Onset of Scouring

7/29/2019 Onset of Scouring

1/23

.Coastal Engineering 42 2001 313335

www.elsevier.comrlocatercoastaleng

Onset of scour below pipelines and self-burial

B.M. Sumer ), C. Truelsen, T. Sichmann, J. Fredse( )Department of Hydrodynamics and Water Resources ISVA , Technical Uniersity of Denmark, 2800 Lyngby, Denmark

Received 3 April 2000; received in revised form 19 October 2000; accepted 8 November 2000

Abstract

This paper summarizes the results of an experimental study on the onset of scour below and self-burial of pipelines in

currentsrwaves. Pressure was measured on the surface of a slightly buried pipe at two points, one at the upstream side andthe other at the downstream side of the pipe, both in the sand bed. The latter enabled the pressure gradient which drives a

.seepage flow underneath the pipe to be calculated. The results indicated that the excessive seepage flow and the resultingpiping are the major factor to cause the onset of scour below the pipeline. The onset of scour occurred always locally but

.not along the length of the pipeline as a two-dimensional process . The critical condition corresponding to the onset of scourwas determined both in the case of currents and in the case of waves. Once the scour breaks out, it will propagate along the

.length of the pipeline, scour holes being interrupted with stretches of soil span shoulders supporting the pipeline. As thespan shoulder gets shorter and shorter, more and more weight of the pipeline is exerted on the soil. In this process, a critical

.point is reached where the bearing capacity of the soil is exceeded general shear failure . At this point, the pipe begins to .sink at the span shoulder self-burial . It was found that the self-burial depth is governed mainly by the KeuleganCarpenter

number. The time scale of the self-burial process, on the other hand, is governed by the KeuleganCarpenter number and the

Shields parameter. Diagrams are given for the self-burial depth and the time scale of the self-burial process. q 2001 ElsevierScience B.V. All rights reserved.

Keywords: Currents; Onset of scour; Pipeline; Scour; Self-burial; Waves

1. Introduction

If the initial embedment of a pipeline laid on aseabed is not very large, and the flow induced by

.currentsrwaves is sufficiently strong, the bed maybe washed away underneath the pipe, the onset of

scour it may be noted that the bed may not bewashed away underneath the pipe, and yet some

slight scour may occur at the pipeline. In this paper,

however, the term Aonset of scourB will be used for

)

Corresponding author. Fax: q45-45-932860. .E-mail address: [email protected] B.M. Sumer .

the case when the bed is washed away underneath.the pipe . The onset of scour is basically related to

the seepage flow in the sand beneath the pipeline,

which is driven by the pressure difference between

the upstream and downstream sides of the pipe.

The critical conditions for the onset of scour have . .been studied by Mao 1986 , Chiew 1990 , Sumer . .and Fredse 1991 and Klomp et al. 1995 .

.Mao 1986 has described the role of vortices thatform in front and at the rear of the pipe. He has also

discussed the seepage flow underneath the pipe in

relation to the onset of scour. The latter has been .further elaborated by Chiew 1990 . The latter author

0378-3839r01r$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. .P I I : S 0 3 7 8 - 3 8 3 9 0 0 0 0 0 6 6 - 1


2/23

( )B.M. Sumer et al.rCoastal Engineering 42 2001 313335314

has also linked the onset of scour to the process of

piping. Although the previous work has given a

considerable insight into the process of onset of

scour, the precise impact of the above mentioned

pressure difference on the soil behaviour was not

fully described.

Another problem regarding the onset of scour

concerns the critical condition defining the onset of .scour. Sumer and Fredse 1991 conducted experi-

ments to determine the critical conditions in the case

of waves, and expressed it in terms of two parame-

ters, namely the KeuleganCarpenter number, KC,

and the initial embedment-to-diameter ratio, erD. .Klomp et al. 1995 later extended the Sumer and

.Fredse 1991 study to the case of combined wavesand current. However, no study is yet available

investigating this matter for the case of currents, a

common case which is of large practical importance,

considering pipelinesrcables laid on a riverrseastrait bed.

The first part of the present study addresses the

two issues mentioned in the preceding paragraphs, .namely: 1 the mechanism of the onset of scour, and

the role of the pressure gradient in the latter process .in wavesrcurrents; and 2 the critical condition for

the onset of scour incurrents.

Once the scouring commences, it will propagate

along the length of the pipeline, as sketched in Fig.

1. A three-dimensional scour pattern emerges in

which the scour holes are interrupted by stretches of

Fig. 1. General scour picture around a pipeline.

soil, called span shoulders, where the pipe obtains its

support, section A-A in Fig. 1a.

Various modes of self-burial of the pipe may

occur, depending on the flow, the soil, and the pipe

stiffness:

1. Scour, sagging, backfilling and eventual self-burial of the pipeline between span shoulders.

2. The soil supporting the pipeline may fail due to

liquefaction, leading to the self-burial of the

pipeline.

3. The self-burial of the pipeline occurs at span

shoulders due to the so-called general shear

failure.

The first case has been investigated by Fredse et .al. 1988 . Various accounts of the spreading process

the spreading of scour along the length of the.pipeline have been given in Leeuwenstein et al. . .1985 , Bernetti et al. 1990 , and Hansen et al. .1991, 1995 .

The second case has been investigated by Sumer .et al. 1999 , and various quantities such as the

sinking depth, the time scale, the influence of the

pipes specific gravity, the influence of wave charac-

teristics, etc. have been discussed. It was demon-

strated that a pipe initially sitting on the bed could

sink to a depth of 22.5 D in a soil confined with an

impermeable base below.

The third case, i.e. the self-burial of pipelines at

span shoulders, has been investigated by Sumer and .Fredse 1994 . However, in this latter work, the

flow environment was limited only to steady current.

In the second part of the present study, attention

is concentrated on the self-burial of pipelines at span

shoulders in waves. It turns out that the self-burial

depth is a function of KC, and the variation of the

self-burial depth with KC is the same as that for the

scour depth for a fixed pipeline.

2. Experimental set-up

.Two kinds of experiments were conducted: 1The experiments related to the onset of scour; and .2 those related to the sinking of pipeline at spanshoulders.


3/23

( )B.M. Sumer et al.rCoastal Engineering 42 2001 313335 315

2.1. Experiments related to onset of scour

.Two kinds of experiments were carried out: 1 .current experiments; and 2 wave experiments.

The current experiments were conducted in an

open flume, 2 m in width, 0.5 m in depth and 23 m

in length. The water depth was maintained at 0.30 m.

A 5.5-m-long and 0.10-m-deep sand-bed section was

established in the flume, protected at two ends by .sections of crushed stones 3.5 cm in size with 1:10

slope. The upstream end of the sand-bed section was

12 m from the inlet section of the flume. The test

section itself was 3 m from the upstream end of thesand-bed section. A vertical, guiding wall made of

.plywood divided the working section into two partsalong the length of the sand-bed section so that one

section had the same width as the length of the test

pipe in the wave flume, namely 0.6 m. Two pipe

sizes were used in the experiments, diameter Ds10and 5 cm. The pipe was rigidly fixed in this section

to the side wall of the flume at one end, and to the

guiding wall at the other. The pipe surface was

smooth except in one test where the surface of the

10-cm diameter pipe was roughened, as will be

detailed later. The junction between the pipe and the

side wall may be a critical section for the onset of

scour. This is because a half horseshoe vortex may

form due to the separation of the boundary layer on

the side wall, and cause scour. To avoid this, the

upstream part of the junction between the pipe andthe side wall was filled with sand with an extent ofabout one diameter, both along the length of the pipe

.and along the side wall , moulded in the form of astreamlined surface. This prevented the scour at the

two ends of the pipe.

The wave experiments were carried out in a flume,

0.6 m in width, 0.8 m in depth and 26.5 m in length.

The water depth was maintained constant at 0.33 m.

Monochromatic waves were produced by a piston-

type wave generator. Similar to the current experi-

ments, a 0.10-m deep sand section was established in

the flume, 3-m-long, protected at the ends by crushed

stones. The offshore end of the sand section was 11

m from the wave generator. The test section was

halfway through the length of the sand section. The

pipe was rigidly fixed to the two side walls of the

flume. A wave absorber at the onshore side of the

wave flume was used to minimize the reflection. The

flow velocity was measured by a bi-directional mi-

cropropeller.

The pipe was equipped with two pressure tap-

pings, 5 mm in diameter and covered with 40 mm

nylon filters, 328 apart, as sketched in Fig. 2. They

were connected to pressure transducers. The pres-

sures were recorded automatically at a sampling

frequency of 30 Hz. The length of recording was . .O 10 s for the current experiments, and O 30 s for

the wave experiments, corresponding to the length of

time from the start of the flow to the instant when

the scouring commences. The purpose of the pres-

sure measurement was to obtain the pressure gradi- .ent that causes the seepage flow at the instant of

the onset of scour, as will be detailed later in the

paper. In these measurements, the pipe was slightly

buried with a burial depth of es0.64 cm, as sketched

in Fig. 2.

Two kinds of sand were used in the experiments:d s0.18 mm and geometric standard deviation s50 g

.1r2s d rd s1.2, and d s1.25 mm and ss84 16 50 g1.2.

In the wave experiments, flow visualization tests

were also made. For this, a laser sheet of light

scanned the experimental section vertically, and the

flow was made visible with the sand itself.

The test conditions regarding these experiments

are given in Table 1.

Fig. 2. Set-up for the pressure measurement.


4/23

Table 1

Test conditions for the onset of scour

2 . Test Flow Burial Pipe Wave U or U , Bed friction Sand Shields Pipe U r gm . .num be r de pth, de pt h, di am ete r, pe riod, c mrs velocity U or size, parameter, Reynolds 1y n Df

2 . . . . . . h cm erD D cm T s U , cmrs d mm u number, U r gw fm 50 m . Re 1y n D

( )a Steady current experiments smooth pipe4

O1.1 30 0.064 10 Increased 0 2.5 0.18 0 0.20 0 5.0= 10 0 0.30

O1.12 gradually

from 0 up

to about 50

4

O2 30 0.01 10 22 1.0 0.18 0.03 2.2= 10 0.06

4O3 30 0.02 10 26 1.2 0.18 0.05 2.6= 10 0.09

4O4 30 0.03 10 28 1.3 0.18 0.06 2.8= 10 0.10

4O5 30 0.05 10 33 1.5 0.18 0.08 3.3= 10 0.14

4O6 30 0.10 10 56.5 2.6 0.18 0.23 5.7= 10 0.42

4O7 30 0.15 10 72.5 3.3 0.18 0.38 7.3= 10 0.69

4O8 30 0.04 5 27 1.3 0.18 0.06 1.4= 10 0.17

4O9 30 0.07 5 37 1.8 0.18 0.12 1.9= 10 0.35

4O10 30 0.10 5 41 2.0 0.18 0.14 2.0= 10 0.44

4O11 30 0.08 10 54 3.2 1.25 0.05 5.4= 10 0.38

4O12 30 0.10 10 58 3.4 1.25 0.06 5.8= 10 0.44

4O13 30 0.125 10 66 3.9 1.25 0.08 6.6= 10 0.57

4O14 30 0.15 10 70 4.2 1.25 0.09 7.0= 10 0.64


5/23

( ) y2b Steady current experiments. Rough pipe k rDs 6.0= 10s4

O15 30 0.10 10.0 76 3.4 0.18 0.40 6.0= 10 0.72

( )c Wae experiments4

O16 33 0.064 10 4 45 2.4 0.18 0.19 4.5= 10 0.27

4O17 33 0.07 10 1.8 12.0 1.5 0.18 0.08 1.2= 10 0.02

3O18 33 0.01 10 5 9.0 1.0 0.18 0.04 9.0= 10 0.01

4O19 33 0.02 10 4.8 10.0 1.1 0.18 0.04 1.0= 10 0.01

4O20 33 0.10 10 5.2 14.1 1.2 0.18 0.05 1.4= 10 0.03

4O21 33 0.03 10 4 20.0 1.1 0.18 0.04 1.0= 10 0.05

4O22 33 0.01 10 7.4 13.2 1.1 0.18 0.04 1.3= 10 0.02

4O23 33 0.07 10 3.2 30.5 2.1 0.18 0.15 3.0= 10 0.12

4O24 33 0.05 10 4.3 26.0 1.8 0.18 0.11 2.6=

10 0.09

4O25 33 0.04 10 6.9 21.6 1.4 0.18 0.07 2.1= 10 0.06

4O26 33 0.10 10 6.3 25.0 1.6 0.18 0.09 2.5= 10 0.08

3O27 33 0.10 5 2.6 13.0 1.4 0.18 0.07 6.5= 10 0.04

4O28 33 0.10 5 4.4 21.0 1.6 0.18 0.09 1.1= 10 0.17

4O29 33 0.10 5 4.8 25.0 1.7 0.18 0.10 1.3= 10 0.12

4O30 33 0.15 5 4.3 25.3 1.7 0.18 0.11 1.3 x 10 0.17

4O31 33 0.15 5 3.6 40.4 2.3 0.18 0.18 2.0= 10 0.43


6/23

Table 2

Test conditions for self-burial of pipelines. Sand size was d s0.18 mm and angle of internal friction was ws43850

Test Flow Pipe Wave Wave U or U Bed friction Shields Pipe Reynoldm

.number depth, diameter, period, height, cmrs velocity U or parameter, number, f . . . . .h cm D cm T s H cm U cmrs u Rew fm

( )a Steady current experiments4S1 25 10 45 1.7 0.09 4.5=10

( )b Wae experiments4S2 33 10 1.5 10.0 19.6 2.0 0.14 2.0=104S3 33 10 1.5 11.7 25.3 2.3 0.18 2.5=103S4 33 5 2 6.4 13.0 1.5 0.08 6.5=103S5 33 5 2 6.9 18.2 1.8 0.11 9.1=104S6 33 5 2 10.1 20.6 1.9 0.13 1.0=104S7 33 5 2 10.3 23.1 2.0 0.14 1.2=104S8 33 5 2 11.6 28.0 2.2 0.17 1.4=10 4S9 33 5 2.5 12.1 26.5 2.0 0.14 1.3=10 4S10a 33 5 2.5 14.6 31.3 2.2 0.17 1.6=10 4S10b 33 5 2.5 14.6 31.3 2.2 0.17 1.6=10 4S10c 33 5 2.5 14.6 31.3 2.2 0.17 1.6=10 4S10d 33 5 2.5 14.6 31.3 2.2 0.17 1.6=10 4S10e 33 5 2.5 14.6 31.3 2.2 0.17 1.6=10 4S11 33 5 3 10.5 27.1 2.0 0.14 1.4=10 4S12 33 5 3 12.1 30.5 2.1 0.15 1.5=10 4S13 33 5 3 12.6 32.0 2.2 0.16 1.6=10 4S14 33 5 3 14.3 37.2 2.3 0.19 1.9=10 4S15 33 5 3 15.2 41.3 2.4 0.21 2.1=10 4S16 33 5 3 15.7 42.3 2.5 0.21 2.1=10 4S17 33 5 3 16.3 47.1 2.6 0.23 2.4=10 4S18 33 5 3 17.2 50.0 2.7 0.25 2.5=10 4

S19 33 5 3.5 18.5 48.1 2.5 0.22 2.4=10 3S20 33 2 3 8.2 22.2 1.8 0.11 4.4=10 3S21 33 2 3 9.3 30.0 2.1 0.15 6.0=10 3S22 33 2 3 13.6 40.1 2.4 0.20 8.0=10 4S23 33 2 3 16.6 50.2 2.7 0.25 1.0=10


7/23


In Table 1, U is the undisturbed flow velocity at

the top of the pipe in the case of the steady current,

U is the maximum value of the undisturbed, orbitalmvelocity of water particles at the bed, U is thefundisturbed friction velocity in the case of the steady

current, and U is the maximum value of the undis-fmturbed friction velocity in the case of waves, u is the

Shields parameter defined by

U2fus 2.1 .

g sy1 d . 50

in which s is the specific gravity of sand grains, g is

the acceleration due to gravity. In the case of the

waves, U is replaced by U . Also, in Table 1, Re isf fmthe Reynolds number

UDRes 2.2 .

n

the velocity U is replaced by U for the case of them.waves , and KC is the KeuleganCarpenter number

U Tm wKCs 2.3 .

D

in which T is the wave period. Furthermore, k inw sTable 1 is Nikuradses equivalent sand roughness.

The porosity of the sand used in the tests was

ns0.53 for d s0.18 mm sand and ns0.47 for50d s1.25 mm sand.50

Finally, as seen from Table 1, almost all the tests

correspond to the live-bed conditions, i.e. u)u .cr

2.2. Experiments related to sinking of pipeline at

span shoulders

.Two kinds of experiments were carried out: 1 .current experiments; and 2 wave experiments.

The current experiments were conducted in the

same current flume as that for the onset-of-scour

experiments with the same test setup but without the

splitter wall, yielding a width of the test section of 2

m. The mean water depth was 0.25 m.

An aluminium, 10 cm diameter pipe with hy-

draulically smooth surface was used in the current

experiment. It was 1.98 m in length, with a 1-cm gap

between the pipe and the side wall at each end.

These gaps were designed on purpose, to enable the

scour process to start at the two ends of the pipe, and

.propagate towards the center of the pipe Fig. 13a , .similar to that in Sumer and Fredse 1994 . This

enabled controlled tests.

The pipes were mounted to a vertical frame. The

frame itself was mounted to another frame with

frictionless supports, enabling the pipe to move freely

in the vertical direction. The details of the system .can be found in Sumer and Fredse 1994 . The

vertical displacement of the pipe was measured with

the aid of a potentiometer.

The wave experiments were carried out in the

same wave flume as in the onset-of-scour experi-

ments. The test setup was the same as that in the

current experiments described in the preceding para-

graph. The water depth was 0.33 m. Three kinds of

pipes were used in the tests, with diameters Ds2, 5

and 10 cm, all measuring 59.4 cm in length, allow-

ing 0.3 cm gap at the ends. The gap was large

enough for the scour to start at the two ends of thepipe in the same way as in the current experiments.

The time development of the scour along the length

of the pipe was recorded with the aid of two video

cameras, one viewing the entire length of the span

shoulder in plan view, and the other viewing the .process a close-up view at the junction between the

.pipe and the scoured bed Fig. 13a . Experimentswere done for different values of the specific gravity

of the pipe. This was achieved by applying addi-

tional weights to the frame to which the pipe was

mounted. The flow velocity was measured by abi-directional micropropeller, similar to the onset-

of-scour experiments.

The same sand was used in these tests as for the

onset-of-scour tests. The angle of internal friction of

the sand was measured in a vacuum tri-axial test and

was found to be ws438.

Test conditions for these tests are summarized in

Table 2.

3. Mechanism of onset of scour

3.1. Seepage flow and piping underneath the pipe

When a pipeline is laid on a sediment bed, and .subject to a current Fig. 3 , the pressure difference

between the upstream and the downstream of the

pipe will induce a seepage flow underneath the pipe.


8/23


.Fig. 3. Seepage flow underneath the pipe cf. Fig. 2 .

When the current velocity is increased, a critical

point is reached where the discharge of the seepage

flow will be increased more rapidly than the driving

pressure difference dictates, and simultaneously, the

surface of the sand at the immediate downstream of

the pipe will rise, and eventually a mixture of sand

and water will break through the space underneaththe pipe. This process is called piping, and is well-

known in soil mechanics in conjunction with the

so-called piping failures at hydraulic structures such .as dams, cofferdams, etc. Terzaghi, 1948 .

. .Mao 1986 , Chiew 1990 and Sumer and Fredse .1991 considered the piping as the main mechanismresponsible for the onset of scour below pipelines.

. .Piping or quicksand conditions occur Fig. 3 ina cohesionless granular material when the pressure

.gradient E prg rEx exceeds the floatation gradient . .sy1 1yn :

E pG sy1 1yn 3.1 . . . /Ex g

. .in which Ep r Ex is the pressure gradient driving .the seepage flow just underneath the pipe Fig. 3 , s

.is the specific gravity of sand grains ssgrg , gs sis the specific weight of sand grains, g is the spe-

cific weight of water, and n is the porosity at the

.moment when these two quantities in Eq. 3.1 areequal, the soil element at the exit has lost its internal

.shear strength .The previous investigators Mao, 1986; Chiew,

.1990; Sumer and Fredse, 1991 emphasized, how-ever, that the vortices that form in front of the pipe

and in the lee-wake may contribute to the process of

the onset of scour. We shall return to this point later

in the paper.

3.2. Current case

Fig. 4 shows the time series of the pressure .gradient E prg rEx in the case of the steady cur-

Fig. 4. Time series of the pressure gradient just underneath the pipe that drives the seepage flow. Current case. Test O1.6.


9/23


Fig. 5. Sequence of piping process captured by video. Time

instants correspond to those in Fig. 4.

rent. In this test, the flow velocity is increasedgradually until the critical point where the mixture

of sand and water breaks through underneath the.pipe is reached. The pressure gradient is calculated

from the two pressure time series recorded at points .A and B Fig. 2 :

E p p ypA Bs 3.2 . /Ex g gAB

It may be noted that the pressure distributionalong the surface of the pipe in the soil measured in

a separate test, by rotating the pipe at small incre-.ments showed that the pressure distribution, when

.plotted as a function of the distance x Fig. 3 , islinear, revealing the way in which the pressure gradi-

..ent is calculated Eq. 3.2 .In the test, the junction between the downstream

side of the pipe and the bed was videotaped simulta-

neously with the pressure measurements with a mini .underwater camera Fig. 5a . To enable the onset of

scour to occur precisely at the section of the pressure

measurements, the bed was loosened by removing

the sand at this section, and then replacing it in a

very gentle way. In addition to that, a small channelon the bed 15 cm long, and with decreasing depth,

.from 3 to 0 mm was established, as sketched in Fig.6 note that the figure is not to scale; the dimensions

.of the channel are grossly exaggerated . With thisarrangement, the onset of scour occurred precisely at

the same section where the pressure measurements

were made. This arrangement enabled us to relate the

measured pressure gradient to the videotaped onsetof scour. The obtained picture from the video record-

ing is displayed in Fig. 5b and c cf. the time instants.in Figs. 4 and 5 .

From Figs. 4 and 5, the following deductions can

be made. .1 There are two stages in the process of piping,

.leading to the onset of scour Fig. 5b and c . As the .pressure gradient increases with increasing velocity ,

a point is reached where the surface of the sand at

the immediate downstream of the pipe begins to rise

.Fig. 5b , consistent with the description of the pip-ing process described in conjunction with dams in

. Terzaghi 1948 it may be noted that the videorecording showed clearly that this change in the bed

level was not in the form of piling-up of the sand

due to the lee-wake vortex, but rather in the form of.rise of the bed en masse .

.Fig. 6. Small channel 15-cm long, and with decreasing depth from 3 to 0 mm on the bed, enabling the onset of scour to occur precisely at

the section of the pressure measurements. The figure is not to scale; the dimensions of the channel are grossly exaggerated.


10/23


.2 This stage continues for some period of time .about 5 s, Figs. 4 and 5bc , and is subsequentlyfollowed by the process where a mixture of sand and

.water breaks through Fig. 5c . The instant when thesurface downstream starts the rise marks the instant

when the pressure gradient exceeds the floatation

gradient. Subsequently, grains are progressively re-

moved and a breakthrough develops. The process

will depend on the porosity, internal friction, andlength of flow path the longer the path, the longer it

.takes for the breakthrough to develop . .3 The onset of scour never occurred concur-

rently along the length of the pipe in a two-dimen-

sional fashion, rather it always occurred locally, as

illustrated in Fig. 7. If the bed were absolutely

homogenous, the piping would occur over the full-

length simultaneously. The local occurrence is asso-

ciated with the weakest point.

.4 Fig. 4 shows that, for the piping condition to .occur, the pressure gradient E prg rEx has to reach

. . ..the value equal to 1yn sy1 cf. Eq. 3.1 . Note .that 1 the porosity value used here is ns0.53, and

it was determined for the sand in the loosest condi-

tion, consistent with the condition experienced in the .actual tests; 2 a total of 12 experiments were made,

and the mean value of the pressure gradient .E prg rEx was found to be 0.74 with a standard

deviation 0.14; the slight variation of the pressure

gradient from one experiment to the other may be

attributed to the turbulent wake behind the pipeline; .and 3 as seen the mean value of the pressure

.gradient E prg rEx, namely 0.74, is slightly smaller . .than the floatation gradient 1yn sy1 s0.77.

As described in the preceding paragraphs, the bed

was loosened at the measurement section, and conse-

quently, the floatation gradient was probably less

than 0.77 with a porosity larger than the measured

value 0.53, consistent with the expectation that the

piping occurs when the pressure gradient just ex-

ceeds the floatation gradient. However, we were

unable to measure what exactly the porosity was for

the loosened sand at the measurement section.To facilitate comparison, a supplementary test

was conducted somewhat similar to the staticpres-.sure-gradient test of Chiew, 1990 . In this test, the

pipe was placed in the same flume on the sand bed

Fig. 7. Onset of scour.


11/23


with the same burial depth, namely es0.64 cm

corresponding to erDs0.064. The sand bed was

prepared in exactly the same way as in the current

experiment, corresponding to the loosest condition.

Then, both sides of the pipe were filled with waterhalfway through the pipe height see the small sketch

.in Fig. 8 . Subsequently, the water level at Side A of .the pipe Fig. 8 was gradually increased, and the

pressures at Points A and B were continuously

recorded. Fig. 8 displays the time series of the .pressure gradient E prg rEx obtained from these

.records. In the test, it was observed that 1 thepiping occurred in much the same way as in the

.current experiment, and 2 for the piping to occur, .the pressure gradient E prg rEx has to reach the

. . value 1yn sy1 as seen in Fig. 8, cf. Figs. 4. .and 8 , revealing the criterion in Eq. 3.1 .

Comparison of this result and that in the case of

the current experiment indicates that, in the current .case Fig. 4 , although the pressure-gradient force is

apparently the major mechanism, there is also an

additional mechanism which contributes to the onset

of scour. This mechanism may be related to thevortices mentioned earlier see the small box in Fig.

.4 . These vortices do not exist in the supplementarytest, however, they do exist in the current test, and

therefore they may have contributed to the piping

process exhibited in Fig. 4. However, no clear expla-

nation has been found as to how these vortices

contribute to the onset of scour.

Finally, it should be noted that visual observations

made in the current test showed that the vortices

generated at the downstream and upstream parts of .the pipe see the small box in Fig. 4 did not

undermine the pipe prior to the onset of scour whichwould otherwise lead to a slight reduction in the

length of the streamline of the seepage flow, presum-.ably resulting in larger pressure-gradient forces .

3.3. Wae case

Fig. 9 shows the time series of the pressure .gradient E prg rEx in the wave case. The experi-

mental setup was precisely the same as that in the

current case. For the onset of scour to occur, the

wave height had to be selected very large, and thisled to a highly asymmetric wave asymmetric be-

. .tween the crest and the trough Fig. 9 . As seenfrom the figure, the onset of scour takes place in the

crest half period; clearly, the pressure gradient in the

trough half period is not large enough to cause

piping.

As seen from Fig. 9, the onset of scour occurs .when the pressure gradient E prg rEx reaches the

Fig. 8. Time series of the pressure gradient just underneath the pipe that drives the seepage flow. No current. The seepage flow is caused by

the rising water level at side A.


12/23


Fig. 9. Time series of the pressure gradient just underneath the pipe that drives the seepage flow. Wave case. Test O16.

. .value sy1 1yn , and even exceeds it. This resultis different from that obtained for the current case .Fig. 4 . This difference may be attributed to thetime over which the sand is exposed to the critical

pressure-gradient force. In the case of the current,

this time is quite large, namely in the order of .magnitude of 5 s Fig. 4 , the mixture of sand and

.water breaks through only after O 5 s upon the

application of the critical pressure-gradient force inthe case of the supplementary test mentioned in

connection with the current test, this time is also

large, even larger than that experienced in the case of.the current, Fig. 8 . By contrast, in the case of the

waves, the pressure gradient necessary for the onset

of scour is available only for a very short period of .. .time O 0.5 s for each crest half period, Fig. 9 . It

seems that apparently this small exposure to the

critical pressure gradient is not long enough for the

piping to occur. It is only when the pressure gradient

is increased further, and after some number of expo-

sures, the piping takes place, resulting in the onset of

scour. It may be added that the breakthrough is a

progressive process; each wave loosens some grains

on the exit side.

Simultaneous measurements of the surface eleva-tion h not shown in Fig. 9 to keep the figure

.relatively simple and the pressure gradient

.E prg rEx showed that there is a phase difference .between h and E prg rEx: the pressure gradient

.Fig. 9 lags about 20258 behind the surface eleva-tion. Fig. 10 shows a sequence of flow picturesfrom the laser-sheet flow visualization study for the

Fig. 10. Sequence of flow pictures over one period of wave. Test

O16. h is the surface elevation. A new vortex, vortex N, forms . .frame 3 after vortex M is washed over the pipeline frame 2 .


13/23


.same wave conditions as in Fig. 9 over one waveperiod. The instant where the onset of scour occurs

coincides almost with the passage of the wave crest .frame 1 in Fig. 10 where the flow is in the direc-

tion of wave propagation and the lee-wake with.vortex M is well established. This observation rec-

onciles with the flow pattern in the case of the .steady-current see the small sketch in Fig. 4 . Al-

though the flow picture is similar when the trough is .passing frame 3 in Fig. 10 , the onset of scour did

not occur in this half period because the magnitude

of the pressure gradient was not large enough, as has

been pointed out in conjunction with Fig. 9.

4. Criterion for the onset of scour

4.1. In steady current

..The criterion for the onset of scour Eq. 3.1 canbe written in the following non-dimensional form:

Onset of scour occurs if

Ep ) U2

qR G1 4.1 .) 5Ex gD 1yn sy1 . .

cr

in which

p x) )p s , x s 4.2 .2

DrU

r is the water density, U is the undisturbed flowvelocity at the top of the pipeline the top velocity

rather than the center-line velocity is adopted here,

considering the cases where the pipeline may be.buried with erD larger than 0.5 , and g is the

acceleration due to gravity. The term R is a small,

non-dimensional term, and is included here to repre-

sent the effects other than the pressure-gradient forcemainly the effect of the vortices forming in front ofthe pipe and, particularly, in the lee-wake discussed

. ) . ) .in the preceding paragraphs . Both Ep r Ex andR are essentially a function of the burial-depth-to-di-

ameter ratio, erD. Therefore, the criterion for the

onset of scour can be written in the following form.

2U eGf 4.3 . /gD 1yn sy1 D . .

cr

.where the function f erD is to be determined fromexperiments. It may be noted that f is actually a

function of not only the gap-to-diameter ratio, erD,

but also the pipe Reynolds number, ResUDrn,

and the relative roughness krD in which n is theskinematic viscosity and k is the surface roughnesssof the pipe. However, it is expected that the influ-

ence of these latter parameters will not be very

significant, if there is no significant change in the

flow regime, i.e. if the flow around the pipe does not

change from the subcritical regime to the supercriti-

cal regime, or from the supercritical regime to thetranscritical regime see, e.g. Sumer and Fredse,

.1997, Chapter 1 , as will be demonstrated later in thesection. Also, it may be mentioned that cohesionless

granular material is considered in the present analy-sis. Otherwise, soil properties including permeabil-

. ity will also influence the onset of scour clearly, in

the case when the permeability0, the break-.through will never occur . The focus in this subsec-

tion will be on the variation with erD.

The data obtained in the present investigation for .the onset of scour is plotted in the form of Eq. 4.3

in Fig. 11. The procedure used in the tests is as

follows. .1 Level off the bed. . 2 Place the pipe on the sand bed gently without

.pressing it , and fix it to the side walls. Then, fill thetwo sides of the pipe with sand up to the level

corresponding to the burial depth, e, to be studied inthe test. Make sure that the bed at the two sides of

the pipe is more or less horizontal. .3 Increase the flow velocity in small increments

until the onset of scour occurs. Identify this criticalvelocity at this point keep the time of increasing the

flow velocity as short as possible to ensure that no

buildup of sand at the downstream side of the pipe

occurs; the latter would obviously change the picture

regarding the seepage flow and the piping, and there-.fore not desired .

.4 Repeat the exercise in items 1 3 for the nextburial depth to be investigated.

Fig. 11 shows that the larger the burial depth, the

higher the critical velocity for the onset of scour, as

expected. This is because, as the burial depth in-

creases, the pressure gradient will be decreased,

therefore relatively higher velocities will be required

to cause piping.


14/23


Fig. 11. Critical condition for the onset of scour. Current case. Tests O1O14.

.Fig. 11 further shows that 1 the results for twodifferent pipe diameters, namely Ds5 and 10 cm,

seem to coincide, when plotted in terms of the .non-dimensional quantities in Fig. 11, and 2 like-

wise, the results for two different sand sizes, namely

d s0.18 and 1.25 mm, seem to collapse on a50single curve, revealing that the results are unaffected

by the sand size. Note that the experiments forcoarser sand were not conducted for burial depths

smaller than erDs0.08. This is because, for such

small values of erD, the sand will no longer act as acontinuous medium. Therefore, the results will not

.make sense .The data in Fig. 11 can be represented by the

following empirical expression2 0 .5U ecr

s0.025 exp 9 4.4 . /gD 1yn sy1 D . .in which U is the critical undisturbed flow velocitycr .measured at the level of the top of the pipeline forthe onset of scour.

Finally, it may be noted that the time required for

the flow to remove the grains and open a AbreachBwill be appreciably longer for larger diameter pipes

than for those used in the present study.

4.2. Effect of change in flow regime

To see the effect of change in the flow regime

around the pipeline, the 10 cm diameter pipe was

coated with 0.3 cm diameter and 0.3 cm height

cylinder-shaped plastic grains. The burial depth tested

in this experiment was erDs0.1. The grains were .glued in a densely packed manner to the cylinder,

and the roughness height measured from the base.pipe surface to the top of the roughness elements

was 0.3 cm, or alternatively the Nikuradses equiva-

lent sand roughness k +2=0.3s0.6 cm, giving asrelative roughness of krDs6=10y2 . To keep thesboundary condition in the sand the same as in the

case of the smooth pipe, the holes between theroughness elements were filled with plastic for the

portion of the pipe that stays in the sand bed. The

only difference between the rough-pipe test and the

smooth-pipe test is that, in the smooth-pipe case, the

flow around the pipe was in the subcritical regime 4 .Res5.7=10 , whereas, in the rough-pipe case, it

4was in the transcritical regime Res6=10 , krDsy2 . .s6=10 Sumer and Fredse, 1997 .

The result of this experiment is compared with its

smooth-pipe counterpart in Table 3.

As seen, the critical value of the parameter2 . ..U r gD 1yn sy1 is now a factor of 1.7 larger

than that for the smooth-pipe case. This is because,

in the case of the rough pipe, the flow is in the

transcritical regime, therefore the pressure gradientwill be smaller due to the relatively larger wake

.pressure, see, e.g. Sumer and Fredse, 1997, p. 41 ,and hence, relatively larger velocities will be re-


15/23


Table 3

Comparison of critical condition for the onset of scour for two different flow regimes. Burial depth, erDs0.1

2Test Pipe Critical Pipe Reynolds Pipe Flow regime U rcr .number velocity for number at the roughness, gD sy1 ..the onset of scour, critical velocity, krD 1yns

.U cmrs ResU Drncr cr4O6 Smooth 56.5 5.7=10 Subcritical 0.424 y2

O15 Rough 76.0 6.0=

10 6=

10 Transcritical 0.72

quired for the onset of scour. This result suggests

that, for extremely large pipelines with smooth sur- 5..face Re)O 10 , or for mediumrlarge size

4 .pipelines with very large roughness Re)O 10 , y2 .. krD)O 10 where the flow regime is trans-s

.critical, see, e.g. Sumer and Fredse, 1997 , thecritical curve for the onset of scour displayed in Fig.

11 may be shifted upwards so that the critical value

2 . ..of the parameter U r gD 1yn sy1 would be afactor of 1.52 larger than depicted in Fig. 11.

4.3. In waes

In the case of waves, the criterion given in Eq. .4.3 can be adopted provided that the following willbe followed.

Fig. 12. Critical condition for the onset of scour. Tests O16O31. Steady-current result is taken from Fig. 11.


16/23


.1 U is replaced by U , the maximum value ofmthe orbital velocity of water particles at the bed.

.2 There will be an additional parameter regard- .ing the function f, namely f erD, KC . This is ) . ) .because, in this case, the terms Ep r Ex and R

.in Eq. 4.1 are also governed by the KeuleganCarpenter number KC see, e.g. Sumer and Fredse,

.1997 .The dependence of the onset of scour on KC has

.been discussed by Sumer and Fredse 1991 . In thelatter study, the variation of the critical burial depth

for the onset of scour with KC was obtained; how-2 .ever, the role of the parameter U r gD 1yn sy

..1 was not recognized. .The data obtained by Sumer and Fredse 1991

has been recast, and plotted in Fig. 12 together with

the present data. It is seen that both parameters,2 . ..namely KC and U r gD 1yn sy1 , are equallym

significant.For a given value of KC, the critical value of the

2 . ..parameter U r gD 1yn sy1 increases with in-mcreasing erD. This can be explained in the same

way as in the case of the steady current. Likewise,

for a given value of erD, the critical value of the2 . ..parameter U r gD 1yn sy1 increases with in-m

creasing KC. This is because the pressure gradientdecreases with increasing KC cf. the pressure dia-

gram given in Sumer and Fredse, 1991, Fig. 3, and.that in Bearman and Zdravkovich, 1978, Fig. 1 ,

therefore larger and larger velocities will be neededfor the onset of scour, meaning that the critical value

2 . ..of U r gD 1yn sy1 will increase with in-mcreasing KC.

Fig. 12 indicates that, as the KeuleganCarpenter2 number increases, the critical value of U r gD 1ym

. ..n sy1 approaches that in the case of the steady .current. For example, for erDsO 0.05 , the critical

2 . ..value of U r gD 1yn sy1 approaches that form .the steady current for KC)O 20 . This is linked to

the fact that the pressure gradient in the case of the

waves approaches that experienced in the case of the

steady current.

The present study focuses on the variations with

respect to KC and erD. The variation with the .number of waves or the time required for the

piping to occur has not been studied. Similar to the

case of steady current, the time required for the

piping to develop will be appreciably longer for

larger diameter pipes than for those used in the

present study.

5. Self-burial of pipeline at span shoulder

After the scour breaks out underneath the pipe, it

propagates along the length of the pipeline, as

sketched in Fig. 1. A three-dimensional scour pattern

emerges in which the scour holes are interrupted by

stretches of soil, called span shoulders, where the

pipe obtains its support, section A-A in Fig. 1a. As

has been mentioned in Section 1, various cases may

occur, depending on the flow, the soil, and the pipe

stiffness. The present study focuses on the self-burial

of pipelines at span shoulders. As indicated in Sec-

tion 1, attention will be concentrated on the case of

waves.

5.1. Mechanism of self-burial

The process of self-burial occurs as follows. The

scour begins to propagate along the length of thepipeline after the onset of the process Hansen et al.,

.1991 . As the process continues, the length of thefree span will be larger and larger at the expense of

the span shoulder. Therefore, more and more weight

of the pipe will be exerted on the soil over a shorter .and shorter length of the span shoulder Fig. 13a .

This process may reach such levels that the bearingcapacity of the soil is exceeded, and therefore the

soil fails. The failure occurs by sliding in the two

outward directions, as indicated in Fig. 13b. This

type of failure is known as a general shear failure in .soil mechanics Terzaghi, 1948 . Clearly, as the scour

continues, the bearing capacity of the soil will be

exceeded constantly due to the continuous reduction

of the bearing area, leading to the permanent sinking

of the pipe. The process will stop, only when the

pipe sinks to such depths that it will be protected

against the scour. When the scour stops, obviously

the constant failure of the soil will stop, and conse-

quently the sinking of the pipe will come to an end.

As implied in the preceding paragraph, the scour .at the two ends of the span shoulder Fig. 13a is the

key mechanism for the process of pipe sinking. The

scour process itself is governed mainly by the Keule-ganCarpenter number Sumer and Fredse, 1994,


17/23


Fig. 13. Definition sketch. Sinking of pipeline at span shoulder.

.1999 . This is essentially linked to the lee-wake,precisely in the same way as in the case of two-di-

mensional scour below a pipeline; the higher the

KeuleganCarpenter number, the longer the lee-wakethat forms behind the pipe in each half period of the

. motion , the larger the scour see Sumer and Fredse,.1990, for a detailed discussion . This suggests that,

.first of all, the sinking depth the self-burial depth ,e, normalized by the pipe diameter D, should be a

function of the KeuleganCarpenter number KC;

and secondly erD should increase with increasing

KC. The following sections will basically discuss

this issue.

5.2. Self-burial depth

Fig. 14 presents the results of a self-burial testmade in the present study. Here KC was 16 Table

.2 . There are three stages in the process.

.1 During the first 40 s, the scour spreads alongthe length of the pipe until the length of the bearing

.area is reduced to ls40 cm Fig. 14b . .2 At this point, the pipe begins to sink in the

.sand Fig. 14a due to the general shear failure, asdescribed in the preceding paragraphs. This stage

continues for about a little more than 400 s. .3 Subsequently, the space between the pipe and

the scour hole is gradually backfilled with sand, and

the length of the span shoulder begins to increase by

virtue of the backfilling process. This stage takes .place from 480 to 540 s Fig. 14b . With the comple-

tion of this stage, the pipe is eventually buried to a .depth of 2.0 cm erDs0.39 .

The process occurs in precisely the same manner .as described by Sumer and Fredse 1994 for the

case of the steady current.

Fig. 15 displays the data regarding the equilib-

rium self-burial depth obtained in the present experi-


18/23


. .Fig. 14. a Time series of sinking of the pipe and b that of the length of span shoulder. Test S10c.

ments. The existing steady current data from the .present work and from Stansby and Starr 1991 isalso included note that only the data of Stansby and

. .Starrs work with u)u live-bed is included .crFirst of all, Fig. 15 shows clearly that the self-

burial depth is a function of the KeuleganCarpenter

number, KC. It increases with increasing KC, asexpected see the discussion in the previous Section

.5.2 . Secondly, the influence of the pipes specificgravity, s, on the end results is insignificant see the

data point for KCs16, the cross, and also the.legend in Fig. 15 , for this KC number, five tests

were conducted with five different values of s in the

range 1.256, and it was found that the sinking

depth was practically unchanged. Sumer and Fredse .1994 reached the same conclusion in the case ofthe steady current. The sinking is uninfluenced, be-

cause the key element in the process is the scour;

when the scour stops, the sinking will also stop, as

discussed in the preceding subsection. Since thepipes specific gravity is not an influencing factor for

the scour, it will therefore not affect the self-burial

depth.

Although not included here, the present wave

results compare well with those of Stansby and Starr .1991 . However, this is for KC larger than about20. For KCQ20, the self-burial depths of Stansby

and Starr begin to assume smaller and smaller values

with decreasing KC for KCQ20. This may be

attributed to the small pipe size in Stansby and

Starrs experiments; for KC numbers smaller than

about 20, the self-burial depth measured by the latter .authors is esO 0.20.3 cm , and clearly, such

small values of e may be subject to considerable

uncertainty.

Fig. 16 compares the present self-burial data with .the data of Sumer and Fredse 1990 for the scour

depth below a fixed pipeline with an originally zero


19/23


Fig. 15. Self-burial depth vs. KC. Tests S1 S23. Live bed. u)u .cr

.clearance between the pipe and the bed ; see thelegend in Fig. 16. As seen, these two sets of data

agree quite well. This is an interesting result. It can

be explained as follows.

Now, as the sand at the span shoulder fails pro-

gressively, the pipe sinks in the sand, and, at the

same time, it falls in the scour holes at the two sides .of the span shoulder Fig. 13a . The scour process

comes to an end when the pipe reaches the bottom of .these scour holes Fig. 17b . At this moment, the

.scour depth, S Fig. 17b will be fairly close to thatobtained for a fixed pipe originally in contact with

. .the bed Fig. 17a , Fredse et al. 1988 . This im-plies that the self-burial depth at the span shoulder

should be the same as the latter, as revealed by Fig.

16.

Although not tested directly due to the experi-.mental constraints , the preceding results imply that:

1. a pipeline may be self-buried completely for .KC larger than O 100 ; and

2. the self-burial depth of pipelines may reach

values as high as erD, 3, for very large KC .numbers such as O 1000 , representing the tidal

flow conditions.

The following empirical expression, given origi- .nally by Sumer and Fredse 1990 for the equilib-

rium scour depth below a fixed pipeline with an.initial zero gap between the pipe and the bed , can be


20/23


Fig. 16. Self-burial depth, and scour depth vs. KC. Live bed. u)u .cr

used to assess the self-burial depth of pipelines at .span shoulders for KCQ100 Fig. 16 :

e 's0.1 KC . 5.1 .D

Caution must be exercised when extrapolating the

preceding equation for KC larger than 100, as it has

not been tested for the self-burial of pipelines for

such large KC numbers.

Finally, it may be noted that the process of self-

burial studied here is due to general shear failure of

the soil. However, the self-burial may occur due to

other processes as well, as mentioned in Section 1. .Sumer et al. 1999 report self-burial of pipelines in

the laboratory to depths as much as 22.5 D, due to

liquefaction of soil caused by the buildup of pore .pressure. Sakai et al. 1994 report block subsidence

in the laboratory, due partly to the so-called momen-tary liquefaction where the soil is, over a short

period of time, liquefied during the passage of wave.troughs, see Sakai et al., 1992 , and partly to the

.oscillatory flow action. Raudkivi 1976, p. 365 re- .ports a pipeline settling in the surf zone in the field

4 m under the bed level, due to liquefactionrfluidi-zation of bed under waves.

Fig. 17. Definition sketch.


21/23


5.3. Time scale of self-burial process

The sinking of the pipe develops towards theequilibrium stage through a transitional period Fig.

.14a . The time scale of the process may be definedby the following equation

`1Ts eye d t 5.2 . .H t

e 0

.see the definition sketch in Fig. 18 . Here, e is theequilibrium sinking depth and e is the sinking depthtat time t. The time scale T can be interpreted as the

time over which a substantial amount of self-burial

takes place.

The data regarding the time scale is plotted in Fig.

18 as a function of two parameters, namely the

KeuleganCarpenter number, KC, and the Shields

parameter, u. Here, T) is the normalized time scale

defined by

1r23g sy1 d .)T s T 5.3 .2D

.Fredse et al., 1992 , considering that the time scale

of the self-burial process is similar to that of thescour process that induces the self-burial. Fredse et

.al. 1992 gives the background regarding the non-dimensional time scale T) . This non-dimensional

quantity can easily be obtained by normalizing the

equation of sediment continuity. .1 As seen from Fig. 18, the time scale decreases

with increasing u. This is because the larger the

value of u, the higher the sediment transport in the

scour process, the faster the sinking of the pipe in the

sand; therefore, the time scale should increase with

Fig. 18. Time scale of sinking process as a function of KC and u)u .cr


22/23


increasing u. On the other hand, the figure shows

that the larger the KeuleganCarpenter number, the

larger the time scale. This is because the larger the

value of KC, the larger the scour depth, therefore the

larger the volume of the sand undergoing scour,

hence the larger the time scale. .2 Although there is only one data point for the

case of the steady current, apparently the time scale

of the self-burial process in the case of the steady

current seems to be quite close to that for the case of

waves with KCs24. This may be linked to the

self-burial depth. Fig. 16 suggests that the self-burialdepth for the two cases namely, the steady-current

.case and the case of KCs24 are rather close.Therefore, the time scale of the self-burial process

should also be close to each other.

6. Conclusions

.1 The pressure difference between the upstreamand downstream sides of a pipeline drives a seepage

flow underneath the pipe. When this seepage flow

becomes excessive, piping occurs; a mixture of water

and sand breaks through underneath the pipe, result-

ing in the onset of scour below the pipeline. .2 The previously mentioned pressure difference

together with other effects of secondary importancesuch as vortices forming in front of and at the

.lee-wake of the pipe are the agitating forces for thepiping process.

.3 In the case of the steady current the criticalcondition for the onset of scour is determined by two

parameters, the burial depth of the pipe, erD, and a2 parameter involving the flow velocity, U r gD 1y

. ..n sy1 . The critical condition can be assessed fora given pipeline and a given current climate from

Fig. 11. .4 In the case of the waves, there is an additional

parameter, namely the KeuleganCarpenter number,

KC. The critical condition in this case can be deter-

mined, using Fig. 12. .5 Once the scour breaks out, it will propagate

along the length of the pipeline. Scour holes are .interrupted with stretches of soil span shoulders

supporting the pipeline. As the span shoulders get

shorter and shorter, more and more weight of the

pipeline is exerted on the soil. In this process, a

critical point is reached where the bearing capacity .of the soil is exceeded general shear failure . At this

point, the pipe begins to sink at the span shoulder. . .6 The ultimate equilibrium self-burial depth is

a function of KC. The larger the value of KC, the

larger the self-burial depth of the pipeline. . .7 Eq. 5.1 may be used to assess the self-burial

depth for a given wave climate. In the case of the

steady current, on the other hand, the self-burial

depth is 5080% of the pipe diameter. .8 The time scale of the self-burial process is

d ep en de nt o f two p ara me te rs, n am ely th e

KeuleganCarpenter number and the Shields param-

eter, and it may be assessed, using Fig. 18.

List of symbols

D Pipe diameter

d50 Sand size

e .Embedment burial depth of the pipeline .for the onset of scour tests ; otherwise,equilibrium self-burial depth of pipeline

et .Self-burial depth sinking depth at time tg Acceleration due to gravity

h Water depth

KC KeuleganCarpenter number, U T rDm wn Porosity of sand

p Pressure

p ) 2 .Non-dimensional pressure, pr rURe Reynolds number, UDrn, or U Drnm

s Specific gravity of sand, rrrssp Specific gravity of pipeline, rrrpt Time

T Time scale of self-burial process

T) Nondimensional time scale of self-burialw . 3x1r2 2process, g sy1 d TrD

Tw Wave period

U Undisturbed flow velocity at the top of the

pipeline

Um Maximum value of the orbital velocity of

water particles at the bed

Uf

Friction velocity in the case of currents

Ufm Maximum value of the friction velocity in

the case of waves

x distance along the surface of the pipeline in .the sand Fig. 3

x ) Non-dimensional distance, xrD

g Specific weight of water

gs Specific weight of sand grains


23/23


h Surface elevation

u Shields parameter

n Kinematic viscosity

w Angle of internal friction of sand

Acknowledgements

This study was partially funded by the Commis-

sion of the European Communities, Directorate-Gen-

eral XII for Science, Contract No. MAS3-CT97-097, .Scour Around Coastal Structures SCARCOST , and

.by the 5-year 19992004 Framework Programme

AComputational HydrodynamicsB of the Danish

Technical Research Academy, STVF.

References

Bearman, P.W., Zdravkovich, M.M., 1978. Flow around a circular

cylinder near a plane boundary. J. Fluid Mech. 109, 3348.

Bernetti, R., Bruschi, R., Valentini, V., Venturi, M., 1990.

Pipelines placed on erodible seabeds. Proc. 9th International

Conference on Offshore Mechanics and Arctic Engineering

Conference, ASME, Houston, TX, vol. V, pp. 155164.

Chiew, Y.-M., 1990. Mechanics of local scour around submarine .pipelines. J. Hydraul. Eng., Am. Soc. Civ. Eng. 116 4 ,

515529.

Fredse, J., Hansen, E.A., Mao, Y., Sumer, B.M., 1988. Three-di-

mensional scour below pipelines. J. Offshore Mech. Arctic

Eng., Am. Soc. Mech. Eng. 110, 373379.Fredse, J., Sumer, B.M., Arnskov, M.M., 1992. Time scale for

wavercurrent scour below pipelines. Int. J. Offshore Polar .Eng. 2 1 , 1317.

Hansen, E.A., Staub, C., Fredse, J., Sumer, B.M., 1991. Time-

development of scour induced free spans of pipelines. Proc.

10th Offshore Mechanics and Arctic Engineering Conference,

ASME, Stavanger, Norway. Pipeline Technology, vol. 5, pp.

2531.

Hansen, E.A., Klomp, W.H.G., Smed, P.F., Bijker, R., Bryndum,

M.B., 1995. Free span development and self-lowering of

pipelinesrcables. Proc. 14th Offshore Mechanics and Arctic

Engineering Conference, ASME, Copenhagen, Denmark.

Pipeline Technology, vol. 5, pp. 409417.

Klomp, W.H.G., Hansen, E.A., Chen, Z., Bijker, R., Bryndum,

M.B., 1995. Pipeline seabed interaction, free span develop-

ment. Proc. 5th Int. Offshore and Polar Eng. Conf., The

Hague, Netherlands, June 1116, vol. II, pp. 117122.

Leeuwenstein, W., Bijker, E.A., Peerbolte, E.B., Wind, H.G.,

1985. The natural self-burial of submarine pipelines. Proc. 4thInternational Conf. on Behavior of Offshore Structures .BOSS , vol. 2. Elsevier, pp. 717728.

Mao, Y., 1986. The interaction between a pipeline and an erodi-

blebed. Series Paper 39, Tech. Univ. of Denmark, ISVA, in

partial fulfillment of the requirement for the degree of Doctor

of Philosophy.

Raudkivi, A.J., 1976. Loosed Boundary Hydraulics. 2nd edn.

Pergamon.

Sakai, T., Hatanaka, K., Mase, H., 1992. Wave-induced effective

stress in seabed and its momentary liquefaction. J. Waterw., .Port Coastal Ocean Eng., Am. Soc. Civ. Eng. 118 2 , 202

206, See also Discusions and Closure in vol. 119, No. 6, pp.

692697.

Sakai, T., Gotoh, H., Yamamoto, T., 1994. Block subsidence

under pressure and flow. Proceedings of the 24th Conference .on Coastal Engineering ICCE 94 , 2328 October, Kobe,

Japan. pp. 15411552.

Stansby, P.K., Starr, P., 1991. On a horizontal cylinder resting on

a sand bed under waves and current. Int. J. Offshore Polar .Eng. 2 4 , 262266.

Sumer, B.M., Fredse, J., 1990. Scour below pipelines in waves.

J. Waterw., Port Coastal Ocean Eng., Am. Soc. Civ. Eng. 116 .3 , 307323.

Sumer, B.M., Fredse, J., 1991. Onset of scour below a pipeline .exposed to waves. Int. J. Offshore Polar Eng. 1 3 , 189 194.

Sumer, B.M., Fredse, J., 1994. Self-burial of pipelines at span

.shoulders. Int. J. Offshore Polar Eng. 4 1 , 30 35.Sumer, B.M., Fredse, J., 1997. Hydrodynamics Around Cylindri-

cal Structures. World Scientific, xviiiq530 pp.

Sumer, B.M., Fredse, J., 1999. Wave Scour Around Structures. .In: Liu, P.L.-F. Ed. , Advances in Coastal and Ocean Engi-

neering, vol. 4. World Scientific, Chapter, 51 pp.

Sumer, B.M., Fredse, J., Christensen, S., Lind, M.T., 1999.

SinkingrFloatation of pipelines and other objects in liquefied .soil under waves. Coastal Eng. 38 2 , 5390, October.

Terzaghi, K., 1948. Theoretical Soil Mechanics. Wiley, New

York.

Documents

Onset of Scouring