assessment of pipeline stability in the gulf of mexico during hurricanes using dynamic analysis

Cassidya,∗ aCentre for Offshore Foundation Systems and ARC CoE for Geotechnical Science and Engineering, University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia

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Theoretical and Applied Mechanics Letters

journal homepage:www.elsevier.com/locate/taml

Letter

Assessment of pipeline stability in the Gulf of Mexico during

hurricanes using dynamic analysis

Yinghui Tiana, Bassem Youssefb, Mark J Cassidya,∗

aCentre for Offshore Foundation Systems and ARC CoE for Geotechnical Science and Engineering, University of Western Australia, 35 Stirling Highway,

Crawley, WA 6009, Australia

bAtteris, Level 3, 220 St Georges Terrace, Perth, WA, 6000, Australia

a r t i c l e i n f o

Article history:

Received 23 October 2014

Accepted 9 January 2015

Available online 25 February 2015

*This article belongs to the Solid Mechanics

Keywords:

Pipeline

On-bottom stability

Dynamic lateral stability analysis

Force-resultant model

Hydrodynamic load

a b s t r a c t Pipelines are the critical link between major offshore oil and gas developments and the mainland Any inadequate on-bottom stability design could result in disruption and failure, having a devastating impact

on the economy and environment Predicting the stability behavior of offshore pipelines in hurricanes

is therefore vital to the assessment of both new design and existing assets The Gulf of Mexico has a very dense network of pipeline systems constructed on the seabed During the last two decades, the Gulf of Mexico has experienced a series of strong hurricanes, which have destroyed, disrupted and destabilized many pipelines This paper first reviews some of these engineering cases Following that, three case studies are retrospectively simulated using an in-house developed program The study utilizes the offshore pipeline and hurricane details to conduct a Dynamic Lateral Stability analysis, with the results providing evidence as to the accuracy of the modeling techniques developed

© 2015 The Authors Published by Elsevier Ltd on behalf of The Chinese Society of Theoretical and Applied Mechanics This is an open access article under the CC BY-NC-ND license (http://

creativecommons.org/licenses/by-nc-nd/4.0/)

Introduction The Gulf of Mexico is a small oceanic basin

sur-rounded by continental land masses and a relatively simple and

roughly circular structure approximately 1500 km in diameter [1

As shown inFig 1, the Gulf of Mexico basin resembles a large pit

with a broad shallow rim Approximately 38% of the Gulf comprises

shallow and intertidal areas (<20 m deep) The area of the

conti-nental shelf (<180 m) and continental slope (180–3000 m) are 22%

and 20% of the total area, respectively Abyssal areas deeper than

3000 m make up the final 20% [2] The northeast Gulf of Mexico is

the region with the most reported damaged pipelines This region

extends from east of the Mississippi Delta near Biloxi to the eastern

side of Apalachee Bay The majority of this region is characterized

by soft sediments [3

Five hurricanes hit the Gulf of Mexico between 1992 and 2005:

Andrew in 1992, Lili in 2002, Ivan in 2004, Katrina and Rita in 2005

and their paths are shown inFig 1 These hurricanes caused severe

destruction and the economic loss is estimated to be worth 75

bil-lion US dollars due to Katrina alone [4 Table 1summarizes

de-struction of the 5 hurricanes The majority of the pipeline failures

∗Corresponding author.

E-mail addresses:yinghui.tian@uwa.edu.au (Y Tian),

bassem.youssef@atteris.com.au (B Youssef), mark.cassidy@uwa.edu.au

(M.J Cassidy).

are in areas perpendicular to the maximum current and in water depths less than 60 m Large displacements of pipelines have been highlighted by Gagliano [5] and this agrees with the reported data

inTable 1 For example, an 18 inch (0.457 m) unburied oil pipeline with a specific gravity of 1.6 drifted southward 910 m from its orig-inal location during Hurricane Ivan During Hurricane Katrina, a 26 inch (0.66 m) buried gas pipeline with a specific gravity of 1.4 in a water depth of 15 m was displaced about 1219 m to the north over 14.5 km of its length A sonar survey after Hurricane Ivan presented

in Thomson et al [6] revealed that an 18 inch (0.457 m) pipeline, approximately 44.25 km long, that ran from an oil gathering plat-form westward to near the Mississippi River Delta was found dis-placed by 580 m In addition, approximately 100 pipeline failures due to hurricanes were reported from 1971 to 1988, whereas about

600 cases of pipeline damage were reported after Hurricanes Kat-rina and Rita in 2005 [7

Pipeline on-bottom stability assessment post Hurricane Ivan After the enormous destruction to the offshore oil and gas

facilities by Hurricane Ivan, many research publications assessed and reviewed the design of the damaged pipelines [4,7–12]

As reported by Det Norske Veritas (DNV) [7], three on-bottom pipeline stability studies were conducted to model pipelines under Hurricane Ivan using the PONDUS software [13] In the analysis, the pipelines were assumed to be oriented perpendicular to the path

of Hurricane Ivan.Table 2summarizes the input parameter values

http://dx.doi.org/10.1016/j.taml.2015.02.002

2095-0349/ © 2015 The Authors Published by Elsevier Ltd on behalf of The Chinese Society of Theoretical and Applied Mechanics This is an open access article under the CC

Table 1

Summary of the 5 hurricanes in the Gulf of Mexico.

Hurricane Hurricane

scale *

to excessive disp.

Andrew 4 Hs≈10.7–12.2 m 485 pipelines and flow lines were damaged Eight seven percent (87%) of the pipeline

damages occurred in small diameter pipes and most in water depths<30.5 m.

44 Lili 4 120 pipelines were damaged Eight five percent (85%) of the pipeline failures occurred in

small diameter pipelines and there was no apparent correlation with pipeline age.

Ivan 4–5 Hs>2500 year

return period

168 pipeline damages report with an estimated 16093 km out of the 53108 km of the Outer Continental Shelf pipelines in the direct path of the hurricane.

38

Katrina 5 Hs≈16.8 m 299 pipelines and flow lines were damaged Approximate 35405 km out of the 53108

km of pipelines were in the path of Katrina and Rita.

61

* See DNV [ 4 ] for details about the hurricane scale based on Saffir–Simpson scale standard.

Table 2

Three pipeline analysis cases in DNV [ 7

Submerged weight/N·m − 1 892 (water-filled) 372 (empty) 871 (water-filled)

Fig 1 Gulf of Mexico location and the path of the main hurricanes.

used in the PONDUS simulations and the pipeline displacements

measured in the field In the first two cases, pipelines experienced

massive lateral displacements of 914 m and 518 m, respectively,

and the third pipeline case did not experience any displacement

under Hurricane Ivan The numerical simulation predicted that

all three pipeline cases would experience lateral movement,

1446 m, 628 m, and 254 m, respectively It is clear that PONDUS

overestimated the pipeline displacement of the three pipeline

cases

In-house developed dynamic finite element program Tian

and Cassidy [14–16] and Tian et al [17] developed an integrated

fluid–pipe–soil modeling Dynamic Lateral Stability package

Dy-namic Lateral Stability analysis is considered to be the most

comprehensive method because a complete three-dimensional

pipeline simulation can be performed for any given combination of

waves and currents in time domain analysis (see DNV [18] for de-tails) This in-house package adopted advanced plasticity pipe–soil force-resultant models [19–22] and Fourier hydrodynamic load models [23] to evaluate soil resistance and hydrodynamic load-ing, respectively The commercially available finite element pack-age ABAQUS/Standard was used (implicit analysis), with modules for pipe–soil interactions and hydrodynamic loading implemented

as user subroutines UEL and DLOAD, respectively (see Dassault Sys-tem for technical details [24])

The pipe–soil interaction module implements available force-resultant models on calcareous sand [19–21] and clay soil [22] as ABAQUS user-defined elements through the user subroutine UEL

Figure 2illustrates the symbolic convention for loading acting on

a segment of a pipeline The vertical component of the resultant

force is V = Ws − Fv, where Ws is the pipeline submerged

weight and Fvis the vertical hydrodynamic loading The horizontal

component is H = FH, where FH is the horizontal hydrodynamic loading Most available pipe–soil interaction models are based on the simplistic Coulomb friction concept [25–27] and link H directly

to V through only one simplistic friction factor More advanced

force-resultant models have been presented in the last decade, allowing a more fundamental understanding of pipe–soil behavior

by relating the resultant forces(V,H)directly to the corresponding displacement (w,u) within a plasticity framework Schotman and Stork [28] initially proposed the force-resultant concept to pipe–soil modeling Subsequently, other fully developed force-resultant pipe–soil models have been presented by Zhang [19], Zhang et al [20], Calvetti et al [29], Di Prisco et al [30], Hodder and Cassidy [22], Tian et al [21], and Tian and Cassidy [16] through experimental and numerical studies Among these, Hodder and Cassidy [22] conducted centrifuge testing at 50g with a pipeline model 0.5 m in diameter and 2.5 m in length in prototype The tested soil samples of kaolin clay were commercially available but can well represent the undrained behavior of clayey soil These

Fig 2 Pipe load and displacement convention.

Fig 3 Yield surface.

force-resultant models provide an understanding of the complex

pipe–soil behavior with a more fundamental theoretical basis

Based on strain hardening plasticity theory, the force-resultant

model has a yield surface to describe the allowable resultant force

(V,H) SeeFig 3, the yield surface size V0, is directly related to the

vertical plastic embedmentwpin a hardening law to describe the

expansion/shrinkage See Hodder and Cassidy [22] for details about

the model and refer to Tian and Cassidy [15], Tian et al [17] for the

detailed introduction of the development of the Dynamic Lateral

Stability package

In the hydrodynamic loading calculation module, a

three-dimensional ocean surface is first generated using a wave

spec-trum (significant wave height Hs and peak time period Tp) and

spreading function The water particle velocity and acceleration

are then evaluated at the pipeline level, or, alternatively, input

ve-locity and acceleration time series are accepted by the program

The Fourier model developed by Sorenson et al [23] was adopted

to calculate the hydrodynamic loading on the pipeline More

ad-vanced than the traditional Morison equation (which is based on

ambient flow velocity and time-invariant coefficients), the Fourier

models are proven to have better accuracy for the prediction of

time-variable hydrodynamic forces on a subsea pipeline [31–34]

The Fourier model uses a composition of harmonic sine waves, 9

for regular wave and 5 for irregular wave, to calculate the drag

force FDand lift FLon a pipeline The inertia force FIin the Fourier

model is calculated the same as in the traditional Morison

formu-lation but with a fixed inertia coefficient value of 3.29 The

to-tal horizonto-tal hydrodynamic load FHequals the superposition of

drag force FDand inertia for FI, i.e., FH = FD+FI, while the

ver-tical load FVis considered equal to the uplift force FL The

devel-oped integrated fluid–pipe–soil model has the capability to reduce

the hydrodynamic loads based on the pipe vertical and horizontal

displacements during the simulation (see Youssef et al [35] and

Youssef [36] for details about the hydrodynamic load reduction)

With one force-resultant model simulating a small section

of pipe–soil interaction, a three-dimensional long pipeline can

be represented by attaching numerous models in a ‘‘Winkler

foundation style’’ As illustrated in Fig 4, the pipeline structure

is modeled as beam elements, and the force-resultant models

Fig 4 Illustration of program integration.

attached to the pipe nodes represent the surrounding soil behavior Hydrodynamic loads are applied along the pipeline and vary with time and location

Environmental loads A three hour storm was numerically

generated to represent Hurricane Ivan based on the environmental conditions provided inTable 2 A 3000 m long pipeline is used

to represent the pipeline The hydrodynamic loads acting on the pipeline in case 1 after 20 min of the storm are shown inFig 5for illustration Plotting the pipe self-weight of case 1 on the vertical load diagram,Fig 5(b) shows that the uplift loads exceed the pipe self-weight in three spots along the pipeline at the moment Numerically, this load must be shared and distributed along the pipe

As a preliminary estimation, the hydrodynamic vertical loads are averaged over the pipeline length of 3000 m.Figure 6shows the averaged hydrodynamic vertical load history for the three pipeline cases The corresponding pipe self-weights are also plotted on the diagrams It is clear that the pipe self-weight of the first two pipeline cases is much less than the uplift loads The pipe self-weight of case 3 is almost double the uplift load Therefore, the first two pipelines are more likely to have had experienced large uplifting load during Hurricane Ivan In this scenario, the pipeline may have been lifted from the seabed and drifted laterally with the flowing stream Therefore, this preliminary analysis suggests that the first two pipelines are unstable However, the self-weight of the pipeline in case 3 is large enough to counterbalance the estimated hydrodynamic vertical load

Comparing the hydrodynamic loads and the initial yield surface gives a rough indication of the applied loads and the expected resistance capacity To perform this comparison, the generated

hydrodynamic loads, FHand FV, at an arbitrarily selected location,

500 m from the pipeline end, are plotted in V − H space by considering that V =Ws−FVand H =FH, as shown inFig 7for the three pipeline cases For the first two pipeline cases, there are

many loading points located on the negative side of the V axis that

exceed the uplift capacity of the yield surface Even expanding the yield surface during the simulation could not accommodate these loading values Therefore, the soil should not be able to support this loading scenario Based on the comparisons presented in this section, the first two pipeline cases may not be stable during a full

3000 m pipeline simulation, though the pipeline case 3 is expected

to be stable However, during numerical simulation there is the possibility that the hydrodynamic load may be shared along the pipeline length, taken by the dynamic response of the pipe or reduced due to the pipe movements

Retrospective modeling using the in-house package To

numerically simulate the three pipeline cases using the integrated hydrodynamic-pipe–soil program, the pipeline was assumed to be

3000 m long and a flat seabed was assumed Load concentration

Fig 5 Hydrodynamic loads acting along pipeline Case 1 after 20 min.

a

b

c

Fig 6 Average vertical load along the three pipeline cases and the pipe self-weight.

during pipeline was assumed to be twice the pipeline weight

(for a study of the effect of load concentration please refer to

Youssef [36]) Thus, the initial pipeline embedment was calculated

The pipeline was divided into 150 beam elements that were 20 m

long (for a study of the influence of element length please refer

to Youssef [36]) As the Gulf of Mexico mainly has clayey soil, the

Hodder and Cassidy [22] model is adopted to describe the soil and

151 force-resultant models were attached to structural nodes to

Fig 7 Hydrodynamic loads 500 m from the pipeline end compared to the yield

surface.

Fig 8 Influence of self-weight.

Fig 9 Influence of load concentration factor.

model the pipe–soil interaction See Hodder and Cassidy [22] for

details about the model parameters

In the first two pipeline analysis cases, the numerical analysis

can not complete the entire 3 h storm because the pipeline was

lifted completely off the seabed In both cases, the yield surface of

some force-resultant models first shrunk to zero and thus became

‘‘inactive’’ in the numerical package as the pipe self-weight was

insufficient to counterbalance the uplift loads The loads acting at

the inactive pipe–soil element zones are shared by the remainder

of the pipe nodes along the pipeline length This caused these nodes

to reach the inactive state just afterward These analysis results

of the first two pipeline cases indicate that these pipelines are

unstable in the Hurricane Ivan environment On the other hand,

the 3 h analysis of pipeline case 3 was completed with a maximum

horizontal displacement of 19.25 m

To explore what pipe self-weight would be required for these

pipeline cases to be stable during Hurricane Ivan, pipeline case

1 and case 2 were reanalyzed with self-weight values varying

2.0, 2.5, 3.0, and 3.5 times the original pipe self-weight shown in

Table 2.Figure 8shows the maximum lateral displacement results

for the reanalyzed cases As can be seen, the simulation of using a

pipe weight of two times the original weight results in maximum

horizontal displacements of 92.0 m and 48.0 m for cases 1 and 2,

respectively

The analysis of case 3 predicted a maximum horizontal

dis-placement of 19.25 m However, during Hurricane Ivan the pipe

did not experience any horizontal displacement One of the pos-sible reasons for this difference between the numerical predicted and the field measurement is assumed to the load concentration factor during the pipeline laying, which essentially implies the ini-tial yield surface size As explained in Westgate et al [37], the load concentration factor is the ratio of the vertical load transmitted in the touchdown zone during the pipelaying to the pipe self-weight The value of the load concentration factor depends on many factors during the pipelaying, which include the sea state, water depth, wind speed and direction Load concentration factor values of 2.0 and 4.2 have been suggested by Cathie et al [38] for the cases of weak soil and strong soil, respectively

The load concentration factor used in the previous simulation was set as 2 To investigate the effect of the load concentration factor on pipeline case 3 stability, four simulation cases are conducted by varying 2.5, 3, 3.5, and 4 The results for these simulation cases are presented inFig 9 The simulation with load concentration factor of 4 results in an almost static pipeline with a final horizontal displacement of 0.01 m

The numerical modeling results presented in this section demonstrate the capability of the integrated hydrodynamic-pipe–soil modeling program to reasonably simulate the on-bottom stability under strong hydrodynamic environment conditions

Conclusions The developed in-house package was used to

investigate the hydrodynamic loads acting on three pipeline cases during Hurricane Ivan and reported in the literature In two of the cases, 1 and 2, the pipe-weight and soil resistance was not enough

to resist the applied loads and a displacement scenario is suggested

as these two pipeline cases were lifted from the seabed and drifted with the flowing stream (confirming the enormous displacements

of 914.4 m and 518.2 m reported in the literature, respectively)

To assess the on-bottom stability of the three pipeline cases, the developed integrated program was used to conduct a 3-hour pipeline simulation The simulation analysis of the first two pipeline cases terminated because the pipelines were lifted from the seabed The analysis results indicated that pipelines with greater self-weight might be stable Repeating the analysis of the first two pipeline cases considering pipelines with greater self-weight confirmed the conclusion above Using a pipe self-self-weight double the original weight results in horizontal displacement values of 95.5 m and 48.7 m for pipeline case 1 and case 2, respectively

The 3-hour analysis of pipeline case 3 revealed a horizontal displacement of 19.23 m Repeating the analysis of pipeline case 3 with different load concentration factors during the pipeline laying resulted in a maximum horizontal displacement of 0.01 m for a load concentration factor equals 4

It is concluded from the analyses presented for the three pipeline cases that the developed integrated program can simulate complex cases with reasonable accuracy

Acknowledgments

This work was supported by the Research Development Awards of University of Western Australia, Australia–China Nat-ural Gas Technology Partnership Fund and Lloyd’s Register Foun-dation Lloyd’s Register Foundation supports the advancement of engineering-related education and funds research and develop-ment that enhance the safety of life at sea, on land, and in the air The work also forms part of the activities of the Centre for Offshore Foundation Systems (COFS) above, currently supported as a pri-mary node of the Australian Research Council Centre of Excellence for Geotechnical Science and Engineering

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