3d model of flexible risers

Wet and Dry Collapse of Straight and Curved Flexible Pipes: a 3D FEM Modeling

Alfredo Gay Neto1

Clóvis de Arruda Martins1

Eduardo Ribeiro Malta1

Carlos Alberto Ferreira Godinho2

Teofilo Ferreira Barbosa Neto2

Elson Albuquerque de Lima2

1Department of Mechanical Engineering. University of São Paulo.

São Paulo, SP, Brazil 2Prysmian Cables and Systems.

Cariacica, ES, Brazil

ABSTRACT

Flexible pipes for offshore applications can operate in deep water. In

this situation the pipe must resist to the external pressure without

collapse. Two different failure modes must be analyzed: the dry and the

wet collapse. The first is possible to occur when the external polymeric

layer of the flexible pipe has no damages. In the wet collapse scenario

the external polymeric layer is damaged, permitting that the water

floods the annulus. So, the internal polymeric layer receives the

external pressure. In this case the limit external pressure to that the pipe

can resist is usually smaller than in the former one. This work deals

with both the failure modes, comparing their characteristics and

collapse pressure values. For that purpose, a full 3D finite element

model was constructed, including the interlocked carcass, the internal

polymeric layer, the pressure armor and the external polymeric layer.

The model considers all the cross section details of the pressure armor

and interlocked carcass and contemplates self-contacts and interactions

between layers. The length of pipe simulated corresponds to dozens of

pitches of the interlocked carcass. The developed model can deal with a

straight or curved flexible pipe to study the effect of curvature in the

collapse pressure limit. Case studies are presented, compared and

discussed.

KEY WORDS: flexible pipes, curvature, collapse, buckling

INTRODUCTION

Flexible pipes are structures composed by many layers used for

offshore oil exploration. The layers are usually made of different

materials. A typical arrangement includes some important metallic

layers:

• The interlocked carcass layer that is the innermost one. Its

function is to provide a way to internal fluid flow and to resist to

the external pressure loads.

• The pressure armor layer, which is designed to ensure the internal

pressure resistance. It also acts as an external pressure barrier

when the external plastic layer is not damaged.

• The tensile armors that are usually the outermost metallic layers.

Their function is to provide axial rigidity to the flexible pipe. They

are usually rolled in pairs to improve torque balancing when the

whole pipe is tensioned.

Flexible pipes can present many failure modes, being many of these

related to structural causes. This work deals with two failure modes,

named “dry collapse” and “wet collapse”. Both are related to the

flexible pipe failure when it is subjected to external pressure loads.

The “dry collapse” failure mode can occur when the external polymeric

layer has no damages. All the internal layers work together resisting to

the external pressure loading. One can simplify this problem assuming

that only the pipe core (composed by the interlocked carcass, the

internal polymeric layer and the pressure armor) resists to the loading.

Obviously the tensile armors and the other layers such as tapes can

increase the whole pipe capacity to avoid the dry collapse.

A different situation refereed as “wet collapse” occurs when the

external polymeric layer has damages, permitting the annulus flood.

Then, almost all of the external pressure acts at the internal polymeric

layer wall. In this scenario the situation is more severe than in the dry

collapse, once only the carcass has to resist all the external loading.

However, the other layers can play a role as constraints to the

interlocked carcass, helping to avoid the collapse.

The dry and the wet collapse are structural stability problems. If one

face the flexible pipe, simply as a “pipe”, the instability external

pressure value would depend on the stiffness of it, on the yielding

strength of the pipe material and on the initial imperfections

considered. As a first approximation, the dry collapse of a flexible pipe

can be faced as the collapse of an equivalent tube or ring. This problem

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Proceedings of the Twenty-second (2012) International Offshore and Polar Engineering ConferenceRhodes, Greece, June 17–22, 2012Copyright © 2012 by the International Society of Offshore and Polar Engineers (ISOPE)ISBN 978-1-880653-94–4 (Set); ISSN 1098-6189 (Set)

www.isope.org

was discussed and solved using analytical models by Timoshenko and

Gere (1961). This classical reference served as basis to other

publications about the same topic, however with some modifications

depending on the nature of the problem being analyzed. Bai (1998)

used the Timoshenko’s equations, changing the thickness of the pipe

for considering corrosion effects. Bai et al. (1999) also modified the

analytical model for considering anisotropy effects in the tube.

For predicting failure of flexible pipes, a possible approach of

analytical model is to use Timoshenko’s equations in a fictitious

equivalent ring (that represents the carcass layer or other layers of

interest). Martins et al (2003) presented a methodology to calculate the

equivalent thickness of the carcass layer of flexible pipes utilizing the

principal moment of inertia of the cross section shape. The same

approach was modified by Gay Neto and Martins (2012) to include a

better approximation of the superposition of the subsequent cross

sections. Different approaches to evaluate the equivalent thickness of

helical rolled layers can be found also in de Sousa et al. (2001) and Lu

et al. (2008). The equivalent thickness approach was not only used for

collapse problems, but was also addressed when dealing with other

failure modes. For example, Gay Neto et al. (2010) used this approach

to deal with the pressure armor in the burst failure mode, and Alsos et

al. (2010) for developing an orthotropic elastic-plastic model for

representing the carcass and pressure layers in flexible pipes impact

modeling.

The collapse problem of flexible pipes was treated by Gay Neto and

Martins (2012) neglecting the presence of the pressure armor. It was

showed that there is a limit safe external pressure. When it is achieved,

a snap-through loss of stability is showed to occur. The presence of the

pressure layer as a constraint to the carcass loss of stability plays an

important role, as showed by Gay Neto and Martins (2011). However,

it was considered only the possibility of a two symmetry planes

collapse mode (named “eight collapse mode”). Another collapse mode

name “heart collapse mode” can also occur. This was commented by

Paumier et al. (2009) when they present the two possible collapse

failure modes for flexible pipes.

Li and Kyriakides (1991) presented the fundamental problem of two

concentric rings, when the inner one is loaded externally. Two kinds of

initial imperfection are considered: a singly symmetric and a doubly

symmetric. These are for inducing different failure modes. It is

concluded that the preferred buckling mode depends on the ratio

between the thickness of both the considered rings and also on the

amount of initial imperfection adopted.

The present work can be viewed as a continuation of Gay Neto and

Martins (2011). The simplifications made for considering only the

“eight collapse mode” were not made. Furthermore, the pressure layer

was now considered with its actual rolled shape and, no more as an

equivalent ring. A finite element model was developed to take into

account the cross section details of the pressure armor and the

interlocked carcass. Self-contacts and contact between layers were

considered. Dozens of pitches samples were simulated using the

developed model that can deal with a straight pipe but also with a

curved one. This aims the study of the effect of the flexible pipe

curvature in the collapse pressure limit.

The present study focuses on 2.5” and 4.0” flexible pipes, but the same

methodology should be used for larger sizes.

GEOMETRY MODEL DESCRIPTION

This section presents the characteristics of the finite element models

that were solved using ANSYSTM 13 software.

It was assumed that the structural nucleus is the most important region

of the flexible pipe when dealing with the collapse problems. Thus, the

present models consider the carcass, the internal polymeric and the

pressure armor layers. Additionally, an external polymeric layer was

considered in order to avoid rotational movements in the pressure

armor, once actually it is restrained by the presence of the outermost

layers.

The geometry developed does not consider any symmetry plane and,

also, can be done with as many pitches as necessary. The metallic

layers are rolled in a helical shape. Their actual geometries do not

present any symmetry plane. One possible simplification to be done is

considering these layers as sets of rings, instead of a helix. This would

induce a symmetry plane, making possible the usage of simpler FEM

models. However, the objective of the present model is to serve as a

reference for future simplified models considering the curvature of the

pipe, for example. Thus, no symmetry simplifications were done.

The Fig. 1 shows the geometry considered in the model. It encompasses

the structural nucleus of the flexible pipe and the external polymeric

layer. The details of the cross sections of the layers are shown in Fig. 2.

The cross section profiles are swept through a spatial curve,

constructing four helixes. Each polymeric layer is then converted into

one only cylindrical solid (once they are not actually a helix). The

layers can be considered to be ovalized, in order to induce an initial

imperfection to initiate some collapse modes. The input of initial

ovalization (and also the measurement of ovalization during the

collapse simulation process) is done through API (2002) ovalization

definition:

D�� D��

D�� D��

(1)

• D�� is the maximum diameter.

• D�� is the minimum diameter.

Fig. 1 - Geometry of the model. From inside to outside of the pipe: the

carcass layer, the internal polymeric layer, the pressure armor layer and

the external polymeric layer.

Fig. 2 - Geometry of the cross sections of the layers of the model.

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The model can consider the carcass and internal polymeric layers with

a given value of initial ovalization and the pressure armor and the

external polymeric layers with a different initial ovalization. This can

be used to study the sensitivity to initial perturbations for the wet and

dry collapse problems.

MESH

The mesh considered for all the layers is constructed through a sweep

method. A 3D mesh example is shown in Fig. 3 and its cross section

plane meshes patterns are shown in Fig. 4.

Fig. 3 - An example of mesh generated using the model developed for

collapse models.

Fig. 4 - Cross section mesh patterns examples.

MESH200 elements were used for developing the 2D mesh pattern.

The 3D element used for all the layers considered is the SOLID186. It

is a second order element that can be used with nonlinear material

models. More details about the element formulation can be found in

Ansys (2011).

The mesh density used for the present models were not varied due to

the very large size of the models (actually, one single simulation can

take about a month running in a good computer). However, the

experience learned in the former works dealing with simpler models

permitted doing one only good mesh for representing the collapse

problem of the whole flexible pipe. One should take care with the hoop

direction discretization, to ensure enough elements that would not make

the structure too stiff (this could increase the collapse pressure values

predictions). In this work 80 second order elements were used in hoop

direction for all simulations. This was acceptable for dealing with the

collapse problem.

MATERIAL MODELS

The material models for all the layers include nonlinearities. The

carcass and pressure armor layers materials are considered to have a bi-

linear elastic-plastic behavior with isotropic hardening (BISO). The

polymeric materials are modeled using multilinear elastic plastic with

isotropic hardening models (MISO). Once the loading that causes

collapse is considered not to be variable in time, the multilinear curve is

only used to evaluate the stress vs. strain behavior of the polymer. If a

reverse loading was considered, this procedure would not be correct

once, actually, the polymeric materials do not suffer plasticity as a

metallic material. The material data for the carcass layer is shown in

Table 1:

Table 1 - Carcass layer material properties

Material Young's modulus 193 GPa

Material Poisson's ratio 0.3

Material yielding strength 600 MPa

Material tangent modulus (after yielding stress) 2000 MPa

The material data for the pressure armor layer is shown in Table 2:

Table 2 - Pressure armor layer material properties

Material Young's modulus 207 GPa

Material Poisson's ratio 0.3

Material yielding strength 650 MPa

Material tangent modulus (after yielding stress) 53,712 MPa

The internal polymeric layer material curve (PA11) is shown in Fig. 5

and the external polymeric layer material curve (HDPE), in Fig. 6.

Fig. 5 - Internal polymeric layer (PA11) material curve.

Fig. 6 - External polymeric layer (HDPE) material curve.

INTERACTIONS BETWEEN LAYERS AND SELF-

CONTACTS

All the layers considered in the model have some interactions with the

others through contact regions. Furthermore, the carcass and pressure

layers also have self-contacts. All these contact possibility regions were

considered in the model. They are shown from Fig. 7 to Fig. 11.

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Fig. 7 - Self-contact regions considered for the carcass layer.

Fig. 8 - Contact regions considered between the carcass layer and the

internal polymeric layer.

Self-contacts in the carcass and in the pressure armor are considered to

be frictionless. These interactions permit structure accommodations

during loading application in the model. The frictionless behavior

assumes implicitly that the most important self-contact contributions to

the problem are the loading transferring due to normal direction contact

forces, neglecting any resistance to slipping.

The contact between the internal polymeric layer and carcass is

considered to be bonded. This is helpful for convergence issues and,

being the polymeric layer very soft, its most important function is to

transfer normal loading between the metallic layers and its contribution

to the flexible pipe resistance to collapse is negligible. As the actual

pipe is unbonded, the interaction between the internal polymeric layer

and the pressure layer was considered to be frictionless. This

assumption considers that any shearing is transferred between layers in

this interaction, which induces each pipe metallic layer to work

independently in terms of local bending during collapse, only with the

compatibility for no inter-penetration. For collapse pressure prediction

this assumption looks to be conservative. It is not possible to say the

same for different problems, such as flexible pipes lateral impact, as

studied by Alsos et al. (2010), in which a 0.15 Coulomb model friction

coefficient was assumed between layers interactions. The authors say

that different friction coefficient values cause variations in axial

tension.

Between the pressure armor layer and the external polymeric layer a

bonded interaction was assumed. Actually, the external polymeric layer

is not glued in the pressure armor. However, the tensile armors are

located between these layers, but they are not included in this model.

Putting together the pressure armor and the external polymeric layer

helps dealing with some rotation movements that occur in the pressure

armor when it is loaded and does not have any circumferential restraint.

The friction between the pressure layer and the outermost layers causes

difficulty to these rotation movements in the real flexible pipe. The

bonded interaction considered in this interface is a way to represent this

constraint.

The frictionless contacts properties are shown in Table 3.

Table 3 - Frictionless contact properties

Contact behavior Standard

Pinball radius 0.25 mm

Contact Algorithm Pure Penalty Method

Normal penalty stiffness factor 0.01

Penetration tolerance factor 0.1

Friction coefficient 0.0

Fig. 9 - Contact regions considered between the pressure armor and the

internal polymeric layer.

Fig. 10 - Self-contact regions considered for the pressure armor.

Fig. 11 - Contact regions considered between the pressure armor and

the external polymeric layer.

In the bonded contacts, to avoid movements of the polymeric layers

into the voids of metallic layers, some contact special options had to be

used. For the internal polymeric and carcass interaction, the PA11 is

extruded over the whole carcass during manufacturing. This makes this

layer not exactly like a polymeric pipe but, it has some penetrations

into the voids of the metallic layer. These were not modeled

geometrically, but were taken into account numerically assuming that a

rigid body exists in the carcass layer voids. To achieve it using

ANSYS, a pinball radius parameter was modified, considering the

bonded contact not only between the faces on initial contact but, also,

between faces with a non-zero gap, driven by the pinball radius

tolerance. The same procedure was addressed to the external polymeric

layer and pressure armor layer interaction. The details of the bonded

contact regions are resumed in the Table 4.

Table 4 - Bonded contact properties

Contact behavior Bonded (always) Contact Algorithm Augmented Lagrange Method Normal penalty stiffness factor 10 Penetration tolerance factor 0.1

BOUNDARY CONDITIONS

The boundary conditions considered in the model are two rigid regions

in both the tips of a flexible pipe segment. This is done through the

creation of two pilot-nodes in the model that can be moved due to

imposed displacements and rotations. Each pilot node movement is

coupled to the rigid regions, shown in Fig. 12. The pilot-nodes can be

used to constrain the displacements and rotations of both the tips of the

flexible pipe, considering that it is clamped in both sides. It can also be

used to impose an initial curvature to the sample, in order to study its

influence in the collapse pressure. The Fig. 12 shows the two pilot

nodes and the rigid regions, whose nodes are shown using cyan and

blue symbols.

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Fig. 12 - Boundary conditions of the model.

PRESSURE LOADING

In addition to the constraints, the external pressure loading was

considered in the model. Two possibilities of loading were addressed:

for wet and dry collapse.

For the wet collapse, the pressure is applied on the outer face of the

internal polymeric layer, assuming that the annulus is flooded. For the

dry collapse, the pressure is applied in the outer face of the external

polymeric layer. Fig. 13 shows the wet and dry collapse pressure

loading conditions.

(a) (b)

Fig. 13 - External pressure loading applied in the: (a) wet collapse

condition (b) dry collapse condition.

STUDY OF THE SAMPLE LENGTH

A study of the sample length was made to find out how many pitches

would be necessary for the evaluation of the collapse pressure of an

“infinite length” sample. This was done to isolate the influence of the

boundary conditions in the collapse pressure result. For this study, only

the wet collapse of a straight flexible pipe without pressure armor and

external polymeric layer was done. It was assumed that the conclusion

of the number of pitches here obtained is valid for all the other flexible

pipe conditions (wet and dry collapse, with or without curvature). A

100.6 mm of internal diameter of carcass layer was considered. An

initial API ovalization of 0.5% was imposed to the carcass layer.

The Table 5 shows the results of collapse pressure for various numbers

of carcass layer pitches. Fig. 14 shows the same results graphically,

where an asymptotic behavior can be clearly seen for the collapse

pressure. For the purposes of collapse prediction, the conclusion is that

a sample of 30 pitches is enough to a good approximation of the

collapse pressure, not being necessary to consider larger samples. This

sample length was used for all the results present in this work.

Table 5 - Sample length study for the collapse pressure

Number of carcass layer pitches Collapse pressure (MPa)

10 24.57

12 23.45

14 20.65

16 18.39

20 16.04

24 15.03

30 14.35

40 14.05

The Fig. 15 shows a sample of 24 pitches in the collapse imminence. It

is possible to observe the effects of the boundary conditions (in this

case, the pilot nodes were simply fixed).

Fig. 14 - Collapse pressure vs. Number of pitches for the wet collapse

with only carcass and internal polymeric layers.

Fig. 15 - A sample of 24 pitches in the collapse imminence with the

radial displacements colored. The deformed shape is 10 times scaled.

VERIFICATION OF ASSUMPTIONS IN THE WET

COLLAPSE PROBLEM

As explained before, in the wet collapse problem a failure occurs in the

external polymeric layer. For safety, a correct approach would be to not

consider this layer in the analysis, neglecting any residual contribution

after its failure. However, the tensile armor and the tapes keep

restraining the nucleus of the pipe, even on wet collapse situations.

As the here presented model does not consider the action of the tensile

armor and tapes, neglecting the presence of the external layer would

permit any rotational movements in the pressure layer, once it would

not be restrained in the circumferential direction. However, this restrain

would exist in the real situation due to the action of the tapes and

tensile armor presence. Thus, a study of three situations was performed

using the wet collapse model with 30 pitches of carcass layer:

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• A: Wet collapse of the pipe considering only the carcass,

polymeric and pressure layers, with total absence of external

layers, permitting rotational movements of the pressure layer;

• B: Wet collapse of the pipe considering a fictitious PA11 5 mm

thick external polymeric layer bonded to the pressure layer, in

order to avoid the non-realistic rotational movements of the

pressure layer;

• C: Wet collapse of the pipe considering a fictitious PA11 1 mm

thick external polymeric layer bonded to the pressure layer, in

order to avoid the non-realistic rotational movements of the

pressure layer.

The comparison of the collapse between the models A, B and C helped

to understand the effect of the external polymeric layer in the wet

collapse model as a constraint to the pressure layer movement.

Fig. 16 - Ovalization versus external pressure for the wet collapse

Models A, B and C.

Fig. 16 shows that Model A collapses for small levels of external

pressure when compared to Models B and C. This is due to the

rotational movements of the pressure layer. Models B and C have

almost the same behavior; the thickness of the external polymeric layer

didn’t affect the results.

This study showed that it is possible to considerer the external

polymeric layer presence in the wet collapse problem, once the only

important effect it shows is to avoid the rotational movements of the

pressure layer as its structural stiffness does not affect the external

pressure collapse value.

CASE STUDIES OF WET COLLAPSE

The present section show some case studies performed. Two flexible

pipes types were considered: 2.5” and a 4.0” of internal diameter. Both

have the same pressure armor but different carcass layer profiles. The

Table 6, Table 7 and Table 8 show the properties for the layers of the

pipes.

To deal with the wet and dry collapse problems (for the straight and

curved pipes) a carcass layer model with 30 pitches length was

considered. The thickness of both the polymeric layers was 5 mm. A

0.2% bi-symmetric initial ovalization was imposed on the carcass layer

in this model (trying to induce an “eight collapse mode”, once actually

the initial shape was elliptical).

The volumes and the elements of the model are plotted in Fig. 17 and

Fig. 18, respectively. The 4.0” flexible pipe model mesh contains

2.674.327 nodes and 2.115.992 elements. The 2.5” flexible pipe model

mesh contains 2,010,705 nodes and 1,652,551 elements.

Table 6 – Pressure armor layer geometrical properties (2.5” and 4.0”

flexible pipes)

Cross section area (profile) 53.792 mm2

Minimum moment of inertia (profile) 105.68 mm4

Length of profile 14.5 mm

Table 7 – Carcass layer geometrical properties (2.5” flexible pipe)




Table 8 – Carcass layer geometrical properties (4.0” flexible pipe)




The curved flexible pipe problem is solved in two subsequent steps,

being:

• Curvature imposition rotating the pilot nodes in both extremities

of the sample;

• External pressure loading.

Fig. 17 – Volumes of half the model utilized for collapse problems (the

model actually considers no symmetry planes, being the cut view used

only for visualization purposes).

For the 4.0” flexible pipe, a curvature radius of 2.06 m was assumed

and, for the 2.5” flexible pipe, 2.24 m.

Fig. 18 – Detailed cut view of the elements of half the model utilized

for collapse problems (the model actually considers no symmetry

planes, being the cut view used only for visualization purposes).

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The wet collapse simulations for the straight pipe showed two different

collapse modes for the 2.5” and 4.0” flexible pipes, as one can see in

the deformed shape colored by the displacement field in Fig. 19 and

Fig. 20. This interesting fact occurs because both pipes have the same

pressure armor but different carcass layer profiles and so different

stiffness ratios between these layers. When the external layer is too stiff

when compared to the inner carcass layer, the “heart collapse mode” is

naturally chosen by the structure, even with a doubly symmetric

perturbation.

Fig. 19 – Deformed shape of the middle section of a straight 4.0”

flexible pipe showing the buckling mode for wet collapse. Results

showing the radial displacements (mm) related to the last simulation

sub-step (closest to the limit point).




sub-step (closest to the limit point).

When one looks to the deformed shapes of the curved flexible pipe in

the wet collapse results (Fig. 21 and Fig. 22), it is possible to notice

that both the models present the “heart collapse mode”. This occurs

because the curvature acts as an imperfection with only one symmetry

plane. It is also possible to visualize the influence of the curvature in

the wet collapse pressure prediction. It is really important to consider it

in the pipe design, once it can decrease the wet collapse pressure by an

important amount when compared to the straight flexible pipe. This can

be visualized in Fig. 23 and Fig. 24, which compare the API ovalization

vs. external pressure for both flexible pipes simulated. In these plots the

collapse pressure value can be identified as a limit point, associated to a

maximum pressure value. For the presented models, the 4.0” flexible

pipe showed an 8.4% collapse pressure reduction due to curvature, and

the 2.5” flexible pipe, a more severe reduction of 13.2%.

Fig. 21 – Deformed shape of the middle section of a curved 4.0”


related to the last simulation sub-step (closest to the limit point) - plot

is 10 times scaled.

Fig. 22 – Deformed shape of the middle section piece of a curved 2.5”



is 10 times scaled

Fig. 23 - API Ovalization versus external pressure for the wet collapse

of the 4.0" flexible pipe.

The Fig. 25 shows a curved sample of flexible pipe. The curvature

osculator plane was used to cut the model to easily visualize the

deformed shape of the structure. It is possible to visualize one of the

curvature effects in the pipe: the decrease of the pitch of each rolled

layer in one side (region 1) and the increase of the pitch in the opposite

region of the tube (region 2). This causes a stiffness change in the

radial direction of the pipe in each region. The region 1 presents a

stiffness increase and, the region 2 a stiffness decrease. This

collaborates for the reduction of the wet collapse pressure in a curved

pipe, when compared to a straight one. Once the less stiff region

collapses first and suffers plastic strains, it induces the “heart collapse

mode”, because at the onset of buckling the stiffer region (1) still did

not suffer the same amount of plastic strain. It is similar to induce the

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collapse in a tube with the imperfection in only one symmetry plane (as

done by Li and Kyriakides (1991) for two concentric contacting rings).

Fig. 24 - API Ovalization versus external pressure for the wet collapse


Fig. 25 – Curved pipe showing two different changing pitch regions

CASE STUDIES OF DRY COLLAPSE

The same flexible pipes chosen for the wet collapse case studies were

considered in the dry collapse. A 0.42% initial ovalization of pressure

layer was imposed to 4.0” flexible pipe and a 0.40 % initial ovalization

of the same layer was imposed to the 2.5” flexible pipe.

For the straight flexible pipes, the Fig. 26 and Fig. 27 show the

deformed shape colored by the displacement field. One can see that the

2.5” and 4.0” straight flexible pipes present the same qualitative

displacement field. Additionally, the curved flexible pipes displacement

field can be seen in Fig. 28 and Fig. 29. These results show that the

curvature presence does not change the dry collapse mode as occurred

in the wet collapse study. All the dry collapse mode shapes obtained are

of the kind “eight collapse mode”.


flexible pipe showing the buckling mode for dry collapse. Results


sub-step (closest to the limit point)

Fig. 27 – Deformed shape of the middle section piece of a straight 2.5”



sub-step (closest to the limit point)




is 10 times scaled.




is 10 times scaled.

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The Fig. 30 and Fig. 31 show the API ovalization vs. external pressure

for both flexible pipes simulated. It is possible to see that the initial

curvature effect did not influence significantly the collapse pressure

prediction, as occurred in the wet collapse problem.

Fig. 30 - API Ovalization versus external pressure for the dry collapse


Fig. 31 - API Ovalization versus external pressure for the dry collapse


The Fig. 32 shows the ovalization pattern for the 4.0” flexible pipe,

showing the repetition pattern of displacements close to the mid of the

sample considered. One can see a clearly “eight shape mode”

appearance.

Additionally, the “heart shape mode”, can be seen in Fig. 33, which

shows a repetition pattern of displacements close to the mid of the

sample considered.

Fig. 32 – Y direction displacements (mm) in the dry collapse of a

curved 4.0” flexible pipe showing the ovalization pattern. Results

related to the last simulation sub-step (closest to the limit point)

It is possible to notice that in the deformed shape, at the onset of the

dry collapse, the external pressure modifies the curvature in the middle

region of the sample. This occurs because the external pressure tries to

restore a straight configuration of the pipe when it is curved. It was also

observed that the external pressure effect in the wet collapse cannot

change the whole flexible pipe curvature as in the dry collapse

problem. Actually, the “heart shape mode”, as seen in Fig. 33, can be

understood as this tendency to restore a straight pipe configuration for

the system composed by the internal polymeric layer and carcass layer.

However, the pressure layer presence tries to keep the pipe curvature,

acting as a constraint to this movement. The final result of this

interesting mechanical interaction is the “heart shape mode” inside a

curved external set of layers composed by the pressure armor and the

external polymeric layers.

Fig. 33 – X direction displacements in the wet collapse of a curved 4.0”

flexible pipe showing the ovalization pattern. Results related to the last

simulation sub-step (closest to the limit point)

CONCLUSIONS

This work presented a FEM modeling approach for dealing with the

wet and dry collapse failure modes of flexible pipes. The idea is to

simulate a sample of a flexible pipe in external pressure conditions to

induce collapse. The developed models have few assumptions about

possible movements and imperfection inclusions for collapse induction.

This was done in order to permit the structure to choose its less energy

buckling mode for each case. It was concluded that the different

collapse modes can naturally be chosen by the structure, depending on

the inducing initial imperfections and the relation between the stiffness

magnitudes of the layers of the flexible pipe. Furthermore, a discussion

about the effects of the curvature in the wet and dry collapse was made,

indicating that in the wet collapse the curvature has a decreasing

collapse pressure effect. For the dry collapse problem, the present

model does not consider a constant curvature during the pressure

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loading as the curvature was imposed before the pressure. Due to its

restoring effect from a curved to a straight pipe, it is possible to

visualize that curvature varies during the external pressure loading.

Thus, to address the problem of a constant curvature along the pipe a

different model must be considered.

FUTURE WORKS

The present model can be compared with simpler numerical models,

which could be solved in shorter time when compared with the solution

time spent for solving the here presented models. Experiments for

testing the collapse of flexible pipes including the curvature effects

would be welcome for comparisons.

ACKNOWLEDGEMENTS

The authors thank FAPESP, for funding the PhD studies of the first

author (grant 2006/06277-0); CNPQ, for the research grant of the

second author (310105/2009-9) and Petrobras/ANP for funding the

PhD studies of the third author.

REFERENCES

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