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

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1 Fatigue Assessment Analysis of a Jack-up Platform Pile Leg Structure Zuo Xin College of Shipbuilding Engineering, Harbin Engineering University, Harbin , 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

2 Vol. 20 [2015], Bund 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 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,

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

5 Vol. 20 [2015], Bund 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 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,

6 Vol. 20 [2015], Bund 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 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 % 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.

7 Vol. 20 [2015], Bund 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) BM BRACE-SID ABS-D-CP BM BRACE-SID ABS-D-A

8 Vol. 20 [2015], Bund BM BRACE-SID ABS-D-A BM BRACE-SID ABS-D-A BM BRACE-SID ABS-D-A BM BRACE-SID ABS-D-CP BM BRACE-SID ABS-D-A BM BRACE-SID ABS-D-CP BM BRACE-SID ABS-D-CP BM BRACE-SID ABS-D-CP BM BRACE-SID ABS-D-A BM BRACE-SID ABS-D-A BM BRACE-SID ABS-D-A BM BRACE-SID ABS-D-CP BM BRACE-SID ABS-D-A BM BRACE-SID ABS-D-CP BM BRACE-SID ABS-D-A BM BRACE-SID ABS-D-A BM BRACE-SID ABS-D-A BM BRACE-SID ABS-D-CP BM BRACE-SID ABS-D-CP BM BRACE-SID ABS-D-CP 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, 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: [3] Almar-Naess, A., Fatigue Handbook: Offshore Steel Structures. Trondheim. [4] Dover, W.D. and A.G. Madhava Rao, Fatigue in Offshore Structures vol. 1. A.A. Balkema, Rotterdam/Brookfield.

9 Vol. 20 [2015], Bund [5] Etube, L.S., F.P. Brennan and W.D. Dover, Modeling of jack-up response for fatigue under simulated service conditions. Marine Structures, 12: [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, ejge

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