Analysis of Safe Span Length and Fatigue Life of Submarine Pipelines

Owing to the complex environmental conditions, suspension could induce complicated forces on submarine pipelines and even cause vortex-induced vibration, resulting in fatigue damage of pipelines. Through aiming at the 28-inch submarine pipeline in the East China Sea, the pipeline was segmented according to the similarity, considering the factors of pipe assembly, typhoon, current, wave and seabed topography. The effects of span length on natural frequency in each section of submarine pipeline were analyzed by finite element model. The maximum safe span length allowed by each pipeline section was verified by fatigue cumulative damage theory, and the fatigue life of each pipeline section were predicted. The results showed that each order natural frequency of the pipeline decreased with the increase of span length. The calculated results of empirical formulas were much smaller than those of the FEM analysis. The increase of the gap between the suspended pipeline and the seabed was beneficial to enhance the fatigue life of the suspended pipeline.


Introduction
Oil and gas pipelines are usually laid under complex environmental conditions. When lying on uneven seabed, the submarine pipelines would be suspended (Celant et al., 1982). Vortex-induced vibration (VIV) and fatigue failure are easy to occur in suspended pipelines. It is of great significance to study the maximum safe span length and fatigue life of different span sections to ensure the reliability of pipelines.
Stephens and Mandke (1981) used a probabilistic method to get the fatigue damage of pipeline in deep water. Tsahalis (1983) found that the seabottom proximity could change the vortex-induced vibration of suspended spans and improve longer fatigue lives. Kansao et al. (2008) developed a fluid-structural model and found that slug characteristics would reduce the fatigue life of offshore pipes. Dominguez et al. (2016) analyzed the dynamic behavior of a submarine pipeline section by 1-DOF and 2-DOF models, and found that the 1-DOF model was good for fatigue life prediction. Dong et al. (2015) discussed the VIV with the influence of stiffness and damping of soil. The results showed that soil stiffness could affect the natural frequency highly. Zhang et al. (2016) investigated the XFEM fatigue simulations on pipelines with an elliptical embedded crack under cyclic tension loadings. Han et al. (2017) discovered that soil damping could highly affect levels on fatigue damage of pipe. Gao et al. (2011) analyzed the thermal buckling phenomenon of pipelines by finite element analysis.
Sea condition is one of the main factors to affect the safe span length, but the effects of pipeline segmentation are still lacking at present. In this paper, aiming at the 28-inch submarine pipeline in the East China Sea, the pipeline is divided into 27 sections according to the similarity, considering the factors of pipe assembly, typhoon, current, wave and seabed topography. The influence of span length on natural frequency of each section of submarine pipeline is studied by finite element model analysis, and the maximum safe span length of each section without vortex-induced vibration is summarized. The maximum safe span length allowed by each pipeline section is verified according to the fatigue cumulative damage theory.

Pipeline model
For the free spanning submarine pipeline, if it is simply regarded as a beam fixed or twisted at both ends, ignoring the restraint effect of the soil at the shoulder part, the calcu-lation results would not conform to the actual situation. In order to obtain the accurate natural frequency of the submarine pipeline, this paper regards the soil in the shoulderspanning part as a linear soil spring, and establishes threedimensional soil springs connecting the soil and pipeline in the axial, in-line and cross-flow directions, so as to simulate the interaction between the soil and the pipeline. Fig. 1 shows the soil-pipe interaction model of the submarine pipeline. The real loading on the pipe segment is obtained from the original design data of submarine pipeline.
For a discrete free spanning submarine pipeline system, the vibration equation can be expressed as follows (Su et al., 2002;Wei and Liu, 2019;Xiao et al., 2019): where M is the mass matrix, C is the damping matrix, K is the stiffness matrix, F(t) is the external excitation force vector, . Natural frequency is the inherent property of the system, so it can be obtained by analyzing the dynamic response of pipeline under static conditions without external loads, that is F(t) =0. Generally, when solving the natural frequencies of structural systems, damping has little influence on the results. Then, Eq. (1) can be simplified to the free vibration equation neglecting the damping term: (2) The stiffness of soil spring is determined by soil properties and pipe parameters. As the pipeline vibration being a small amplitude simple harmonic vibration, a vector array φ i changing harmonically with phase angle is introduced.
By substituting Eq. (3) into Eq. (2), the corresponding characteristic equation can be obtained as follows: As , and the eigenvalue λ i and the non-zero solution φ i are determined by the mass matrix M and the stiffness matrix K, the eigenvalue equation can be used to solve the natural frequency.
2.2 Computational model 2.2.1 Pipe element selection According to the data of theoretical research and engineering practice, beam element can not only simulate the stress condition of pipeline better, but also save calculation time and improve calculation efficiency compared with other elements in the finite element analysis of submarine pipeline. ABAQUS provides a large number of beam elements, which are divided into plane beam elements and space beam elements. The stress and vibration of the pipeline suspension section analyzed in this paper are mainly distributed in the in-line and across-flow directions, and the axial stress and strain of the pipeline are also taken into account. Therefore, the spatial beam element is chosen as the basic element of pipeline modeling. Pipe31H is a two-node linear beam element. It can not only withstand tension, pressure and bending, but also simulate the ocean current and wave forces. So Pipe31H linear beam element is used to model the ocean pipeline. Table 1 shows the design parameters of the submarine pipeline. Taking the 68m suspended pipeline in the CEP-KP28 km section as an example, the finite element model is established by taking the span length at both ends as half of the span length, and then giving the uniform cross-section and material properties of the whole pipeline.

Finite element model of pipeline-soil interaction
The medium transported by the pipeline is natural gas, not liquid oil. The interaction between water, natural gas and pipelines is considered in the finite element analysis and simulation. Among them, water is attached to the pipeline as an additional mass according to DNV standard, as for the gas in the pipeline, the pressure on the inner wall of the pipeline is also considered in the calculation. At the shoulder of the finite element model, a node is set every 0.5 m in length, and three-direction soil spring is added to each node to simulate the effect of soil on the pipeline at the shoulder. Because of the large number of nodes, it is too complicated to add springs one by one. So first, establishing the line characteristics from each node to the ground, and then, the vertical, horizontal and axial stiffness of all lines can be given uniformly. That is the stiffness of soil springs in all directions calculated above. The established model of pipe-soil interaction is shown in Fig. 2.
The main considered loads include the residual tension and the internal pressure of the pipeline. The average operating pressure of the pipeline is 6 MPa. On the basis of the above model, two kinds of loads are added respectively, as shown in Fig. 3. PIPE31H element is selected for the type of pipeline element, and the grid is well divided.

Modal analysis
In modal analysis, external loads such as waves and currents are not considered, and the plastic deformation of pipeline is mainly caused by the weight of the pipeline itself. Therefore, the plastic deformation of pipeline is in-cluded by adding gravity in the simulation process. The first three natural frequencies and corresponding modes of the suspended pipeline can be seen in Fig. 4. It can be observed that the first and third natural frequencies are in-line, the second natural frequency is cross-flow, and the first and second natural frequencies are similar as the pipelines are symmetrical structures. The natural frequencies and modes of the two directions are the same in theory, but the natural frequencies of the two directions are different due to the different stiffness of the vertical and horizontal soil springs in the span part.
Based on the above modal analysis, the first three natural frequencies of the span length of different sections from 8 m to 80 m are analyzed. The main relationship curve between the span length and the first three natural frequencies can be     Zhang-feng et al. China Ocean Eng., 2020, Vol. 34, No. 1, P. 119-130 shown in Figs. 5-7. It can be observed that with the increase of the span length, the natural frequencies of the pipeline decrease. In the short span section, the natural frequencies change largely, and the natural frequencies change slowly with the increase of the span length.

Verification of method
DNVGL-RP-F105 (Det Norske Veritas, 2017a) regards the suspended pipeline as a beam with twisted ends or fixed ends. The empirical formula for calculating the first order natural frequency of the suspended pipeline is expressed as: where C 1 and C 3 are the boundary condition coefficients; for different boundary conditions, the range of values are given in Table 2. E is the Young's modulus of pipeline, I is the moment of inertia of pipeline, C SF is the stiffness enhancement factor of concrete, L eff is the effective span length, m e is the effective mass, D is the outer diameter of pipeline, P cr is the critical buckling load, , δ is the static deflection, and S eff is the effective axial force.
The corresponding higher order natural frequencies are calculated according to the frequency doubling relationship, as shown in Table 3.
For the section of CEP-KP28 km, the natural frequencies of the suspended pipeline with 72 m in length are calculated by DNV empirical formula and finite element model analysis method, respectively. The results are shown in Table 4.
From the above results, it can be seen that the results calculated by the two methods are quite different. According to the response model of DNV vortex-induced vibration, the smaller the natural frequency of pipeline is, the easier the vortex-induced vibration and resonance will be caused under the action of current and wave, so the shorter the service life of pipeline will be. For the gas pipeline mentioned herein, CNOOC has calculated it by FATFREE software of DNV. The results show that when the span length reaches 40 m, the fatigue life of the pipeline is only 1.93 years. However, at present, the maximum span has reached more than 60 m, so the calculation results of the pipeline frequency based on the DNV empirical formula are relatively   conservative (CNOOC, 2017). In actual situation, the crossshoulder part of the suspended pipeline interacts with the soil. The fixed boundary condition at both ends strengthens the restraint effect of the soil on the pipeline, while the twisted boundary condition at both ends weakens the restraint effect of the soil, so the real situation is between the two of them (CNOOC, 2017). In this paper, the soil spring modal analysis method recommended by DNVGL-RP-F114 (Det Norske Veritas, 2017b) is used to simulate the restraint effect of soil at the shoulder span with linear soil spring. The basic frequency of the suspended pipeline is 0.9365 Hz, which is between the fixed boundary condition and the twisted boundary condition, and it is more accordant with the actual situation.

Numerical analysis and discussion
3.1 Analysis of vortex shedding frequency

Calculation of vortex shedding frequency
According to the Strouhal vortex shedding law, when the vortex-induced vibration does not occur in the suspended pipeline, the frequency f s of the vortex shedding is proportional to the current reduction velocity V R . With the increase of the current reduction velocity, the frequency f s of the vortex shedding will increase when the Strouhal number St is a constant. The relationship between them can be expressed by the following equation: With the increase of the vortex shedding frequency, when the frequency f s of the vortex shedding increases to near a certain order of natural frequency f n of the suspended pipeline, the VIV will occur in the pipeline.

Reduced velocity
Reduced velocity V R is a dimensionless parameter, which is used to express the effect of fluid velocity range on vortex-induced vibration.
where, U c is the steady current velocity, U w is the effective current velocity caused by waves, and f n is the natural frequency of a given vibration mode. From the above, the vortex shedding frequency can be expressed as follows: The frequency of vortex shedding is mainly related to the environmental load, the natural frequency of pipeline, and the outer diameter of pipeline in the sea area where the pipeline is suspended. The variation range of the vortex shedding frequency in different sections needs to be determined with detailed structural parameters and sea condition parameters.
3.2 Analysis of the maximum safe span length

Methods avoiding VIV
According to the mechanism and characteristics of VIV and frequency locking, two methods avoiding VIV are proposed in this paper from the two aspects of vortex shedding frequency and reduced velocity.
(1) Control the vortex shedding frequency From Eq. (9), the frequency of vortex shedding can be calculated as follows: Then, According to DNVGL-RP-F105, the minimum natural frequencies of suspended pipelines in different sections are calculated by substituting U ext into Eq. (11) in different sections.
where U c,i-year is the current velocity with a recurrence period of i years near the pipeline, and U w,i-year is the effective velocity caused by significant waves with a recurrence period of i years near the pipeline.
(2) Control the reduced velocity Then, Similarly, by introducing the extreme ocean current condition U ext into Eq. (14), the minimum natural frequencies of suspended pipelines in different sections can be obtained. From the equation of vortex shedding frequency and reduced velocity, it can be seen that in order to reduce their values, it only needs to increase the natural frequency of the pipeline. From Figs.5 to 7, it can be seen that in order to increase the natural frequency of the pipeline, only the span length of the pipeline needs to be reduced.
Above all, two different natural frequencies of suspended pipelines can be obtained by controlling the frequency of vortex shedding and the range of reduced velocity. Conservatively, the larger of the two can be taken as the natural frequency of the minimum suspended pipeline. Combined with the curve of the relationship between the length of pipeline span and the natural frequency in the above analysis, the maximum safe span length for avoiding vortex induced resonance in different sections can be obtained.

Maximum safe span length
The maximum safe span length for avoiding VIV in different sections is calculated as shown in Table 5. It can be seen from the table that although the parameters and environmental loads of KP112-KP118 km section and KP118-KP127 km section are identical, the maximum span length of the two sections to avoid eddy-induced resonance is different because the former is sandy soil and the latter is clay. When it is sandy soil, the stiffness is greater and the restraint effect on the pipeline is stronger than that of clay. Therefore, the natural frequency of the pipeline under the same span length is higher than that of clay. The soil types and environmental loads of KP110-KP112 km section and KP137-KP147 km section are the same. The allowable span lengths of 951 mm and 911 mm pipelines are 68 m and 56 m, respectively. This is in accordance with the calculation formula. If the outer diameter of steel tube is unchanged, when the concrete protective layer becomes thicker, the outer diameter of the pipeline would be larger, the allowable minimum natural frequency becomes smaller, and the allowable maximum span length to avoid VIV correspondingly becomes bigger. Table 5 shows the span length to avoid VIV. Nevertheless, the pipeline may not meet the safety requirements and may not meet the fatigue life criteria. Fatigue failure of suspended pipelines is the result of long-term environmental loads. VIV cannot be avoided even if there is no resonance. Therefore, fatigue life verification is still needed to avoid the VIV with the maximum span length. If the designed fatigue life of pipelines is not satisfied, the span length should be further reduced until the requirement of fatigue life is reached.

Fatigue life analysis
The fatigue damage mechanism of submarine pipeline is the same as that of other metal structures. It can be defined as cyclic cumulative damage process under fluctuating stress or strain. The remarkable feature of fatigue is that the load will not cause the failure of structural components immediately, but will go through a certain number of cycles to make the cumulative damage reach the critical point. Therefore, fatigue damage is one of the most important failure modes in mechanical structure production practice involving loading cyclic stress. Palmgren-Miner linear cumulative fatigue damage criterion has been widely used in the fatigue research of offshore engineering structures, especially for submarine pipelines, due to its easy use and practical efficiency. This study mainly uses Palmgren−Miner criterion to evaluate the fatigue damage of suspension span of offshore pipelines. The methods of fatigue strength analysis for offshore engineering structures are basically divided into four parts: (1) load calculation; (2) stress calculation; (3) S-N curve determination; (4) fatigue cumulative damage calculation. In addition to the fourth part, the forecasting methods of the major classification societies in the world are quite different. The DNV used multi-modal crossflow, in-line response model, and impact force model to calculate the stress amplitude of the pipeline overhang section. Combined with the ocean current environment data, the fatigue life assessment using two-segment S-N curve is better than that of other classification societies in terms of authenticity, accuracy, and calculation efficiency. Therefore, this paper mainly carries out the fatigue life analysis and assessment of the overhang pipeline based on the theory and experience model of DNVGL-RP-F105 specification. Combined with the Palmgren-Miner fatigue damage accumulation theory and DNVGL-RP-F105 specification, the specific flowchart of fatigue life verification for suspended pipelines is shown in Fig. 8.

S-N curve
In this paper, the Palmgren-Miner cumulative fatigue damage theory is used as the basic principle of fatigue life assessment. The fatigue damage caused by alternating stresses at all levels is calculated separately and linearly superposed.
where D f is the cumulative fatigue damage, and 0≤D f ≤1, n i is the number of cycles under the i-th order stress, and N i is the maximum number of cycles under the i-th order stress.
The typical double-line S-N curve is shown in Fig. 9. From Fig. 9, it can be inferred that the number of failure cycles N under the action of stress amplitude S is:

Palmgren-Miner fatigue damage theory
If the steady-state response frequency of VIV is f v , the corresponding cyclic stress amplitude is S, and the cyclic time is T, then the number of stress cycles corresponding to the steady-state response of VIV in the whole cycle is: N (S ) =ā · S −m According to S-N curve, , and the Palmgren-Miner cumulative fatigue damage theory, the formula of fatigue damage caused by VIV in the suspension span at this reduced velocity can be deduced: According to the definition of cumulative fatigue dam-age theory, when D f reaches 1, the structure will suffer from fatigue failure, and the corresponding period T life is the fatigue life of the structure under the cyclic stress. The fatigue life formula of VIV response in the suspension span can be obtained by slightly changing Eq. (18) under the sea condition corresponding to a single reduced velocity: In the actual situation, the sea state cannot remain unchanged, and the VIV response and long-term distributed load of the suspension section will be different due to the interaction of different currents and waves. The long-term distributed VIV load is composed of cyclic stress amplitudes at all levels. The damage degree in the fatigue life cycle is the result of the linear superposition of fatigue damage caused by cyclic stress amplitudes at all levels. Therefore, the three-parameter Weibull distribution model is used as the probabilistic model of long-term ocean current distribution load for the VIV of the suspension span, so as to calculate the fatigue damage contribution and the fatigue life of the system corresponding to the stress amplitudes at all levels in the life cycle. 20) where D i is the fatigue damage corresponding to the i-th order sea condition in the life cycle, f v,i and S i is the frequency and stress amplitude of the VIV under the i-th order  HE Zhang-feng et al. China Ocean Eng., 2020, Vol. 34, No. 1, P. 119-130 sea condition, respectively, and f VR,i (V R,i ) is the probability of the occurrence of i-th order reduced velocity following the Weibull distribution.
Based on the response model provided by DNVGL-RP-F105, the response stress amplitude and frequency under each sea condition are calculated, and then the fatigue damage caused by each sea condition is calculated according to Palmgren-Miner fatigue damage accumulation theory. Finally, when the total damage is one, the corresponding statistical period is the fatigue life of the suspended pipeline.

Wave data
The wave data in this paper are derived from the omnidirectional waves in 30 years from the statistics of pipeline design data. Each wave is defined by two parameters: wave height and wave period. Omnidirectional wave scatter plot is adopted, so the effect of reducing the angle between wave direction and pipeline is neglected. That is to say, assuming all wave directions are perpendicular to the pipeline, the calculation results are relatively conservative.
As the wave spectrum method can reasonably reflect the wave characteristics at sea surface under extreme sea conditions such as wind, tide and storm, Pierson-Moskowitz wave spectrum method based on linear wave theory is used to describe short-term and irregular wave sea conditions. Its spectral function, the sea surface spectral density function S ηη (ω), is as follows: In order to obtain the Popper function near the pipeline depth, the first order wave theory is used to transform the spectral density function S ηη (ω) of the sea surface into the spectral density function S UU(ω) near the sea tube through the frequency transfer function G(ω), and to calculate the wave velocity U W near the pipeline: The n-th order spectral moment can be defined as M n : Thus, the effective wave velocity U S near the pipeline can be obtained.
The average cross-zero period T U is:

Ocean current data
Considering that the steady current velocity of tidal cur-rent obeys three-parameter Weibull distribution in each section, the Weibull distribution parameters are shown in Table 6.
The three-parameter Weibull probability distribution function F X and probability density function f X can be expressed as: The integral of probability density function in different intervals represents the probability of current velocity in the interval. The whole interval is divided into several sections, and the probability of different intervals is calculated respectively. The maximum value of the interval is used to calculate the velocity in the interval. The probability of velocity in (a, b) interval is: Based on the above formula, the probability of steady seabed current velocities in different ranges can be obtained as shown in Tables 7-9.

Fatigue life verification
In this paper, according to DNVGL-RP-F105 VIV response model and force model, the fatigue life analysis of pipelines with the maximum safe span length to avoid VIV in different sections is carried out. The VIV response model includes the cross-flow response model and the in-line response model.
From DNVGL-RP-F105, the fatigue life of suspended pipeline is verified according to the following expression: where T is the fatigue life of the suspended pipeline, T des is the design life, η is the allowable fatigue damage ratio, The fatigue life of each section of submarine pipeline is analyzed for the maximum safe span length to avoid VIV. The fatigue life of each section is shown in Table 10.
The gap e between the suspended pipeline and the seabed will affect the fatigue life of the pipeline to a certain extent. Since the lack of detailed data, the gap is set 0.2 m here. According to the response model of DNV VIV, when the gap between pipeline and seabed is large, the correction factor ψ proxi, onset would be large, and the starting speed of cross-flow VIV would become high. As shown in Eqs. (31) and (32), the fatigue life of suspended pipeline will be improved.
When the gap between pipeline and seabed increases, the correction factor and of in-line force model will decrease. As shown in the following expression, when the drag coefficient C D and inertia coefficient C M is small, the impact force of wave on pipeline would be small and the fatigue life of in-line force model will be enhanced.
(36) Table 11 shows the fatigue life of the suspended pipeline in the KP112-KP118 km section, the span length is 80 m, the gap between the pipeline and the seabed is 0.2 m and 1.5 m, respectively. In the in-line direction, the fatigue life of the VIV response model is smaller than that of the force model, so the in-line fatigue life remains unchanged.    It can be observed from Fig. 10 that the CEP-KP80 km section is close to the central platform, and the sea water is deep. The velocity of seabed current caused by waves and the impact force on the suspended pipeline are relatively small, while the velocity of seabed steady current is relatively slow. Fig. 11 shows the probability density distribution function curves of seafloor velocity in different sections of Weibull distribution. It can be seen that in KP80-KP254 km section, the seafloor velocity mainly distributes in the range of 0-0.6 m/s, while in CEP-KP80 km section, the seafloor velocity concentrates in the range of 0-0.3 m/s. Environmental load has little effect on the suspended pipeline. Fatigue damage mainly comes from the impact of wave load on the suspended pipeline. With the further extension of the suspended pipeline, the natural frequency of the suspended pipeline decreases. Fatigue damage mainly comes from the cyclic stress caused by the transverse and VIV.
From Figs. 12 and 13, in the KP80-KP270 km section, the water depth decreases gradually, and the fatigue damage of the suspension section mainly comes from the in-line VIV. The fatigue life of suspended pipeline decreases sharply with the increase of suspension span length. There is a sudden change in part length and a great decrease in life. Through comparative analysis of fatigue damage calculation data, it is found that when the natural frequency of suspended pipeline drops to a critical point, the second mode of suspended pipeline starts to be stimulated by low     flow velocity to participate in the VIV of pipeline. From the above-mentioned response model, it can be observed that in the in-line direction, because of the influence of the crossflow VIV, the stress amplitude of the in-line VIV will increase. Once the second-order mode of the in-line flow is activated, the influence will intensify, resulting in the joint response stress of the in-line flow being greatly increased. At the same time, the probability of occurrence of low flow rate is getting high. In the long-term distributed load, the cumulative fatigue damage even exceeds the high flow rate. Therefore, the fatigue life of the suspended pipeline decreases rapidly. Fig. 14 shows that in KP270-KP306 section, fatigue damage mainly comes from cross-flow VIV due to shallow seawater and high velocity of seabed current. As the soil in this section is mainly very soft clay and has little restraint on the pipeline, the natural frequency of the suspended pipeline is relatively small. Under the excitation of ocean currents, it is easy to cause Vand resonance, and fatigue damage occurs in long-term working environment. The limit span lengths of KP270-KP283 km, KP283-KP306 km and KP306-LP sections are 48 m, 32 m and 20 m, respectively. These sections are close to landing points, shallow seawater and high seabed current speed. Although the span is small and short, there are risks of multiple adjacent span series connection. It should pay close attention to the development trend of the close span section and take timely measures to avoid the long span formed by series connection.
The simulation procedure adopted in this paper is carried out according to the most recognized DNV standards. Each step of calculation and operation herein are mainly in accordance with the references (Det Norske Veritas, 2017a, 2017b), including the equivalent parameters of pipelines, the stiffness calculation of soil springs, etc. Therefore, the results of finite element modal analysis are credible.

Conclusions
This paper segments the submarine pipeline in the East China Sea considering the factors of pipe assembly, typhoon, current, wave and seabed topography according to the similarity. The maximum safe span length of each section is investigated by finite element model analysis. The fatigue life and the maximum safe span length allowed by each pipeline section are predicted further. The following conclusions are summarized.
(1) With the increase of the span length, each order natural frequencies of the pipeline gradually decrease, the span is short, and the decline is obvious. With the increase of the span length, the in-line trend is gradually smooth.
(2) The calculated results of empirical formulas are much smaller than those of finite element model analysis. If the natural frequency is lower, it is easier to cause the vortex-excited resonance. So the empirical formula results are too conservative, and the finite element model analysis method is more in line with the actual situation.
(3) When the gap between the suspended pipeline and the seabed increases, the starting speed of cross-flow VIV will become larger, but the in-line drag coefficient and inertia coefficient will decrease, and thus make the impact force of waves on the pipeline decrease. Therefore, increasing the gap is helpful to improve the fatigue life of the suspended pipeline.
(4) With different environmental loads and pipeline parameters, the fatigue failure reasons of each section are different. In CEP-KP80 km section, the fatigue damage mainly comes from the in-line impact force and the transverse VIV. In KP80-KP270 km section, the fatigue damage mainly comes from the in-line VIV. In KP270-CEP section, the fatigue damage mainly comes from the transverse VIV.