• The pipeline operational pressure and temperature should be included in the on-bottom stabilitymodel as the pipeline is more susceptible to displace laterally when the operational pressure andtemperature are accounted for. Moreover, the predicted pipeline maximum tension forces andstresses are higher when the operational pressure and temperature are considered.

• Special consideration should be given to modelling the pipeline end conditions and the pipelineactual route. The pipeline is shown to experience higher tension loads when the pipeline ends arerestrained. Furthermore, the full pipeline route including the correct end restraints and any changein the route heading should be included in the model to correctly estimate the pipeline lateraldisplacement and the maximum tension forces.

• The pipeline axial stiffness and bending stiffness have significant effect on the pipelinedisplacement and the maximum tension loads. Therefore, for flexible pipelines, umbilicals andcables the Generalised stability method of the recommended practice DNV-RP-F109 may lead tounconservative on-bottom stability designs as the displacement of a flexible pipeline or cable (withlow axial stiffness) could be higher than the displacement of a similar rigid pipeline.

• The wave boundary layer affects the wave velocity in the vicinity of the seabed. The recommendedpractice DNV-RP-F109 does not provide any guidelines on the wave velocity calculations forsmall diameter pipelines or cables. Ignoring the effect of the wave boundary layer in on-bottomstability analysis of small diameter pipelines or cables can lead to overly conservative designresults. However, caution needs to be exercised in implementing the effect of the wave boundarylayer effect in the design as it is not listed in the recommended practice.

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