Fatigue Assessment Analysis of a Jack-up Platform Pile Leg Structure

Fatigue Assessment Analysis of a Jack-up Platform Pile Leg Structure Zuo Xin College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China ABSTRACT Fatigue has long been recognized as an important consideration for designing offshore structures.. In this paper, fatigue life assessment for welded tubular joints of a jack-up platforms is numerically assessed as part of mitigation for platform life time. The analysis procedures are presented for numerical fatigue assessment methods based on S-N curve approach for ABS standard utilizing the spectral (stochastic) method. The objective of this analysis is to verify that the pile leg of a jack-up platform has the appropriate fatigue life referring to the expected design life of twenty (20) years. The results are discussed and summarized through tables. KEYWORDS: Fatigue Assessment, Jack-up Platform, Pile Leg, Tubular Joints INTRODUCTION Generally, jack-up platform structures are used for production drilling and exploration of ocean oil which is an important structure style in the offshore industry over the last 40 years. Fatigue is inevitable when it operates for a long time. Fatigue is the process of damage accumulation in material due to stress fluctuation caused by variation of loads in service time. The fatigue failure occurs when accumulated damage has exceeded a critical level [1]. Research on the fatigue of offshore structures has attracted much attention during recent decades [2-5]. Nolte and Hansford [2] developed closed-form mathematical expressions for determining the fatigue damage of structures due to ocean waves. Almar-Naess [3] discussed the most important subjects related to fatigue of the offshore steel structures, such as calculation of fatigue stresses and fatigue lives. Dover and Madhava Rao [4] reviewed and summarized the knowledge in the area of SCF (stress concentration factor), fatigue and fracture mechanics of the tubular joints, damage assessment and reliability analysis of joints. Etube et al. [5] presented a modeling of jack-up response for fatigue calculation. By analyzing a mathematical model to obtain the transfer function of the dynamic response for a typical - 1025 -

Vol. 20 [2015], Bund. 3 1026 jack-up platform, they found out that the complex leg-soil interaction can be adequately modeled using springs and assuming a rigid foundation. In this study, the fatigue analysis was performed using SESAM software, in which, stochatic method was employed, and the water depth was taken as 100m. In the calculation of the cumulative fatigue damage of the leg of the platform, the Middle East sea states were used. The critical joints of the chords and the braces were selected and reviewed for the fatigue life calculation. APPROACH This fatigue analysis by using spectral analysis method was based on a dynamic analysis in Sestra of SESAM software, and the methodology and process in this fatigue analysis are described as follows: In the dynamic analysis, effect of equipment is taken into account with loads, and other weights are reflected by mass elements. RAOs of legs are calculated through frequency domain spectral analysis method by using Wajac of SESAM. In these calculations, range of wave periods is from 4.40s to 30.12s, and sixteen wave approaching directions(see table 1) are considered. Wave periods are select based on: Eigenfrequencies (eigenperiods) of the platform; Cancellation and attenuation effects; With the high wave energy; Including a reasonable range of wave periods with high wave energy. T(s) Table 1: Wave periods of loads calculation 4.40 4.61 4.97 5.20 5.54 5.97 6.35 6.80 7.53 8.34 9.12 10.91 12.21 15.00 17.82 24.37 30.12 The stress range transfer functions of the leg's structure are generated from a dynamic structural analysis in each wave heading by using Sestra of SESAM. Fatigue analysis through stochastic method for the selected joints are carried out by using Framework of SESAM. FINITE ELEMENT MODEL The idealized model of the jack-up platform is shown in Figure 1 and Figure 2. Air gap used in the analysis is 10m for the water depth of 100m, and the length of the leg penetrated into seabad is taken as 3.40m. Pinned type supports at the spud cans are used and the leg pin point is conservatively assumed at 3.40m below the mudline. Members and locations of the selected chords and braces are shown in Figure 3. Fatigue critical locations identified by reviewing the stress responses under the design operating conditions are found near the lower guides, spud cans and waterline,

Vol. 20 [2015], Bund. 3 1027 Figure 1: The whole model of jack-up Figure 2: Leg model Figure 3: Fatigue critical locations

Vol. 20 [2015], Bund. 3 1028 FATIGUE LOADING Dead loads Maximum elevated weight is 9800t, which includes 5000t of ship hull and 3000t of VDL, and also included in the analysis are the leg weight of 1500t and spud can weight of 300t. Drag coefficient The contribution of hydrodynamic loads due to individual k-braces and interior braces is lumped to the three leg chords. Wave loads were applied to the Finite Element model as a series of distributed loads producing the correct force and overturning moment. Loads are computed using Morison s equation. Wave particle kinematics are computed based on Airy wave theory. The equivalent chord drag and inertia coefficients are found to be: CD1= 1.2, CM1 = 2. The brace drag and inertia coefficients are found to be: CD2= 0.65, CM2 = 2. The jet line drag and inertia coefficients are found to be: CD3= 1.95, CM3 = 6. STRESS TRANSFER FUNCTIONS Stress concentration factors Stress concentration factors (SCFs) are calculated according to DnV Rules for all joints, and the calculated results are included in table 1. Stress transfer functions Since the fatigue damage is primarily due to cyclic load action, the non-cyclic loads including buoyancy and gravity are not considered in this fatigue analysis. The frequency of current and wind loads are largely lower than that of wave loads, so the effect of them can be ignored, and only the fatigue damage resulted form wave loads are calculated. The relationship between stress range and wave height was assumed to be linear. Although this relationship is more close to a quadratic polynomial, it is sure that the linear approximation is accurate enough for the fatigue assessment. RAOs of legs of the jack-up platform are calculated by using Wajac of SESAM, and the stress transfer functions are calculated by using Sestra of SESAM. Rayleigh damping may be given for all forced response methods: C= α M+ α K, 1 2

Vol. 20 [2015], Bund. 3 1029 where: C is the damping matrix; M is the mass matrix; K is the stiffness matrix; α 1 is the Coefficient of proportionality related to the system mass matrix; α 2 is Coefficient of proportionality related to the system stiffness matrix. According to the natural period of the Jack-up platform, the values of α 1 and α 2 are chosen as α 1 = 0.3 and α 2 = 0. STOCHASTIC FATIGUE ASSESSMENT Long term distribution of sea states An annual wave scatter diagram provided for the Middle East sea state. Based on the diagram, a distribution of the sea states defined by the mid-range significant wave height, averaged zero crossing period (weighed by their occurrences) and the corresponding percent occurrences are derived. All these data are imported into Framework of SESAM for fatigue analysis. Wave energy spectral density function The Pierson-Moskowitz spectrum for fully developed seas is selected for the current analysis. A convenient form of the spectrum is expressed as follows: 2 HT s z 5 1 4 ηη ( ) = ( z ) exp ( z ) S f Tf Tf 4π π, where Hs is the significant wave height, Tz is the average (mean zero-crossing) waves period, and Sηη ( f ) is the P-M power density function for wave surface elevation (unit:m 2 /Hz). Stress range response spectra The stress range response spectra are obtained by: σσ 2 ( ) = ( ) ( ) S f T f S f where T(f) is the stress range transfer function. The statistical properties of the response were then evaluated as follows: The nth order spectral moment: ηη,

Vol. 20 [2015], Bund. 3 1030 n mn f S ( f ) df 0 =, The standard deviation of the stress range: σrms The effective frequency of the stress response: = m 0, f e = m m 2 0. Distribution of stresses The stress range history at a joint can be assumed to be a narrow-banded Gaussian Process whose peaks are Rayleigh distributed. Knowing the standard deviation of the stress range for a given sea state, a Rayleigh probability density function p ( σ r ) against stress range can be obtained: ( ) p σ r 2 σ r σ r = exp. m0 2m0 The total area under the function is unity. It is shown that the probability of the occurrence at the stress range greater than 5 standard deviations becomes negligible small. m0 Thus, the stress range from 0 to 5 can be divided into small stress range blocks. The probability of the occurrence of the stress block i is the corresponding strip area under the function and can be found by: σri+ 1 σ σ p ( σ = σ ) = p ( σ < σ < σ ) = p ( σ ) dσ = exp. r ri ri 1 r ri+ 1 r r σri 1 2 2 ri+ 1 ri 1 exp 2m0 2m0 Miner s cumulative fatigue damage The number of cycles applied in a year from sea state j and at stress range block i is calculated by: ( ) n = P P σ f, 3 ji 31536 10 % ri e where P% is the total fraction occurrences of the wave in a year for j sea state and P ( σ ri ) is the probability of the occurrence of the stress range block i and fe is the effective stress response frequency for j sea state.

Vol. 20 [2015], Bund. 3 1031 ABS fatigue criteria The fatigue stress under constant amplitude loading is expressed through a S-N curve. The S-N curves given in ABS Guide for The Fatigue Assessment of Offshore Structures [6] are be used here. The effect of thickness and the relative corrosiveness of the environment in which the structural detail is being subjected to variable stress are considered. The fatigue performance of a structural detail depends on member thickness. For the same stress range the detail s fatigue strength may decrease, as the member thickness increases. This effect (also called the scale effect ) is caused by the local geometry of the weld toe in relation to the thickness of the adjoining plates and the stress gradient over the thickness. The basic design S-N curves are applicable to thicknesses that do not exceed the reference thickness tr = 22 mm (7/8 in). For members of greater thickness, the following thickness adjustment to the S-N curves applies: S f q tr = S t, where S is unmodified stress range in the S-N curve; t is plate thickness of the member under assessment; q is thickness exponent factor (= 0.25). Damage accumulations The Middle East sea state has been used in this analysis. The cumulative fatigue damage in one year is then calculated by summing each stress range block i, each sea state j and each wave direction. D n P N =, ji j j i ji where P j is the appearance probability of the sea state j. Then the fatigue life is calculated byy = 1/ D. RESULTS AND CONCLUSIONS Fatigue lives for the operating water depth of 100m are summarized as follows: Table 2: The results and conclusions of fatigue assessment Element ID Joint ID Weld Side SCF SCF ax SCF ipb SCF opb S-N Curve Damage Life (years) BM2017 1277 BRACE-SID 17.131 3.802 5.078 ABS-D-CP 0.188 107 BM2227 1580 BRACE-SID 17.131 3.802 5.078 ABS-D-A 0.163 123

Vol. 20 [2015], Bund. 3 1032 BM2118 1580 BRACE-SID 17.131 3.802 5.078 ABS-D-A 0.129 155 BM2886 965 BRACE-SID 17.131 3.802 5.078 ABS-D-A 0.122 164 BM3005 965 BRACE-SID 17.131 3.802 5.078 ABS-D-A 0.121 166 BM1869 427 BRACE-SID 17.131 3.802 5.078 ABS-D-CP 0.101 198 BM2763 275 BRACE-SID 17.131 3.802 5.078 ABS-D-A 0.082 244 BM1945 248 BRACE-SID 17.131 3.802 5.078 ABS-D-CP 0.071 282 BM1880 970 BRACE-SID 17.131 3.802 5.078 ABS-D-CP 0.070 285 BM2771 1301 BRACE-SID 17.131 3.802 5.078 ABS-D-CP 0.067 299 BM2903 1304 BRACE-SID 17.131 3.802 5.078 ABS-D-A 0.065 308 BM2815 1302 BRACE-SID 17.131 3.802 5.078 ABS-D-A 0.061 326 BM2859 1303 BRACE-SID 17.131 3.802 5.078 ABS-D-A 0.061 326 BM2727 1300 BRACE-SID 17.131 3.802 5.078 ABS-D-CP 0.057 354 BM2559 997 BRACE-SID 17.131 3.802 5.078 ABS-D-A 0.052 386 BM2751 272 BRACE-SID 17.131 3.802 5.078 ABS-D-CP 0.051 393 BM2759 274 BRACE-SID 17.131 3.802 5.078 ABS-D-A 0.047 422 BM2755 273 BRACE-SID 17.131 3.802 5.078 ABS-D-A 0.047 427 BM2454 997 BRACE-SID 17.131 3.802 5.078 ABS-D-A 0.045 446 BM1800 1553 BRACE-SID 17.131 3.802 5.078 ABS-D-CP 0.043 469 BM2683 1299 BRACE-SID 17.131 3.802 5.078 ABS-D-CP 0.043 470 BM1893 1004 BRACE-SID 15.714 3.802 5.078 ABS-D-CP 0.042 473 Using the fatigue analysis procedures discussed in this report, the shortest fatigue lives of a jack-up platform have been conservatively assessed to be 107 years for 100m water depth based on ABS fatigue criteria. REFERENCES [1] Naser Shabakhty, Pieter van Gelder. Reliability analysis of jack-up platforms based on fatigue degradation. Proceedings of OMAE 02 21st International Con and Artic Engineering June 23-28, 2002,Oslo, Norway [2] Nolte, K.G. and J.E. Hansford, 1976. Closed-form expressions for determining the fatigue damage of structures due to ocean waves. In: Proceedings of the Eighth Annual Offshore Technology Conference, Offshore Technology Conference Dallas, TX, 2: 861-872. [3] Almar-Naess, A., 1985. Fatigue Handbook: Offshore Steel Structures. Trondheim. [4] Dover, W.D. and A.G. Madhava Rao, 1996. Fatigue in Offshore Structures vol. 1. A.A. Balkema, Rotterdam/Brookfield.

Vol. 20 [2015], Bund. 3 1033 [5] Etube, L.S., F.P. Brennan and W.D. Dover, 1999. Modeling of jack-up response for fatigue under simulated service conditions. Marine Structures, 12: 327-348. [6] ABS Rules for Building and Classing Mobile Offshore Drilling Units 2008 Edition. [7] Chinese Classification Society Rules for the Classification and Construction of Mobile Offshore Drilling Units, 2005. 2015 ejge