IPC2014 33552 Structural Reliability Free Spans

1 Copyright © 2014 by ASME

Proceedings of the 2014 10th International Pipeline Conference IPC2014

September 29 – October 3, 2014, Calgary, Alberta, Canada

IPC2014-33552 DRAFT

STRUCTURAL RELIABILITY OF FREE SPANNING PIPELINES

F. Van den Abeele Fugro GeoConsulting Belgium

Brussels, Belgium

F. Boël Fugro GeoConsulting Belgium

Brussels, Belgium

J-F Vanden Berghe Fugro GeoConsulting Belgium

Brussels, Belgium

ABSTRACT

When installing subsea pipelines on an uneven seabed, the free spans can be vulnerable to fatigue damage caused by vortex induced vibrations (VIV). Indeed, even moderate currents can induce vortex shedding, alternately at the top and the bottom of the pipeline, at a rate determined by the flow velocity. Each time a vortex sheds, a force is generated in both the in-line and cross-flow direction, causing an oscillatory multi-mode vibration. This vortex induced vibration can give rise to fatigue damage of submarine pipeline spans, especially in the vicinity of the girth welds. Traditional design for VIV is recommended in DNV-RP-F105, which limits the allowable free span length and implies whether (and when) seabed interventions are required.

The traditional DNV-RP-F105 design method is based on a

semi-empirical approach, where the allowable span length depends on the pipe properties (diameter, wall thickness, coating, steel SN_curves, …), the sea state (current velocity, wave induced velocity and period) and the soil conditions (submerged unit weight, undrained shear strength, bearing capacity,…). All these input parameters, however, exhibit a certain extent of scatter and uncertainty.

This paper presents a risk based evaluation of free spans,

by applying the principles of structural reliability theory to the problem of long free spanning pipelines subjected to VIV. First, a fully deterministic on-bottom roughness analysis is performed to introduce numerical tools for free span analysis. Then, a sensitivity analysis on soil parameters is presented to show significant influence of soil properties on free span predictions.

To study the implications of uncertainty in soil properties,

a First Order Reliability Method (FORM) analysis is presented at the end of this paper, where the soil properties are introduced as stochastic variables.

TOOLS TO ANALYSE ON-BOTTOM ROUGHNESS Offshore pipeline installation is performed from a lay

barge, typically in S-lay configuration. For smaller diameters, pipeline reeling can be the most cost efficient solution, whereas J-lay is the only feasible approach in (ultra) deep water. Depending on the installation method, the pipeline is subjected to different load patterns during installation, including hydrostatic pressure, lay tension and bending on the stinger and in the sagbend. A comprehensive overview on the mechanics of installation design can be found in [1]. Figure 1 shows a subsea pipeline leaving the stinger of a laybarge during an S-lay installation process.

Figure 1: Pipeline leaving stinger during S-lay installation

The simulation of the pipelaying process is one of the most

challenging tasks once the pipeline route has been selected. Implementing pipeline installation in a general purpose finite element package can be a time consuming and tedious job, in particular when importing vast amounts of seabed data. Most often, advanced scripting techniques are required to define the seabed profile, select the optimum pipeline route and simulate the laydown process. In addition, the available constitutive models for pipe-soil interaction may not comply with industry standards.


In this paper, the SAGE Profile software suite [2, 3] is used to simulate pipelaying on an uneven seabed. SAGE Profile is the industry standard software for on bottom roughness analysis. A comprehensive overview of the software is given in [3], and its application to fatigue analysis of free spanning pipelines subjected to vortex induced vibrations is presented in [4]. SAGE Profile has been tailored to assist the pipeline engineer during offshore pipeline design. Using a transient dynamic explicit solver, it can accurately mimic the actual pipeline installation process, like schematically shown in Figure 2.

The pipe is simulated by discretising the entire pipeline into section of finite length. These sections are represented by beam elements with 12 degrees of freedom (DOF), bounded at either side by nodes. The distributed mass of the pipe is lumped at these nodes. The finite element kernel uses an explicit integration algorithm, which computes the dynamic motion of the pipe and is therefore ideally suited to simulate the pipe laying process.

Figure 2: Pipeline catenary shape during S-lay installation

During this pipeline installation process, new pipe

elements are continuously created and the pipe is laid along the target path defined on the seabed. The residual lay tension at the seabed is used as an input and the unstressed length of the last element is updated such that the axial force corresponds to the applied lay tension. When the growing element becomes longer than twice the initial length, the element is split in two new elements. An additional node is placed along the last element such that the newly formed element obtains the original unstressed length.

This algorithm accurately reflects the continuous supply of

welded pipe joints from a moving lay barge. The gravity, applied during the pipelay simulation, will force the newly created pipe elements into place. Indeed, Figure 2 shows the typical catenary shape during pipeline installation.

For long pipelines and significant water depths, simulating the entire laydown process (from the barge down to the seabed) tends to be time consuming and is computationally expensive. The sophisticated architecture of the SAGE Profile solver allows for a significant reduction in the resources required to simulate pipeline laydown. By default, the lay barge and most of the free hanging pipe is replaced by a single feeding point in the water column moving close to the seabed, like shown in Figure 3.

Figure 3: Definition of feeding point and target path This feeding point acts as a submarine lay barge,

generating new pipe joints as it moves forward. The lay tension is now applied at the feeding point, generating a residual on bottom tension in the laid pipe section. Assuming a catenary shape [10], the lay tension at the feeding point can be expressed in terms of the submerged weight per unit length

tan1 1 tan (1)

where is the angle between the pipe and the target path, and is the height of the feeding point above the seabed. Replacing the lay barge with a feeding point close to the seabed allows for a significant reduction in calculation time, without losing accuracy. Given the inherent complexity of pipeline laying, an accurate and robust steering mechanism of the feeding point is of paramount importance. In SAGE Profile, this steering mechanism is governed by a Proportional-Integrating-Differentiating (PID) controller, providing a smooth movement of the feeding point and ensuring that the pipeline is installed on the pre-defined target path (shown in red on Figure 3).

In addition to the concept of a feeding point, an efficient element killing procedure has been implemented to control the computational effort during pipeline laydown. Indeed, it would be too expensive to simulate the entire length of the pipe from its starting point up to the feeding point. In order to reduce the required calculation time, elements that are already lying on the seabed and are no longer moving will be removed from the simulation. If the magnitude of the velocity vector for a node is lower than a pre-defined threshold, the associated element has little or no contribution to the simulation results and can be killed without losing accuracy. On Figure 3, the elements that have been killed are shown as well.


IDENTIFICATION OF FREE SPANNING PIPELINES Accurate prediction of free spans (location, length and

height) is an important prerequisite in offshore pipeline design. Indeed, free span lengths should be maintained within an allowable range [5], which is determined during the design phase. Pipelines installed on a very rough seabed can cause a high number of free spans that can be difficult to rectify. A judicious assessment of free spans can dramatically reduce the costs associated with seabed intervention (trenching, rock dumping and span supports).

Figure 4: Free spanning pipeline on an uneven seabed

Figure 4 demonstrates that SAGE Profile is capable of simulating pipeline installation on an uneven seabed, and subsequently detecting free spans.

In this paper, the case study presented in [4] is used to

demonstrate the application of structural reliability theory to the problem fatigue damage predictions for free spanning pipes. An X70 flowline with an outer diameter = 10-¾” (273.05 mm) and a wall thickness = 7/8” (22.225 mm) is installed in the Gulf of Mexico in water depths exceeding 2400 meters. The irregular seafloor topography, shown in Figure 5, indicates that this pipeline may be prone to free spans and hence vulnerable to vortex induced vibrations.

Figure 5: Seabed roughness along the pipeline route

The pipe is coated with a Fusion Bonded Epoxy (FBE) coating and a Glass Syntactic Polyurethane (GSPU) coating with mechanical properties summarized in Table 1.

Table 1: Mechanical properties of the coating layers

Coating Thickness

[“] Density [kg/m³]

Water Absorption

[%]

FBE 0.018 1440 0

GSPU 3 833 5

The soil conditions along the route consist mainly of very

soft clay, typical for deepwater soils encountered in the Gulf of Mexico. For the base case scenario, we assume a very soft clay with a submerged unit weight of = 7.5 kN/m³ and an undreamed shear strength of =2.2 kPa. The catenary shape of the suspended pipeline during laying (schematically shown on Figure 2) has been taken into account to accurately capture the pipe embedment at the touchdown point.

Simulation of the pipe laying process has been performed with an element length of 1 meter, and assuming a residual bottom tension = 100 kN. After the pipelay simulation has been completed, SAGE Profile automatically detects the spans over the entire pipeline route, and plots the span location, length and height in comprehensive and easy-to-read design charts, like shown in Figure 6.

FATIGUE ANALYSIS OF SPANS SUBJECTED TO VIV Once the laydown simulation is performed, SAGE Profile

automatically detects the spans over the entire pipeline route, like shown on Figure 11. The plots of seabed roughness, pipeline profile, span height and span length clearly indicate the presence of a long free span starting at KP ~ 1940m. This free span, with a length of 82 m and a maximum gap of 1.9 m, is shown on Figure 12, where the color code reflects the span gap.

SAGE Profile offers a DNV-RP-F105 [5] span check to

evaluate whether such free spans are susceptible to fatigue damage induced by VIV. For each detected span, the span check algorithm calculates the associated reduced velocity

(2)

where is the mean current velocity (normal to the pipe), the significant wave-induced flow velocity, and an approxi-mation for the lowest natural frequency given by

√1 1 (3)


Figure 6: Overview of span location, height and length with the stiffening effect of the concrete coating, the effective span length [10], the effective mass, the effective axial force, the static deflection and the end boundary coefficient. The moment of inertia for the hollow circular pipe is given by

64 (4)

Figure 7: Long free spanning pipeline vulnerable to VIV

and the critical buckling load can be calculated as

1 (5)

where is an end boundary coefficient as well. In addition to the reduced velocity (2), the stability parameter

4

(6)

is calculated for each span, where is the total modal damping ratio, comprising structural damping, hydrodynamic damping and soil damping. Based on the values of the reduced velocity (2) and the corresponding stability parameter (6), the in-line vibration amplitude can be estimated based on the response model shown in Figure 8, and presented in the Appendix.

Figure 8: Amplitude Response model for in-line VIV motion

For the (ultra)deep water pipeline, presented in this paper,

the contribution of wave induced velocities is neglected, i.e. we assume 0 m/s. The current velocity is typically specified as a Weibull probability density function [6], which can be estimated from the 1, 10 and 100 y return period. Since no detailed metocean data was available, and given the magnitude of the water depth (exceeding 2400 meter), we have used a uniform current velocity distribution of 0.1 m/s in this paper.


Under these hydrodynamic conditions, the reduced velocity for the long span, shown in Figure 7, exceeds the threshold for the onset of in-line VIV:

1.18 0.909 , (7)

SAGE Profile calculates the maximum allowable span

length that satisfies , as = 65.8 meter. The in-line vibration amplitude can be determined from the response model (shown in Figure 8) as the value of that corresponds with the design value of the reduced velocity

(8) with the safety factor for the natural frequency, which depends on the safety class and whether the span is (very) well defined or not [5].

The dimensionless vibration amplitude ⁄ can then be translated into a stress range

2

(9)

with a safety factor, the reduction factor for the current flow ratio

(10)

and the unit stress amplitude, i.e. the stress due to unit diameter in-line mode shape deflection. According to DNV-RP-F105 [6], the unit stress amplitude may be approximated as

1

(11)

with the mid-span boundary condition coefficient and the stiffness of steel. The number of cycles to failure at a stress range is defined by an SN-curve of the form

∙∙

(12)

where , are fatigue exponents (i.e. the inverse slope of the bi-linear SN curve), , are characteristic fatigue strength constants, and

10

(13)

is the stress at the intersection of the two SN-curves, with the number of cycles for which the change in slope appears. Typically, log is either 6 or 7.

The SN-curves may be determined from dedicated laboratory test data, accepted fracture mechanics theory, or the values recommended in [7].

For fatigue calculations in SAGE Profile, the pipeline

design engineer can either define his own SN curve, or select the SN-curves , , , from DNV-RP-C203. The latter curves have a different shape for free corrosion (only one slope) or when cathodic protection is present (two-slope curve). For instance, the SN curves in seawater when cathodic protection is present are shown on Figure 14. The change in slope occurs at 10 . For the fatigue analysis, presented here, we have used the SN-curve from [7], assuming cathodic protection is present.

Figure 9: SN curves for cathodically protected pipelines

The marginal fatigue life capacity against in-line VIV in a

single sea-state is calculated by integrating over the long-term distribution of the current velocity. As we assume a uniform current velocity distribution, the fatigue life calculation simplifies to

⁄

365 ∙ 24 ∙ 3600

(14)

For the critical free span shown in Figure 12, this leads to a remaining fatigue life of 116 years, which is well above the design life of the flowline.

In addition to the in-line VIV assessment, SAGE Profile also constructs the response model for cross-flow VIV, based on the current flow ratio (17), and the Keulegan Carpenter number

(15)

with the significant wave-induced velocity, and the corresponding frequency. Given the significant water depths, exceeding 2400 meters, fatigue analysis for both cross-flow VIV and cross-flow induced VIV can be omitted.


SENSITIVITY TO SOIL PROPERTIES

For the deterministic benchmark, presented in the previous section and elaborated in [4], sensitivity analyses were performed to investigate the influence of the element length, the weight of the suspended catenary and the estimation of the on-bottom residual lay tension on the ability to predict free spanning pipes. These analyses indicate that

Reducing the element length enhances the accuracy of the simulated spans. The lower bound for the element length is governed by the seabed resolution.

The suspended catenary has to be taken into account to capture the actual pipeline embedment at the touch-down point.

The applied residual lay tension has a pronounced influence on the span predictions. The simulated span lengths increase with increasing lay tension. This is in line with the observations reported in [8] on influence of the effective axial force on free spanning pipes.

The predicted span length and height were shown to be

even more sensitive to the constitutive soil model. An elastic soil model tends to over-estimate the span length. Hence, an elasto-plastic soil model is recommended. Moreover, the shear strength proves to have a significant influence on both the number of predicted spans and the corresponding span lengths.

Indeed, the soil reaction is dictated by a vertical soil spring,

which reflects the bearing capacity and for clays, DNV-RP-F105 [5] recommends

5.14 (16)

where is the pipe penetration, and

2 0 2⁄

otherwise

(17)

the bearing width. The bearing capacity (16) is often calculated assuming a constant shear strength, which is the average value of the shear stress profile measured in the top ~400 mm of the undisturbed seabed.

However, predictions of the initial pipeline embedment based on a merely static load generally under-estimate the actual pipe penetration, because they do not account for the stress concentration at the touchdown point, nor the dynamic movement induced by the vertical catenary oscillations. Cheuk and White [9] have suggested to modify the original shear strength to reflect the level of soil disturbance and remoulding expected during the lay process. Introducing a soil sensitivity

, the remoulded shear strength is written as a fraction of the original undisturbed shear strength:

(18)

The soil sensitivity can vary between 1 (insensitive

clays) and 16 (quick clays) and hence has a significant influence on calculated bearing capacity. The influenced of soil sensitivity on the vertical soil spring (16) is shown in Figure 10.

Figure 10: Influence of soil sensitivity on bearing capacity

On-bottom roughness assessment and free span analysis is

often performed in feasibility studies and during the route selection process, where detailed geotechnical data and accurate pipe-soil interaction parameters are not always available. To study the effect of incomplete data on the soil properties, we have re-run the pipeline laydown simulations for different values of the remoulded shear strength.

Table 2: Sensitivity analysis on soil parameters

St [-]

Sensitivity

[kPa]

[kPa]

1 Insensitive 2.2 2.2

2 Medium 2.2 1.1

4 Sensitive 2.2 0.55

The parameters used in the sensitivity analysis are

summarized in Table 2, and the results are shown in Figure 11. Both the number of identified spans and the total span length over the proposed pipeline route increase significantly with the undrained shear strength of the soil. Indeed, considering a sensitivity of 1 rather than 4 raises the number of spans from 27 to 83, and implies a 20% increase in the accumulated span length.

From this fairly simple and straightforward sensitivity

analysis, it is obvious that the soil properties are of paramount importance for the accurate prediction of free spans and the corresponding fatigue lifetime of the pipeline when subjected to vortex induced vibrations.


Figure 11: Influence of soil properties on span predictions

Yet, the soil properties are not always known in the early

design stages, or at least subject to uncertainty. In the next section, we introduce a probabilistic model to estimate in-line VIV fatigue, where the soil properties are represented by stochastic variables. This is the perimeter of engineering where structural reliability analysis provides the tools that allow calculating the cost of ignorance.

RELIABILITY ANALYSIS APPLIED TO FREE SPANS Reliability methods deal with the uncertain nature of loads

and resistance, and lead to the assessment of the reliability [10-11]. Reliability methods are based on analysis models for the structure in conjunction with available information about loads and resistances, and their associated uncertainties. The analysis models are usually imperfect, and the information about loads and resistances is usually incomplete [12]. The reliability as assessed by reliability methods is therefore generally not a purely physical properties of the structure in its environment of actions, but rather a nominal measure of the safety of the structure, given a certain analysis model and a certain amount and quality of information.

According to [12], the structural reliability is defined as the

probability that the system will not attain each specified limit state. The limit state or performance function may be generally defined by the stochastic loads and resistances

as the condition where the load equals the system’s resistance:

0 (19)

The loads and resistance of a system possess inherent

uncertainties in their magnitude for different periods of time in the design life. For a given time period, the limit state can be represented graphically as shown in Figure 12-a. The structural reliability of the system is therefore the area under the resistance curve that is greater than the load (Figure 12-b).

Mathematically, it is more convenient to calculate the reliability of a system in terms of its complement: the probability that failure will occur, like shown on Figure 12-c. The probability of failure is calculated as

0

(20)

with and the probability density functions for the resistance and load respectively.

(a) Limit State Definition

(b) Stuctural Reliability

(c) Probability of Failure

Figure 12: Structural reliability and probability of failure


The reliability index is defined as [10-12]

Φ (21) where Φ is the standard normal (cumulative) distribution function. The probability of failure and the corresponding reliability index can be solved by Monte Carlo simulations [13] or using first or second-order reliability methods [14].

In this paper, application of the First Order Reliability Method (FORM) is demonstrated to predict the probability of (fatigue) failure for a free span subjected to in-line VIV, when the soil properties are treated as stochastic variables.

Stochastic Basic Variables

Standardised Normal Variables

Figure 13: Transformation of the limit state surface

In a FORM analysis, the limit state surface in the space spanned by the basic variables is transformed to a corresponding limit state function by normalization of the random variables into standardized normally distributed variables:

(22)

with and the mean value and standard deviation of the original stochastic variable . As a result, the transformed random variables follow a normal distribution with zero mean and unit standard deviation. The transformation of the limit state function is schematically shown in Figure 13.

The design point ∗ is the point on the transformed limit state surface which is closest to the origin, and hence the most likely failure point. For a non-linear limit state surface

, Hasofer and Lind [15] suggest performing a linearization of the failure surface represented at the design point (hence first order reliability method).

Hence, the FORM solution provides a geometrical

interpretation of the reliability index as the distance between the origin and the design point ∗ in the standard normal space, like shown in Figure 13.

To apply the First Order Reliability Method to the problem of fatigue failure of free spans subjected to VIV, we follow the approach recommended in [12]:

Identify all significant failure modes For each failure mode, formulate a failure criterion

which can be expressed as a limit state function In the limit state functions, identify all the stochastic

variables and parameters and specify their probability distributions

Calculate the probability of failure for each failure mode

Assess whether the estimated reliability is sufficient, i.e. meets the target reliability

A comprehensive and elaborate reliability analysis for free

spanning pipelines has been presented in [8]. In our investigation at hand, the analysis is constrained to in-line VIV fatigue. The limit state function for fatigue failure after years can then be expressed as

1 (23)

where is the stochastic fatigue damage at year . For demonstration purposes, the deterministic parameters have been selected to produce an onerous scenario with a high probability of failure. For a bilinear SN-curve like shown in Figure 9, the stochastic fatigue damage can be expressed as


where is the dominating frequency of the vibrating span, and

is the stochastic long-term stress range probability density function, capturing the uncertainty in the amplitude response model.

The sensitivity analysis on soil properties, summarized in Figure 11, has shown that the span prediction is to a very large extent dependent on the accuracy of the geotechnical input data. To study the importance of uncertainty in soil properties, we have chosen all variables and parameters in (23) to be deterministic, except the ones that relate to geotechnical data. For the damage induced by in-line VIV [6], this reduces to the coefficient for the lateral soil stiffness and the uncertainty on the stability parameter (6), which captures the effect of soil damping.

For the lateral soil stiffness, we assume that is normally distributed with a mean value = 1200 kN/m5/2 and a coefficient of variability

0.3 (24)

These values are representative for a soft clay and in line

with the recommendations given in [8] and [16]. As is assumed to be normally distributed, it can be converted into a standard normal variable through the transformation (22). Figure 14 shows the variation of the limit state function (23) as a function of the expected value for when all other variables are fixed. The fatigue damage quickly becomes important for increasing values of the lateral soil stiffness.

Figure 14: Influence of soil stiffness on limit state function

In order to account for the uncertainty on the model used

for calculating the stability parameter , an additional stochastic variable is multiplied with (6).

This stochastic variable is assumed to follow a lognormal distribution with = 1 and = 0.12. The lognormal distribution implies that ln follows a normal distribution:

exp (25) where is the standard normal variable and and are the mean and the standard deviation of . The mean of a lognormal variable can be computed as

exp 2

(26)

and the variance can be expressed as

exp 1 exp 2

(27)

and hence, by very definition of (26),

exp 1

(28)

Inverting (26) and (28) yields an expression for the variance

ln 1 (29)

and the mean value

ln 2

(28)

of the normally distributed variable . These expressions finally allow transforming the uncertainty on the stability parameter into the standard normal variable

ln (30)

Figure 15: Influence of stability XKS on limit state function


The influence of on the performance function (23) is shown in Figure 15. Since we are only investigating uncertainty in soil properties, the vector in the transformed limit state function reduces to , . Assuming that these stochastic variables are not correlated, the joint probability distribution can be visualized as the product of the both normal standard probability density functions, like shown in Figure 16.

Figure 16: Joint probability density function in U-space

The FORM analysis now reduces to the minimization problem

min (31) provided 0. This can be visualized in the space spanned by the standard normal variables , , as demonstrated in Figure 17. The design point is found as the root of the minimization problem (31) as

∗ ∗ , ∗ 0.08, 0.438 (32)

The most likely point of failure thus corresponds to a soil stiffness coefficient = 1171 kN/m5/2 and an uncertainty on the stability parameter 1.046. The reliability index is calculated as 0.445 and the corresponding probability of failure is found as

Φ 0.328 (33) which can be interpreted as the area under the joint probability density surface intersected by the failure set 0. These results lead to an unacceptable reliability of ~67%, because we have deliberately designed an extremely onerous scenario to clearly illustrate the FORM methodology (like shown in Figure 16 and 17).

Figure 17: FORM analysis for free span subjected to VIV

CONCLUSIONS

In this paper, a risk based evaluation of free spans was presented, by applying the principles of structural reliability theory to the problem of long free spanning pipelines subjected to in-line VIV.

First, an integrated numerical framework was presented to predict and identify free spans that may be vulnerable to fatigue damage caused by vortex induced vibrations. An elegant and efficient algorithm was introduced to simulate offshore pipeline installation on an uneven seabed. Once the laydown simulation has been completed, the free spans can be automatically detected.

When free spans are judged to be prone to VIV, amplitude response models are constructed as per DNV-RP-F105 to predict the maximum steady state VIV amplitudes. The vibration amplitudes are translated into corresponding stress ranges, which then provide an input for the fatigue analysis.

A sensitivity analysis on soil properties has shown that the span prediction is to a very large extent dependent on the accuracy of the geotechnical input data. As the soil properties are not always known –or at least subject to uncertainty- in the early design stages, a First Order Reliability Method (FORM) was presented, where the soil properties are introduced as stochastic variables. It has been demonstrated that structural reliability theory the tools that allow calculating the cost of ignorance.


APPENDIX: RESPONSE MODEL FOR IN-LINE VIV The in-line response of a pipeline span in current dominated conditions (like the one shown on Figure 7) is associated with either alternating or symmetric vortex shedding. Contributions from the first instability region and the second instability region are included in the response model proposed in [6]. This response model, schematically shown on Figure 13, can be constructed based on the design value of the stability parameter

⁄ , where is a safety factor. The onset velocity , is the value for the reduced velocity where in-line VIV starts to occur:

,

1.00.4

0.60.4 1.6

2.21.6

(34)

and the end velocity can be written as

, 4.5 0.8 1.0

3.7 1.0 (35)

The reduced velocities for the other two points indicated in Figure 13 are given by

, 10 , , (36)

, , 2 ,

(37)

where , and , are the corresponding vibration amplitudes

, max 0.18 11.2

; , (38)

and

, 0.13 1 1.8

(39)

These amplitude values depend on the reduction factors 0 , 1 and 0 , 1 who account for the effect of the turbulence intensity and the angle of attack ( , in radiance) for the flow [6]. Also note that DNV-RP-F105 introduces an additional reduction function to account for reduced in-line VIV in wave dominated conditions:

0.0 for 0.50.5

0.3for 0.5 0.8

1.0 for 0.8

(40)

Thus, if 0.5, in-line VIV may be ignored.

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Installation Design, pp. 597-636 (2005) [2] Witgens J.F., Falepin H. and Stephan L., New Generation

Pipeline Analysis Software, Offshore Pipeline Technology, OPT 2006

[3] Van den Abeele F. and Denis R., Numerical Modelling and Analysis for Offshore Pipeline Design, Installation and Operation, Journal of Pipeline Engineering, Q4, pp. 273-286 (2011)

[4] Van den Abeele F., Boël F. and Hill M., Fatigue Analysis of Free Spanning Pipelines subjected to Vortex Induced Vibrations, Proceedings of the 32nd International Conference on Ocean, Offshore and Arctic Engineering, OMAE2013-10625 (2013)

[5] Det Norske Veritas, Recommended Practice on Free Spanning Pipelines, DNV-RP-F105 (2006)

[6] Fyrileiv O., Aronsen K. and Mork K., DNV FatFree Verification Document, Report No. 2000-3283 (2010)

[7] Det Norske Veritas, Recommended Practice on Fatigue Design of Offshore Steel Structures, DNV-RP-C203 (2010)

[8] Hagen O., Mork K.J., Nielsen F.G. and Soreide T., Evaluation of Free Spanning Design in a Risk Based Perspective, Proceedings of the 22nd Conference on Offshore Mechanics and Arctic Engineering, OMAE-37419 (2003)

[9] Cheuk C.Y. and White D.J., Centrifuge Modelling of Pipe Penetration due to Dynamic Lay Effects, Proceedings of the 27th International Conference on Offshore Mechanics and Arctic Engineering, OMAE2008-57923 (2008)

[10] Thoft-Christensen P. and Baker M.J., Structural Reliability and its Applications, Spinger Verlag, Berlin, Heidelberg (1982)

[11] Ditlevsen O. and Madsen H.O., Structural Reliability Methods, Wiley, Chichester (1996)

[12] Det Norske Veritas, Classification Notes CN30.6, Structural Reliability Analysis of Marine Structures (1992)

[13] Rubinstein R.Y., Simulation and the Monte-Carlo Method, Wiley, New York (1981)

[14] Schueller G.I. and Stix R., A Critical Appraisal of Methods to Determine Failure Probabilities, Structural Safety vol. 4, pp. 293-309 (1987)

[15] Hasofer A.M. and Lind N.C., An Exact and Invariant First Order Reliability Format, Journal of Engineering Mechanics, pp. 111-121 (1974)

[16] Sigurdsson G., Mork K.J. and Fyrileiv O., Calibration of Safety Factors for DNV-RP-F105 Free Spanning Pipelines, OMAE2006-92099 (2006)

IPC2014 33552 Structural Reliability Free Spans

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