Randolph White OTC 19128

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OTC 19128-PP

Pipeline Embedment in Deep Water: Processes and QuantitativeAssessmentMark F. Randolph and David J. White, Centre for Offshore Foundation Systems, University of Western Australia

Copyright 2008, Offshore Technology Conference

This paper was prepared for presentation at the 2008 Offshore Technology Conference held in Houston, Texas, U.S.A., 5–8 May2008. 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 of the paper have not beenreviewed by the Offshore Technology Conference and are subject to correction by the author(s). The material does not necessarily reflect any position of the Offshore Technology Conference, itsofficers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Offshore Technology Conference is prohibited. Permission toreproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of OTC copyright.

AbstractThe paper outlines the processes that determine pipeline embedment in soft sediments typical of deep water, and describesquantitative methods for assessing the contribution to pipeline embedment from each process. The main processes consideredare: self-weight, force concentration during installation, and cyclic lateral and vertical motion during pipe-laying. For eachprocess, non-dimensionalized solutions are provided to evaluate embedment for given pipeline and soil properties, anddifferent conditions operative during pipe-laying. Methods to establish a penetration resistance profile using modernpenetration testing techniques are described, and the up-scaling of these measurements to pipeline behavior is discussed. Theimportant effects of heave and soil self-weight are also quantified, and the effects of remolding and subsequent reconsolidationfollowing a cyclic event are also demonstrated. Finally, the influence of cyclic motion within the touchdown zone duringpipe-laying is explored. Examples of numerical and physical modeling of the lay process show that these dynamic effects canhave a dominant influence on the as-laid embedment. Approaches for quantifying this aspect of behavior in design arediscussed.

IntroductionEngineering design of a pipeline in respect of external interactions, such as stability, lateral buckling, axial friction, heattransfer and exposure to submarine slides, requires an assessment of the as-laid pipeline embedment. In deep water, pipelinesare commonly laid on the seabed without specific actions directed at embedding the pipeline, and without additional overlyingprotection. As such, embedment or partial penetration of the pipeline into the seabed is a function of the self-weight of thepipeline relative to the strength of the seabed, but is complicated by the laying process, which leads to enhanced contactstresses in the region where the pipeline meets the seabed (the so-called touchdown zone), and during which dynamic motionof the lay vessel and suspended part of the pipeline can lead to significant additional penetration as the seabed soils areremolded locally.

It is necessary to bound the pipeline embedment, and hence the anticipated axial and lateral pipe-soil resistance, in order toensure a safe design. It is not possible to adopt ‘conservative’ extreme design values, since low and high resistance can workfor or against a particular design consideration, depending on the limit state under consideration. For example, the different

influences of high and low pipe-soil interaction forces on the phenomena of buckling and walking are summarized by Brutonet al. [1]. Another example where embedment has a conflicting influence on design requirements is stability versus thermallosses. High embedment and therefore high lateral resistance improves on-bottom stability. However, it also reducesconvective heat losses, leading to higher operating temperatures distant from the wellhead, and therefore greater thermalexpansion.

The feasibility of a particular design solution is strongly affected by the design values for pipe-soil interaction forces. If acontrolled lateral buckling solution cannot be adopted to accommodate the thermal pipeline loading, then alternative solutionsof seabed anchors or expansion spools are required. These devices increase the installation cost of the pipeline significantly,since additional construction processes and seabed interventions are needed. In a recent development offshore West Africa, itwas found that significant cost savings, in excess of US$50 million, could arise for the pipeline system from relatively minorrefinements of the design parameters for pipe-soil interaction. Improved methods are necessary to raise the reliability of thesedesigns in marginal cases, enhancing the viability of offshore hydrocarbon developments in deep water.

The lateral resistance that the pipeline has to overcome during buckle initiation depends strongly on the embedment.

Accurate prediction of the as-laid pipeline embedment is the greatest challenge during the assessment of buckling behavior,


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and is the parameter that most significantly affects the feasibility of a design [1]. Empirical and theoretical solutions forpredicting pipeline embedment are available, but are consistently found to under-estimate the embedment when compared withfield survey data, primarily due to additional penetration caused by the static load concentration at the touchdown point, anddynamic oscillations of the pipeline as it is laid [2].

This paper examines recent developments in estimating pipeline penetration, including theoretical studies based on largedeformation finite element analysis, and physical model tests to evaluate the effect of cyclic deformations on pipelinepenetration.

Seabed CharacterizationImproved reliability in estimating pipeline penetration hinges on accurate measurement of the shear strength profile,particularly in the upper 0.5 m of the seabed. Techniques to achieve this include: (a) in situ testing; (b) ship-based vane orpenetrometer tests in box-cores recovered from the seabed; (c) laboratory tests on samples obtained from the seabed. All suchmeasurements become more challenging in very soft sediments, either because of disturbance to the recovered samples or, forthe in situ testing, due to minor errors in the depth datum or load cell zero readings, both of which become much moresignificant at shallow depths and low strength material.

Modern techniques for obtaining large diameter piston cores have led to improvement in sample quality over most of thesample length [3,4], but any slight delay in triggering the piston of gravity corers will lead to gross disturbance of the veryshallow soils, and also to uncertainty in the depth datum [5]. The development of a static sampler activated from a fixed frame[6] should lead to further improvement, provided the shallow material has sufficient strength to allow samples to be preparedfor laboratory testing.

Box-corers have been used for a number of years, particularly to obtain bulk samples of the upper 0.5 m of the seabed forgeochemical testing, but strength testing within box-core samples has typically been limited to a few hand-held or motorizedvane tests. Development of a manually operated penetrometer, the DMS [5,7], provides the ability to obtain continuousprofiles of penetration resistance, using miniature full-flow (T-bar or ball) penetrometers. In addition, cyclic penetration andextraction allows assessment of the soil sensitivity, which is directly relevant for assessing dynamic effects during the pipelinelay process. More extensive use of ship-based penetrometer testing in box-cores is recommended as a means of improvedassessment of pipeline embedment.

In situ testing provides the best potential to obtain accurate assessment of the shear strength profile, or more specificallythe penetration resistance profile, in the uppermost sediments. Full-flow penetrometers such as the cylindrical T-bar andspherical ball may be viewed as model elements, and the penetration resistance data may be used directly in assessing thepenetration resistance of pipelines or risers. Their advantage, relative to a conventional cone penetrometer, lies in the muchsmaller corrections required for (a) pore pressure acting behind the penetrometer head and (b) overburden stress [5,8].However, a number of steps are necessary in order to ensure accuracy in the measured data:

1. The penetrometer must remain above the mudline once the seabed frame has stabilized on the seabed, with visualevidence (provided visibility allows this) used to supplement load cell readings in assessing a true depth datum.

2. Any load cell drift or zero offset should be monitored for a period prior to advancing the penetrometer into the seabed,in order to ensure full temperature equilibration; this should be repeated following extraction of the penetrometer.

3. At least one, but preferably more, cyclic penetration and extraction tests should be carried out during everypenetrometer test, as a further check on the accuracy of the load cell zero [5]; typically 5 to 10 cycles are required toremold the soil fully, over a minimum cyclic range of three times the penetrometer diameter.

A more detailed set of recommendations emerged from a joint industry project conducted in collaboration between theNorwegian Geotechnical Institute and the Centre for Offshore Foundation Systems [9]. That project assembled a largedatabase of offshore and onshore penetrometer data, together with corresponding data from laboratory tests on high-qualitysamples. Statistical analysis of the data led to recommended empirical correlations between penetration resistance and theshear strength measured in different testing modes, and these were supplemented by numerical studies. The latter allowedquantification of the separate effects of the high strain rates associated with in situ testing, and the gradual softening thatoccurs as soil flows past the advancing penetrometer. Publications are being prepared to disseminate the results of the project.

Results of in situ full-flow penetrometer tests may be interpreted in terms of a shear strength profile, using a penetrometerfactor, Nk , which is typically taken as about 11 for T-bar or ball penetrometers. Some adjustment is appropriate to allow fornear surface effects, which will generally not extend below 3 to 5 diameters (120 mm to 200 mm for a standard 40 mmdiameter T-bar). Alternatively a T-bar may be viewed as a model pipeline segment, thus providing a direct estimate of theresistance profile in the upper meter of the soil to assess pipeline embedment. Again, though, the difference in scale betweenthe T-bar of 40 mm diameter, and a typical pipeline with diameter in the range 0.2 m to 0.8 m, needs to be considered. Testingat different scales, for example with a T-bar and a small pipeline segment (as in the Smartpipe development [10]), can providean effective means of refining estimates of pipeline penetration resistance at shallow depths.

Cyclic Remolding. The effects of cyclic remolding, which may be achieved through penetration and extraction cycles of full-flow penetrometers, are particularly relevant for assessing dynamic lay effects for pipelines. The reduction in penetrationresistance as the soil is remolded will be less than the reduction in the soil strength itself, partly due to the partial softening thatoccurs already during the initial penetration and partly due to changes in the flow mechanism [5,11]. As such, the final


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remolded penetration resistance is more directly relevant for considering dynamic effects on pipeline embedment thansubstituting of the remolded soil strength into solutions for static penetration.

There are two further complications, which affect the change in strength during cyclic penetration: water entrainment (andconsequent swelling), and re-consolidation between cyclic events. Water can be gradually entrained as the pipeline remoldsthe soil, or when a penetrometer emerges then repenetrates the surface. This entrainment leads to further remolding andsoftening, as the moisture content of the soil increases. This is illustrated in Fig. 1 for a cyclic T-bar test where the T-bar isbrought right to the mudline with each cycle, thus allowing access to free water. Softening at (approximately) constant water

content appears to occur over the first few cycles, but then the penetration and extraction resistance starts to degrade further,with a linear gradient (see cycles 7 to 11 in Fig. 1b). Such behavior would occur almost from the start for a pipelineundergoing dynamic motion, leading to greater embedment than might be estimated without allowing for the local increase inwater content of the soil.

The remolding process tends to generate positive excess pore pressures in normally consolidated (or lightly-overconsolidated) soils. The initial laying of a pipeline is likely to be sufficiently fast for this reconsolidation to be neglected.However, the touchdown zone of a catenary riser may be subjected to cyclic motion only during storm events, and so the pipe-soil interaction involves episodes of cyclic motion interspersed with intervals of reconsolidation.

0

0.1

0.2

0.3

0.4

0.5

0.6

-100 -50 0 50 100 150

qTbar (kPa)

D e p

t h ( m )

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1 2 3 4 5 6 7 8 9 10 11 12

Cycle number

D e g r a d a t i o n f a c t o r

(a) Cycles of T-bar penetration and extraction (b) Degradation of resistance with cycles

Fig.1 Cyclic miniature T-bar penetrometer test in a box core sample

(a) Effect of remolding and re-consolidation on strength (b) Degradation of resistance over two episodes of cycling [12]

Fig.2 Cyclic strength behavior, with intervals of reconsolidation


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The dissipation of positive excess pore pressure leads to the expulsion of water and therefore a reduction in moisturecontent and a rise in undrained strength. This behavior is illustrated schematically in Fig. 2a on axes that are used to describethe critical state framework of soil strength. The reconsolidation process leads to a reduction in moisture content and aconsequent increase in the ‘critical state’, or remolded strength.

Soil strength measurements that match this pattern of behavior are shown in Fig. 2b. These results are from a cyclic T-barpenetrometer test conducted in the UWA geotechnical beam centrifuge [12]. The test involved an initial phase of cyclicremolding, followed by a period of reconsolidation during which the excess pore pressures generated by the initial cyclic

episode were permitted to dissipate. The post-consolidation remolded strength exceeded the initial value by 50%. Subsequentphases of re-consolidation led to further increases in remolded strength.

This observation implies that estimates of vertical pipe-soil stiffness – for example to assess the touchdown response of acatenary riser – cannot be assumed to remain low after an initial phase of remolding. Although experimental observationsshow that dramatic softening occurs during cyclic riser motion [13], reconsolidation of the seabed can raise the stiffnesssignificantly. Experimental data is needed to explore this type of behavior. This may be achieved through laboratory floor orcentrifuge model tests conducted in reconstituted samples of seabed soil, or may be undertaken in the field throughsophisticated apparatus such as the Smartpipe development [10]. The waiting period required for re-consolidation around alarge-scale model pipe is likely to be prohibitive for tests conducted at the seabed, but the reduced size of the T-barpenetrometer means that episodic cyclic penetrometer tests can be completed in the same duration as a sequence of monotonicpipe-soil interaction tests. The general mechanisms of remolding and re-consolidation are similar for pipes and penetrometers.Current projects that rely on accurate prediction of as-laid pipeline embedment to underpin analyses of lateral bucklingtypically involve a blend of laboratory, centrifuge and in situ testing techniques to evaluate pipe-soil interaction.

Static Penetration ResistanceExisting methods to estimate pipeline embedment may be grouped into empirical correlations and theoretical solutions. In both

approaches, the key parameters are the shear strength, su, and effective unit weight, γ ', of the soil, the pipeline diameter, D, andthe vertical force (per unit length), V, imparted by the pipeline to the seabed. Verley and Lund [14] fitted data from a varietyof industry studies, expressing the normalized (static) pipeline penetration, w/D, in terms of two dimensionless groups, as:

7.03.0

u

2.33.0

u

GDs

V06.0G

Ds

V007.0

D

w

+

= (1)

where G was given as su / γ sD, with γ s being the (saturated) unit weight of the soil. Neither the form of this empirical fit, nor the

use of saturated unit weight, γ s, rather than the effective unit weight, γ ', have any theoretical logic.Comparison of this expression with upper and lower bound plasticity solutions [15] showed that the empirical fit gave

much higher pipeline penetration for normalized loads V/Dsu less than about 3 [16]. The plasticity solutions were laterextended for more general linear variations of shear strength with depth using finite element analysis [17], and showed that thenormalized load was best expressed in terms of the shear strength at the pipeline invert, su,invert. The limiting load at a givenpenetration was then expressed as

b

invert,u D

wa

Ds

V

= (2)

Fitted values of the power law parameters, a and b, depended primarily on the relative roughness of the pipe-soil interface, and

to a lesser extent on the strength homogeneity parameter, ρD/sum (where ρ is the strength gradient and sum is the mudlinestrength). Values of the coefficients, a and b, in Eq. 2 that gave a reasonable fit to the numerical results throughout the range of

ρD/sum, are summarized in Table 1.

Table 1. Power law coefficients [17] Table 2. Pipeline penetration [18]

Interface condition w/D ≤ 0.5 w/D > 0.5Smooth a = 4.97, b = 0.23 a = 4.88, b = 0.21

Rough a = 6.73, b = 0.29 a = 6.15, b = 0.15

Relationship Parameters

g

uDs

Vf

D

w

=

15

Sf t= , g = 2

A similar expression to Eq. 1, but re-arranged to give w/D directly, was proposed by Bruton et al. [18] on the basis ofexperimental data gathered during the SAFEBUCK joint industry project. The expression and parameters are given in Table2, with St being the sensitivity of the soil. Comparing the two expressions, it may be observed that the empirical fit givessignificantly greater penetrations, as acknowledged [18]. Thus even taking a sensitivity of unity, a normalized load ofV/Dsu = 2 would lead to a penetration of 0.27D, whereas Eq. 2 would give penetrations of around 0.02D. The discrepancy

between the empirical fit (which was calibrated against experimental data) and the plasticity solutions can be attributed to:


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(i) unreliable quantification of the undrained strength at shallow depths in the experimental data; and (ii) additionalembedment being present in the experiments, through consolidation and lay effects (which are described later in this paper).Recent high quality experimental data of static penetration resistance, when back-analyzed using undrained strength data fromminiature T-bar penetrometers, generally lie close to the theoretical solutions [19-21].

For design, it is suggested that the theoretical solutions should form the basis for estimating the static penetrationresistance, adopting rounded values of the power law coefficients, for example assuming a = 6, b = 0.25. As noted below,however, it is important to consider the pipeline buoyancy relative to the soil, allowing for the effect of local heave, which will

tend to give additional buoyancy.

Heave Effects. As the pipeline penetrates into the soil, it will become increasingly buoyant, due to the higher density of theseabed sediments relative to seawater. If heave is ignored, the correction for this buoyancy would be to reduce the submerged

weight by an amount γ 'As, where γ ' is the effective unit weight of the soil and As is the (nominal) area of the pipe lying belowmudline level. The latter may be expressed as

( )( ) ( ) ( )[ ]ŵ1ŵŵ212ŵ1ŵ4sin4

DA 1

2

s −−−−=− (3)

where ŵ is the normalized penetration, w/D. The effect of local heave will be to enhance this buoyancy effect by some factor,

f b, so that the penetration resistance becomes

invert,u2sb

b

invert,u sD

DAf

Dwa

DsV γ ′+

= (4)

This may also be expressed in terms of more familiar bearing capacity factors as [22]

Dw

Af Nand

D

waN where

s

wNN

Ds

V sbb

b

cinvert,u

bcinvert,u

=

=

γ ′+= (5)

Illustrations of heave calculated from large deformation finite element analyses, comparing results from two different softwarepackages [23] are shown in Fig. 3. The maximum height of heave, relative to the original seabed, is just over 50 % of the(nominal) pipeline penetration. Although the additional soil above the mudline has little effect on the penetration resistanceterm, Nc, the buoyancy effect is increased significantly by the heave, and should not be neglected in the calculation of totalvertical resistance. Example resistance curves are shown in Fig. 4, where results from large deformation finite element (LDFE)

analyses [23] are compared with resistance curves obtained using Eq. 5. A buoyancy factor of f b = 1.5 is needed to match theLDFE results (corresponding to a value of Nb ∼ 1 at w/D = 0.5), with the buoyancy resistance then representing up to 16 % (atan embedment of 0.5D) of the total resistance.

A further important implication of heave is that the ‘local’ embedment of the pipe relative to the adjacent soil surface(i.e. point A on Fig. 3) may be significantly greater than the ‘nominal’ embedment relative to the original soil surface. Thenominal embedment is conventionally used in analysis of vertical and lateral resistance, but when considering the thermalinsulation and axial sliding resistance of the pipe, the pipe-soil contact length is the relevant parameter, which is related to thelocal embedment. It may also be more logical to consider the level of exposure to debris flows and turbidity currents in termsof the local embedment, although erosion and scour may alter both the local and nominal embedment over time. Neglecting

erosion and scour, the local pipe embedment typically exceeds the nominal embedment by ∼50% due to heave [19,22,23].

0.0

0.1

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0.5

0 1 2 3 4 5 6

Normalised vertical resistance, V/Dsu,invert

E m b e d m e n t , w / D

LDFE (ABAQUS)

LDFE (AFENA)

Buoyancy

(f b = 1)Nc term

(a = 6, b = 0.25)

Total resistance

(f b = 1.5)

Input data

ρD/sum = 1.25; γ 'D/sum = 2.26;

τinterface = 0.3sum

Fig. 3. Deformation pattern at w/D = 0.45 Fig. 4. Penetration resistance curves


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Lateral Motion. The effects on penetration of dynamic motion of the pipeline during laying are discussed later in the paper,but it is worth noting here that any lateral movement of the pipeline will generate lateral resistance, and hence a decrease in theavailable penetration resistance due to the interaction between vertical and horizontal capacity. Yield envelopes for pipelinesunder combined horizontal and vertical loading indicate that the vertical capacity during steady lateral displacement isapproximately half the vertical capacity during purely vertical motion [24]. This feature alone would lead to a significantincrease in predicted penetration, essentially computing the penetration by taking a = 3 (rather than 6) in the Nc term in Eq. 5.

Cyclic Vertical Motion. The component of vertical resistance due to buoyancy is significant if the soil becomes heavilyremolded, raising the ratio γ′w /su which controls the relative contributions of the strength and buoyancy terms in Eq. 5. Thestrength profile after heavy remolding near the soil surface is typically 0.5 kPa/m in centrifuge experiments using kaolin clay.

This gradient implies a ratio γ′w /su in the range 5 – 10. In this case, the majority of the vertical resistance arises frombuoyancy rather than soil strength. Since buoyancy always acts upwards on the pipe, whereas the soil strength contributionopposes motion, there is always a compressive reaction between the pipe and the soil during shallow vertical cyclic motion, asillustrated in Fig. 5 [12]. This response contrasts with the models commonly used for cyclic vertical pipe motion, for examplein the analysis of catenary risers, which assume that the soil exerts a downwards reaction on the riser during upwards motion.

Fig. 5. Buoyancy-dominated vertical cyclic response at shallow pipe embedment [12]

Lay EffectsMechanisms of Pipeline Embedment. Observations show that the as-laid pipeline embedment is typically much greater thanwould be expected from the static weight alone in combination with the solutions for penetration resistance described above.The additional embedment results from two mechanisms: stress concentration at the touchdown point, and cyclic embedmentdue to dynamic effects.

During pipe laying, whether by J-lay or S-lay, the contact stresses (or vertical force per unit length) between the pipe andthe soil in the vicinity of the touchdown point will exceed the submerged self-weight of the pipe and any contents. The degree

of ‘over-stress’ is affected by the water depth, the stiffness of the seabed, the bending rigidity of the pipeline and the effectivetension in the pipeline in the touchdown zone. Parametric solutions for the static lay conditions are discussed below.The second process that creates additional pipe embedment is the dynamic movement of the pipe within the touchdown

zone, driven by the vessel motion and hydrodynamic loading of the hanging pipe. These loads will induce a combination ofvertical and horizontal motion of the pipeline at the seabed [2,16]. In addition to vessel motion due to swell and waves at thesea surface, cyclic changes in tension may occur if the offloading of the pipe is not smoothly coincident with advancing the layvessel. The changes in tension will result in changes in the touchdown point and cycles of vertical motion of the pipeline atthe seabed in the touchdown zone. Any cyclic movement of the pipeline during laying will lead to local softening of theseabed sediments. In particular, any lateral motion will push soil away to either side of the pipe alignment, creating a narrowtrench in which the pipe becomes embedded. The net effect can lead to pipeline penetration that is an order of magnitudegreater than estimated from static loading, even allowing for over-stressing during the lay process.

It is common to assess the separate effects of the touchdown stress concentration and the dynamic touchdown motion byapplying multiplicative adjustments to the static embedment approach described previously [12, 18]. The as-laid pipe weight,

p, is multiplied by a concentration factor due to the catenary shape, f lay, to yield the maximum anticipated vertical force


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between the pipe and the soil, f layp. This maximum touchdown load is then used in a conventional bearing capacity type ofcalculation to assess the pipe embedment, wstatic, based on the anticipated maximum static touchdown load. Dynamic layeffects are then accounted for by multiplying wstatic by a dynamic touchdown factor, f dyn, to finally reach the predicted as-laidembedment, allowing for lay effects [18].

This approach is common practice, but necessarily empirical. Typical values of f dyn lie in the range 2 – 10, based oncomparisons between as-laid surveys and static embedment calculations, for pipes laid in relatively shallow water (< 500 mdepth) [2]. The additional lay-induced embedment in exceedence of wstatic depends on the details of the lay process and the

response of the seabed to the imposed cyclic loading. New approaches to capture these lay processes for design calculationsare needed to reduce this wide uncertainty, by providing a more robust basis for assessing f dyn.

Non-Dimensional Solutions for Static Conditions. Solutions for the suspended shape of a pipeline during laying, togetherwith key design data such as maximum bending moments and shear force, and the local contact force at the touchdown point,have been obtained analytically, albeit with some approximations, or through numerical analysis. Most analytical solutions arebased on what is referred to as a boundary-layer approach, whereby the main portion of the hanging pipeline is treated as acatenary, while separate solutions are developed for the region close to, or in contact, with the seabed where the effects of thebending stiffness become important [25-28].

Figure 6 shows a schematic of the pipeline during laying. Following Pesce et al. [26] it is useful to introduce non-

dimensional groups of the controlling parameters, the most important of which is the characteristic length, λ. This isexpressed as:

0TEI=λ (6)

where EI is the bending rigidity of the pipeline and T0 is the horizontal component of the effective tension in the pipeline; asfor any catenary, T0 is constant throughout the suspended section of the pipeline, and thus equal to the tension at thetouchdown point (where the pipeline is close to horizontal). The pipeline diameter itself does not affect the solution directly(other than through EI), and the remaining parameters are the submerged pipeline weight (per unit length), p, the water depth,

zw, the lay angle, φ, and an equivalent seabed stiffness, k. Note that zw need not be the actual water depth (for example, where

an S-lay configuration is used), but should be consistent with the angle, φ, at a point on the suspended pipeline where thebending moment is small. The standard catenary solution relates these geometry parameters to the tension, T0, by

φ−

φ=

cos1

cos

pz

T

w

0 (7)

φ

zw

Pipeline: Diameter, D;

Bending rigidity, EI

Submerged weight, p

Tension, T0Seabed: Stiffness, k

Sea surface

See expanded

view

φ

zw



Submerged weight, p


Sea surface

See expanded

view

φ

zw



Submerged weight, p


Sea surface

See expanded

view

Tension, T0

Seabed

Pipeline

Touchdown region

Peak contactforce, V

Tension, T0

Seabed

Pipeline

Touchdown region

Peak contactforce, V

(a) Complete pipeline (b) Expanded view of touchdown region

Fig. 6 Schematic of static pipeline configuration during laying

The extent to which the pipeline behaves as a catenary, and also the accuracy of the boundary-layer solutions such as

described by Lenci and Callegari [28], may be quantified by the dimensionless group, T0 / λp, which is expressed directly interms of the water depth and lay angle as

2 / 12 / 3

w0

EI

pz

cos1

cos

p

T

φ−

φ=

λ (8)


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For typical pipelines, with diameters of 0.2 to 0.7 m, values of T0 / λp will rarely fall below 3 except in shallow water (less than

500 m) or very steep angles (greater than 85 degrees). As will be illustrated later, for T0 / λp ¥ 3, the maximum shear force in

the pipeline, and contact force in the touchdown zone, become essentially independent of T0 / λp, and key performance data canbe estimated with good accuracy from analytical solutions or simple expressions.

The maximum bending moment in the pipeline occurs in the suspended part of the pipeline at some distance from thetouchdown point, and is independent of the seabed stiffness [26]. The maximum bending moment can be expressed in non-

dimensional form as Mmax / λ2p, and is shown as a function of the normalized pipeline tension at the mudline, To / λp, in Fig. 7.

The analytical solution of Lenci and Callegari [28] is compared with numerical results obtained with the commercial software,

OrcaFlex [29], with close agreement obtained for values of T0 / λp ¥ 1. An approximate fit to the analytical and numericalsolutions is given by

( ) 9.002max

p / T1

11

p

M

λ+−≈

λ (9)

This expression is sufficiently accurate for use in assessing extreme stresses in the pipeline wall during the lay process.

0

0.10.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.1 1 10 100 1000

Normalised pipe tension, T0 / λp

M a x i m u m m o m e n t , M

m a x

/ λ 2 p

Analytical solutionNumerical (OrcaFlex)

Curve fit

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.1 1 10 100 1000 10000

K0.5

= λ(k/T0)0.5

M a x i m u m s h e a r , S

m a x

/ λ p Curve fit

OrcaFlex

Analytical

solution

(T0 / λp ≥ 10)

T0 / λp =

0.3

1

3

0.1

Fig. 7 Maximum moment in suspended pipeline Fig. 8 Maximum shear force in touchdown zone

1

10

100

1 10 100 1000 10000

K0.5

= λ(k/T0)0.5

M a x i m u m c o n t a c t f o r c e , V

m a x

/ p

Analytical

solutions

(T0 / λp ≥ 10)

Curve fit

T0 / λp = 0.10.31

OrcaFlex

results

0

0.5

1

1.5

2

2.5

3

-50-40-30-20-100

Horizontal distance (m)

N o r m a l i s e d c o n t a c t f o r c e ,

V / p

Water depth 500 m

Water depth 2000 m

Seabed stiffness 100 kPa

Seabed stiffness 10 kPa

Fig. 9 Maximum contact force in touchdown zone Fig. 10 Example profiles of contact force

The maximum contact force (per unit length), Vmax, in the touchdown zone, and the associated peak shear force, Smax, inthe pipeline are affected primarily by the seabed stiffness, k, expressed as the ratio of contact force, V, to penetration, w.During initial penetration, the appropriate value of k should be determined as a secant stiffness, allowing for plasticpenetration, and will therefore be much lower than customarily used for fatigue assessment during the operational life of thepipeline. For soft, lightly over-consolidated, seabed sediments, with a small strength intercept and a strength gradient of 1 to2 kPa/m, the relevant value of k may be as low as 10 kPa. By contrast, for sandy conditions or where there is a significantstrength intercept at the mudline, the stiffness may be 2 orders of magnitude higher.


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The appropriate non-dimensional stiffness may be expressed as [26]:

02 T / k K λ= (10)

For normalized pipeline tensions of T0 / λp ¥ 3, the maximum shear force, Smax, becomes independent of T0 / λ and may beapproximated as:

( )[ ] 5.1K10log4.0maxe1p

S −−≈λ (11)

A comparison of this expression with results from OrcaFlex and the analytical solution of Lenci and Callegari [28] is shown in

Fig. 8, with results for high T0 / λp coalescing into a single curve.Corresponding results for the maximum normalized contact force, Vmax /p (equivalent to f cat) are shown in Fig. 9. As for the

shear force, the analytical and OrcaFlex solutions coalesce (to each other, and to a single curve) for values of T 0 / λp greaterthan 3. The resulting (normalized) maximum contact force may be approximated as:

( ) 25.00225.0max T / k 4.06.0K4.06.0p

Vλ+=+≈ (12)

It is helpful to consider the likely practical range of Vmax /p for water depths in the range 500 to 2000 m, assuming submergedpipe weights of 1 to 1.5 kN/m and a lay angle of 83 degrees. From Eq. 7, the range for T0 is then 70 to 420 kN. For typical

values of bending rigidity, based on a pipeline diameter to wall thickness ratio of 20 and pipeline diameters of 0.3 to 0.61 m,the corresponding values of T0 / λp lie in the range from just below 3 to over 20. For a seabed stiffness of 10 kPa, thenormalized stiffness range is 6 to 450, but the range in Vmax /p is only 1.2 to 2.5. Increasing the seabed stiffness to 100 kPaleads to a corresponding range for Vmax /p of 1.7 to 3.9. Within these ranges, high normalized contact forces result from largediameter (assumed heavier) pipelines laid in shallow water, and vice versa. This is illustrated in Fig. 10, which shows exampleprofiles of contact force.

The reduction in lay factor, f lay = Vmax /p, in deep water means that the maximum static loading may occur during thehydrotest after laying the complete pipeline. However, penetration of the pipeline is still likely to be dominated by the layprocess, because of the combination of the static catenary contact forces and the dynamic effects due to cyclic pipeline motion.Estimating an equivalent seabed stiffness during initial penetration of the seabed, allowing for plastic deformation of the soil,is a key step in estimating f lay, and hence the static pipeline penetration. Estimation of k is an iterative process, involvingcompatibility between the resulting value of Vmax and hence penetration, Vmax /k, and the penetration resistance expected at thatpenetration for the given strength profile. It may be shown that for zero strength intercept, and a strength gradient of

~1.5 kPa/m, the resulting ‘plastic’ value of k may be as low as 2 to 4 kPa, with the pipeline penetrating by a diameter or more.However, even a small strength intercept of, say, 3 kPa results in k values of 100 to 300 kPa, with pipeline penetrations of lessthan 0.1D. It should also be noted that, although it is suggested that the value of the seabed stiffness is chosen in order tomatch the secant stiffness of the non-linear seabed response, in practice different stiffnesses are relevant for different parts ofthe touchdown region. As the pipeline is gradually laid, the seabed in advance of the maximum contact force deformsplastically with increasing force, while points on the pipeline beyond the current maximum contact force will be unloading,and thus following a much stiffer response (as V/p reduces back towards unity).

Cyclic Motion. Dynamic motion of the pipe within the touchdown zone during laying increases the pipeline embedmentbeyond that created by the static load imposed at the maximum stress concentration within the catenary, f layp. Small-amplitudeoscillations of the pipe within the touchdown zone, originating from the lay-vessel motion and hydrodynamic loading of thehanging pipe section, lead to remolding and displacement of the seabed soil creating a trench and leading to deeper pipeembedment than would arise if the pipe were laid statically. The dynamic lay process not only gives rise to extra embedment,

but also significantly remolds the soil surrounding the pipe, and allows the entrainment of water, leading to softening. In softfine-grained seabed sediments, excessive dynamic motion can create a substantial reduction in the soil strength, whichinfluences the breakout resistance.

The increase in embedment due to dynamic effects is often neglected in design calculations. However, as discussedpreviously, recent design guidance suggests that dynamic effects can be accounted for by multiplying the static embedment byan empirical dynamic embedment factor, f dyn, where this factor is typically in the range 2 – 10, based on back-analysis of as-laid surveys [2, 18].

An alternative approach to the single f dyn adjustment factor is to consider the lay process in detail, making an assessment ofthe accumulation of pipe embedment as an individual element of pipe first comes into contact with the seabed, then passesthrough the touchdown zone (or more accurately, the touchdown zone moves past the pipe element), and finally reaches astable position on the seabed.

Figure 11 shows the touchdown zone schematically, depicting the vertical and horizontal dynamic effects. Quantitativeobservations of the dynamic motion within the touchdown zone has not been published, so the magnitude of the movement,

and the resulting pipe-soil force, are not well understood. Lund [2] suggests that although the dynamic oscillation of the


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hanging pipe is generated by the lay-vessel motion, the dominant frequency of the movement is related to the natural period ofthe hanging pipe, rather than the period of the vessel motion. A more severe sea state will lead to increased amplitude ofoscillation within the touchdown zone. It has also been suggested that the horizontal component of the oscillation is a moresignificant driver of dynamic embedment compared to the vertical oscillation [2]. At shallow embedment (w/D = 0.5) thisbehavior is consistent with the creation of a trench, with the soil pushed aside and remolded by the horizontal cyclic movement(Fig 12a).

At deeper embedment, and when the soil is weakened by remolding, any soil that is displaced away from the pipe

centerline by the dynamic motion will fall back, and the ‘trenching’ mechanism is less effective. Instead, the dynamic motion– whether vertical or horizontal – will remold and weaken the soil, leading to increased settlement under the pipe weight. Thiseffect is illustrated as the ‘softening’ mechanism in Fig. 12b.

Quantification of these dynamic effects is limited by the lack of field observations and the difficulty of modeling theprocess numerically due to the interaction between the soil and the structural responses. The dynamic motion is neither load-controlled nor displacement-controlled, and the actual movement within the touchdown zone will depend on the excitationfrom the lay vessel, the structural behavior of the hanging pipe, and the stiffness (and cyclic behavior) of the soil response.Figure 11 arbitrarily depicts the vertical effect as a load oscillation of the force profile relative to the static catenary solutiondiscussed previously, and the horizontal effect as an oscillatory motion between displacement limits.

To explore dynamic lay effects without recourse to a full analysis involving the hanging pipe and vessel motion, it isnecessary to consider the process as seen by a single pipe element. Figure 13 illustrates the displacement path followed by apipe element within the touchdown zone. The horizontal oscillation is progressively attenuated by the increasing soil restraintas the embedment increases and as the freely-moving hanging end becomes more distant. As the pipe moves through the

touchdown zone the applied vertical load rises to the peak force concentration then falls toward the pipe weight – with avertical oscillation imposed on this pattern. These processes lead to the time history shown in Fig. 14. This idealized behaviorcan be used as in input to numerical or physical modeling of the dynamic lay process, although the selection of appropriateparameters to characterize the oscillation is difficult.

Lund [2] back-analyzed the as-laid embedment for the Zeepipe 2B pipeline in the North Sea in which the lay process wasidealized as horizontal oscillations under constant vertical load. It was found, based on numerical analysis, that the observed

dynamic embedment was consistent with 20 cycles of horizontal oscillation with an amplitude of ±0.5D, under a vertical loadwhich remained constant at 2.5 times the pipe weight.

Recently-developed tools for numerical analysis of risers and pipe laying allow more sophisticated cycle-by-cycle back-analyses to be conducted, although most software is restricted in scope, for example to only in-plane movements of the pipe orriser, and linear pipe-soil interaction. Advanced physical modeling techniques have also been developed recently, allowingarbitrary load or displacement histories to be imposed on an element of pipe, allowing dynamic lay effects to be simulated inan idealized manner. The following two sections of this paper illustrate the potential of these new numerical and physicalmodeling techniques to simulate dynamic pipe movement during laying.

(a) ‘Trenching’

(b) ‘Softening’

Fig. 11. Schematic illustration of dynamic behavior in touchdown zone during pipelay Fig. 12. Dynamic embedment mechanisms


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Fig. 13. Longitudinal view of dynamic pipe embedment Fig. 14. Time history of dynamic pipe embedment

Numerical Simulation of Lay Effects. Commercially available software for pipeline and riser analysis is mostly limited tosimple linear response of the seabed, although extensions to non-linear seabed response are starting to be developed. Anexample is shown here from a trial version of OrcaFlex, incorporating a non-linear seabed response with a hysteretic cyclicmodel that leads to incremental penetration with each cycle even under purely vertical motion, in a similar manner to thatobserved in model tests [29]. The pipeline properties were: diameter, D = 0.51 m, bending rigidity, EI = 240 x 103 kNm2 and

submerged weight, p = 1.2 kN/m, with water depth of 1500 m and lay angle of φ = 84 º. These properties result in λ = 33.7 m,

T0 = 210 kN and T0 / λp = 5.2. The analysis simulated the effect of 10 cycles of vertical movement of the vessel (or upper endof the pipeline), with a displacement amplitude of ±3 m and frequency of 0.05 Hz, with the pipeline assumed to be pinned atthe vessel (so zero bending moment) maintaining the lay angle of 84 º constant.

The seabed was assigned a strength profile of su = 1 + 1.2z kPa, and the non-linear response was modeled using ahyperbolic approach [20,30] with a maximum normalized stiffness, K, of 200 times the ultimate penetration resistance at thatdepth, the latter being calculated from Eq. 2, with a = 6 and b = 0.25. The maximum uplift resistance was taken as 30 % of thecorresponding penetration limit, and an exponential decay function was used to model breakaway.

Using OrcaFlex, the initial touchdown point was found to be at an arc distance of 1683 m, measured from the upper end ofthe pipeline (at sea level). Figure 15 shows the calculated cyclic response at two arc distances within the touchdown zone

during the simulated cyclic motion. The hyperbolic model, in conjunction with a slight delay in rejoining the previousmaximum resistance during repenetration, gives incremental embedment of the pipeline from initial embedments of 0.16D and0.20D at the two locations, to maximum values in excess of 0.7D after 10 cycles (see Fig. 15).

Profiles of the pipeline penetration, expressed as w/D, and also of the normalized contact force, V/p are shown in Fig. 16and Fig. 17. The initial maximum penetration of 0.2D corresponds to a local contact force of 1.7p, equivalent to V/D = 4 kPa(hence a secant stiffness of k = 4/0.2 = 20 kPa). During the cycles of vertical motion the maximum envelope of the pipelineprofile increases to reach an embedment of 0.8D, with the smallest arc distance to the touchdown point reducing to 1660 m.The envelope of maximum contact force reaches a local maximum of V/p = 3.2 (so nearly double the static value of 1.7) whilethe envelope of minimum contact force reaches a ‘suction’ of V/p = -0.8.

0

0.10.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-5 0 5 10 15

Pipe-soil resistance, V/D (kPa)

P e n e t r a t i o n , w / D

Ultimate penetration

resistance

Limiting

uplift resistance

Cyclic response at arc

distance of 1690 m

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-5 0 5 10 15

Pipe-soil resistance, V/D (kPa)


Ultimate penetration

resistance

Limiting

uplift resistance

Cyclic response at arc

distance of 1700 m

(a) Response at arc distance 1690 m (b) Response at arc distance 1700 m

Fig. 15. Pipeline-seabed response in the touchdown zone


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0

0.1

0.2

0.30.4

0.5

0.6

0.7

0.8

0.9

1650 1700 1750 1800

Arc distance (m)


Initial profile

Final

profile

Minimum

envelope

Maximum

envelope

-1

0

1

2

3

4

1650 1700 1750 1800

Arc length (m)

N o r m a l i z e d c o n t a c t f o r c e ,

V / p

Initial

profile Final

profile

Minimum

envelope

Maximum

envelope

Fig. 16. Pipeline penetration profiles Fig. 17. Profiles of pile-soil contact stress

The extreme values of embedment and local contact force discussed above can be compared with values obtained using alinear seabed stiffness. For lower and upper estimates for k of 20 kPa (corresponding to the secant stiffness at the deepest

embedment point for the non-linear seabed model) and 1000 kPa (corresponding approximately to 200 times the ultimatepenetration resistance at a depth of 0.2D), the maximum static contact forces, Vmax, are 1.9p and 4.2p respectively. During thecyclic motion these increase to maximum values of 2.2p and 5.0p (so dynamic amplification factors of 1.17 and 1.19,compared with 1.87 for the non-linear seabed model). The maximum of 3.7p obtained from the non-linear seabed model liesbetween these two values, suggesting that an intermediate seabed stiffness would be appropriate for fatigue calculations.

Physical Modeling of Lay Effects. Over the past 12 months, a variety of experiments simulating dynamic lay effects havebeen conducted using the geotechnical beam centrifuge at the University of Western Australia (UWA), both for genericresearch and site-specific project studies. This centrifuge is equipped with two-directional actuators that feature a sophisticatedfeedback control system which allows rapid cyclic load or displacement-controlled operation of each axis, independently.

This control allows pipelaying to be simulated by imposing on the model pipe a time history of vertical load whichrepresents the catenary solution through the touchdown zone whilst imposing horizontal oscillation in a pattern that aims toreplicate the motion induced by the vibration of the hanging pipe. An example of the experimental set-up is shown in Fig. 18.

An element of model pipe – which can be equipped with miniature pore pressure transducers to monitor the development anddissipation of excess pore pressure against the pipe – is rigidly fixed to a loading arm, and lowered onto the model seabed,which is prepared by re-consolidation from a slurry. For recent industry studies, the full lay process, as illustrated in Fig. 14,has been simulated to replicate the site-specific lay conditions as closely as possible.

A more general parametric study aimed at understanding the mechanisms underlying dynamic lay effects is reported byCheuk and White [21] as part of a collaborative research project between UWA and the University of Hong Kong. Two seriesof pipe lay simulations were conducted, in different soil samples. One soil sample consisted of kaolin clay (denoted KC), andthe second sample was a natural high plasticity clay (denoted HP), taken from a deep water site off the coast of West Africa(supplied by BP Angola). Both samples were reconsolidated from a slurry, and had a strength profile which increased linearlywith depth from a small intercept (< 1 kPa) at the mudline. In each simulation the pipe was lowered onto the seabed until aspecified vertical load was reached. This load was then held constant, a series of packets of horizontal displacement cycleswere applied, increasing then decreasing in amplitude (as described in Table 3). The model pipe was 20 mm in diameter, andrepresented a 0.8 m diameter section of pipeline at the applied centrifuge acceleration of 40 g.

The results from a test on kaolin clay representing a pipe imposing a vertical load of 2.2 kN/m on the seabed aresummarized in Figs. 19 and 20. The pattern of controlled horizontal movement and the resulting embedment is shown inFig. 19, and the controlled vertical load and the resulting horizontal load are shown in Fig. 20. In this test (denoted KC-05) theinitial settlement under the applied vertical load alone was only 0.12D, whereas after stage 1 of the lay effect (20 cycles of

±0.05 D amplitude) the embedment had increased to 0.52D. Further increases in embedment arose from the higher-amplitudestages, but once the horizontal movement was reduced the pipe embedment stabilized. Initially the embedment increasedrapidly, doubling after 2 cycles, and tripling after 5. This increase in embedment can be attributed primarily to the ‘trenching’process shown in Fig. 12a. In the later stages, when the pipe was deeper, the rate of embedment reduced and the ‘softening’mechanism shown in Fig. 12b is likely to have been the dominant driver of the increasing embedment.

The results from four tests, two in each type of clay, are shown in Fig. 21. These summarize the influence of vertical loadon the rate of embedment for the selected sequence of horizontal motion, and also highlight a significant difference in thebehavior of the two clay types. During the first packet of cycles the pipe invert reached an embedment in the range w/D =0.3 - 0.7, roughly in proportion to the imposed vertical load. The majority of this increased embedment can be attributed to

‘trenching’, and the behavior observed in the two different soils was similar.


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Table 3. Idealized dynamic lay effect [21]

Lay effectstage

Horizontal cyclicamplitude, ∆u/D

Number ofhorizontal cycles

imposed

1 ±0.05 40

2 ±0.1 40

3 ±0.2 40

4 ±0.1 20

5 ±0.05 20Vertical load maintained constant throughout simulated lay process

Fig. 18. Typical centrifuge model test arrangement

Fig. 19. Lay effect model test (KC-05): displacements [21] Fig. 20. Lay effect model test (KC-05): normalized loads [21]

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 1 2 3 4 5

Normalised vertical load, V/suD

P i p e i n v e r t e m b e d m e n t ,

w / D

HP06 HP07

KC04 KC05

Initial After stage 1

After stage 2 After stage 3

Curve fit to

plasticity

solutions for

monotonic

embedment

Fig. 21. Accumulation of pipe embedment during lay effect model tests [21]

D = 0.8 mV = 2.21 kN/m


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However, contrasting behavior was observed during the second and third stages of the simulated lay process. Over thisperiod the embedment in the HP clay approximately doubled, whereas in the kaolin clay the embedment increased by only

∼25%. This suggests that the HP clay is more susceptible to the ‘softening’ mechanism (Fig. 12b) which is considered to bethe dominant mechanism at depth.

Although the idealized lay effect used in these tests is not exactly representative of the real lay process, the results indicatethat the HP clay has a far higher tendency to allow dynamic pipe embedment, beyond the initial few cycles of the ‘trenching’stage. The challenge for design is to identify a method for detecting soils that have this tendency for more dramatic strength

loss when remolding occurs (and free water can be entrained). Conventional cyclic T-bar penetrometer tests (conductedbeneath the soil surface, thus eliminating the possibility of water entrainment) revealed nearly identical values of sensitivityfor the kaolin and HP clays. Cyclic T-bar tests that pierce the soil surface may provide a better indication of the increasedbrittleness evident in the response of the HP clay to the lay-induced oscillations.

Quantitative Assessment of Dynamic Lay EffectsThe numerical and physical modeling examples described above demonstrate that the as-laid embedment of a pipeline isstrongly influenced by dynamic effects. The theoretical techniques described in the first part of this paper allow pipelineembedment under monotonic loading to be predicted using the robust framework of plasticity that underpins bearing capacityassessments for shallow foundations. However, the challenge of incorporating dynamic effects remains to be solved, and thecurrent approach based on a multiplier on the monotonic embedment – the dynamic embedment factor, f dyn – does not capturethe underlying influences of:

1. the sea-state, the resulting vessel motion, and the consequent motion or load imposed at the hanging end of the

touchdown zone; 2. the profile of vertical stress through the touchdown zone;3. the attenuation of the dynamic motion through the touchdown zone;4. the non-linear response of the soil during the cyclic motion imposed within the touchdown zone, including the

susceptibility to lose strength due to remolding and water entrainment.To advance from a lumped f dyn adjustment factor to a cycle-by-cycle analysis, in which these factors are considered

individually, is analogous to the historical evolution of approaches for assessing the cyclic bearing capacity of offshoreshallow foundations – for example for gravity-based structures. Early methodologies for the inclusion of cyclic effects in theassessment of capacity were based on the selection of a single factor by which the in situ soil strength should be downgradedin order to account for the reduction in undrained strength due to cyclic pore pressure build-up. More modern approachesinvolve the assessment, on a cycle-by-cycle basis, of the cumulative degradation of shear strength (and any recovery, throughdissipation of excess pore pressure) [31]. In contrast to the foundation analysis of large gravity-based structures, the pipe layprocess has the added complication of involving soil-structure interaction causing the loads to vary according to the soilresponse. Morris et al. [32] described an approach for assessing the cyclic accumulation of pipeline embedment underhydrodynamic loading which adopts a similar framework to models for cyclic strength degradation.

A full three-dimensional soil-structure analysis of the lay process is currently beyond the capability of riser and pipelinesoftware and there are no widely accepted constitutive models to describe cyclic pipe-soil interaction, accounting for bothvertical and horizontal movement. An intermediate approach is to attempt to model the behavior of a single pipe elementduring the lay process, based on appropriate assumptions regarding the imposed loads and displacements. This approach hasbeen used to guide parametric centrifuge modeling studies for recent projects, to provide bounds on the anticipated as-laidembedment. Cyclic histories of vertical load and horizontal oscillation of the form shown in Fig. 13 were selected based on thefollowing inputs, extending the approach suggested by Lund [2]:

1. the profile of vertical load through the touchdown zone (and the length of this zone) from a catenary analysis;2. a profile of horizontal oscillations assumed to act along the touchdown zone, or a maximum amplitude which is

assigned at the soil surface and assumed to reduce linearly with pipeline embedment;3. upper bound (fast) and lower bound (slow) values for the lay rate based on the anticipated welding periods and potential

causes of downtime;4. the natural period of the hanging pipe section, based on a catenary analysis.The length of the touchdown zone combined with the anticipated lay rate indicates the time period that the pipe remains

within the touchdown zone. The number of imposed displacement cycles can then be calculated from the natural period of thehanging pipe. The adopted cyclic histories of vertical load and horizontal motion are imposed on a model pipe section which isembedded in a sample of reconstituted soil taken from the project site. Although significant assumptions are involved in thisapproach, physical modeling provides a useful basis for bracketing the anticipated range of dynamic embedment. Since theaccumulation of embedment varies non-linearly with the lay process input parameters, and a relatively stable embedment canbe reached for some lay conditions (as shown in Fig. 19), a broad range of lay process input parameters can yield a reasonablynarrow range of dynamic embedments.


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ConclusionsPredictions of the as-laid embedment of on-bottom pipelines feed into a variety of design issues related to the response of thepipeline during laying and operation. Low embedment is favorable in relation to some design issues, whereas others requirehigh embedment. It is therefore not possible to make a single conservative assessment.

The current state-of-the-art approach to the assessment of as-laid embedment is to use static embedment solutions whichare either based on plasticity theory or have been calibrated to databases of model tests. These solutions require accurateassessment of the undrained strength profile close to the soil surface. The static load assumed in these calculations is enhanced

by a touchdown lay factor, f lay, which accounts for the maximum force concentration in the touchdown zone and the resultingstatic embedment is multiplied by a dynamic embedment factor, f dyn, to account for the additional penetration that arises fromcyclic movement of the pipe as it becomes grounded during the lay process.

This paper has presented recent analyses and approaches which can be used to refine each of these three calculation stages.Firstly, new theoretical solutions for static pipe embedment were summarized. These solutions include modest improvementson previous plasticity solutions and a more correct approach to account for heave and buoyancy. The significant differencebetween ‘nominal’ and ‘local’ embedment arising from heave was also highlighted, which is an important consideration forthe analysis of thermal heat losses.

Secondly, recent developments in penetrometer testing for assessing the near-surface soil strength profile required for thesesolutions were described. The potential to explore remolding and re-consolidation through penetrometer tests was highlighted.

Thirdly, a summary of the catenary solutions for the static distribution of vertical load within the touchdown zone waspresented. These solutions rely on a linear model for the vertical soil response, but can be reduced to simple analyticalexpressions in order to allow assessment of the maximum structural loading within the pipe. The length-scale of the

touchdown zone and the peak force concentration within this zone can be calculated using simple relationships involving thelay tension (or angle) and the relative pipe-soil stiffness. These solutions provide a simple approach to the estimation of f lay,but rely on an iterative approach to assess an appropriate soil stiffness, which remains a significant source of uncertainty.

Finally, the origin of the dynamic embedment factor was discussed, and examples in which the dynamic pipe movementwithin the touchdown zone dominates the as-laid embedment were shown. Recent research that sheds light on the underlyingmechanisms of dynamic embedment was summarized, and approaches by which dynamic embedment can be simulatednumerically and experimentally were described.

The static solutions for the maximum vertical load within the touchdown zone, and the consequent monotonic embedment,are now well-established. The primary remaining challenges related to the assessment of pipeline embedment in deep waterare (i) to accurately evaluate the near-surface soil strength and (ii) to develop a robust understanding of the dynamic aspects ofthe lay process. This second tasks encompasses the generation of dynamic movement through lay-vessel motion leading tooscillation of the hanging pipe and the response of the seabed to the resultant cyclic loading within the touchdown zone.These developments will reduce the current wide uncertainty associated with predictions of as-laid embedment, which has

significant repercussions for many design issues related to deepwater pipelines.

AcknowledgementsThe work described here forms part of the activities of the Centre for Offshore Foundation Systems (COFS), established underthe Australian Research Council’s Research Centres Program and now supported under grants FF0561473 and DP0665958and Centre of Excellence funding from the State Government of Western Australia. The authors would also like to thankOrcina Ltd for the loan of their OrcaFlex software during collaboration in respect of non-linear seabed contact models.

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Randolph White OTC 19128