Stiffness characteristics of buried and on-bottom pipelines loaded axially

K. Kruk1 Fugro Engineers B.V., Leidschendam, the Netherlands

ABSTRACT

A testing apparatus was designed and constructed to conduct small-scale physical modelling research on pipe-soil interaction problems. The apparatus allowed investigating the force-displacement behaviour of exposed and buried pipelines under axial loading. The very simplified method of calculation of axial soil resistance of on-bottom pipelines is presented in standards. It does not take into account the actual amount of soil-pipe surface contact. The equation presented in this paper accommodates the latter. There are 3 main methods of estimating axial resistance of buried pipelines. Results of experiment suggest that existing equations, which currently use ‘at rest’ K0 and active Ka coefficients may greatly underestimate axial resistance in denser, dilative soils. In terms of mobilisation distances, standards propose fixed values for sand. It does not take into account any other conditions that can have significant effect on the distance at which full pipe-soil resistance is mobilised. Literature review and experimental work showed that similar parameters used in calculation of axial resistance such as angularity of soil, which can be correlated with angle of friction, also affect mobilized distance. Also it was revealed that larger pipe would mobilise peak axialresistance at larger displacement which is an enhancement to the current approach of constant mobilised distance irrespective of pipe diameter. Keywords: buried pipelines, on-bottom pipelines, buckling, pipe-soil interaction, axial soil resistance

1 Fugro Engineers B.V., Veurse Achterweg 10, 2260 AG Leidschendam, the Netherlands. k.kruk@fugro.nl

1 INTRODUCTION

After the Second World War oil was found in the Gulf of Mexico and the era of offshore pipelines begun. By the 1990s pipelines were laid in 3 km deep waters. The length between the wells and delivery points increased. Longer pipelines mean larger cumulative friction, which has to be overcome by applying even greater pressure to push the fluid through.

For liquids, which are technically not compressible, the increase in the pressure is proportional to the increase in temperature, which exceeds 150°C for some pipelines. This leads to the expansion of the pipeline, which can

result in the most interesting phenomenon happening to buried pipelines: upheaval buckling.

Buckling is a negative effect induced by a compressive force, which distorts pipeline. It is the same as buckling phenomenon in the column loaded axially. But the pipeline’s slenderness ratio is much larger and there is uneven distribution of restrain provided by soil. Additionally, due to difficult conditions of laying pipeline in the seabed the out-of-straightness is unavoidable. Due to these factors pipelines are much more at risk of buckling. Lack of care may lead to, at the very least, costly and eventually dangerous consequences.

Figure 1. Upheaval buckle of 1020mm onshore pipeline in

Uzbekistan [1]

For detailed calculations we need 4 types of soil resistances [2], which are used to model the pipeline movement in the ground: - Downward; - Upward; - Lateral; - Axial. In design, every unit of length of the pipeline is restrained by means of springs attached to the pipeline, which govern its movement (Figure 2).

Figure 2. The model of pipeline response induced by lateral and axial forces and restrained by lateral, vertical and axial

springs, each one with its own unique non-linear force-displacement characteristics [3]

2 SOIL RESISTANCE

The movement of buried or on-bottom pipeline is restricted by the soil. The lateral movement is limited by the soil, which the pipeline tries to push (Figures 3 and 4). The axial movement is limited by the soil-pipeline friction (Figure 5).

Figure 3. Vertical displacement of the buried pipeline and

build-up of soil resistance

Figure 4. Horizontal displacement of the on-bottom pipeline

and build-up of soil resistance

Figure 5. Axial displacement of the on-bottom and buried

pipelines with friction along the perimeters

2.1 Axial resistance

The formulae proposed by previous researchers differentiate between axial resistances for partially embedded and buried pipelines (Table 1). A simplified method of calculation of axial soil resistance of on-bottom pipelines is presented in BS 8010:1993 [4]. It is a model of the body of mass sliding on the surface with particular interface friction between them. However, it does not take into account the actual amount of soil-pipe surface contact.

There are three main methods of estimating axial resistance of buried pipelines. The first one was presented by Schaminee et al. in 1990 [5]. Neither the clue for the estimation of interface friction nor the choice of an appropriate soil pressure coefficient was presented in their paper. Later Finch et al. (2000) [6], Cathie (2005) [7] proposed methods for derivation of interface friction angle and they used an active soil pressure coefficient for Schaminee’s formula.

Another method (ALA, 2001 [3]) is quite similar to the first one. A difference is that it uses at-rest soil pressure coefficient, which is higher than the active one, but the method neglects the submerged weight of the pipe. Tab. 1 Summary of common practice for derivation of soil axial resistance

Method (year) Soil axial resistance, Fa

Partially embedded

BS 8010 (1993)

Drained conditions Fa = µ·W’ Non-cohesive µ = 0.55 to 1.2

Cohesive µ = 0.3 to 1 W’ = pipe submerged weight

revision by Cathie et al. (2005)

Undrained conditions α⋅⋅= ua cLF

L = arc length in embedded soil cu = undrained shear strength

α = alpha factor (coefficient of friction) Buried

Schaminee et al. (1990)

Non-cohesive δγγπ tan)'

41

2)2/(''( ⋅⋅+

+⋅+⋅=

DWDHKHDFa

D = diameter of pipe γ’ = submerged unit weight of soil

H = depth of buried pipe Recommendation for K not given

Cohesive απ ⋅⋅⋅= ua cDF α > 0.2

American Lifelines Alliance (2001)

Non-cohesive δγγπ tan)

2)2/(')2/('( 0 ⋅

+⋅++⋅=

DHKDHDFa

K = K0 φδ ⋅= factorcoating _

Cohesive απ ⋅⋅⋅= ua cDF

α = f(cu)

Finch et al. (2000), revision by Oliphant & Maconochie (2007) [8]

Non-cohesive & cohesive

pa

a DWDHKH

DF µγγ

π ⋅⋅++⋅+

⋅= )'41

2)2/(''

(

K = Ka ppp f φµ tan⋅=

Recommendation for fp not given φp = f(Ip or Id, grading and grain angularity)

2.2 Mobilization distances

In terms of coarser soil ALA (2001) proposes 3mm for dense sand and 5mm for loose sand as mobilization distance. It does not take into account any other conditions, which can have significant effect on the distance at which full pipe-soil resistance is mobilised. Finch et al. obtained a smaller value of 2 mm for sand. The same 2 mm but for loose sand interacting with small-diameter pipe with shallow embedment was obtained by Shupp et al. (2006) [9].

Figure 6. Model of pipe-soil interaction in axial direction for sand; σv = effective vertical soil pressure, σh = effective

lateral soil pressure, σavg = effective average soil pressure, N = normal force, Rfriction = friction force, δ = friction angle

3 EXPERIMENTAL WORK

A testing apparatus was designed and constructed to conduct small-scale physical modelling research on pipe-soil interaction problems. The apparatus allows investigating the force-displacement behaviour of exposed and buried pipelines under axial loading.

The test is very similar to the one used by Wijewickreme (2008) [10] with one major difference (applied in the experimentation for this paper): the pipe was able to move freely in vertical direction. This enabled the investigation of pipe weight effect on axial friction resistance.

Figure 7. Test configuration showing the soil box and the

actuator set for an axial push-in test

4 DISCUSSION

4.1 Exposed pipes

A number of tests were performed during laboratory stage in which axial resistance of fully exposed pipes (so-called ‘on-bottom pipes’) and partially embedded pipes (i.e. buried by half diameter) were investigated.

0

10

20

30

40

50

60

70

0 20 40 60 80 100 120

Weight of the pipeline, W'/L (N/m)

Res

ista

nce

Fa/L

(N/m

)

µ = 1.2

µ = 0.55

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

351.3g

Coe

ffici

ent o

f res

ista

nce,

µ

Partially embedded

Partially embedded

Partially embedded

Partially embedded

On-bottom

On-bottom

On-bottom

On-bottom

Loose GravelMedium dense Gravel Loose Sand

Medium dense Sand

Figure 8. Upper graph shows the results of laboratory test for

different types of soil and different weights of pipe (askew lines indicate lower and upper boundaries according to

equation from Table1 for exposed pipes). Lower graph zooms

in on 351.3g pipe (horizontal lines indicate upper and lower boundaries).

Multiple tests showed good repeatability for the given pipe as well as the same pipe with additional ballast to simulate different pipe weight. Heavier pipe gave larger axial resistance.

The difference between a partially embedded and an on-bottom pipe is noticeable. Equation for cohesive soil in Table 1 does take it into account, whereas for granular material it is omitted (i.e. Fa = µW’, irrespective of embedment depth). This increase in axial resistance may be due to larger area of friction for partially embedded pipe.

In general, the axial resistances achieved in laboratory were closer to calculations based on ‘lower boundary’ coefficient (i.e. µ = 0.55). An exception is the lightest pipe, for which case the results matched the predicted values well (Figure 8).

4.2 Buried pipes

The values of axial resistance achieved during testing with 38mm pipe installed in gravel are well within the range of predicted values based on equations in Table 1. The larger force was needed to push the heavier pipe, which implies that pipe weight is a factor that needs to be taken into account. In terms of density, no substantial increase of axial resistance was observed in medium dense gravel.

Buried pipe tests were also performed on a 38 mm pipe in sand. In this case the values measured were higher than predicted ones. Similarly, resistances larger than expected were measured in dense sands by Wijewickreme et al. (2008) who suggested that passive coefficient of lateral pressure Kp would be more suitable for denser soils. Existing equations (Table 1) currently use ‘at rest’ K0 and active Ka coefficients, which may underestimate axial resistance in denser, dilative soils.

To further investigate, the coefficient of lateral pressure was back-calculated in order to determine the value of K that would match measured and theoretical resistance. The back-calculated K was larger for medium dense sand and much larger than K0 and Ka used in current design.

To investigate the effect of different pipe diameter, the last set of tests was performed on a 76 mm pipe, twice the diameter of the smaller pipe. As before, the effective coefficient of lateral earth pressure K was back-calculated and found to be 0.4 for loose sand and 2.5 – for medium dense sand. This supports the earlier findings.

Both in gravel and in sand an increase of pipe weight gave larger axial resistance. This confirms the importance of pipe weight in calculations of axial resistance, which is not considered in the equation proposed by American Lifelines Alliance (ALA, 2001) [3].

4.3 Mobilization distances

On average, the mobilization distance for 38 mm pipe was 0.9 mm whereas for 76 mm pipe 1.75mm. The results of push-in test were correlated with Wijewickreme (2008) [10] who used a larger pipe and with the values from ALA (2001) standard.

In terms of angularity, which can be correlated with angle of friction of given material the more angular the particles are the smaller the mobilised distance. This was confirmed by tests in which gravel with an angle of friction of 42° and sub-angular particles tend to mobilise at smaller distances i.e. 0.55 mm on average compare to sand (33°) and 0.9 mm for the same pipe.

0

5

10

15

20

0 100 200 300 400 500

Diameter of the pipe, mm

Mob

iliza

tion

dist

ance

, mm

Clay

Sand

Gravel

SoftStiff

LooseDense

LooseDense

Figure 9. Mobilisation distance for a given pipe diameter for clay, sand and gravel. Dotted line represents extrapolation of

results.

A dimensional design chart was created based on experimental results of this study and of Wijewickreme et al. (2008). The data pool is however too small to make accurate predictions for other soils. However, further research could investigate whether similar relationship applies to clay and gravel. The extrapolation of results obtained on sand was performed to other types of soil and presented in Figure 9.

4.4 Correction for exposed pipes

In order to facilitate the difference in friction between on-bottom and embedded pipe observed in tests the following equation is proposed by the author:

])2

('[' 20

DKWFa ⋅⋅⋅+⋅= γχµ (1)

where the expression in square brackets is applicable to embedded pipe and χ is the ratio of embedded circumference to diameter of pipe. The equation was crosschecked with test results. The error between on-bottom and embedded pipe was reduced from 100% (no equation) to below 18% (using equation).

5 CONCLUSIONS

Three main findings were obtained: - First finding relates to exposed pipelines.

According to BS 8010: Part 3 (1993) only the submerged weight of the pipe is important. However, this research shows clearly that the latter is not valid. The larger embedment yields larger resistance. The author proposed the equation, which would accommodate this fact.

- Second finding relates to buried pipelines. As Wijewickreme et al. (2008) mentioned the proper coefficient of lateral friction under certain conditions would be a passive i.e. Kp. In such cases, the peak axial resistance, using standard methods, would be greatly underestimated. The results of push-in test performed in the course of this research confirmed his results. Whereas Wijewickreme et al. (2008) achieved passive

coefficient of lateral friction in dense sand the results obtained from this research suggest that Kp would be more applicable to medium dense sand.

- The last important finding relates to mobilise distances. Such distances were found to be strongly correlated to pipe size and density of soil. The larger pipe would mobilise peak axial resistance at larger displacement. The author proposed a design chart for stiff and soft clay, loose and dense sand as well as gravel. The data set on which it is based is however small and further research would need to apply pipes with larger diameter than the ones used in this research.

ACKNOWLEDGEMENT

The author is grateful to Andrew Brennan for his support and for the valuable ideas for this project. Indrasenan Thusyanthan is gratefully acknowledged, particularly for his industrial view on the topic and his advice on conducting physical tests.

REFERENCES

[1] AC. Palmer and R.A. King, Subsea Pipeline Engineering, Penn Well, USA, 2006.

[2] DNV-RP-F110, Global Buckling of Submarine Pipelines: Structural Design due to High Temperature/High Pressure, Norway, 2007.

[3] ALA, Guidelines for the Design of Buried Steel Pipe, ASCE, USA, 2001.

[4] BS 8010: Part 3, Code of practice for Pipelines, Part3: Pipelines subsea: design, construction and installation, BSI, London, 1993.

[5] P.E.L. Shaminee, N.F. Zorn and G.J.M. Schotman, Soil Response for Pipelines Upheaval Buckling Analyses: Full-Scale Laboratory Tests and Modelling, OTC 6486, 22nd Annual Offshore Technology Conference, May 7-10, 563-572, Houston, 1990.

[6] M.F. Finch, R. Fisher, A. Palmer and A. baurgard, An integrated approach to pipeline burial in the 21st Century, Deep Offshore Technology, Houston, 2000.

[7] D.N. Cathie, C. Jaeck, J.-C. Ballard and J.-F. Wintgens, Pipeline geotechnics – state-of-the-art, Frontiers in Offshore Geotechnics: ISFOG, taylor & Francis Group, London, 2005.

[8] J. Oliphant and A. Macanochie, The Axial Resistance of Buried and Unburied Pipelines, Proceedings of the 6th Internation Offshore Site Investigation and Geotechnics Conference: Confronting New challenges and Sharing Knowledge, London, 2007

[9] J. Shupp, B.W. Byrne, N. Eacott, C.M. Martin, J. Oliphant, A. Maconochie and D. Cathie, Pipeline unburial behaviour in loose sand, International Conference on Offshore Mechanics and Arctic Engineering, Hamburg, 2006

[10] D. Wijewickreme, H. Karimian and D. Honegger, Response of buried steel pipelines subjected to relative axial soil movement, Canadian Geotechnical Journal, 2008