Effect of seabed stiffness on fatigue life of steel catenary risers due to random waves

Abstract

Today’s oil and gas industry is facing deeper waters and harsher environmental conditions. Offshore platforms and marine risers, as the main parts of this industry, have many challenges and design issues. Steel Catenary Riser (SCR) connected to Floating, Production, Storage, and Offloading unit (FPSO), is a preferred and commonly used solution to the challenges. It is needed to have more understandings of SCR behavior. So in this study, the significance of SCR-seabed interaction is investigated. Also, the effect of seabed stiffness on the structural behavior of the SCR is studied. Results show that the seabed stiffness makes considerable differences in dynamic and fatigue responses of SCRs in the touch down zone (TDZ) and reveal the importance of proper seabed stiffness modeling. Model (I), which represents weak soils with very low stiffness, could resist on continuously applied harsh environmental condition for 139.6 days. Model (IV) which represents a very stiff seabed, had a minimum fatigue life of about 6.5 percent of the model (I). The results indicated that the SCR responses were highly separated in terms of fatigue performance especially for weak to normal soils.

Keywords

Riser seabed fatigue random waves soil stiffness

1. Introduction

Risers and mooring systems are the most important parts of all offshore structures, especially in deep sea condition. Risers are prone to oscillatory motion caused fatigue and other dynamic failures in the structure, while the mooring system reduces the motions and consequently participates in increasing reliability of the operations. Different types of riser and mooring system have been developed to satisfy specific requirements related to special environmental conditions and operational demands. So the interaction between riser and mooring system is an interesting research subject affecting the operation and economy.

The growing trend of global demand for hydrocarbon energy sources has put oil and gas exploration into more advanced technology, deeper water depths, and more hostile environments. A direct result of this trend has been the design of different mobile and semi-mobile offshore platforms, like Tension Leg Platform (TLP), Semi-submersible, Floating Production, Storage and Offloading unit (FPSO), etc. For the purpose of deepwater activities, FPSOs have been considered as one of the most appropriate systems because of their advantages in huge storage capacity, ample deck space giving better layout flexibility, cost efficiency for the short-life fields, mobility, and no need of neighboring pipeline infrastructure [22].

As a part of the offshore platform, offshore marine risers, which connect the platform on the water surface to the wellhead production stream located on the seabed, have been highly developed in aspects of material composition, fabrication technologies and engineering design in recent years. The main function of the riser is to transport fluids or gas from seabed to a host platform. The riser system is a vital element in providing safety, and its failure results in spillage or pollution and could endanger lives. Hence, significant design effort is required to have a high degree of reliability for riser design.

Steel catenary riser (SCR) has been a preferred riser solution for deepwater field developments due to its simple engineering concept, cost-effective, flexibility in using different host platform and flexibility in geographical and environmental conditions [4]. SCR concept allows the use of large diameter, which is suitable for deepwater and high pressure and high temperature (HPHT) field development [20].

Risers are not fixed and robust bodies, these slender flexible structures exhibit complex dynamic behavior which has been investigated through various numerical and experimental methods in the last few decades [10]. Matsunaga and Ohkusun (1994) showed that precise prediction of the dynamic behavior of risers is of primary importance [14]. Therefore, it is necessary to define all the significant sources of the environmental loads and the external forces. Royer et al. (2014) compared dynamic responses of different SCR configurations and highlighted the differences of each riser concept’s behavior and provided an understanding of the limitations of riser concepts [19]. Taheri and Alizadeh (2017) investigated the length of the riser on its structural behavior [25]. Seungjun and Moo-Hyun proved that the conventional SCRs connected to an FPSO hull exhibit significant dynamic responses and negative tensions, which may induce large structural stress amplification, local dynamic buckling, and serious fatigue damage at the members nearby touch down (TD) region [22]. Siahtiri and Taheri (2017) studied the dynamic behavior of SCR near the touch down zone and investigated the effect of the trench formation on the structural performance of risers [23]. Ljuština et al. (2004) showed that the vessel motion and waves are the dominant sources of riser bending moment and stress which are from the main cyclic loads affecting the fatigue life of the riser [13].

Cyclic stress caused by cyclic wave loading and vessel motion result in low fatigue performance. As fatigue studies show, there are two critical areas which have the minimum fatigue life over SCR total length; they are located near the vessel hang-off point (HOP) and in the touch down zone [12,21]. An accurate estimation of fatigue damage is crucial as SCR failure can have significant environmental and economic effects. Moreover, interventions or repairs in deep water are very complex, particularly in touch down zone (TDZ) [1,3]. So it can be concluded that the touch down zone has the most criticality in terms of dynamic behavior and fatigue performance. Lucile Queau (2015) in her researches improved the knowledge of the structural response of SCRs and proposes efficient strategies to simplify the early stages of fatigue design of SCRs in the TDZ. She examined the fatigue damage due to first order wave motions which usually has the highest contribution to overall fatigue life [18].

When the SCR is subjected to oscillating movement, there is a complex interaction between SCR and seabed, so this interaction should be considered appropriately in the dynamic and fatigue analyses. There are different approaches to model the seabed behavior. Many of SCR studies assumed the seabed as rigid flat or linear elastic spring. A rigid surface generally gives a conservative result since it is unyielding, while the linear elastic surface is a better approximation of a seabed [2]. A high value of seabed stiffness models an almost rigid surface such as rock; a low value models a soft surface such as mud. Intermediate values can represent different soil types; very soft to hard clays, very loose to dense sands.

In this study, the significance of the SCR–seabed soil interaction and the influence of seabed vertical and lateral stiffness, which represents different soil types behavior, on structural and dynamic responses and also fatigue performance of SCRs in deepwater are investigated.

2. Theory and modeling

2.1. Static and dynamic analysis

A Finite Element (FE) approach is normally considered for global riser system analysis. Static analysis is always the first step in global riser analysis and defines the starting point for subsequent dynamic analyses. Static riser analyses are normally performed using a nonlinear FE approach. The purpose of the static analysis is to establish the static equilibrium configuration due to static loading (weight, buoyancy, top tension, current) for given locations of riser terminations to rigid structures (e.g. terminations to the seafloor and floater) [5].

Commonly used dynamic FE analysis techniques are; nonlinear time domain analysis, linearized time domain analysis, and frequency domain analysis [5]. Nonlinear time domain (NLTD) analysis allows for consistent treatment of load, as well as structural nonlinearities. Nonlinear simulations will typically be needed for systems undergoing large displacements, rotations or tension variations, or in situations where the description of variable touch down locations or material nonlinearities is important [6].

Waves can be defined either as regular or irregular waves. Ocean waves are irregular and random in shape, height, length, and speed of propagation. A real sea state is best described by a random wave model [7]. There are several spectrum theories to describe an irregular wave, which are used in the analysis and design of offshore structures. The most commonly used wave spectra are the Pierson-Moskowitz model, Bretschneider or ITTC two parameter spectrum, JONSWAP model, and the Ochi-Hubble spectrum model. The considered wave spectra model should give a good representation of the typical waves found at the service location [4]. Assumed wave spectra for the environmental condition modeled in this study is JONSWAP model to represent the environment of Gulf of Mexico.

Most specialist state-of-the-art riser analysis codes use either rigid or linear elastic contact surfaces to simulate the seabed, which model vertical soil resistance to pipe penetration, horizontal friction resistance, and axial friction resistance. In the Linear seabed model the seabed behaves as a linear spring in the normal direction, with spring strength equal to the vertical seabed stiffness specified in the Table 3. The normal (vertical) stiffness reaction force has a magnitude of $K_{n} . A . d$ and is applied in the outwards normal direction, where $K_{n}$ is seabed normal stiffness, A is penetrator contact area, and d is depth of penetration into the seabed. The Lateral seabed stiffness ( $K_{s}$ ) is used by the friction calculation. The friction force acts in the direction tangential to the seabed plane and towards the friction target position, whether in riser longitudinal direction or any other direction. Friction is modelled as modified Coulomb friction in the seabed plane. The friction force can be thought of as being linearly ramped from 0 to a maximum value of $μ R$ as the deflection increases. In this formula, μ is the friction coefficient ( $= 0.2$ in this study) and R is the contact reaction force. $K_{s}$ is equal to the slope of the ramp. Higher values of $K_{s}$ lead to the ramping taking place over a shorter distance, and vice versa. In OrcaFlex, both normal and axial friction coefficients can be defined. If these values are different, OrcaFlex uses a vector of μ for each direction. In this study, a same value of friction coefficient is used for both directions.

OrcaFlex is a fully 3D non-linear time domain finite element program capable of dealing with arbitrarily large deflections of the flexible pipes from the initial configuration. A lumped mass element is used which simplifies the mathematical formulation and allows quick and efficient development of the program to include additional force terms and constraints on the system in response to new engineering requirements. The pipe is divided into a series of line segments which are then modeled by straight massless model segments with a node at each end. The model segments only model the axial and torsional properties of the line. Other properties (mass, weight, buoyancy etc.) are all lumped to the nodes [16]. A schematic of the finite element model used in OrcaFlex is shown in Fig. 1.

Fig. 1.

Finite element model used in OrcaFlex [16].

2.2. Fatigue analysis

The fatigue assessment methods can be categorized into S-N curve and fatigue crack propagation based methods. Normally, the methods based on S-N curves are used for fatigue life assessment [5]. The fatigue design which is based on the use of S-N curves are obtained from fatigue tests. The design S-N curves are based on the mean-minus-two-standard-deviation curves for relevant experimental data. The S-N curves are thus associated with a 97.7% probability of survival [9]. These experimental curves are the basis of fatigue calculations in a lot of numerical simulation softwares like OrcaFlex.

An S-N curve defines the number of cycles to failure, N; when a material is repeatedly cycled through a given stress range S. Eqs. (1), and (2) show the relation between S and N; “a” and “m” are material type constants [9]. Each S-N curve specifies a stress endurance limit, $F_{L}$ which is the stress range below which no damage occurs. $\begin{array}{l} (1) & N = {a S}^{- m} \\ (2) & {log}_{10} (N) = {log}_{10} (a) - m {log}_{10} (S) \end{array}$

Damage can be calculated by using the S-N curve approach which indicates stresses and cycles up to the endurance limit for a homogeneous pipe (metal riser), and Deterministic irregular wave fatigue analysis using the rainflow cycle counting method.

The stress to be considered for fatigue damage accumulation in a riser is the cyclic principal stress. The governing cyclic nominal stress component, σ for pipes is normally a linear combination of the axial and bending stress given by Eq. (3). This combined stress varies around the circumference of the riser pipe [5]. $\begin{matrix} (3) & σ = \frac{T_{e}}{π (D - t_{fat}) t_{fat}} + \frac{32 M (D - t_{fat})}{π (D^{4} - {(D - 2 t_{fat})}^{4})} \end{matrix}$

In this equation, $T_{e}$ is effective tension (axial force), D is nominal outside diameter, $t_{fat} = t_{Nominal} - 0.5 t_{Corrosion}$ , $t_{Nominal}$ is nominal riser wall thickness, $t_{Corrosion}$ is corrosion allowance of the pipe, and M is bending moment.

The stress range to be applied in fatigue damage calculations is found by application of a stress concentration factor as well as a thickness correction factor to the nominal stress range as shown in Eq. (4) [8]. $\begin{matrix} (4) & S = σ . SCF . {(\frac{t_{fat}}{t_{ref}})}^{k} \end{matrix}$

$SCF = Stress Concentration Factor$

$t_{ref} = Reference Thickness (25 mm)$

$k = Thickness Exponent$

The response time history, for each load case, is then calculated at fatigue points. The damage value, $Damage (S)$ , is defined at that fatigue point due to one occurrence of that load case as Eq. (5) [9]. $\begin{matrix} (5) & Damage (S) = \{\begin{matrix} 1 / N (S) & if S > F_{L} \\ 0 & if S ⩽ F_{L} \end{matrix}\} \end{matrix}$

$F_{L}$ is the fatigue endurance limit, which no damage occurs under stress ranges below that. The fatigue criterion, which shall be satisfied, can be written [8]: $\begin{matrix} (6) & D_{fat} . DFF ⩽ 1 \end{matrix}$

$D_{fat} = Accumulated fatigue damage$

$DFF = Design Fatigue Factor$ ( $= 6$ , for Normal Safety Class)

Spectral methods provide closed-form fatigue damage estimates in terms of statistics for stationary random stress processes. Cycle-counting methods, such as rainflow cycle counting, provide an alternative damage estimation approach that is generally applicable and requires simulation of stress time series. The cycle-counting approach requires more computation than spectral methods. There is general agreement that rainflow cycle counting gives the best estimate of fatigue damage when the stress time history is known, as in the case of recorded time series data [11].

The fatigue of SCRs should be assessed by considering all of the causes of fatigue damage; they are for instance the first order and second order wave motions, the vortex induced vibrations (VIV), the thermal and pressures changes, the fabrication and installation phases [8]. This research examines the fatigue damage due to first and second orders wave motions, and current induced loads which usually have the highest contribution to overall fatigue life. A deterministic irregular wave fatigue analysis using the rainflow cycle counting method is used to assess the fatigue damage, as it is more appropriate for structural systems presenting nonlinearities [5,15–17,24]. Rainflow counting is a process to convert the actual stress time history, to an equivalent time history with constant amplitude cycles. Then rainflow extracts the number of cycles, and their respective range and mean value. The analysis is performed using OrcaFlex 9.7a.

3. Case study

Four models of SCRs connected to FPSOs are considered. The FPSOs are moored by 16 lines with a $4 \times 4$ taut-spread configuration in a water depth of 1000 m. An irregular wave with a significant height of 15.85 m and wave period of 15.4 s based on JONSWAP spectrum, with combination of current loading, are applied which represent typical deep water and harsh environmental conditions such as in the Gulf of Mexico. The FPSO is free to move under first and second order wave loads, current loads and is only limited by its mooring constraints. The seabed is assumed to behave like linear springs in both vertical and lateral directions as is shown in Fig. 2.

Fig. 2.

Seabed modeling.

Hence different soil types have different stiffness components which affect the SCR-seabed interaction. In order to compare the effects of seabed soil type on the dynamic response and the fatigue life of SCR, the only difference of the models is the linear seabed stiffness in both vertical and lateral directions. Model (I), which has the lowest stiffness, represents weak soils with very low stiffness, and model (IV) represents a very stiff seabed.

Tables 1–3 list the riser, mooring lines, and environmental conditions respectively for all four cases. Figure 3 shows the configuration of the mooring lines and riser, position of the touch down point (TDP) in arc length, and the direction of the wave and current.

In this table, SMYS is significant minimum yield stress, SMTS is significant minimum tensile stress, and $B 1$ is the S-N curve class based on DNV classification of the S-N curves.

Table 1

SCR modeling data

Parameter	Value	Parameter	Value
Length (m)	2500	Poisson Ratio	0.293
Inner Diameter (m)	0.254 ( $10^{″}$ )	Content Density ( $kg / m^{3}$ )	800
Wall Thickness (m)	0.019 ( $3 / 4^{″}$ )	Coating Density ( $kg / m^{3}$ )	800
Material Density ( $kg / m^{3}$ )	7850	Coating Thickness (m)	0.100
Young’s Modulus (GPa)	212	Welding Type	Seamless
SMYS (MPa)	555	S-N Curve (DNV)	B1
SMTS (MPa)	625	SCF	1.00

4. Results

The difference in the seabed stiffness had a little influence on the TDP position and also the TDZ length of SCR. Increasing the seabed stiffness, which means stiffer soil type, caused a little more hanged length of SCR and longer touch down area. Table 4 reports the mean position of the TDP in arc length of the SCR relative to the top end and the TDZ length for each model.

Since the touch down zone and the top end of the SCRs are critical areas along the length, and on the other hand, SCR-seabed interaction significantly affects the TDZ, this study has focused on the riser response in TDZ and its neighborhood (approximately the range of 1200 m to 1600 m in arc length).

Table 2
Mooring lines modeling data

Section Material Diameter (m) MBL 1 (kN) Length (m)

Top Steel (Chain) 0.0952(Bar) 7553 100

Mid. Polyester (Rope) 0.160 7429 1800

Bot. Steel (Chain) 0.0952(Bar) 7553 100

Section	Material	Diameter (m)	MBL 1 (kN)	Length (m)
Top	Steel (Chain)	0.0952(Bar)	7553	100
Mid.	Polyester (Rope)	0.160	7429	1800
Bot.	Steel (Chain)	0.0952(Bar)	7553	100

Minimum Breaking Load

Table 3

Environmental modeling data

Water depth (m)	1000	Wave Data	$H_{s} (m)$	$T_{p} (s)$	γ

			15.85	15.4	2.4
Current data	Depth (m)	Surface	38.1	76.2	1000
	Speed (m/s)	7	5.2	0	0
Seabed data	Model No.	(I)	(II)	(III)	(IV)
Vertical stiffness ( $kN / m / m^{2}$ )		1.672	16.72	167.2	1672
Lateral stiffness ( $kN / m / m^{2}$ )		1.152	11.52	115.2	1152

Fig. 3.

Illustration of analyzed model.

The governing parameter affecting the SCR response is the bending moment. The effect of seabed vertical and horizontal stiffness on the induced bending moment is shown in Fig. 4, and its variation during the time, is shown in Fig. 5 as the variation affects the fatigue performance of the riser. Stiffer soils had much more bending moments and bending moment variations. As it can be seen from the figure, the models (III) and (IV) bending moments and variations were very close to each other.

Table 4

Touch down position

Parameter	Model (I)	Model (II)	Model (III)	Model (IV)
Mean TDP (m)	1461.356	1476.633	1482.947	1485.887
TDZ length (m)	182	189.5	192	192.5

Fig. 4.

Maximum bending moment in TDZ.

Fig. 5.

Bending moment variation in TDZ.

Due to weight of the SCR, there were some initial penetrations in each soil. It is obvious that, this penetration in stiffer seabed is less. Initial penetrations of the models are: Model (I); 1.7471 D, model (II); 0.1747 D, model (III); 0.0175 D, and model (IV); 0.0017 D.

Dynamic analysis showed more penetrations, because of environmental loads and dynamic interactions of the riser. The maximum penetration of SCR over time in TDZ under 30 minutes interactions for all models are illustrated in Fig. 6.

Fig. 6.

Maximum SCR penetration in TDZ.

As shown in Fig. 7, the SCR lateral displacement was also affected somewhat by the seabed stiffness. Stiffer soils had more lateral displacements and looser soils allowed less lateral movements. The reason can be understood by comparing the SCR penetrations; The SCR penetrated more in weaker soils, so it was surrounded by the soil, while in stiffer soils, it was free to move and the only resisting component was the seabed friction.

In another point of view, consider the relation of riser penetration and seabed normal reaction force; as the penetration increases, seabed vertical spring force (= contact reaction force, R) increases.

On the other hand, the maximum value of friction force is $μ R$ . So the increase of penetration results in increase of R, hence increase of maximum value of friction force which is resisting on lateral riser displacement. Consequently, lateral riser displacement decreases with increase of penetration.

So weaker soil experiences more riser penetration, more contact reaction force, more friction force, and less lateral riser displacement.

Fig. 7.

SCR lateral displacement in TDZ.

As mentioned before, the stress to be considered for fatigue damage accumulation in a riser is the cyclic principal stress. Figure 8 shows how seabed stiffness affected the variation of this stress over time in TDZ. Stiffer seabed caused high variation of the stress which can considerably affect the fatigue life of SCR.

Fig. 8.

Cyclic principal stress variation in TDZ.

The overall trend of fatigue life Vs. SCR arc length curves for the SCRs are the same. The fatigue results of the model (IV) as an example are presented in Fig. 9. The reported fatigue lifetimes mean that how much time the SCR points can withstand against continuously applying mentioned harsh environmental condition. Minimum lifetimes were in the vicinity of the SCR top end and TDZ. The criticality of these two regions was pointed in terms of fatigue performance.

Fig. 9.

Fatigue life of model (IV) SCR.

The effect of soil stiffness on SCR fatigue life in TDZ are investigated and the results plotted in Fig. 10. Models with different seabed stiffness components had significant difference in fatigue lives. Higher seabed stiffness, resulted in lower fatigue lifetime of SCR in touch down zone. In other words, dense sand and stiff clay lead the SCR to experience more fatigue damages than loose sand and low stiff soil considering their relative stiffness components. It was predicted by the analyses that model (I) which had the smallest stiffness between models, can resist on continuously applied harsh environmental condition for 139.6 days. This fatigue survival time for model (II) was only 11.5 days, which is 8.3 percent of model (I). Model (III) and model (IV) which had much more seabed stiffness, like very dense sand and rock, had a minimum fatigue life of about 6.6 and 6.5 percent of model (I). The results indicated that the SCR responses, were highly separated in terms of fatigue performance especially for weak to normal soils.

Fig. 10.

Fatigue life of models in TDZ.

5. Conclusions

Results show that the seabed stiffness can make considerable differences in dynamic and fatigue responses of SCRs in TDZ and reveal the significance of proper seabed modeling. The differences for small values of stiffness (e.g. less than $10 kN / m / m^{2}$ ), are extremely high. So for weak soils, special attention must be paid to choose an appropriate value of seabed stiffness, to represent the behavior of the soil as accurate as possible. Stiffer soils (e.g. more than $100 kN / m / m^{2}$ ), have negligible difference in their responses and are almost rigid.

The most important results of this study are listed below:

Stiffer soils have much more bending moments in SCR touch down zone.

Lower seabed stiffness, inherently means more initial and dynamic penetrations, which decreases the bending moment variations in TDZ.

Stiffer soils lead to more lateral displacements of SCR and looser soils allow less lateral movements, because of more penetration of SCR in weaker soil and being surrounded by the soil, while in stiffer soils, the riser is almost free to move and the main resisting component is the seabed friction.

Weaker soil with higher penetrations lowers the variation of the cyclic principal stress which considerably affects the fatigue life of SCRs.

SCR top end and TDZ are the most critical areas vulnerable to fatigue failure.

The differences in SCR performance caused due to the seabed stiffness, are obviously observed by comparing the fatigue responses. Higher seabed stiffness resulted in lower fatigue lifetime of SCR in touch down zone. In other words, dense sand and stiff clay lead the SCR to experience more fatigue damages than loose sand and low stiff soil considering their relative stiffness components.

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