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This paper focuses on a theoretical approach to access the fatigue life of flexible pipes. This methodology employs functions that convert forces and moments obtained in time-domain global analyses into stresses in their tensile armors. The stresses are then processed by well-known cycle counting methods, and

Unbonded flexible pipes or simply flexible pipes, as in Figure

Typical unbonded flexible pipe.

Flexible pipes are composite structures made of several steel and plastic concentric layers designed to meet specific requirements. The polymeric layers work as sealing, insulating, and/or antiwear components, whilst basically three types of metallic layers withstand the imposed structural loads [

These pipes typically operate in water depths up to 2000 m, but recent plans to extend their use to water depths up to 3000 m [

One of the advantages of using flexible pipes instead of rigid steel pipes in offshore systems is the compliance of the formers with the movements of floating facilities and, furthermore, the ability to absorb harsh environmental loads. These characteristics derive from its internal structure in which the individual layers are allowed to slide relative to each other. These movements and environmental loads, however, may provoke high tension and curvature variations in the pipe, which may lead to fatigue failure and/or the wear of the metallic layers. Among all metallic layers of a flexible pipe, its tensile armors are especially prone to fatigue failure [

Despite the large use of flexible pipes in the offshore oil industry, the determination of their fatigue limits still deserves great attention and, similar to the procedure employed for rigid risers, involves five steps [

collection of environmental loading data and definition of the load case matrix,

global analysis of the riser system, that is, the evaluation of axial forces (tension, as torsion is usually neglected) and bending moments (curvatures) that act on the pipe due to the loads defined in Step 1,

transposition of the tensions and moments determined in the global analysis to theoretical local models devoted to calculate the stresses in each layer of the pipe,

local stress analysis of the pipe focusing on the evaluation of the stresses in the tensile armor wires,

estimation of the fatigue life relying on the stresses calculated in the last step.

This procedure, easily followed in the analysis of rigid steel pipes, implies some difficulties when flexible pipes are analyzed. The computation of stresses is one of the key problems; for rigid pipes, stresses are calculated by simple formulas, and this calculation can be performed directly in the global analyses. For flexible pipes, the evaluation of stresses in their internal layers is not that simple, due to their multilayered structures and complex responses to mechanical loads, mainly when friction between their internal layers is considered. In this way, specific programs have to be employed, and the transposition of tensions and bending moments from the global analyses programs to these programs is needed.

Additionally, many local analyses have to be carried out in order to generate time histories of stresses that are employed to estimate their fatigue lives, but programs devoted to perform local analyses are usually not prepared to carry out thousands (and sometimes millions) of such analyses and store this data for further fatigue assessment.

Finally, according to Grealish et al. [

Annulus conditions: the annulus of a flexible pipe is the space between the inner and outer polymeric sheaths that contains the pressure and tensile armors. The characterization of the annulus environment directly influences the choice of the fatigue

Global analyses: neither the nonlinear bending response of flexible pipes nor bending hysteresis effects, which will be discussed later in this paper, are usually considered. The energy dissipation during loading is normally represented with an equivalent viscous damping.

Local analyses: the application of response parameters, such as curvature and tension determined from a global analysis, may not be consistent with the manner that the stresses in the wires of the tensile armors are calculated.

Fatigue methodology: traditional approaches rely on the use of minimum and maximum curvature values that have been derived from regular wave analyses in order to calculate stress ranges. Irregular wave loading, rainflow counting techniques, weather directionality, and frequency domain screening are frequently neglected or inconsistently employed. Moreover, current methods do not usually account for variations of the dynamic tension, which may be significant in ultradeepwater applications, and also do not generally consider the variation of stresses in the armor wires around the cross-section of the pipe. Finally, locations such as the touchdown zone (TDZ) or bending stiffener areas may not be treated with sufficient rigour.

Therefore, in order to address some of these issues, this paper presents an approach to evaluate the fatigue life of flexible pipes focusing on the calculation of stresses in their tensile armors. This approach employs preestimated functions that convert time histories of forces and moments obtained in global analyses into time histories of stresses in the wires of the tensile armors. The use of these functions speeds up the calculation of stresses, allowing that a great number of cross-sections along the flexible pipe are analyzed with low computational effort. Moreover, these transfer functions also account for load directionality and friction between layers and, consequently, are capable of representing the hysteretic response of flexible pipes subjected to cyclic three-dimensional bending. Finally, time histories of stresses are processed by well-known cycle counting methods and

Next, firstly, the proposed approach is presented in detail. After that, various analyses are performed in order to estimate the fatigue life of a flexible riser, and a study is conducted in order to assess the importance of four main aspects in the fatigue response of flexible pipes: the friction between their layers, the annulus conditions, the number of points in the cross-section at which the damage is calculated, and the effect of mean stresses.

The approach proposed in this paper can be summarized in the following steps.

Environmental loading cases for global analyses are selected from the location scatter diagram.

Global time-domain analyses of the flexible pipe are performed. Time series of tensions and moments at selected locations along the flexible pipe are generated and stored.

A group of coefficients that convert loads imposed to the pipe into stresses in its layers is derived in parallel with (or previous to) the global analyses.

Time series of stresses are automatically generated from the loads evaluated in Step 2 and using the coefficients estimated in Step 3.

Rainflow stress cycle counting for each point of each section of the pipe is performed; fatigue damage is calculated and also accumulated, and, finally, fatigue life is evaluated.

Each of these steps is described in detail next.

The environmental loads that most influence the analysis and design of offshore structures, such as risers and mooring lines connected to floating units, are waves, wind, and current (see Figure

Environmental loads in flexible risers.

From a statistical point of view, these time-dependent environmental loads are random processes. In long-term periods (greater than 1 year), these processes are not stationary; however, for shorter periods (usually 3 h), the parameters that characterize each environmental load present a statistical regularity that allows to consider the stationarity assumption. Each set of environmental parameters for a short-term period of 3 h is called a seastate. A seastate

Joint probability distribution functions that include all parameters that characterize a seastate are not usually found in the literature [

Example of a scatter diagram for waves.

In order to obtain seastates for fatigue analysis from the individual and independent scatter diagrams for waves, wind, and current, a method to combine the environmental loads has to be chosen. This choice can be simplified by recognizing that waves are the most important loads in fatigue calculations [

Due to the importance of the wave loading in the evaluation of the fatigue life of a riser, its correct numerical simulation is of fundamental importance in the global analyses of flexible pipes. There are basically two ways of representing waves in such analyses: the regular and irregular wave approaches. The regular wave approach is associated with deterministic global riser analyses, whilst the irregular wave approach leads to stochastic global analyses.

In a deterministic global analysis, each pair (

On the other hand, a stochastic global analysis directly considers each seastate of a stochastic scatter diagram, but long simulation times are necessary to stabilize statistical parameters of the response (tensions and moments). These analyses thus demand total simulation times and computational effort much higher than those required in a deterministic analysis, but the loads are more representative of the field environment leading to more realistic results.

The deterministic approach, due to its low computational cost and conservatism, is traditionally used in the computation of the fatigue life of flexible (and rigid) risers. However, recently, stochastic analyses have become more attractive due to the increasing computational capacity and, mainly, the need to reduce the conservatism in fatigue life assessment.

Once the environmental parameters are defined, the whole set of seastates,

The fatigue approach proposed in this work deals with either deterministic or stochastic analyses, but, in performing these analyses, a key point is the generation of time histories of tensions and curvatures, as these time histories are converted to time histories of stresses that are used to compute the fatigue life of flexible pipes. This approach accounts for time variation of the axial forces and bending moments as well as the phasing between these responses thereby reducing the number of simplifying assumptions associated with the transposition of forces and moments, which is discussed next.

As mentioned before, the evaluation of stresses in the layers of a flexible pipe is not straightforward, and forces and moments calculated in global analyses programs have to be transposed to programs capable of computing these stresses.

The local analyses of flexible pipes are performed with programs based on one of the various theoretical models available in the literature (see Witz [

the tensile axial stiffness of a flexible pipe is different from its compressive axial stiffness [

these stiffnesses, for moderate loads, do not vary with the magnitude (positive or negative) of the axial displacement (translation or rotation).

In the design of flexible pipes, axial compression is not desirable as it may cause the excessive bending of these structures or the buckling of their tensile armors wires [

On the other hand, the bending stiffness of the pipe depends on its curvature. Various authors [

For small curvatures, friction between the wires and the adjacent layers prevents their slippage. As a consequence, axial forces are induced in the wires, and these forces are opposed by friction forces with the same magnitude. This leads to a linear bending moment versus curvature relationship with a very high tangent stiffness. This tangent stiffness is usually called no-slip bending stiffness,

As curvature increases, interlayer friction is overcome and progressively allows the relative movement of the layers. This slippage reduces the tension increase in the extrados of the pipe and compression decrease in its intrados thereby reducing the tangent stiffness of the pipe. This stiffness keeps decreasing until friction forces are fully overcome and the tensile armors are free to slip. At this point, the tangent stiffness reaches a limit value much lower than the no-slip one. This lower limit is called full-slip bending stiffness,

Schematic representation of the hysteretic response of flexible pipes under bending.

If a flexible pipe is loaded and unloaded with curvatures lower than the critical value, the bending moment versus curvature relationship is linear (path OAB in Figure

This nonlinear and hysteretic bending response has a substantial impact on the fatigue life computation of flexible pipes mainly due to two aspects [

bending motions imposed to the pipe are reduced as the high preslip bending stiffness sustains small changes of curvature at each curvature reversal, and, moreover, there is a significant energy dissipation associated with higher curvatures,

different stress components and amplitudes may arise in the tensile armor wires during the no-slip and full-slip phases.

Concerning the second aspect, three different types of stresses arise in the tensile armors wires during bending [

Normal (axial) stresses due to friction, which are uniformly distributed across the section of the wire. These stresses are positive (tensile stresses) in wires located in the extrados of the bent pipe and negative (compressive stresses) in wires located in the intrados of the pipe and also have a limit value associated with the critical curvature.

Bending stresses due to normal curvature variations, which vary linearly from tension to compression along the thickness of the wire.

Bending stresses due to transverse (binormal) curvatures, which vary linearly from tension to compression along the width of the wire.

As a result of the helical path of the wires, a sinusoidal distribution along the cross-section of the pipe is typically assumed for these stresses. Considering the bending moment,

Tensile armor wires in a cross-section of a flexible pipe.

Despite its importance in fatigue life computation, the simulation of this nonlinear and hysteretic bending response is not a simple task and is often, conservatively, not considered in global and local analyses of flexible pipes. It is worth mentioning that most programs devoted to perform global analyses have been initially developed to analyze rigid steel pipes and cables or mooring lines. In these structures, the bending moment versus curvature relationship is typically linear, and energy dissipation is mainly due to viscous and hydrodynamic dampings. Therefore, when analyzing flexible pipes with these programs, the usual approach is to consider a tangent bending stiffness (usually the full slip value, as it is provided by the manufacturers) associated with an equivalent viscous damping, which is set by designers relying on their own practice. Local analyses may be performed considering that the stresses are related to the no-slip phase [

Only in the recent few years, programs capable of considering the described hysteretic response in the global analyses of flexible pipes have been developed [

In this work, bending moments (or curvatures) calculated either with a linear or nonlinear bending moment versus curvature relationship can be transposed to the local model, but the model always assumes a bilinear and hysteretic relation between stresses and curvatures. If a linear relation is employed in the global analyses, this assumption will reduce the conservatism of the analysis (mainly if the global analyses are performed using the full-slip bending stiffness of the pipe). On the other hand, if a nonlinear relation is employed in the global analyses, this approach will lead to consistent results as long as the friction moment and the critical curvature informed in the bilinear bending moment versus curvature curve are the same of the bending stresses versus curvature curves. The whole procedure is described in detail next.

It is common practice in the analysis of flexible pipes to split the total stresses in the wires into two components: stresses associated with axisymmetric loads and stresses induced by the imposed bending moments or curvatures [

There are several models available in literature devoted to the cross-section (local) analysis of flexible pipes [

In this work, (

In particular, for a typical unbonded flexible pipe with a high-strength tape to prevent axial compression instability of the tensile armor wires, two different types of nonlinearities were observed in the analyses:

loss of contact between some layers of the pipe,

material nonlinearities due to the high-strength tape, which only works when tensioned.

The responses obtained for this type of flexible pipe were grouped in 16 possible deformed shapes, as indicated in Table

Possible contact pressures and stress in the high-strength (HS) tape for a typical unbonded flexible pipe considering different annulus conditions and axisymmetric loading.

Shape | Interface^{†} |
Stress (HS tape) | Annulus | ||||
---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | |||

1 | Contact | Contact | Contact | Contact | Contact | Unloaded | |

2 | No contact | Contact | Contact | Contact | Contact | Tensioned | |

3 | No contact | Contact | Contact | Contact | Contact | Unloaded | |

4 | No contact | Contact | Contact | No contact | Contact | Tensioned | Dry |

5 | No contact | Contact | Contact | Contact | No contact | Unloaded | |

6 | No contact | Contact | No contact | No contact | Contact | Tensioned | |

7 | Contact | Contact | Contact | Contact | No contact | Unloaded | |

| |||||||

8 | Contact | Contact | Contact | Contact | Contact | Unloaded | |

9 | No contact | Contact | Contact | Contact | Contact | Tensioned | |

10 | No contact | Contact | Contact | Contact | Contact | Unloaded | |

11 | No contact | Contact | Contact | No contact | Contact | Tensioned | |

12 | No contact | Contact | Contact | Contact | No contact | Unloaded | Flooded |

13 | Contact | Contact | Contact | Contact | No contact | Unloaded | |

14 | Contact | No contact | Contact | No contact | Contact | Tensioned | |

15 | Contact | No contact | Contact | Contact | No contact | Unloaded | |

16 | Pure external pressure |

^{
†}Interface 1: inner carcass and internal plastic sheath; interface 2: internal plastic sheath and pressure armor; interface 3: pressure armor and antiwear tape (or tensile armor); interface 4: pressure armor (or antiwear tape) and internal tensile armor; interface 5: external tensile armor and polymeric layer upon it. In all other interfaces, contact between layers was observed.

Load characteristics for each possible deformed shape of a typical unbonded flexible pipe considering different annulus conditions and axisymmetric loading.

Shape | Load characteristics^{†} |
Annulus |
---|---|---|

1 | High tension (no axial compression), low internal pressure, high external pressure, moderate torsion | |

2 | Low tension or axial compression, high internal pressure, low external pressure, low torsion | |

3 | High tension, high internal pressure, moderate external pressures (internal pressure higher than external pressure), low torsion | |

4 | High axial compression (no tension), high internal pressure, low external pressure, low torsion | Dry |

5 | High tension and internal pressure, no external pressure, moderate torsion | |

6 | High axial compression, low internal and external pressures, low torsion | |

7 | High tension and low internal and external pressures, low torsion | |

| ||

8 | Analogous to shape 1 | |

9 | Analogous to shape 2 | |

10 | Analogous to shape 3 | |

11 | Analogous to shape 4 | |

12 | Analogous to shape 5 | Flooded |

13 | Analogous to shape 7 | |

14 | High axial compression, no internal pressure, high external pressure, low torsion | |

15 | High tension, no internal pressure, high external pressure, low torsion | |

16 | Pure external pressure |

^{
†}The fundamental aspect is to maintain the proportionality between the loads. Therefore, a high load value could be its limit for the studied flexible pipe; a low value may be, for instance, 1% of the limit value, and a moderate value could be 50% of the limit value.

Therefore, for each of the possible deformed shapes, five analyses, which effectively produce the assumed contact and stress conditions presented in Table

This methodology allows the computation of the stresses in the armors with few simple operations and low computational effort. As a consequence, in a typical fatigue analysis, the stresses induced in the armors may be evaluated at each time step of all considered time histories.

The computation of the stresses due to the bending of the pipe is based on a vector hysteresis model. In this model, an in-plane stress versus curvature relationship, which has to be previously defined, is extended in order to account for the three-dimensional bending of the pipe.

The model relies on a set of equations proposed by Fylling and Bech [

If a curvature increment Δ

Fylling and Bech [

Moreover, by hypothesis, the relative slide of the wires starts when the total curvature modulus exceeds the internal friction curvature,

In (

Coefficients

Finally, considering (

In this work, the time series of stresses for each load case are generated from the tension and moments time series calculated in the global analysis using (

The first time step of the time series of tension and curvatures corresponds to the results from the static analysis. From these results, the static stresses are determined considering the methodology previously described. The critical curvature estimated for this step is kept throughout the whole dynamic analysis for each load case.

Dynamic axisymmetric stresses are calculated using (

Bending stresses are calculated by maintaining the critical curvature of each static analysis and considering that the static configuration is the unstressed one. The stress variations, which correspond to the dynamic stresses, are obtained by considering the variation of the curvature related to the static stresses. It means that the total curvatures in the dynamic analyses are the difference between the dynamic curvatures calculated in the global analyses and the static curvature. Hence, the stresses at each corner of a tensile armor wire may be expressed by the following formulas.

The approach proposed in this work computes stresses (and fatigue damage) at several points in the pipe’s cross-section and for each of the environmental load cases considered. The number of stress cycles in each of these time series is counted using the rainflow technique, and the fatigue damage associated with each stress cycle is evaluated using

Finally, fatigue damage is accumulated assuming that the Palmgren-Miner rule is valid, and the fatigue life in each section is represented by the minimum value obtained for all processed points. It is also worth mentioning that mean stress effects may be addressed using the well-known Goodman correction factor.

As mentioned before, the global loads that act on the pipe may be assessed with one of the various programs devoted to perform this task (see Larsen [

In order to speed up the calculation of stresses and evaluation of the fatigue life, a specific tool called FADFLEX was developed. FADFLEX performs the transposition from the global to the local model and computes stresses at each desired point along the flexible pipe. Moreover, stress cycles are counted by this program, and fatigue damage is calculated. Finally, the program estimates the fatigue life of the flexible pipe.

As an example of the proposed methodology for fatigue evaluation of flexible pipes, a 6” oil production riser connected to a FPSO (Floating Production, Storage and Offloading) vessel was selected. The riser is in a free hanging configuration (7° top angle, 185° azimuth) in a water depth of 800 m. It has 8 layers including two tensile armors. The inner tensile armor has 56 wires, whilst the outer tensile armor has 58 wires. All wires are 3 mm in height and 9 mm in width. The axial stiffness of the pipe is 357 MNm/m, and its full slip bending stiffness equals 12.8 kNm^{2}. Figure

General overview of the studied flexible pipe: (a) perspective and (b) lateral view.

The seastates employed in the fatigue analysis were obtained from Campos Basin (offshore Brazil) metocean data [

All environmental loads were supposed aligned (8 directions). Scatter diagrams similar to the one presented in Figure

For each direction, the currents selected to compose each load case were the 1-year extreme currents. The offsets were estimated supposing a value equivalent to 10% of the water depth associated with the largest wave in Campos Basin (

All global time-domain analyses were performed by the in-house tool ANFLEX [

In order to obtain the coefficients

Considering the objectives of the work, which are to illustrate the use of the proposed approach and to evaluate the effect of some parameters in the fatigue response of a flexible pipe, the base case assumed the following premises.

The annulus of the pipe is flooded with seawater.

A friction coefficient of 0.10 between the layers of the pipe is initially considered.

Mean stresses effects are accounted for by the Goodman correction factor.

The

All wires of the tensile armors had their fatigue lives calculated.

Next, firstly, the fatigue life of the 6” flexible riser considering the conditions previously described is computed. After that, relying on the results obtained, the effect of each of the following four parameters on the fatigue response of the pipe is evaluated: friction between layers, annulus conditions, mean stress effects, and number of points considered in each cross-section.

Figure

Fatigue life along the flexible pipe: base case.

The cross-section with the lowest fatigue life is located inside the bend stiffener. Figure

Fatigue life along the critical section: base case.

Figure

Time histories of stresses in wire 10 (corner with the highest fatigue damage) of the inner tensile armor: (a) axisymmetric stresses; (b) normal friction stresses; (c) normal bending stresses; (d) transverse bending stresses.

Time histories of stresses in wire 12 (corner with the highest fatigue damage) of the outer tensile armor: (a) axisymmetric stresses; (b) normal friction stresses; (c) normal bending stresses; (d) transverse bending stresses.

Figure

In order to evaluate the effect of different friction coefficients on the fatigue life prediction of the flexible riser, five different values were considered: 0.00 (no friction), 0.05, 0.10 (base case), 0.20, infinite (fully bonded response). Figure

Fatigue life: effect of different friction coefficients.

Friction coefficient | Fatigue life (years) | ||
---|---|---|---|

Inner armor | Outer armor | Flexible riser | |

0.00 (no friction) | 77387 | 109173 | 77387 |

0.05 | 1054 | 15384 | 1054 |

0.10 | 135 | 3511 | 135 |

0.20 | 19 | 503 | 19 |

Infinite (bonded) | 19 | 19 | 19 |

Fatigue life in the inner armor along the flexible pipe: effect of different coefficients of friction.

Fatigue life in the outer armor along the flexible pipe: effect of different coefficients of friction.

These figures and tables indicate that the choice of the friction coefficient is a key aspect in predicting the fatigue life of a flexible riser. In the analysis with no friction, local and global models assume the same hypotheses, and no hysteresis is expected to occur in the riser response. However, no friction stresses are induced, and, as mentioned before, these stresses largely contribute to the fatigue damage on the riser. Therefore, high and unconservative values for the fatigue lives are predicted in both layers. The assumption of a friction coefficient of 0.05 reduces the fatigue life of the riser in 1/75. It is interesting to observe that this reduction is obtained in the inner armor, but in the outer armor the reduction is of about 1/7, as friction stresses are lower in this layer. The increase of the friction coefficients keeps reducing the fatigue life until a limit value of 19 years is reached in both layers for infinite friction.

It is worth mentioning that, if infinite friction is assumed, the global analysis should be performed considering the no-slip bending stiffness, and, consequently, much lower curvatures would be obtained. Hence, the values obtained with infinite friction maximize the stresses in the wires, and the hypothesis of full slip bending stiffness in the global analyses maximizes the curvatures calculated leading to quite conservative values for the fatigue lives. A possible approach, consequently, would be the choice of a lower friction coefficient, such as 0.05 or 0.10, and the use of the full-slip bending stiffness in the global analysis to ensure some conservatism in the fatigue analysis.

In the previous analyses, the annulus of the pipe was considered to be flooded with seawater. Here, the response of the riser with a dry annulus is assessed considering the base case conditions and an

When the annulus of the pipe is dry, the external pressure acts on its outer sheath leading to high contact pressures between the tensile armors and the adjacent layers in sections located in the TDZ, and, consequently, no slippage between layers occurs in these sections. Therefore, in order to make consistent global and local analyses, the full-slip bending stiffness employed in the global analyses was replaced by the no-slip value in the cross-sections located in the TDZ. In this work, the no-slip bending stiffness, ^{2} was calculated, which is 165 times higher than the full slip bending stiffness.

Considering this new bending stiffness value and the dry

Variation of the fatigue life along the flexible pipe: effect of the annulus conditions (dry values are obtained with the flooded

Table

Fatigue life: effect of the number of wires analyzed.

Number of wires | Fatigue life (years) | ||
---|---|---|---|

Inner armor | Outer armor | Flexible riser | |

All | 135 | 3511 | 135 |

28 | 135 | 3535 | 135 |

14 | 138 | 3536 | 138 |

8 | 146 | 3881 | 146 |

4 | 194 | 3881 | 194 |

The

Fatigue life in the wires of the critical cross-section: effect of mean stresses.

Hence, a key aspect of the fatigue design of flexible pipes is to account for this effect with the use of correction factors, as indicated here, or of

The prediction of the fatigue life of flexible pipes is a key issue that must be addressed in order to employ these structures in harsh operational and/or environmental conditions or, furthermore, to possibly extend the use of structures in operation. In comparison to other offshore structures, such as rigid steel pipes, the computation of the fatigue resistance of flexible pipes has two additional difficulties: the global (evaluation of forces and moments) and local (evaluation of stresses) simulations of the bending hysteretic response of these pipes and the calculation of stresses in their armor layers, which is not straightforward. Therefore, the fatigue life assessment of these pipes is not a simple task, which is usually overcome with theoretical models that assume various simplifying hypotheses leading to quite conservative results. These results may impair their use in the previously stated conditions, and, therefore, less conservative approaches are demanded.

In this work, aiming at reducing the conservatism associated with the fatigue life prediction of flexible pipes, a new theoretical approach was proposed. The main goals of this approach are as follows.

Results from either regular or irregular seastates may be considered.

Various local analyses may be performed with low computation effort.

The fatigue computation is based on the analysis of time histories of stresses generated from the time histories of tensions and bending moments (or curvatures) calculated for each seastate in the global analyses. Therefore, the approach directly encompasses dynamic tension variations, and no additional hypotheses on phasing between tensions and curvatures are necessary.

The possibility of considering either dry or flooded annulus conditions.

The simulation of the bending hysteretic response of flexible pipes in their local analyses in order to generate less conservative time histories of stresses.

Easy computation of the fatigue life in all wires along the flexible pipe. Moreover, fatigue damage is accumulated at each analyzed point in these wires using rainflow counting techniques, adequate

A study on the fatigue response of a 6” flexible riser was carried out using this approach. The fatigue life computation of the riser was based on tensions and moments calculated with a global FE model that did not consider its bending hysteretic behavior, as, usually, programs devoted to perform global analyses of flexible pipes do not handle this issue.

The results obtained showed two critical regions: the top of the riser including the bend stiffener; and the touchdown zone. The critical cross-sections, however, were located at the top of the riser. In all analyses, the fatigue response of the flexible riser was governed by the resistance of the inner tensile armor wires, as stresses induced by friction with adjacent layers are higher in these wires and these stresses have the highest amplitudes.

Aiming at evaluating the effect of friction on the fatigue response of the riser, fatigue analyses considering different coefficients of friction were conducted. These analyses showed that the choice of the coefficient of friction and the simulation of the hysteretic response of the riser strongly affect its fatigue life. The analysis with no friction presented values much higher than the analysis with a low friction coefficient (0.05) and, therefore, is quite unconservative. However, the calculation of forces and moments with the lower bending stiffness of the pipe (highest possible curvatures) followed by the stress computation considering that the wires are prevented from sliding (fully bonded response and maximum stresses) indicated a fatigue life much lower than intermediate values obtained with friction coefficients of 0.05 or 0.10. This approach is thereby quite conservative. The suggested approach is, consequently, to consider friction coefficients between 0.05 and 0.10 and calculate the fatigue life with the simulation of the hysteretic response, at least, in the local analyses or, ideally, in the local and, if possible, global analyses.

This study also indicated that the annulus condition was of fundamental importance. The assumption of a dry annulus, despite the higher stresses obtained in the TDZ compared to the flooded condition, implicates the use of benefic

To sum up, it is authors’ belief that the results presented here serve as a basis to better understand the fatigue response of typical flexible pipes. However, much remains to be done in this area, as, for instance, in this study, the hysteretic response was not considered in the global analyses, and this is a source of conservatism that can be diminished by adapting global FE models to account for this type of responses; there are doubts regarding the friction coefficients and local models for computing the bending and combined (bending and axisymmetric) responses of flexible pipes, and, consequently, experimental tests are needed in order to validate these models, and experimental tests have also to be performed in order to calibrate the whole proposed approach.

Authors from COPPE/UFRJ would like to thank Petrobras for allowing the publication of this work.