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1 INTRODUCTION

Field observations show that ''undrained'' granular soils (silt/fine sand) can be present on theocean floor in the so-called loose state. These soils are prone to liquefaction under waves due to

buildup of pore-water pressure. Likewise, ''undrained'' (silt/fine sand) backfill soils in pipelinetrenches also are prone to liquefaction for the same reason. The stability of pipelines buried insuch soils is of major concern in practice. Of particular interest is the potential for floatation of

gas pipelines. When buried in a soil which is vulnerable to liquefaction, the pipeline can float tothe surface of the soil simply because the density of the pipeline is smaller than that of the lique-fied soil. Therefore it is important to determine the ''critical'' pipeline density for floatation. It isalso equally important to determine the density of liquefied soil so that assessments could bemade whether or not there is potential for pipeline floatation for a given set of soil, wave and

pipeline parameters. There are reported incidents in the literature where sections of pipelinesfloated to the surface during storms, Sumer and Fredse (2002, p. 445). From the literature(Sumer et al., 2004) there appears to be no consensus regarding the reported/recommended val-ues of the critical density for pipe floatation, and the density of liquefied soil. The purpose ofthe present work is to study in a systematic manner (1) the critical floatation density of a buried

pipeline, and (2) the density of liquefied soil.

2 EXPERIMENTS

2.1 The experimental setup

The experiments were carried out in a wave flume, 0.6 m in width, 0.8 m in depth and 26.5 m inlength. Waves were produced by a piston-type wave generator. The water depth was maintained at42 cm. The soil was placed in a 0.175 m deep, 0.59 m wide and 0.9 m long perspex box (withtransparent walls), located at a distance 12 m from the wave generator. The box was placed in theflume so that the soil surface was flush with the false bottom of the flume. Pore-water pressure wasmonitored at four depths, z = 5.5,7.5,12.5 and 17 cm, during the course of the pipe floatation tests,z being the vertical distance measured downwards from the mud line. Rosemount, model 1151 DP

Pipeline floatation in liquefied soils under waves

B. Mutlu Sumer, Figen Hatipoglu and Jrgen FredseTechnical University of Denmark, MEK, Coastal and River Engineering Section (formerly ISVA),

Building 403, 2800 Lyngby, Denmark

Niels-Erik Ottesen Hansen LICENGINEERING A/S, Ehlersvej 24, DK-2900 Hellerup, Denmark

ABSTRACT: This paper summarizes the results of an experimental and theoretical investigationof (1) pipeline floatation in a soil (liquefied under waves) and (2) density of the liquefied soil. Inthe experiments, the soil was silt with d 50 =0.078 mm. Pipeline models of 2 cm diameter wereused. Waves (with 17 cm wave height and 1.6 s wave period, the water depth being 42 cm) wereused to liquefy the soil. The pipes with specific gravity smaller than 1.85 (near the bed surface)- 2.0 (near the impermeable base) floated when the soil was liquefied. A hydrodynamic modelhas been developed to predict the density of liquefied soil. The model is based on the force bal-ance (in the vertical direction) for a soil grain settling in the liquefied soil.

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Alphaline, pressure transducers were used in the pore-water pressure measurements. More infor-mation about the experimental set-up can be found in Sumer et al. (1999). In the tests, the processof liquefaction/compaction was videotaped from the side.

2-cm-diameter perspex pipes were used as pipeline models. The length of these pipeline modelswas 0.57 m, slightly smaller than the wall-to-wall width of the silt box. Small pieces of metalswere placed in the pipes to obtain desired values of the pipe density that were to be tested.

(These small pieces were distributed evenly along the length of the pipe to ensure a uniform dis-tribution of the load on the soil). The two ends of the pipes were then ''sealed'' with rubbercorks. The range of the specific gravity of pipeline tested in the experiments was s p = p/ =1.47-2.05.

The way in which the test set-up was prepared for a typical test is as follows. The silt box wasfilled with water. The pipeline models (three pipelines with different densities for each experimen-tal run) were then placed in the water at a desired depth. They were 18 cm apart. (Three pipelineswere used to reduce the number of runs). The pipelines were held in position by suspending themwith nylon strings. The soil was placed in the water gently by hand, rubbing it between the fingersto get rid of air bubbles, and crushing soil lumps to ensure an even soil texture across the entire

box. Then the flume was filled with water. The strings (which were holding the pipelines) weresubsequently cut, and the waves were switched on. In this way the pipeline models were free tomove when the soil was liquefied. The waves were stopped when the liquefaction/compaction

process came to an end. (The latter lasted about 7 minutes). If the pipeline model was floated to thesurface of the bed, it could be detected quite clearly. Otherwise, the soil was ''excavated'' carefullyto determine the pipe's final burial depth. A total of 24 pipes with different specific gravities weretested in the experiments.

2.2 Test conditions

The soil used in the tests was silt with d 50 = 0.078 mm and the geometric standard deviation =2.7. Other properties of the soil are as follows. The specific gravity of soil grain s = s / =2.721; the coefficient of lateral earth pressure k 0 = 0.41; the maximum void ratio emax = 0.941;the minimum void ratio emin = 0.499; the specific weight of liquefied soil during liquefaction liq = 18.15-19.91 kN/m 3; the specific gravity of liquefied soil during liquefaction sliq = liq / = 1.85-2.03. Before- and after-the-test values of various soil properties, on the other hand, are as fol-

lows.

Before-the-test values: The void ratio e = 0.77; the total specific weight of soil t = 19.35kN/m 3; the total specific gravity t / = 1.97; the submerged specific weight of soil = t - =9.54 kN/m 3; the porosity n = 0.435 and the relative density D r = (emax-e) / (emax-emin) = 0.387.

After-the-test values: The void ratio e = 0.55; the total specific weight of soil t = 20.70 kN/m3;

the total specific gravity t / = 2.11; the submerged specific weight of soil = t - = 10.89kN/m 3; the porosity n = 0.354 and the relative density D r = 0.885

Finally the wave properties are as follows. The wave height is H = 17 cm; the wave period T =1.6 s; the water depth h = 0.42 m; the wave length (from the linear wave theory) L = 2.89 m.

3 EXPERIMENTAL RESULTS3.1 Pipeline floatation

Fig. 1 displays the critical specific gravity of pipeline for floatation obtained from the presentexperiments, represented by Line A. The pipeline floated in the area to the left of Line A in Fig.1, while it sank in the area to the right of Line A. From Fig. 1, it is seen that the ''critical'' spe-cific gravity of the pipeline for floatation, s p,cr (Line A) is not a constant set of value, but rathera function of the burial depth, z, and is represented for the present tests by the following expres-sion

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85.1)(0103.0, += cm z s cr p (1)

with s p,cr = 1.85 at the mud line, increasing to a value of s p,cr = 2.03 at the impermeable base.The pipe floats when s p < s p,cr , and it sinks when s p > s p,cr .

As mentioned previously, the burial depth of the pipeline at the termination of its travel upwards(as well as downwards) also was measured. It was found that this depth, when plotted versus the

specific gravity of pipeline, coincided precisely with Line A in Fig. 1. This implies that the pipestops (in its travel upwards or downwards) at the depth where its specific gravity is equal to thecritical specific gravity for floatation s p = s p,cr , The latter may be interpreted as that the pipelineacted as a hydrometer, the instrument to measure density of liquids.

Fig. 1. Results of pipe floatation test. Fig. 2. Maximum accumulated pore pressure.

3.2 Specific gravity of liquefied soilThe specific gravity of liquefied soil, s liq = liq/ , in the present tests was obtained in three differ-ent ways: (1) From the floatation tests where the pipe is considered to act as a hydrometer; (2)From direct measurements; and (3) From the force balance equation corresponding to the criti-cal condition for the pipe floatation.

In the floatation tests, the pipe can be considered to have acted as a hydrometer. Therefore thedensity of the liquefied soil, s liq = liq / , was obtained from s liq = s p,cr where s p,cr is given in Fig.1, Line A. The latter data indicates that the density of the liquefied soil is not constant, but in-creases with the depth as given in Eq. 1, taking the value of 1.85 at the mud line and reachingthe value of 2.03 at the impermeable base, for the present tests.

The specific gravity of the liquefied soil was also measured directly by collecting samples fromthe soil during liquefaction. The way in which the samples were collected is as follows. Small,thin-wall cylindrical cups (3.8 cm in diameter and 1.9 cm in height and 0.35 mm in wall thick-ness) were used to collect samples from the soil during the liquefaction phase. The sampleswere taken at two different depths, z = 0.5 cm and 5 cm. (Samples could not be taken fromdepths larger than 5 cm because of the experimental constraints). Five samples were collected ateach depth. The samples were dried in the oven. Wet and dry weights of the samples were de-termined. From the latter, the density of the liquefied soil was obtained. The density values didnot vary between the measuring depths. The overall average specific gravity (over a sample ofsize 30) was found to be sliq = liq / =1.925 with a standard deviation of 0.02. The manner in

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which the samples were collected in these tests was not precise enough to resolve the depthvariation exhibited in Fig. 1. Nevertheless, the difference between the value obtained by directmeasurements and that from the floatation tests for the interval z = 0.5-5 cm, is less than 2.5%.

The third method involves the equation of force balance for the pipe (in the vertical direction)corresponding to the critical condition for floatation. This equation reads

z p

p L D

p L D

p p L D

+=

4

2

4

2

4

2 (2)

in which D is the pipe diameter, L p the pipe length, p the pipe specific weight and p the accu-mulated pore-water pressure in excess of the static pore-water pressure. The first term on theleft-hand side of the equation is the weight of the pipe, the first term on the right-hand side ofthe equation is the buoyancy force and the last term is the pressure gradient force on the pipe(directed upwards).

From the preceding equation, the pipe specific gravity corresponding to the critical condition forthe pipe floatation will be

z

pcr p

s

+=

)/(1

,

(3)

This equation enables the critical pipe specific gravity to be calculated from the measured pore-water pressure distribution, corresponding to the liquefaction state of the soil. Fig. 2 displaysthis distribution. As seen, the variation is linear for z < 14 cm and it bends slightly as z increases

beyond z = 14 cm. Since the pipes in the floatation experiments are buried for z (measured fromthe mud line to the centre of the pipe) < 14 cm, the straight-line portion of the variation in Fig. 2can be used to calculate the gradient ( p/)/z.

Once the critical pipe specific gravity is calculated from Eq. 3, this value is set equal to the spe-cific gravity of the liquefied soil, sliq = s p,cr ; see the discussion in the preceding paragraphs. FromFig. 2, the pressure gradient is found to be = 0.93, and therefore the specific gravity of the lique-fied soil will be sliq = 1.93 for the range 5 cm < z < 14 cm. Apparently, the variation of the spe-cific gravity of the soil with the depth illustrated in Fig. 1 is not resolved in this approach. Noclear explanation has been found for this. Nevertheless, the value found for sliq agrees quite well

with those described in the previous two subsections. Particularly, the difference between thespecific gravity obtained from the force balance (1.93, for the range of z = 5-14 cm) and thatfrom the floatation tests (1.9-2.0 for the same range of z, see Fig. 1) is, on average, 1%.

4 A MATHEMATICAL MODEL

As indicated in the preceding section, an upward-directed pressure gradient will be generated inthe liquefied soil (Fig. 2). This pressure gradient will gradually drive the pore water upwardswhile the soil grains settle due to gravity. Now, the force balance equation for a soil grain set-tling in the liquefied soil reads

06

3502

4

250

2

1

6

350

6

350 =

z

pd w

d

DC

d

s

d

(4)

The first term represents the weight of the grain, the second term the buoyancy force, the thirdterm the drag on the grain and the fourth term the pressure-gradient force on the grain (an up-ward force in excess of the static situation). Here, it is assumed that the grains have sphericalshapes (with the diameter equal to d 50). In the preceding equation, s is the specific weight ofsediment grains, C D the drag coefficient and w the fall velocity of grains. It may be noted thatthe drag force is actually ~ ( V -w)2 in which V is the vertical component of the velocity corre-sponding to the seepage-flow driven by the upward-directed pressure gradient. However, it can

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be shown that V is one order of magnitude smaller than w, and therefore can be neglected for the present test conditions (Sumer et al., 2004).

Soil which can undergo residual liquefaction (i.e., the liquefaction caused by the buildup of pore-water pressure as in the present application) is normally an ''undrained'' soil, such as veryfine sand and silt. Therefore, the drag on the grains can be assumed to be in the Stokes regime.Hence, replacing the drag force with the Stokes-regime drag force, the preceding equation reads

02

50

18)/()1( =

gd

w

z

p s

(5)

in which is the kinematic viscosity and g the acceleration due to gravity. The kinematic vis-cosity and the fall velocity w are functions of solid concentration, c:

032

2

c= and

0)1( wncw = (6)

in which 0 and w 0 are, respectively, the kinematic viscosity and the fall velocity with diluteconcentrations. ( c is the volume concentration). For a single grain settling in water with zerosolid concentration, Eq. 5 reduces to

02

50

0018)1( =

gd

w s

(7)

The accumulated pore-water pressure, p, in excess of the static pore-water pressure, reaches theoverburden pressure value at the onset of liquefaction:

30

21'

k z p

+= (8)

From Eqs. 5-8, the following equation is obtained

0)1()1(32

2

30

21)1()1( =

+

snc

c

k t s (9)

This is the first equation of the model. The specific gravity of the liquefied soil, on the otherhand, can be written in terms of the solid concentration as

scc

liq s += )1( (10)

Given the quantities s/ , t / and k 0, the solid concentration c can be calculated from Eq. 9, andsubsequently the specific gravity of the liquefied soil can be obtained from Eq. 10.

The model was calibrated so that the calculated value of s liq matched s liq = 1.94, the depth-average value corresponding to the range 1.85-2.03, measured in the present tests (see Section3.2). In this calibration exercise, the power n was taken as the calibration coefficient. The latterassumes a constant value for very fine sand or silt. Baldock et al. (2004, Fig. 5) give n = 4.5 forsieve grain size d < 0.1 mm. In the previous research, n was determined on the basis of sedimen-tation and fluidization experiments. Cheng (1997) demonstrated that n is also a function of thegrain specific gravity, s, and found that n decreases with decreasing s. The present upward-directed pressure gradient plays essentially a similar role; namely it is as if the grains have a re-duced specific gravity due to the upward-directed pressure gradient. Therefore, it is expectedthat n should assume values smaller than 4.5. The calibration exercise indicated that n = 2.7.

Fig. 3 presents the model results for the specific gravity of liquefied soil for two values of k 0 Inthe figure, Floatation and Sinking areas are also marked. sliq decreases with increasing t / , This

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is explained as follows. The force that keeps the particles in ''suspension'' in the liquefied soil isthe upward-directed pressure-gradient force (the second term on the left hand side of Eq. 5. Thisforce is proportional to / (or alternatively t / ), see Eq. 8. The larger the value of t / , the lar-ger the pressure-gradient force, the more ''dilute'' the mixture of soil and water, and therefore sliq should decrease with increasing t / . The variation with k 0 can also be explained in the sameway.

Fig. 3. Specific gravity of liquefied soil. Model results. s/ =2.65. Silty sand with emax=0.9 and emin=0.3.

5 CONCLUSIONS

Model pipelines were used to investigate the pipe floatation in a soil liquefied by waves.The experiments indicate that pipes with a specific gravity smaller than 1.85-2.0 float, thecritical pipe specific gravity for floatation (the lower bound, 1.85, corresponding to the ini-tial pipe position near the surface of the bed, and the upper bound, 2.0, to that near the im-

permeable base). The pipe floats (or sinks) to a depth where the pipe specific gravity is equal to the critical

pipe specific gravity for floatation. The specific gravity of liquefied soil varies with depth; it is 1.85 at the surface of the bed

and 2.03 at the impermeable base for the present tests. A mathematical model (based on the force balance in the vertical direction for a soil grainsettling in the liquefied soil) has been developed to predict the specific gravity of liquefiedsoil for ''undrained'' soils such as fine sand and silt.

Acknowledgement . This study was partially funded by the Commission of the European Com-munities, Directorate-General XII for Science, Research and Development FP5 specific program''Energy, Environment and Sustainable Development'' Contract No. EVK3-CT-2000-00038,Liquefaction Around Marine Structures LIMAS.

6 REFERENCES

Baldock, T.E., Tomkins, M.R., Nielsen, P. and Hughes, M.G. (2004). Settling velocity of sediments athigh concentrations. Coastal Engineering, vol. 51, 91-100.

Cheng, N.-S. (1997). Effect of concentration on settling velocity of sediment particles. ASCE J. Hydrau-lic Engineering, vol. 123, No. 8, 728-731.

Sumer B.M., Fredse, J., Christensen, S. and Lind, M.T. (1999). Sinking/Floatation of pipelines andother objects in liquefied soil under waves. Coastal Engineering, vol. 38/2, October 1999, 53-90.

Sumer, B.M. and Fredse, J. (2002). The Mechanics of Scour in the Marine Environment. World Scien-tific, 552 p.

Sumer, B.M., Hatipoglu, F., Fredse, J. and Hansen, N.-E.O. (2004). Floatation of pipelines in soils liq-uefied by waves. Submitted for publication.