Self-Burial of Short Cylinders Under Oscillatory Flows and Combined Waves Plus Currents

IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 32, NO. 1, JANUARY 2007 191

Self-Burial of Short Cylinders Under OscillatoryFlows and Combined Waves Plus Currents

Yovanni A. Cataño-Lopera, Salih T. Demir, and Marcelo H. García

Abstract—Self-burial processes of finite-length cylinders underoscillatory flows and waves plus currents were examined with thefollowing two different experimental facilities: a large oscillatingwater-sediment tunnel (LOWST) and a large wave-current tank.More than 130 experiments, with different model cylinders, wereconducted within both facilities. The burial mechanisms studied in-clude burial due to local scour and bedform migration. Burial dueto fluidization in the tunnel was also explored, but only in a qual-itative way. In the case of experiments with LOWST, the equilib-rium burial depth was found to be a power function of the Shieldsparameter (�). In the wave-current tank, the equilibrium burialdepth was also found to be a function of the Shields parameter,albeit with larger scatter. The experimental observations made inboth facilities have similar trends but different magnitudes. Forequivalent values of the Shields parameter, smaller equilibriumburial depths were observed in the wave flume when comparedto the ones in LOWST. After burial induced by local scour takesplace, bedform (ripples and sandwaves) formation and evolutionplay a strong and, in some cases, dominant role on the equilibriumburial depth of the cylinders. Depending on how the vertical di-mensions of bedforms compare to the specimen’s diameter, cyclicalcovering and uncovering of the object may take place due to thepassage of the migrating sandwaves. In such case, burial depth Bd

no longer coincides with the vertical displacement (Vd) of the ob-ject as in the case when the burial process is dominated by localscour.

Index Terms—Bedforms, cylinder burial, fluidization, scour.

I. INTRODUCTION

I N sandy coastal environments, the burial of cylindricallyshaped objects, such as cylindrical containers and mines, re-

mains a complex process that is not completely understood. Theinterrelated fluid-structure, fluid-sediment, and structure-sedi-ment interactions make the burial process difficult to predictnumerically, as recognized by Smith and Foster [1]. As a result,there is a clear need for experimental studies on burial processesof finite-length cylinders as pointed out by Bennett [2] and Voro-payev et al. [3], including both laboratory and field conditions.

Cylindrical objects such as pipelines and finite-lengthcylinders laying on a sandy seafloor can be buried through a

Manuscript received June 24, 2005; revised June 7, 2006; accepted August18, 2006. This work was supported by the U.S. Office of Naval Research(ONR) Coastal Geosciences Program under Grants N00014-01-1-0337 andN00014-01-1-0540 [Defense University Research Instrumentation Program(DURIP)].

Guest Editor: M. D. Richardson.The authors are with the Ven Te Chow Hydrosystems Laboratory, Department

of Civil and Environmental Engineering, University of Illinois at Urbana-Cham-paign, Urbana, IL 61801 USA (e-mail: [email protected]; [email protected];[email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JOE.2007.890968

number of mechanisms, including scour, bedform migration,and fluidization of the bed. Investigations on the burial of shortcylinders due to local scour in an oscillating flow tunnel havebeen previously conducted by Carstens and Martin [4], andmore recently by Demir and García [5], while experiments onscour beneath pipelines under wave action have been reportedby Sumer et al. [6] and Sumer and Fredsøe [7], [8]. Voropayevet al. [3] conducted experiments on burial of short cylindersunder shoaling waves. Investigations combining waves andcurrents include the work of Sumer and Fredsøe [7] for flowaround piles, and Cataño-Lopera and García [9] on scouraround short cylinders. These experimental investigations,along with the help of dimensional analysis, showed that theequilibrium burial depth of the object is primarily afunction of the following: 1) the Keulegan–Carpenter (KC)number, in the case of pipelines as reported by Sumer et al. [6],2) the Shields parameter for pure oscillatory flows (POFs)as reported by Demir and García [5], or 3) both parameters forwaves alone (WA) [3], [9], and for combined flows as found byCataño-Lopera and García [9]. Other properties that might alsoplay a role are the mean grain size , standard deviation

, and density of the sediment and the density ,the length-to-diameter ratio , and the surfaceroughness height of the cylinder. Experimental evidencesuggests that such cylinder properties are less influential thaneither or KC.

Local scour and bedform migration are the most likely pro-cesses that cause the burial of finite-length cylinders, whereasbed fluidization becomes important only for very intense flowand sediment transport conditions as in the case of flows gener-ated by strong storms.

Scour occurs when the fluid shear stress on the seabed ex-ceeds a critical value for initiation of sediment transport [6]. Anobject placed on a seabed disrupts the bottom flow, hence in-creasing the flow velocity around the object as shown by Smithand Foster [1]. If the velocity is larger than the critical valueneeded for initiation of sediment transport, scour pits developlocally around the object [7], [8]. As these scour pits grow, theyadvance from the edges towards the center of the cylinder untilthe object falls, almost suddenly, into the scour pit due mainlyto shear failure of the soil supporting the object. During thisprocess, the cylinder may also exhibit pitch and roll motion [31].As the object sinks, it becomes less and less exposed to the flowaction. Provided that the flow is still strong enough to move andresuspend sediment from around the object, scour fronts regen-erate at the ends of the cylinder and start advancing towards thecenter of the body often followed by a new sudden sinking of thecylinder. This process may repeat itself several times until even-tually the burial process stops and equilibrium conditions are

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192 IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 32, NO. 1, JANUARY 2007

Fig. 1. Local scour pattern around cylinder at equilibrium under WA in the wave tank. Comparison between the (a) real view, and (b) its reproduction afterconducting a survey with the SeaTek array of subaquatic acoustic sensors. Hydraulic conditions: waveheightH = 17.4 cm, wave period T = 2.3 s, wavelengthL = 4.6 m, and mean water depth h = 56 cm. Cylinder #2 in Table II.

reached. In this fashion, the time series of relative burial depthmay consist of several stages as shown later. A typical

view of the local scour pattern around a model cylinder is pre-sented in Fig. 1 for the case of waves alone (WA) in the wavetank. Notice also in Fig. 1 the representation of the bed and ob-ject configuration [Fig. 1(a)] after mapping with a subaquaticarray of sensors [Fig. 1(b)] for which longitudinal ( -direction)and transversal ( -direction) resolutions are on the order of 1and 2 cm, respectively.

The burial of cylinders may also be affected by the formationand evolution of sandwaves. Sandwaves are large seabed mor-phological features, with amplitudes up to several meters andwavelengths of tens of meters and migrating rates up to tens ofmeters per year [10]. Tide-generated sandwaves in the field havebeen studied by Li and Amos [11], among others. Semianalyt-ical models for predicting the geometry, vertical growth rate,and migration speeds of sandwaves are reported by Hulscher[12], Komarova and Hulscher [13], and Komarova and Newell[14]. Despite of their sophistication, most of these models failto provide accurate predictions of the sandwave characteristicsas it was shown in [15].

The bedforms presented herein as sandwaves are comparablein size to the so-called large wave ripples (LWR) studied by Liand Amos [11] and by Williams et al. [16]. These structures aremobile and migrate at different speeds depending on size; largerbedforms travel more slowly than smaller ones. In this manner,they can cover and uncover totally, or partially, an object dueto their own passage as described by Cataño-Lopera and García[17]. In particular, a given object is buried while under the sand-wave crest and is unburied while in the trough.

Fluidization of the bed occurs when the bottom flow velocityis large enough to move the seabed at the sediment-water inter-face as a layer. This condition is generally known as sheet flow,and is observed in coastal environments during strong storms,

as pointed out by Soulsby [18]. At very high velocities, corre-sponding to high Shields parameter values, existing bedformssuch as ripples, sandbars, and sandwaves are washed out andthe bed becomes flat with intense sediment transport. When thenecessary conditions are achieved to initiate sheet flow, the ob-jects on the sea bottom sink quite rapidly.

The aim of this paper is to present the main results obtained onthe burial of short cylinders from experiments conducted in thefollowing two laboratory facilities: large oscillating water-sed-iment tunnel (LOWST) and wave tank. It has been recognizedthat the KC number is one of the main controlling parametersin the burial of cylindrical objects under free-surface oscilla-tory flows [3], [6]–[9], [15]. The range of flow parameters, in-cluding the maximum and minimum KC tested in the tunneland in the wave tank are presented in Tables AI and AII, re-spectively. Herein, however, attention is given to the role of theShields parameter in scour burial. This later parameter hasbeen recognized as the main controlling parameter in experi-ments conducted in the sediment tunnel (LOWST) as describedby Demir and García [5]. Demir and García [5] showed that at-tempts to include KC in the analyses for prediction of final burialdepth resulted in more scatter than if the Shields parameter wasused; so, the idea herein is to explore the differences and sim-ilarities on the burial of objects in both facilities based on therole of .

II. EXPERIMENTAL FACILITIES AND TEST CONDITIONS

Two facilities were used for conducting the experimentaltests. One of them is an LOWST which has a testing section15 m long and 0.8 m wide. Both the sand bed and the waterlayer, above the sand bed, are 60 cm deep. Within the testsection, horizontal velocities up to 2 m/s can be generated andthe oscillation period can be varied from 2 to 18 s. The tunnelis also equipped with two pumps that allow superposition of

CATAÑO-LOPERA et al.: SELF-BURIAL OF SHORT CYLINDERS UNDER OSCILLATORY FLOWS AND COMBINED WAVES 193

TABLE IEXPERIMENTAL RESULTS FOR OC AND COMBINED FLOW IN THE LOWST

TABLE IIPROPERTIES OF TEST CYLINDERS FOR WAVE TANK EXPERIMENTS

mean currents on the oscillatory flow. Experimental tests weredistributed as follows: 30 with POF, three with only current(OC), and six with combined oscillatory plus current flows(CF). Data for the cases of OC and combined flow conditionsare shown in Table I. The facility and the data corresponding tothe POF along with a detailed analysis were presented in [5].

The second experimental facility is the large tilting wave-cur-rent tank that is 49 m long and 1.83 m wide, and is equipped witha piston-type wavemaker and a pump to recirculate the water inthe tank. Along the central portion of the tank, there is a sandpit covering a length of 24 m and having a thickness of 31 cm.More than 95 object burial experiments were conducted in thistank; around 70 for WA and the remaining ones for combinedflow (CF) conditions. Aside from local scour studies, the inter-action of cylindrical models with migrating bedforms was alsoinvestigated. The characteristics of the tested model cylindersare described in Table II. The idea behind using cylinders withdifferent properties was to investigate the role of properties suchmaterial (density) and aspect ratio on the final burial depthof the cylinder. After analysis of the results, it was found thatin most cases the main controlling parameter on the final burialdepth was still the Shields parameter , and the other parame-ters were found to be of less significance, at least for the exper-imental conditions considered in this paper.

The same sediment was used in both facilities. The bed ma-terial was a well-sorted silica sand of mean diameter0.25 mm. The angle of repose and the porosity of the sand wereexperimentally found to be 32.5 and 0.3 , respectively. In allof the experiments, the cylinder axis was oriented perpendicularto the flow/oscillation direction.

An acoustic sensor (model SU7110) with a 12-Hz samplingrate and 0.8-mm vertical resolution was utilized for mea-suring waveheight and wave period . This sensor

Fig. 2. Typical recorded velocity time series under WA. Hydraulic conditions:T = 1.6 s, H = 16 cm, L = 3.6 m, and h = 56 cm. Measurements weretaken 3 cm off the mean level of the bottom.

was mounted upon a movable carriage attached onto rails at thetop of the wave flume. A more detailed description of this fa-cility and the experimental procedure followed for determiningequilibrium burial depth under local scour is given in [9]. The3-D velocity measurements were taken with a standard acousticDoppler velocimeter (ADV) in both facilities. Fig. 2 showstypical time series of 3-D flow velocities recorded in the waveflume. The same device was also utilized in the wave tank totrack the burial of the cylinder since it can measure the distanceseparating its tip and the top of the object. This type of sensorallows measurements of the three velocity components simulta-neously at a frequency of 25 Hz within a measuring cylindrical


volume of approximately 0.1 cm [19]. The ADV was attachedto a frame with the capability of vertical, transversal, andlongitudinal axis displacements.

Bottom topography of the scour pit around the cylinderand the surrounding bedforms (ripples and sandwaves) wascollected using a 32-composite-element array of subaquaticacoustic sensors (developed by SEATek, Inc., Alachua, FL).This instrument allows vertical resolution of the order of

2 mm. The set of sensors was attached to a frame that allowedvertical and horizontals displacement as in the case of theADV. Top photographs of intermediate and final (equilibrium)configurations of the scour hole around the cylinder were alsotaken with a standard digital camera.

III. FRICTION FACTOR CALCULATIONS

The main dimensionless parameter used in this paper for de-scribing the equilibrium burial depth of cylinders due to localscour is the Shields parameter , which is computed using thewidely used formula of Swart [20] as presented by Soulsby [18],that is

(1)

where is the mean grain-size diameter, is the accelerationof gravity and is the submerged specific gravity of the sedi-ment, and is the friction factor. For rough turbulent flow

for (2)

for (3)

where is the orbital amplitude of excursion ofthe water particles right outside the wave boundary layer. Noticein (1) that for combined flow, is replaced by , and

is used instead of in (2) and (3).A more general expression, valid for smooth, transitional,

and rough turbulent flows like the one proposed by Myrhaugand Slaattelid [21], could provide a better approximation for thefriction factor. Furthermore, notice that a more realistic frictionfactor predictor would have to include the form drag associatedwith the potential presence of bedforms in addition to the skinfriction component. Nevertheless, only the skin friction is usedin this paper for comparison purposes since previous empiricalformulas have relied only on this component of the total frictionand also due to the fact that skin friction is the main parameteraffecting sediment erosion and transport [3], [8].

For the case of OC flow experiments the shear velocitywas calculated as

(4)

where is the time-averaged horizontal velocity at a near-bedlevel just outside the viscous boundary layer and is thecurrent friction factor defined by

(5)

in which is the Von Karman constant andis the level (i.e., roughness height) where

the velocity is assumed to be zero. Hence, in (1), for the caseof OC, both and were used instead of and ,respectively.

In the case of combined oscillatory and current flow CF, thedetermination of the friction factor is complicated. The non-linear interaction between waves and currents dictates that theresulting friction factor is not simply a linear superposi-tion of the friction factor due to the oscillatory/wave motionand the friction factor due to currents . In the literature, thereare several expressions such as those of Soulsby [18], Myrhaugand Slaattelid [21], and Madsen and Grant [22]. Such expres-sions are not very accurate and uncertainties still remain. Forthe present experiments with combined flows, such formula-tions were used and similar results were obtained with them.

IV. BURIAL INDUCED BY LOCAL SCOUR

Observations in both experimental facilities showed that equi-librium burial depth was reached within the first 1.5–2 h for mostof the runs. After this, the burial process was no longer attributedto the so-called local scour and is mainly influenced by the for-mation and evolution of bed features larger than ripples (i.e.,the sandwaves). Sandwave formation was only observed in thewave tank for longer experiments with durations ranging from34 to 70 h.

Before presenting computations regarding combined flows,it is worth pointing out that the superimposition of a current onthe oscillatory/wave motion does not necessarily imply an in-cremental increase in the resultant equilibrium burial depth withrespect to the case of wave/oscillation alone. Experimental evi-dence shows that relative burial depths of pipes may or may notbe larger for CF than for WA depending on the ratio

, where is the undisturbed current velocity at the centerof the pipe. Sumer and Fredsøe [8] show that, going from WA,i.e., , to current alone, i.e.,

, the scour depth decreases slightly and reaches a near-con-stant value corresponding to the value of current alone, when

. For , the scour depth first decreases slightly,when , and then increases for

. For ,the scour depth tends to a constant value, independently of KC,which corresponds to the case of current alone. It may be arguedthat a similar process is present when dealing with finite cylin-ders instead of pipelines.

As the current velocity is increased, the flow under thecylinder becomes weaker causing less sediment transport andconsequently reducing the burial depth. For stronger currents,the lee-wake of the upstream side of the cylinder is reduced insize, as the ratio approaches 1. In this case, theeffect of waves is so weak that they no longer play a role andequilibrium burial depth is about the same as in the case forcurrents alone.

More than 80% of the experiments under combined flow con-ducted in both facilities fall within the range for


regardless of the value of KC. This suggests that areason why the trend corresponding to CF falls below the trendof POF and OC (LOWST) and below the one for WA (wavetank) is that the burial depth of cylinders follows a similar pat-tern to that of pipelines as described by Sumer et al. [6]. In thiscase, the superimposed currents are rather weak, i.e., most ofthe current velocities are incapable of moving sediment by theirown action. However, such weak currents help in the transport ofthe sediment that is already placed in suspension due to action ofthe oscillatory motion. On the other hand, very few experimentsunder CF fall within the range andtheir equilibrium burial depths are similar to their counterpartsunder POF and WA conditions.

All measured data points in the LOWST collapsed onto asingle line when the bed shear stresses were calculated by ig-noring the effects of the mean current. This was due to the factthat, in most of the tested cases, the effect of the superimposedcurrent was arguably small. Similarly, all measured data in thewave tank fall onto a curve with a similar slope to that observedin the case of the experiments with LOWST.

The burial processes observed in the experiments show sim-ilar characteristics in both facilities. Scour pits were reasonablysymmetric at both edges of the specimen, along the longitudinalcylinder axis. In the direction of wave propagation in the wavetank, the scour pit was asymmetric presenting a longer depres-sion downstream of the cylinder when compared to its counterside part (Fig. 1). Such asymmetry was more pronounced whena current is superimposed on the wave flow.

A large percentage of the equilibrium burial depth occurredduring the first stages of the experiment. Typically, that tookplace within the first 1 to 5 min (Fig. 3), depending on the flowconditions, cylinder dimensions, and the initial burial depth(Fig. 4). After the first hour, the sinking process slowed downsignificantly and the time required to reach equilibrium condi-tions decreased as the flow energy increased. Before each run,the cylinder was gently placed over the flattened sand bed. Thisinitial burial depth was experimentally estimated to vary from3 to 4 mm for tests conducted in the wave tank (seeTable I). However, in LOWST, some experiments started fromgreater burial depths resulting from previous experiments (to ). In general, the stronger the oscillatory/wave motionis, the sinking of the cylinder becomes faster and there are fewerintermediate stages in the time series of relative burial. The ex-perimental results from both facilities showed that the equilib-rium burial depth under all flow conditions can be expressed as afunction of the Shields parameter , regardless of the cylindricalmodel properties. The resulting data points for versusfollow a lower and parallel trend to the one for POF and WA,for both the tunnel and the wave tank, respectively.

For experiments conducted in the LOWST, the dependence ofthe equilibrium burial depth on the Shields parameterwas very strong (Fig. 5) and best described by

(6)

with a correlation coefficient of .

Fig. 3. Example of time series of relative burial depth B =D for cylinder 3 inTable II. Case of WA with hydraulic conditions: T = 2.6 s, L = 5.6 m, andh = 56 cm.

Fig. 4. Schematic diagram of the burial process starting from flat bed condi-tions. (a) Cylinder with initial burial depthB and (b) subsequent burial depthB . Wave propagation is from right to left.

Fig. 5. Equilibrium burial depth versus Shields parameter for experiments con-ducted in the LOWST for live bed conditions � > � .

Fig. 5 includes all experimental data for POF, OC, and CF.The Shields parameter falls within the range .Notice here that the fitting numerical constants in [5, eq. (20)]differ slightly from those in (6). This difference arises from


Fig. 6. Equilibrium relative burial depth as a function of the Shields parameterfor experiments conducted at the large wave flume. Cases of WA and combinedflow for live bed conditions � > � .

the use of different friction factor equations for computing theShields parameter. In [5], the equation proposed by Myrhaugand Slaattelid [21] was used instead of (2) and (3) employedherein.

In the wave tank, all measured data were found to have atrend with identical slope to the one representing the LOWSTresults (Fig. 6). Again, neglecting the effect of the current in thecase of combined flows caused that the following expressionwas obtained after fitting the whole data set (WA and CF):

(7)

The experimental results obtained in the wave tank experi-ments showed more scatter than in the case of the oscillatingtunnel. Such scatter is believed to have two primary sources:one due greater variations in experimental conditions in thewave tank experiments compared to the experiments in theoscillating tunnel. For example, the flow is more symmetricalin the LOWST, so maximum and minimum orbital velocitiesare practically the same in magnitude and the initial level of thebed can be controlled more easily. In the wave tank, there areother variables that may affect wave conditions. A significanteffect can be wave reflection from the beach since this variable,in particular, differs from experiment to experiment accordingto the actual wave climate. Nonetheless, wave reflection wasmaintained at less than 12% for most of the experiments.

A second source might be associated with changes in the pe-riod of oscillation when asymmetries in the wave profile arepresent. In the case of the wave tank, nonlinearities in the wavevelocity field associated with asymmetries in the surface waterwaves can play a very important role in the whole interactionsbetween fluid structure and bed. Part of the tested hydraulic con-ditions allowed for the development of nonlinear waves that arein turn no longer accurately described by small wave theory (asit was done herein for the sake of simplicity). Nonlinear wavesare characterized by having wave crests higher (in magnitude)and narrower than their counterpart—the troughs. This behavior

Fig. 7. Equilibrium relative burial depth (B =D) as a function of the Shieldsparameter (�). The existence of the two parallel trends also suggests a depen-dence of the burial depth on the oscillation period (T ) for asymmetric waveconditions in experiments conducted in the wave tank.

is reflected in the near-bottom velocities where the forward flowvelocity becomes larger than the backward velocity. Existingrelations developed for symmetric oscillatory flows tend to un-derestimate sediment transport rates when applied directly to theasymmetric case as pointed out by Davies and Li [23]. Further-more, these nonlinear effects have wave period dependencies,which have yet to be well defined, as recognized by Lambkinet al. [24], and that are thought to provide part of the expla-nation for the scatter observed in Fig. 6. Voulgaris et al. [25]showed that to satisfy the threshold of motion for quartz sands,a larger shear force is needed to erode sediment under a shorterwave period. This is exactly what seems to be reflected in thedata points corresponding to 4 s in Fig. 7. Following thefindings of Voulgaris et al. [25], one can arguably attribute theresulting lower equilibrium relative burial depths, for the samevalue of , to the direct effect of the period of oscillation .That is, given the presence of nonlinear waves combined withrather small values of , the shear stress exerted by the flowon the sediment surrounding the object is not strong enough tocause as much erosion as it would cause under longer periods ofoscillation. This would lower sediment transport leading to lessscour, and consequently, less burial of the object.

Notice in Fig. 7 that, for 4 s, the experimental results forwaves are found to match the estimator equation characteristicof the experiments in the LOWST, i.e., (6). The remaining datapoints 1.5 s 4 s are better described by

(8)

The observations are predicted more accurately by (6) and(7), than by any other expressions available in the literature.This is to be expected since the same data were used to de-velop these equations. One of the more widely used expres-


Fig. 8. Measured final relative burial depth. Comparison between predictedvalues from (6), (7), and (9) from HR Wallingford Ltd. model.

sions for burial predictions under current action was proposedby HR Wallingford Ltd. (Wallingford, Oxon., United Kingdom),as cited by Friedrichs [26], using the theoretical background de-veloped by Whitehouse [27]. Although some constants in theequations were derived for unidirectional current experiments,the equations have been modified as a burial estimator underwave action.

In the HR Wallingford Ltd. model, the equilibrium burialdepth depends on the velocity of the current and on the criticalvelocity associated to the initiation of sediment motion on anundisturbed bed. The model equations read as

for

for

for(9)

where is the current velocity above the cylinder (or maximumorbital velocity in the case of waves), is the critical ve-locity required for initial grain movement, and is the cylinderdiameter.

This model has some shortcomings since some constants inthe equations were found by curve fitting of only three experi-mental data points, the validity of the expressions under waveaction was not tested, and the experiments were done with onlyone model cylinder which had a length-to-diameter ratio offive.

Fig. 8 shows a comparison between the predictions from (6)and (7) and the predictions from (9) for the present measureddata. It is readily observed that (9) overpredicts most of the mea-sured data. In fact, for most of the present experimental condi-tions, the HR Wallingford Ltd. model predicts total burial of thespecimens, in particular the maximum allowed burial in (9), i.e.,

. This clearly was not the case and it leads to the conclu-sion that (9) is not suitable for prediction purposes, at least forthe range of conditions tested in this paper.

V. INFLUENCE OF BEDFORMS ON THE BURIAL

OF THE CYLINDER

Bedforms of different length scales are bottom features thatdevelop commonly under oscillatory flows. Size and migrationspeeds depend on hydraulic conditions and bed material charac-teristics. Starting from flat bed conditions, it is often observedthat ripples form very quickly and reach stable conditions afteronly a few minutes. Ripples fields over a flat bed can last up toa couple of hours. During that time, ripples migrate normallyin the same direction of the wave/oscillating and current flowpropagation. If the vertical and/or horizontal dimensions of theripples are comparable to (or longer than) the cylinder diam-eter, the burial of the cylinder is affected by the passage of themigrating ripples. Scour pit morphology is affected by the pres-ence of the bed features that surround it. As ripples migrate,scour pits around cylinders fill, and a given cylinder becomescompletely trapped by the sand and sinking stops. In this situa-tion, the cylinder may undergo periodic burial due to the passageof migrating ripples. This has also been reported by Voropayevet al. [3] when conducting experiments on burial of short cylin-ders under shoaling waves on an inclined bottom. The periodiccovering and uncovering of a cylinder depends directly on thevelocity of migration of the ripples, the size and shape of the rip-ples, and the diameter of the cylinders. Ripples travel at varyingspeeds, but normally averaging 0.01–1.3 cm/min. For longertimes, the uncovering and covering process can be dominatedby the passage of larger bedforms (i.e., sandwaves), when theseare present.

In the experiments run in the wave tank, the interaction be-tween ripples and cylinders was also observed when experi-menting with the smaller cylinder reported in Table II, i.e., steelspecimen. A well-defined scour pit was always observed in thecase of cylinders with larger diameters, i.e., cylinders 1–5 inTable II. The scour pit was not affected by the presence of themigrating ripples in the surrounding area [Fig. 1(a)].

Sandwaves also play a primary role in the global burialprocess of the cylinder. Once they start to develop, it isobserved that they travel in the direction of wave propagation.Under WA, sandwaves show a more symmetrical pattern thanin the case of the ones generated under combined flows thatexhibit asymmetric shapes similar to dunes generated underunidirectional flows, i.e., with a steeper lee side and a less steepstoss side (Fig. 9). The superposition of ripples and sandwavesunder waves is also reported in [15], [16], and [28]. Observedsandwaves in those studies had wavelengths between 2–8.4 mand heights between 2.5–40 cm.

To study the effect of sandwave formation and migration onthe general scour/sinking process, five cylinders were placedon the sandy bottom separated approximately 70 cm from eachother (Fig. 9). Several experiments with a duration ranging from34 to 70 h were conducted for both WA and CF. Cylinders em-ployed were type number 3, as described in Table II. To trackthe evolution of the bottom, an array of 32 subacoustic sensors(SEATek) was utilized. Bottom surveys were made 1 and 4 cm inthe streamwise and transverse directions , respectively.


Fig. 9. Sandwaves and ripples appearance after 34 h under combined flow. Hydraulic conditions: U = 40.2 cm/s,H = 19.5 cm, T = 5.8 s, L = 17.2 m,and h = 56 cm.

Since ripples migrate at significant speeds, it was decided to per-form the measurements after stopping the run at different times.The reach of the survey was 400 cm long (between abscissas 731and 1031 cm, measured from the origin of the sand bed). Thisreach was considered adequate since it covered all five cylindersand gave enough distance, for proper description of the scourpits, upstream and downstream of the first and last cylinder, re-spectively. Evolution of bedforms over time and scour processaround the cylinders are shown for a particular experiment underCF in Fig. 10. It was observed that during the period for whichripples are superimposed upon a flat bed, the scour pits aroundall cylinders show very similar characteristics [Fig. 10(a)]. Aftersandwaves develop, the shape and size of the scour pit are af-fected depending on their relative location over the sandwave[Fig. 10(b)].

Another interesting picture of the process is observed whenconcentrating on the evolution over time of the scour pit aroundthe right-most cylinder in either of the images in Fig. 10.Starting from flat bed [Fig. 11(a)], no scour pit is present; then,after six hours, the presence of a defined scour hole is notice-able, which starts to be affected by the presence of larger ripples,in particular on the upstream side of the specimen [Fig. 11(b)].After 12 h, it is observed that the scour pit is highly disruptedby the growing and migrating sandwaves. Scour depressions onboth edges of the cylinder almost disappear but the downstream

scour depression still remains [Fig. 11(c)]. At 18 and 24 h,downstream scour depression continues its tendency to be lessand less noticeable [Fig. 11(d) and (e)]. After 34 h, the cylinderis trapped by the passing ripples and is close to being totallyburied by the now more mature sandwave [Fig. 11(f)].

In summary, the burial of the cylinder is controlled by thefollowing two processes: 1) process occurring in the first stagesof the experiment where local scour is dominant and 2) processin which the object may become partially or totally buried dueto the migration of the bedforms. Due to the presence of suchbedforms, it becomes necessary to distinguish between the ac-tual vertical displacement and the net burial depthof the cylinder. While the first simply refers to the vertical dis-tance separating the cylinder from its initial position at any giventime, the latter is defined as the distance from the bottom ofthe cylinder to the mean level of the surrounding bed. In thismanner, the total time series of the vertical displacement of thecylinder can be separated into the following two regions: one inwhich equals and one in which no longer coincideswith . Fig. 12 shows a time series of for the case of theleft-most cylinder in Figs. 9 and 10. Notice again that Figs. 4–6refer to equilibrium burial depth due only to local scour, i.e., forcases where .

In real situations, in which cylindrical objects are placedon the seafloors, the sequence flat bed, ripple formation, and


Fig. 10. Evolution over time of scour pattern and migration of ripples superimposed to sandwaves under WA. Conditions: D = 15.2 cm,H = 19.6 cm, L =

4.3 m, T = 2.04 s, and h = 56 cm.

sequent sandwave formation are rarely observed. A more real-istic situation would be the one in which the system of super-

imposed bedforms (ripples and sandwaves) is already present atthe moment of the cylinder deployment. In such a case, the


Fig. 11. Evolution over time of burial of cylinder due to the following. First, local scour, and second, continuous sinking due to passage of sandwave. Conditions:h = 56 cm, H = 19.3 cm, T = 5.8 s, L = 17.2 m. Cylinder 3 in Table II. Case of combined flow U = 40.2 cm/s.

burial of the object after impact will most likely be due to localscour. This is supported by the fact that the time scale associatedwith the object’s burial is much smaller (normally, a significantpercentage of the equilibrium burial depth occurs during the first10 min after deployment) than the time scale associated withbedform migration. It is believed that the previous equationsdeveloped for local scour, i.e., (7) and (8), are still suitable forpredictions of equilibrium burial depth of cylinders deployedover sandwaves. These equations would be more adequate forthe case in which the dimensions of the sandwave are muchbigger than the diameter of the cylinder since in this case thesurroundings of the specimen can be considered “locally” asa flat bed. After local scour, the interaction of the object withlarger bedforms takes place in a similar fashion as describedearlier. Recently, Cataño-Lopera and García [29] have found

Fig. 12. Distinction between relative vertical displacement (V =D) and rela-tive burial depth (B =D) under combined flow with U = 51.0 cm/s,H =19.6 cm, T = 1.9 s, L = 4.4 m, and h = 56 cm.


Fig. 13. Burial due to fluidization for the steel cylinder where U = 88 cm/s and T = 3.6 s. (a) t =0 s, (b) t = 10 s, (c) t = 20 s, and (d) t = 35 s.

that the orientation of the specimen with respect to the mainwave-current flow direction does affect the burial process andthe scour pit morphology.

VI. CASE STUDY OF BURIAL INDUCED BY FLUIDIZATION

Fluidization is a term used for the state of a sediment bedwhere the bedforms are no longer present and the water-sedi-ment mixture moves as a layer (i.e., sheet flow). When the nec-essary conditions are satisfied to fluidize the bed, structures atthe sea bottom experience different movements. Objects lyingfreely on a sandy bed become totally buried and/or change theirlocations; some sections of buried pipelines can get uncoveredand float to the soil surface as reported by Sumer and Fredsøe[8].

To simulate the necessary conditions to obtain fluidization ofthe bed, a few experiments were conducted in the LOWST. Theprimary purpose of these experiments was to properly definethe value of the Shields parameter from where fluidization be-comes the main mechanism for burial of cylindrical objects. Arange for the Shields parameter from 0.7 to 0.8 was identified inthe present experiments, as the transitional zone between burialmechanisms, going from local scour to bed fluidization. Thiscorresponds well with the observations of sheet-flow conditionsreported by Sumer et al. [30] for the case of steady, unidirec-tional currents. Also, this result is not surprising, since Shieldsparameter values near this range have been observed to causethe wash out of existing bedforms and the return to flat bed con-ditions. Here, it should be noted that the calculation of Shieldsparameter values must be done with the procedure defined inthis paper.

Two different responses of cylindrical objects to suchhigh-flow conditions were observed in the experiments,namely, fast burial and rolling motion. If the cylinder density is

high enough to resist rolling due to the flow action (i.e., steelcylinder 7.9 g/cm ), it sinks very rapidly (i.e., in a few sec-onds) as shown in Fig. 13. Typical final burial depths observedin “fast burial” experiments were around half diameter belowthe mean bed surface (i.e., ). However, whencylinders are made up of lighter material (i.e., 2.7 g/cm ),the cylinders rolled back and forth, with the same phase of theflow velocity. The amplitude of the horizontal displacementof the cylinders with respect to its original position was thesame in both directions. This was expected since the oscillatorymotion of the water particles inside the tunnel was nearlysymmetrical. However, in nature, the presence of currentsand wave asymmetries causes different amplitudes of motion,leading to changes in location of the specimens. At this stage,conclusive statements cannot be made and it is recognized thatmore experimental tests have to be conducted that will allowfurther analysis regarding the bed fluidization process and itseffects on burial of cylindrical objects.

VII. CONCLUSION

Two different burial mechanisms were studied during thisstudy, namely, burial induced by local scour and burial due tobedform migration. A third process, associated with bed flu-idization under intense sediment transport conditions (i.e., sheetflow) was also observed. In the case of a local scour, the presentexperimental results show a strong dependency of the equilib-rium relative burial depth on the Shields parameter ,for the case of live bed conditions, i.e., for . Thecritical Shields parameter was calculated with a modifiedcritical Shields parameter equation (see details in [18]). Suchdependency is stronger in the case of experiments conducted inthe LOWST than in the case of the wave tank. For oscillatoryflow experiments (in the LOWST), where no asymmetries in theflow field are involved, the dependence is given by (6). It was


TABLE IIIEXPERIMENTAL RANGES OF FLOW PARAMETERS IN THE LOWST

TABLE IVEXPERIMENTAL RANGES OF FLOW PARAMETERS IN THE WAVE TANK

found that, for the wave tank experiments, the numerical coef-ficient of becomes smaller for 4 s, but very similar for

4 s. This behavior is believed to be associated with non-linear wave effects which were present in the wave tank but didnot exist in the LOWST.

Measured equilibrium burial depth due to local scour datacorresponding to CF were observed to collapse onto those cor-responding to POF (LOWST) and WA (wave tank) when thevelocity of the mean current was neglected in the friction factorcalculations. This was particularly true for the case in whichthe near-bed oscillatory/wave velocity was higher than the ver-tically averaged velocity of the superimposed current. In fact,more than 80% of the experiments conducted in this study cor-respond to this case. More studies on the subject intended todetermine whether or not this is truly the case are needed, espe-cially for the case in which . Application of (6) and (7)is encouraged for quick estimations of final burial depth underoscillatory/wave and combined flows.

A second process that influences the final burial depth is asso-ciated with the presence of migrating bedforms such as ripplesand sandwaves. Interaction between these bottom features andthe object is observed in the case in which the horizontal andvertical dimensions of the bedforms are comparable to the diam-eter of the cylinder. Periodical covering and uncovering of theobject may take place due to the passage of the migrating bed-forms. Due to this interaction, the scour hole around the objectand the net burial depth of the specimen are strongly affected.In this way, proper distinction between net burial depth and netvertical displacement of the cylinder has to be made.

Fluidization of the bed is the main mechanism for burial of theobject for conditions where the Shields parameter is larger than0.7–0.8 according to the present experimental data. However,to be buried by this mechanism, an object has to have a densitylarge enough to resist rolling over the bed due to the action of theflow. Lighter objects, regardless of their dimensions, roll backand forth for a long time due to the action of the flow. In thispaper, the maximum observed equilibrium burial depth was ofthe order of for objects heavy enough to resist rolling backand forth along the sand bed.

APPENDIX IRANGE OF PARAMETERS TESTED IN BOTH FACILITIES

Please see Tables III and IV.

ACKNOWLEDGMENT

The authors would like to thank F. Pedocchi for his valuablecomments and M. D. Richardson for his editorial help duringthe preparation of the final version of the manuscript.

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Yovanni A. Cataño-Lopera received the degree incivil engineering and the M.S. degree in exploita-tion of hydraulic resources from the UniversidadNacional de Colombia, Medellín, Colombia, in 1997and 2000, respectively, and the Ph.D. degree incivil engineering from the University of Illinois atUrbana-Champaign, Urbana, in 2005.

During his permanence in the doctoral program,he was a Research Assistant and conducted ex-perimental work that was financed by the CoastalGeosciences Program of the U.S. Office of Naval

Research. In November of 2005, he became a Water Resources Engineer forthe Hydrologic Systems Inc., San Rafael, CA.

Salih T. Demir was born in Turkey. He received theB.S. degree in civil engineering from the IstambulTechnical University, Istambul, Turkey, in 2002 andthe M.S. degree in hydraulic engineering under thesupervision of Prof. M. H. García from the Universityof Illinois at Urbana-Champaign, Urbana, in 2005.

While at the University of Illinois, he conductedexperimental work that was financed by the CoastalGeosciences Program of the U.S. Office of NavalResearch.

Marcelo H. García received the undergraduateengineering diploma from the Universidad Nacionaldel Litoral, Argentina, in 1982 and the M.S. andPh.D. degrees in civil engineering from the St.Anthony Falls Hydraulics Laboratory, Universityof Minnesota, Minneapolis, in 1985 and 1989,respectively.

Since 1990, he has been on the faculty in theDepartment of Civil and Environmental Engineering,the University of Illinois at Urbana-Champaign,Urbana. He is the Chester and Helen Siess Professor

of Civil Engineering, Professor of Geology, and the Director of the Ven TeChow Hydrosystems Laboratory.

Dr. García is the Editor-in-Chief of the ASCE Sedimentation EngineeringManual of Practice 110 and the recipient of 2006 Hans Albert Einstein Award.

Documents

Self-Burial of Short Cylinders Under Oscillatory Flows and Combined Waves Plus Currents