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  Applied Ocean Research 28 (2006) 291–298www.elsevier.com/locate/apor Steady current induced seabed scour around a vibrating pipeline Fu-Ping Gao ∗ , Bing Yang, Ying-Xiang Wu, Shu-Ming Yan  Institute of Mechanics, Chinese Academy of Sciences, Beijing 100080, China Received 6 September 2006; received in revised form 3 December 2006; accepted 13 January 2007Available online 26 March 2007 Abstract Most of the existing researches either focus on vortex-induced vibrations (VIVs) of a pipeline near a rigid boundary, or on seabed scour arounda fixed pipeline. In this study, the coupling effects between pipeline vibration and sand scour are investigated experimentally. Experimental resultsindicate that there often exist two phases in the process of sand scouring around the pipeline with an initial embedment, i.e. Phase I: scourbeneath pipe without VIV, and Phase II: scour with VIV of pipe. During Phase II, the amplitude of pipe vibration gets larger and its frequencygets smaller while the sand beneath the pipe is being scoured, and finally the pipe vibration and sand scour get into an equilibrium state. Thisindicates that sand scouring has an influence upon not only the amplitude of pipe vibration but also its frequency. Moreover, the equilibriumscour depth decreases with increasing initial gap-to-diameter ratio for both the fixed pipes and vibrating pipes. For a given value of initial gap-to-diameter ratio  ( e 0 /  D ) , the vibrating pipe may induce a deeper scour hole than the fixed pipe in the examined range of initial gap-to-diameterratios  ( − 0 . 25  <  e 0 /  D  <  0 . 75 ) .c  2007 Elsevier Ltd. All rights reserved. Keywords:  Submarine pipeline; Scour; Sandy seabed; Current; Vortex-induced vibration 1. Introduction When a submarine pipeline is laid upon seafloor andsubjected to ocean currents, there exists a complex interactionbetween current, pipeline and soil. Pipeline spans may existin some locations due to the unevenness of the seafloorand (or) soil erosion around the pipeline. When exposed tocurrents or other hydrodynamic loads, such pipeline spans mayexperience vortex-induced vibration (VIV), which has beenwidely recognized as one of the main causes for fatigue damageto pipelines [12]. Therefore, it is highly essential to analyze thedynamic responses of a submarine pipeline near the seabed insevere ocean environments for the proper design of submarinepipelines.During recent decades, the dynamic interaction betweenocean currents/waves, pipelines and the seabed has re-ceived wide interest from submarine pipeline designers andresearchers [2,7,12,21]. Numerous experiments on current- induced vibrations of a pipeline have shown that, when thevortex shedding frequency brackets the natural frequency of an ∗ Corresponding author. Tel.: +86 10 62618499; fax: +86 10 62561284.  E-mail address:  fpgao@imech.ac.cn (F.-P. Gao). elastic or elastically mounted rigid cylinder, the cylinder takescontrol of the shedding frequency in an apparent violation of the Strouhal law. Then the vortex-shedding and pipeline oscil-lation collapses into a single frequency, which is well knownas the ‘lock-in’ phenomenon [15]. A few experimental results for vibrating cylinders with two degrees of freedom indicatedthat the amplitudes of cross-stream vibration are usually muchlarger than those of in-line vibration [3]. For the above rea- sons, many researchers paid their attentions mostly to the cross-stream vibrations of cylinders, such as the work by Khalak andWilliamson [14] and Govardhan and Williamson [9]. However, the aforementioned researches focus on pipeline vibrations neara rigid boundary or under wall-free conditions where the soilscour was not involved.At present, the most reliable approach to predicting scouraround an offshore structure is to conduct model testssimulating the real conditions [2]. Recently, much effort hasalso been devoted on the two-dimensional soil scour aroundfixed pipelines in currents, such as the work done by Hansenet al. [11], Sumer et al. [17], and Chiew [5]. The scour in the middle of the suspended span of a pipeline can beconsidered as a two-dimensional process. The scour aroundthe span shoulders is definitely a three-dimensional one. As 0141-1187/$ - see front matter c  2007 Elsevier Ltd. All rights reserved.doi:10.1016/j.apor.2007.01.004  292  F.-P. Gao et al. / Applied Ocean Research 28 (2006) 291–298  Fig. 1. Sketch of sand scouring around a vibrating pipeline. for the three-dimensional scour case, various scenarios mayoccur in a real-life situation, depending on the conditions of flow, soil and pipe. For example, the pipeline may sink at spanshoulders and sometime be buried by the backfilling soil [19]. The researches on seabed scour around coastal structures havebeen summarized by Sumer and Fredsoe [21]. It should benoted that a pipe with an initial embedment is not alwaysscoured to have itself suspended; it may also lose on-bottomstability when the lateral soil resistance cannot balance thehydrodynamic loads [7,8]. Most of the previous researches either concentrate onsoil scour around fixed pipelines, or on the vortex-inducedvibrations of a pipeline near a rigid boundary, such as thework by Jacobsen et al. [13] and Yang et al. [23]. Unlike wall- free cylinders, a cylinder in the vicinity of a rigid boundarywill not shed regular vortices but still vibrate, as observed byJacobsen et al. [13]. In actual situations, pipeline vibration and soil scour are always coupled. Until now, however, studieson the interaction between a vibrating pipe and soil scourare scarce [16,18]. In the work by Sumer et al. [18], two kinds of experiment were conducted. In the experiments forinvestigating the influence of transverse vibration of pipelineon sand scour, the test pipe was free to vibrate vertically whilesoil scour was taking place from the outset of test; however,in their experiments for investigating the influence of scour onpipeline vibration, the pipe was initially maintained stationaryfor 30 min at a given flow speed during which scour reachedit equilibrium state, and the pipe was subsequently released tovibrate freely above the scour hole. Shen et al. [16] primarily investigated thecross-stream and in-linevibrationsofapipelinenear erodible sands. The previous studies have indicated thatpipe vibration has influences on soil scour and vice versa.Nevertheless, due to the complexity of the physical phenomena,the underlying mechanism of the dynamic interaction betweenpipe vibration and soil scour has not yet been well understood.In this study, the current-induced sand scour around avibrating pipeline was simulated experimentally with a newhydro-elastic facility. Based on similarity analyses, a series of tests was conducted to further investigate the mechanism of thecoupling effects between pipe vibration and sand scour. 2. Dimensionless analyses on current–pipeline–soil interac-tion When a submarine pipeline is laid upon a sandy seabed andexposed to steady currents, there exists a dynamic interactionbetween currents, pipeline and sand. Local scour may becoupled with the pipe vibration under the influence of currents,as illustrated in Fig. 1.In this study, a sandy seabed is considered. The equilibriumscour depth beneath a vibrating pipeline  ( S  )  in a steady currentis mainly dependent on the following characteristic parametersof flow, pipe and seabed, i.e. S   =  f   ( U  ,ν, g ,ρ,ρ s , d  s ,  D r  , e 0 ,  D , m ,  f  n ,ξ, k  s  ...)  (1)where  U   is the flow velocity, which is often taken as theundisturbed flow velocity at the center of pipeline;  ν  is thekinetic viscosity of fluid;  g  is the gravitational acceleration;  ρ is the mass density of fluid;  d  s  is the diameter of sand particles,which is usually chosen as the mean diameter  ( d  50 ) ;  D r   is therelativedensityofsand;  D  istheouterdiameterofpipeline; m  isthe mass of a pipeline per meter;  f  n  is the natural frequency of the pipeline in still fluid;  ξ   is the structural damping factor;  k  s  isthe roughness of pipeline surface;  e 0  is the initial gap betweenthe pipeline and the seabed.According to dimensional analysis for Eq. (1), thedimensionless equilibrium scour depth  ( S  /  D )  beneath avibrating pipeline can be determined by a group of independentdimensionless parameters as S  /  D  =  f   ( V  r  , e 0 /  D ,θ,  D r  , G s ,  Re , m ∗ ,  K  , d  s /  D , k  s /  D  ...) (2)where the reduced velocity  V  r   is defined as V  r   = U  /  Df  n  (3)which is for describing the widths of the lock-in rangeof vortex-induced vibrations of the pipeline;  e 0 /  D  is thedimensionless initial gap between the pipeline bottom and theseabed surface; the Shields parameter  (θ)  is defined as θ   = U  2  f   /( G s  − 1 ) gd  s  (4)which governs the sediment transport, where the undis-turbed bed shear velocity  U   f   can be calculated with theColebrook–White formula, i.e.  U  / U   f   =  8 . 6 + 2 . 5ln (  D / 2 k  b ) ,in which  k  b  is the roughness of the seabed (usually taken as2 . 5 d  s ) [19]; The sand relative density  D r   is defined as  D r   = e max − ee max − e min (5)which is used to express the relationship between the in situvoid ratio  ( e )  and the limiting values  e max  and  e min  of the sand  F.-P. Gao et al. / Applied Ocean Research 28 (2006) 291–298   293 sample [6];  G s  = ρ s /ρ  is the specific gravity of sand particles,which is taken as approximately 2.65 for standard sand; theReynolds number is defined as  Re = UD /ν  (6)which is the ratio of inertia force to viscous force; m ∗ = 4 m /πρ  D 2 (7)is the pipeline mass ratio; K   = 4 ( m + m a )ξ/πρ  D 2 (8)is the stability parameter of a vibrating pipeline, where  m a  isthe added mass,  m a  =  C   A m d   ( m d   is the displaced fluid massper meter,  C   A  is the potential added-mass coefficient,  C   A  = 1 . 0and  m d   =  πρ  D 2 / 4 for a cylinder);  d  s /  D  is the dimensionlessdiameter of sand particles;  k  s /  D  is the relative roughness of thepipeline.The above similarity analyses are for sand scour around avibrating pipeline. When one examines the scour depth arounda fixed pipeline, some parameters related to vortex-inducedvibration of pipeline should not be involved, i.e. S  /  D  =  f   ( e 0 /  D ,θ,  D r  , G s ,  Re , d  s /  D , k  s /  D  ...)  (9)for a fixed pipe. 3. Experimental setup 3.1. A hydro-elastic facility for simulating current–pipe–soilinteraction A hydro-elastic facility was designed and constructed for thepresentexperimentalinvestigation,whichisinconjunctionwitha water flow channel, as illustrated in Fig. 2. The water flow channel is 0.5 m wide, 0.6 m high and 19 m long, and is capableof generating steady currents with velocity up to approximately0 . 4 m / s. The water depth is 0.4 m. The test pipe was attachedto the supporting frame by two connecting poles, two slidingpoles and two sets of springs. The sliding poles can move alongthe four runners, which are connected to the two localizers byfour bearings. Only transverse pipe vibration was simulated inthis study. A laser displacement transducer was employed forthe non-contact measurement of the vertical displacement of the vibrating pipeline. Concurrently, the time development of scour depth was recorded with a digital camera. After the flowwas stopped when the scour reached its equilibrium stage, thelongitudinal scour profile was measured with a depth probe,which was installed upon and could slide along the two side-walls of the flume. One of the main research interests of thisstudy is to examine the effects of the proximity of the pipelineto the seabed upon the dynamic responses of the pipelineand upon the scour depth. As such, the gap between the testpipe and the sand surface was designed to be varied easilywith two vertical slotted portions on the supporting frame (seeFig. 2). Fig. 2. Schematic diagram of experimental apparatus for current–pipeline–soilinteraction. 3.2. Test conditions and procedure Two types of pipeline were taken into account in theexperiments, i.e. Type I: fixed pipes, and Type II: vibratingpipes. For the vibrating pipe, its mass, natural frequencyand structural damping factor are kept constant, i.e.  m  = 3 . 10 kg / m,  f  n  =  1 . 22 Hz,  ζ   =  0 . 0186. Note that thenatural frequency of the pipeline system  f  n  and structuraldampingfactor ζ   aredeterminedbyanalyzingtherecordsofthedisplacements of pipe, which was given a prescribed verticaldisplacement and then released in still water. The test pipe is0.032 m in diameter, 0.47 m in length. Only smooth pipes areconsidered in this study, i.e.  k  s /  D  ≈ 0.In order to make meaningful comparisons of the responsesof aforementioned two types of pipes, only one kind of sandyseabed was adopted, whose grain size distribution is shownin Fig. 3. Its mean particle diameter  d  50  =  0 . 38 mm, andrelative density  D r   = 0 . 66, indicating that the sand sample is amedium-dense one.The velocity of steady flow in the experiments is  U   = 0 . 255 m / s. The corresponding dimensionless parameters are V  r   = 6 . 53,  m ∗ = 3 . 86,  K   = 0 . 09,  θ   = 0 . 039,  Re ≈ 0 . 82 × 10 4 .  294  F.-P. Gao et al. / Applied Ocean Research 28 (2006) 291–298  Fig. 3. Grain size distribution curves of the test sand.Fig. 4. The development of scour depth beneath pipeline with time for a fixedpipe (  D  =  0 . 032 m,  e 0 /  D  =  0,  U   =  0 . 255 m / s,  θ   =  0 . 039, medium-densesand:  d  50  = 0 . 38 mm,  D r   = 0 . 66). In the experiments,  Re  is of the order of 10 4 , being in thesubcritical flow range, whereas in the fields,  Re  is of the orderof10 5 ormore.Nevertheless,theeffectsofReynoldsnumberonthe vortex shedding are negligible, when high Reynolds numberand marine-roughened real-life pipelines are considered [1,17]. 4. Experimental results and analyses 4.1. Sand scour beneath a fixed pipe with various e 0 /  D The flow disturbance by the presence of pipeline may inducelocal scour in the proximity of the pipeline. A typical timedevelopmentofscourdepth ( S  t  ) belowafixedpipelineisshownin Fig. 4. It can be seen from the figure that the sand scouring speedgetsslowerandslowerwithtime.Whenthescouringtimeis long enough (e.g. 120 min, see Fig. 4), an equilibrium stateis finally reached.In this study, the sand scour around a pipe embedded inseabed is also involved. In order to have a knowledge of theeffects of initial gap-to-diameter ratio  ( e 0 /  D )  on the scourdepth, three values of gap-to-diameter ratio are chosen in thetests, i.e.  e 0 /  D  =  0 . 2, 0, − 0.25. The other test conditions arekept unchanged, i.e.  D  = 0 . 032 m, U   = 0 . 255 m / s,  θ   = 0 . 039, d  50  = 0 . 38 mm,  D r   = 0 . 66.For the pipe with an initial embedment, the currents witha certain velocity may induce sand scour beneath the pipe, andthepipeisfinallysuspendedwithagapbetweenthepipebottomand the surface of the scoured seabed, as illustrated in Fig. 5. Fig. 5. Scour underneath a pipe with an initial embedment.Fig. 6. Equilibrium scour profiles around a fixed pipeline with various gap-to-diameter ratios (  D  =  0 . 032 m,  U   =  0 . 255 m / s,  θ   =  0 . 039, medium-densesand:  d  50  = 0 . 38 mm,  D r   = 0 . 66). After that, the soil scour was kept continuing until it reachedan equilibrium state. The sand scour profiles around a fixedpipeline were measured with a depth probe. The equilibriumscour profileis characterized as asteep slop at the upstream sideof the test pipe and a gentle slope at the downstream side (seeFig. 6). It is also indicated in Fig. 6 that the equilibrium scour depth increases with the decrease of initial gap-to-diameterratio. 4.2. Sand scour around vibrating pipes4.2.1. Coupling between pipe vibration and sand scour  In the aforementioned experiments, the sand scour aroundstationary pipes was modeled. In reality, however, soil scouris prone to coupling with the vortex-induced vibrations of thepipeline. Therefore, it is crucial to investigate the couplingeffects between them.In this subsection, the dynamic interaction between thepipe vibration induced by currents and the sand scour aroundthe pipe will be further investigated. Two cases of pipelineare considered, i.e. Case I: a pipeline with an initial gap tothe seabed  ( e 0 /  D  ≥  0 ) , and Case II: a pipeline with initialembedment in the seabed  ( e 0 /  D  <  0 ) . Case  I : A pipeline with an initial gap to seabed   ( e 0 /  D  ≥ 0)The time development of the displacement of a vibratingpipe and the change of scour depth with time are shown inFig. 7(a) and in Fig. 7(b), respectively. It is indicated from the two figures that pipe vibration and sand scour affect eachother. For the case of positive  e 0 /  D , i.e. the vibrating pipewith an initial gap between pipe wall and seabed (e.g.  e /  D  = 0 . 75), the dimensionless equilibrium scour depth ( S  /  D  = 0 . 82,see Fig. 7(b)) is even higher than that for a fixed pipe with e 0 /  D  =  0 ( S  /  D  =  0 . 41, see Fig. 4). It is also found that the
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