Fatigue reliability analysis of jacket-type offshore wind turbine considering inspection and repair

Transcription

1 Fatigue reliability analysis of jacket-type offshore wind turbine considering inspection and repair W.B. Dong, Z. Gao 2 and T. Moan 3 Centre for Ships and Ocean Structures(CeSOS), Norwegian University of Science and Technology (NTNU), Otto Nielsens V., N-749, Trondheim, Norway dong.wenbin@ntnu.no 2 Centre for Ships and Ocean Structures(CeSOS), Norwegian University of Science and Technology (NTNU), Otto Nielsens V., N-749, Trondheim, Norway zhen.gao@ntnu.no 3 Centre for Ships and Ocean Structures(CeSOS), Norwegian University of Science and Technology (NTNU), Otto Nielsens V., N-749, Trondheim, Norway torgeir.moan@ntnu.no Abstract: In this paper prediction of the fatigue reliability of a fixed jacket offshore wind turbine designed for a North Sea site in a water depth of 7 m is performed. The longterm statistical distribution of stress ranges of tubular joints is obtained by combination of time domain simulation for representative sea states. The load histories are normalised to ensure that fatigue design criteria based on the SN-Miner-Palmgren approach is satisfied. Hence the reliability estimates obtained refer to fatigue design of tubular joints that satisfy design criteria. The reliability analysis is based on fracture mechanics (FM) analysis of crack growth. The effect of inspection and repair is quantified based on the quality of inspection in terms of probability of crack detection curves. The sensitivity of the reliability index on random variables is estimated considering the effect of inspection. Keywords: fatigue, tubular joints, time domain simulation, SN-Miner-Palmgren, fracture mechanics, inspection Introduction Offshore wind turbines(owts) are subjected to environmental loads due to waves,current and wind, as well as the effect of corrosion from salt water, and in some cases floating ice; Moreover, they are less accessible than land based turbines. Generally, the operation of OWTs is more than five to ten times more expensive than work on Figure : Offshore wind turbine with jacket support structure.

2 land. Considering these issues, the reliability of OWTs is crucial. Methods for reliability of OWTs are therefore needed. Jacket support structures have been widely used in the offshore oil industry. The operating water depth of jacket support structures is usually less than 3 m. The main failure modes include plastic collapse of braces or legs, tubular joint failure, lateral soil failure, axial pile failure, or combinations of these modes []. In addition fatigue failure would be relevant especially in extra-tropical environments and especially when dynamic effects are present. For jacket support structures located in relatively shallow water, the natural periods of the dominant modes of global lateral vibration of jackets tend to lie well below the periods of the incoming regular waves. This permits quasi-static structural analysis. Dynamic structural analysis is required in deeper water. A significant difference between offshore wind turbines with a jacket support structure and traditional jacket platforms is the superstructure. For offshore wind turbines, it includes tower, nacelle, blades, etc. The height of the tower is governed by the height of the rotor hub above the sea level [2]. e.g. for a 6 m diameter rotor, the sitting height of the hub should be 45m above the sea level. The height of the tower must be larger than this value. Considering the large tower height & deadweight, nacelle and blades weight,the wind load applied to these structures will influence the dynamic response of jackets more significantly than traditional jacket platforms used in offshore oil industry, and this is the focus in this paper. The present paper is concerned with the reliability of wind turbines with jacket support structure in deep water, and mainly considers the fatigue failure of tubular joints of the jackets. The effect of inspection and repair on the fatigue reliability is considered. In fatigue analysis, one of the most important issues is the calculation of the longterm statistical distribution of the response. The Weibull distribution function has been shown to fit many stress spectra for marine structures subjected to wave loads, but for offshore wind turbines, the wind load is much more significant and may influence the longterm distribution of hot spot stress ranges for structural components. In this paper, the longterm distribution of stress ranges of tubular joints is obtained by time domain simualtions, considering only representative sea states to limit the computational effort. The wind loads on wind turbines are obtained with the software HAWC2 which is a tool for simulation of wind turbine response in time domain [3]; the dynamic response of jacket support structure with wind load on wind turbine is obtained with the software USFOS which is tailored to space frame structures and is very efficient for the analysis of such structures [4]. 2. Load Effect Analysis Onshore wind turbines are mainly subjected to aeroelastic loading. Many simulation tools are routinely used to design and analyze them, e.g. HAWC2, FAST, ADAMS, AeroDyn, et al. These tools employ sophisticated models of turbulent and deterministic wind-inflow; aerodynamic, gravitational, and inertial loading of the rotor, nacelle, and tower, etc. For offshore wind turbines both aerodynamic and hydrodynamic loading are important. The analysis of OWTs must account for the dynamic coupling between the support structure platform motions and turbine motions, and this is a challenge. The present paper uses a simplified method to model the Jacket-type offshore wind turbine and calculate the load effect. Wind loads are obtained by HAWC2 and the dynamic response of whole structure due to combined wave and wind loads is obtained in USFOS. In order to make an efficient model in HAWC2, an equivalent monopile wind turbine is constructed, by replacing the storeys of the jacket structure by some equivalent tubular elements structures. The interface structure is also modelled as a pipe structure with relatively high stiffness in the equivalent model. The external diameter and the thickness of the pipes are calculated so that the mass and bending stiffness matches each original storey. The hydrodynamic coefficients, i.e. the drag and the inertia coefficients for the cross section of the equivalent model are estimated by adding all contributions from the slender members at each storey. In this way the phase difference in wave forces on different slender members is not considered. It is reasonable since the horizontal dimension of the jacket at the mean water level is about 5m, while the length of the waves with periods of around s is approximately 6m, which is most important for wave-indued fatigue loads. The wave-induced particle velocity is therefore fully correlated for the slender members at the same height. After the conservative equivalent monopile wind turbine is determined, it can be easily modelled in HAWC2 together with the tower and the blades for aerodynamic analysis. The purpose of the HAWC2 analysis is to obtain a representative aerodynamic force acting on the wind turbine in order to do further analysis in USFOS. When the aerodynamic forces of the wind turbine are calculated and imported to USFOS, we can use more refined model for structural response analysis, where the complete jacket structure can be modelled. Since the force output from the HAWC2 analysis includes the inertia contribution of the blades and the hubs, the USFOS model will not contain these structures. However, the tower and the gearbox in the nacelle are modelled. The forces and moments at the nacelle shaft are taken as external forces for the USFOS analysis(as shown in Figure 2, F and M), which includes the integrated aerodynamic forces on the blades and inertia forces mainly due to the blades and the hubs. In addition USFOS can model the soil-pile interaction, but it is not the

3 wind speed equivalent parts in USFOS point mass F M wind speed mean water level equivalent parts in HAWC2 wave speed wave Equivalent monopile model used in HAWC2 Equivalent Jacket model used in USFOS Figure 2: Sketch of models used in HAWC2 and USFOS. focus of this paper. We assume the jacket is rigidly fixed to the seabed which will be explained in the section of case study. The basic analysis procedure is shown in Figure 2. 3 Fatigue Reliability Analysis Fatigue and fracture are important failure modes of welded offshore structures. Fatigue is a very local phenomenon,influenced by local geometry and weld defects induced by the fabrication process. Crack growth normally start from weld defects with a depth of say. mm and are driven by cyclic, tensile stresses. Cracks in jacket are confined to the tubular joints due to the large stress concentration in such joints (Figure 3).It is noted that the crack size in a shell structure like the tubular joint, increases linearly with time. Hence, a significant reserve life remains when the crack has propagated through the thickness. An overview of experiences with fatigue cracks in offshore structures operating in the North Sea is given by Moan [5] and briefly summarized below.table displays the number of cracks detected and the mean crack depth observed during 34 inspections of 3 jackets in the North Sea. However, in the 99s the limited amount of cracks detected suggested that the prediction methods were conservative and that the likelihood of fatigue cracks was much less than initially anticipated [6]. Prediction methods have later been modified for more precise predictions. However, it should be noted that despite the conservatism in the design method, 2-3% of the fatigue cracks detected, were not predicted. This Figure 3: Crack growth stages and fracture in a tubular K-joint in a jacket platform. Data Propagating cracks / non-propagating cracks First inspection prop. / non-propagating cracks Second inspection prop. / nonpropagating Third inspection prop. / nonpropagating Number of cracks Mean crack depth (mm) 36/ / 2. 44/ /.9 3 / /.7 7 / /.2 Table : Reported crack depths detected in a subset of 34 inspections of 3 jackets installed the North Sea in [6]. fact is attributed to the occurrence of gross fabrication defects. For offshore structures a

4 reliability based fracture mechanics (FM) approach has been presented by Moan et al. [7]. In the present paper this method is implemented to carry out fatigue reliability analysis of tubular joints of jacket-type offshore wind turbines. 3. Crack growth model The crack growth is described by a generalization of the Paris-Erdogans equation, da C( K) m dn = Δ () as introduced by Newman & Raju [8]. The surface crack is assumed to be semi-elliptical with semiaxes a and c at any stage during crack growth, where a is the crack depth, c is the half crack length, N is the number of stress cycles, ΔK is the stress intensity factor range, and C and m are material parameters. For steels, the distribution of the material parameter C approximately follow a lognormal distribution. Parameter C may be reasonably modelled as: lognormally distributed with mean of 3. MPa mm (DNV 984) and a coefficient of variation of.55. Instead of using C as a random variable, lnc is used herein. m is assumed fixed and generally equal to 3. (DNV 984). The stress intensity factor range at any point of the crack front for surface cracks in plane plates subjected to tension and bending loads is expressed as [8] Sb + H S t π a a a c Δ K = ( St + Sb) F,,, S ϕ b + Q c t W St a a c S b = S πayplate,,, ϕ, c t W St (2) where S t and S b are tension and bending stress ranges, respectively. S is the total stress range, t is the plate thickness and W is the width of the plate. ϕ is the parametric angle to identify the position along an elliptical flaw front. In welded joints, consideration also has to be given to the nonlinear stress fields arising from local stress concentrations at the weld toe. These have been modeled using a local stress intensity magnification factor, M k. The stress concentrations due to local weld geometry are especially present in tubular joints. Ideally, both crack growth in depth a (ϕ =π/2) and growth in length 2c (ϕ =) should be calculated, but due to coalescence of cracks the two dimensional model proposed in [8] may give the wrong aspect ratio evolution. For this reason, the aspect ratio of a/c of tubular joints is assumed to be a function of the crack depth a. In the general case, the stress intensity factor range can then be stated as Δ K = S π ay (3) The local stress intensity magnification factor M k is of great importance to tubular joints due to the T-butt welds. Weld toe geometry is often characterized by the weld toe radius ρ and the local weld toe angle θ among other parameters. Thus the local stress intensity magnification factor can be formulated as [9]. M k ( ρθ) = + M, red 22.a 357.a.24 exp exp t t (4) where M red is introduced in order to include effects due to local weld toe smoothing by for example grinding. In addition to the weld toe stress concentration and combined bending and tension stresses, the stress distribution in the circumferential direction is nonlinear. Therefore, the stress field at the tip of a surface crack changes as the crack propagates. The beneficial effect of the nonlinear stress variation in the circumferential direction is neglected and a constant hot spot stress over the cracked region is applied as a conservative assumption. Hence, the geometry function used for tubular joints is a a π S b Y = Yplate γ a c,,,, M c t 2 St k (5) where the crack aspect ratio is randomized by multiplying by a random variable γ a/ c which is assumed lognormal distributed with a mean of. and a COV of % [7]. However, the present method may be extended to account for nonlinear stress variations in the circumferential direction. A representative bending/tension stress ratio of 4. is used for the tubular joints. 3.2 Crack aspect ratio for a tubular joint To account for the coalescence of cracks in tubular joints a forcing function, which makes the crack aspect ratio dependent on the crack depth, is used. As a result of micro-crack coalescence and growth, it is assumed that a small semi-elliptical crack has developed with an aspect ratio of about, not immediately next to another small crack. These cracks develop independently until their crack tips meet. Due to this coalescence one long shallow crack evolves, which then will grow through the wall of the tubular.

5 During crack growth two different stages are considered; one stage before coalescence and one stage during and after coalescence. Assuming that for small crack size the tubular joint can be modelled as a T-plate, the crack aspect ratio before coalescence will develop as follows []: a ka a a = e ; for c t t coalescence (6) where k=.2 mm - []. As coalescence occurs the crack aspect ratio will develop as suggested by Burns et al. [2], in which the shape of the forcing function is dependent upon the bendingtension stress ratio. The shape of the forcing function for (a/t>(a/t) coal. ) is described by the following relationship: Sb a St a = + α2 c S a a b t α + + t t S coal t a + c fail. where α and α 2 are parameters. The combined forcing function, Eq.(7) and Eq.(8), is shown in Figure 4. (7) where A is the scale parameter and B is the dimensionless shape parameter. B is obtained by time domain simulation, and A is obtained by use of design method using the SN approach. Considering time consuming of calculation, the present paper only considers the representative sea states to limit the computational effort. In order to remove the statistical uncertainty, 2 time series of dynamic response of jacket are obtained for each sea state. 3.4 Inspection reliability The inspection reliability is characterized by the relationship between the probability of detection, P D (a D ), and the crack depth, a D. The relationship is of the following form P D D ( a ) = exp D a λ this is the analytical expression for the Probability Of Detection, or POD, curve assumed herein. λ is the parameter used in POD curve,in this paper, λ=. [7]. 3.5 Strategy for inspection and repair The lifetime of the fixed jacket offshore wind turbine designed for a North Sea site in a water depth of 7 m is 2 years. In this paper, it is assumed that inspections basically are performed every fourth year, i.e. after T =4, T 2 =8, T 3 =2,T 4 =6 years. Only one repair strategy is considered; all detected cracks are repaired by welding and grinding. At each inspection a crack may either be missed or detected and then repaired. Thus 6 different repair courses are possible. The event tree is illustrated in Figure 4, in which denotes no detection and denotes repair. The inspection scheme and repair strategy as described above are applicable to each welded tubular joint. (9) Figure 4: Aspect ratio, a/c, of cracks in tubular joints as a function of a/t (forcing function). The aspect ratios are calculated by using α =5, α 2 =.5,(a/t) coal. =.5, (a/c) fail =. and t=2 mm. 3.3 Fatigue loading and uncertainty analysis In this paper, the longterm statistical distribution of stress ranges of tubular joints due to winds and waves is assumed to fit a two parameter Weibull distribution F S B s = A ( s) exp (8) t T T 2 T 3 T 4 = repair = no repair Figure 5: Inspection scheme

6 3.6 Safety and event margins Based on the formula given by Madsen et al. [3], the safety margin for fatigue failure before time t can be approximately expressed as a c da m m M () t = Cν ( t T ) A Γ ( + ) m B a ( γyy πa) () where the initiation period, T, is neglected. ν is number of stress cycles a year. The geometry function is randomized by multiplying by a random variable γ Y which is normally distributed with a mean of. and a COV of % for tubular joints [7]. The critical crack length a c is taken as the plate thickness. The first inspection at time T leads either to crack detection or no crack detection, and the event margin is defined as a D da m m H = Cν ( T T) A Γ + m B a ( γyy πa) () H is negative when a crack is detected and positive otherwise. a D is the detectable crack size which is assumed given by the POD curve. If a crack is detected and repaired at time T 2 and no crack was detected during inspection number 3 the safety margin for failure before t, where T 3 <t <T 4, is ac x da m M () t Cν ( t T2) A m a R m = Γ + B ( γyy πa) (2) a R is the initial crack size after repair, and x is any outcome after first inspection, either or. The event margin for crack detection at time T 4 is ad x da m H () t Cν ( T4 T2) A m a R m = Γ + B ( γyy πa) (3) Safety and event margins are defined similarly for the other branches. 3.7 Failure probabilities and sensitivity analysis The probability of failure before time t is P F (t), with a corresponding reliability index given by β ( t) P ( t) = Φ ( ) (4) F The following three expressions for the failure probability are given as presented by Madsen et al. [3]. Each expression corresponds to a specific interval of the time parameter, t. For T t T : PF () t = P M () t For T < t T2 : P t P T P T t P T t ( ) = ( ) +Δ (, ) +Δ (, ) ( ) F ( ) ( ) ( ) ( ) F F F F (5) = P T + P M T > H > M t + P M T > H M t (6) For T < t T : 2 3 PF ( t) = PF( T2) +ΔPF ( T2, t) +Δ PF ( T2, t) +Δ PF ( T2, t) +ΔPF ( T2, t) = PF ( T2 ) + PMT ( ) > H> M ( T2) > H > M ( t) + PMT ( ) > H> M ( T2) > H M ( t) + PMT ( ) > H M ( T2) > H> M ( t) + PMT ( ) > H M ( T2) > H M ( t) (7) Similar equations can be established for time intervals T3 < t T4 and T4 < t. P F (t) is calculated by FORM (First Order Reliabiity Method) using PROBAN [4]. It is difficult to calculate the intersections by FORM, especially if some of the events are covered by other events. Such problems have mainly been solved by neglecting unnecessary events, which are verified by Monte Carlo Simulation Method. Event margins of a format of the type g=r-s, confer e.g. Eq., may give inconsistent failure probabilities, e.g. the calculated probability of failure after 6 years may be larger than the calculated failure probability after 7 years. the experience is also that using event margins formulated as g=lnr-lns give the correct FORM solution, but in this case the design point in a very limited number of the intersections is found. Thus, the failure margins are given as [7] ζ ( ) g = sign( R) R sign S S (8) where ζ =.25 exponent. ζ is found as the most favourable

7 It is of interest to see the sensitivity of the random variables that appear in the fatigue failure equation on the fatigue reliability index. The sensitivity of any random variable z i, can be derived from the gradient of the reliability index in the normalized space of random variables of the study. i.e. β 2 = ( z ) 2 (9) i z z i i In this paper, the sensitivity of a R and a D is considered. 3.8 Calibration of the fracture mechanics model The purpose is to calibrate a design check: D= ni / Ni Δd so that it implies a consistent life time failure probability by determining the design Miner s sum Δ d as a function of the consequences of failure and relilability of inspection and repair. When an inspection and repair strategy is implemented, the allowable cumulative damage Δ d can be relaxed. To account for the effect of inspection and repair, the initial crack size a and M red are estimated by requiring that the reliability level for the fracture mechanics approach should be the same as that implied by Δ d for the SN approach when no inspection and repair are considered. The safety margin for failure before time t according to the SN approach is M t ν t m =Δ Γ + K B m () A (2) where Δ is the Miner s sum at failure. The scale parameter A is usually determined from ν t m m D= A Γ + =Δ K B c d (2) where K c is a characteristic value, and t is the design life taken as 2 years. 4. Case study A fixed jacket offshore wind turbine designed for a North Sea site in a water depth of 7 m is used in this paper(figure ). The heights of the jacket and the tower are 9m and 63m, respectively. In between, an interface structure with a height of 6m is used. Both the jacket and the tower are modelled by beam elements,while the interface structure is modelled by shell elements. The jacket is composed of tubular members and has five storeys of X braces, while the tower is a simple tubular structure. The jacket is fixed on the sea bed at four corners by 32m*32m. Steel material is considered for the whole structure. The wind turbine sitting on the top of the tower is a 5MW NREL model with the total weight of 4 ton. It is modelled by a point mass in USFOS. As shown in Table 2 the effect of soil-piles on the eigen-periods of this jacket at a North Sea site is small. Therefore, the jacket structure with tower is assumed to be rigidly fixed to the seabed in this paper. Figure 7 shows the spectral density of the overturning moment at the seabed in the operational condition, where the mean wind speed at nacelle is 5m/s with a turbulence intensity of.5. The significant wave height is 4m and the spectral peak period is 9s. Some preliminary conclusions can be drawn from these results. Wind-induced responses obtained using equivalent beam models in HAWC2 and USFOS are identical. It means that the wind force acting on the rotor can be calculated in HAWC2 and then imported to USFOS for further structural response analysis using the full structural model. The wave-induced response is quasi-static and therefore can be decoupled from the windinduced responses. The responses of the monopile model are almost the same as those of the jacket model in USFOS. However, the computational time of the monopile model is about % of that for the full model. In order to limit the computational effort, the monopile model (Figure 6: b)) is finally used to obtain the longterm distribution of stress ranges of tubular joints in present paper. From Figure 7 we can also see that the excited second global mode contributes to fatigue damage. Mode (secs.) with soil-pile without soil-pile st (2 nd ) rd Table 2: Eigen-periods of jacket models with soilpiles and without soil-piles in USFOS, respectively. Interface structure, the height is 6 m 9 m 63 m a) b) Figure 6: Models of case study in USFOS. a) jacket structure with tower ; b) equivalent monopile structure with tower.

8 Wind-induced quasi-static response Wave-induced quasi-static response Wind-induced dynamic response of the first global mode Wind-induced dynamic response of the second global mode Figure 7: Overturning moment in the operational condition Mean Std.Dev. Variable Distribution μ σ Log K Normal Δ Lognormal..3 a Exponential.. a R Exponential.. a D Exponential ν Normal lnc Normal m Fixed 3. ) 3.7 2) lna Normal ).997 /B Fixed.35 γ Y Normal.. thickness Normal a/c Fixed Eq.(7)+(8) γ a/c Lognormal.. S b /S t Fixed 4. M red Fixed.9 ) Used in SN approach 2) Used in FM approach 3) Corresponding to Δ d =. Table 3: Probabilistic data for welded joints in jacket. Stresses and geometrical sizes are given in MPa and mm, respectively. Figure 9: Reliability index for welded joints in jacket as a function of time. The target level is given by Δ d =.2 and no use of inspection and repair, corresponding to a =.mm. The inspection and repair scheme is characterized by 4 inspections, a D =2.mm and a R =.mm. Figure : Reliability index for welded joints in jacket as a function of time. The target level is given by Δ d =.3 and no use of inspection and repair, corresponding to a =.mm. The inspection and repair scheme is characterized by 4 inspections, a D =2.mm and a R =.mm. Figure 8: Reliability index for welded joints in jacket as a function of time. No inspection and repair. Figure : Reliability index for welded joints in jacket as a function of time. The target level is given by Δ d =.4 and no use of inspection and repair, corresponding to a =.mm. The inspection and repair scheme is characterized by 3 inspections for Δ d =.5 and 4 inspections for Δ d =.6, a D =2.mm and a R =.mm.

9 Figure 2: Reliability index for welded joints in jacket as a function of time. The target level is given by Δ d =.5 and no use of inspection and repair, corresponding to a =.mm. The inspection and repair scheme is characterized by 3 inspections for Δ d =.6 and 4 inspections for Δ d =.7, a D =2.mm and a R =.mm. Figure 3: Reliability index for welded joints in jacket as a function of time. The target level is given by Δ d =.3 and no use of inspection and repair, corresponding to a =.mm. The inspection and repair scheme is characterized by 2 inspections, a D =2.mm and a R =.mm. Figure 4: Reliability index for welded joints in jacket as a function of time.the inspection and repair scheme is characterized by 4 inspections, a R =.mm. Figure 5: Reliability index for welded joints in jacket as a function of time.the inspection and repair scheme is characterized by 4 inspections, a D =2.mm. Based on the time domain simulation results of the equivalent monopile model in USFOS, the value of /B is taken as.35. By use of the formula (2), the value of the scale parameter A can be determined corresponding to specific allowable cumulative damage Δ d [7]. In present paper, different cases of Δ d are considered, as shown in Figure 8. The parameters used in reliability calculations are given in Table 3. The target safety levels used in Figures 9-3 are obtained by using the SN Miner-Palmgren approach with no effect of inspection. The detectable crack size a D is assumed to have an exponential distribution and a mean value equal to 2. mm in Figure 9 - Figure 3. This implies that there is a 86.5% probability of detecting it based on the POD curve. In the analysis reported in Figures 9-3 the allowable cumulative damage Δ d, when no inspection and repair is implemented, is assumed to be.2,.3,.4,.5 and.7 respectively. Figure 9 shows that approximately the same reliability level can be obtained with Δ d =.2 and no inspection as with Δ d =.3 combined with inspection. This implies that the design criterion in terms of Δ d can be relaxed when a relevant inspection and repair strategy is implemented. For the case of Δ d =.3, the design criteria Δ d may be relaxed to.4, as shown in Figure ; for the case of Δ d =.4, it may be relaxed to.5-.6,as shown in Figure ; for the case of Δ d =.5, it may be relaxed to.6-.7, as shown in Figure 2; for the case of Δ d =.7, it may be relaxed to.8, and only 2 inspections may be implemented, as shown in Figure 3. Figures 4 and 5 show the sensitivity of random variables a R and a D on the reliability index β, when inspection and repair are implemented. The effect of inspection is increased with the detectable crack size a D is decreased, as shown in Figure 4, and is decreased with the initial crack size after repair a R is increased, as shown in Figure 5.

10 5. Conclusions In the present paper the effect of inspection depending upon its quality for a given inspection strategy for welded tubular joints in jacket-type offshore wind turbine structures has been quantified by using probabilistic methods. The conclusions are based on the following assumptions: welded joints in North Sea structures; the tubular joints, loaded by bending and tensile stresses with a bending-tension stress ratio of 4.; 4 year inspection interval; mean crack size after repair a R =.mm and mean detectable crack size a D =2. mm. The effect of design criteria, in terms of allowable cumulative damage Δ d in the range of.2-.7, when no inspection and repair are implemented, is investigated. The effect of inspection is increased and the inspection interval may be increased with increasing allowable cumulative damage, Δ d, as shown in Figures 9-3. The sensitivity of random variables a R and a D to the reliability index β is also analyzed (Figures 4 5). The reliability is much more sensitive to the detectable crack size a D than the initial crack size after repair a R. Based on the experience in the offshore oil and gas industry in North sea, the inspection reliability is rather ambitious, especially for tubular joints in jackets, therefore, the relaxation in design criteria shown represents a maximum effect of inspection on design criteria. Acknowledgements The authors wish to acknowledge the support from the Research Council of Norway through the Centre for Ships and Ocean Structures at the Norwegian University of Science and Technology in Trondheim, Norway. References [] Mathisen, J., O.Ronold K., Sigurdssion G.. Probabilistic modelling for reliability analysis of jackets, Proc. the 23th OMAE Conf.,Vancouver, Canada, 24 [2] Tong,K.C., Technical and economic aspects of a floating offshore wind farm, Journal of Wind Engineering and Industrial Aerodynamics, 998, 74-76, [6] Vårdal, O.T. and Moan, T., Predicted versus Observed fatigue Crack Growth. Validation of Probabilistic Fracture Mechanics Analysis of Fatigue in North Sea Jackets, Proc. 6th OMAE Conf., Yokohama, 997 [7] Moan,T., Hovde, G.O. and Jiao, G.Y., Fatigue reliability analysis of offshore structures considering the effect of inspection and repair, Proc. the 6th ICOSSAR Conf., Innsbruck, Austria, 994 [8] Newman, J.C. and Raju, I.S., An empirical stress-intensity factor equation for the surface crack, Engineering Fracture Mechanics, 98,Vol. 5, No. -2, [9] Marine Technology Directorate Limited, Probability-based fatigue inspection planning. MTD Ltd Publication 92/, London, England,992 [] Vosikovsky et al., Fracture mechanics Assessment of Fatigue Life of Welded Plate T- Joints Including Thickness Effect, Proc. of 4th BOSS, Amsterdam: Elsevier, Amsterdam,985 [] Moan T., Hovde, G.O. and Blanker, A.M., Reliability-Based Fatigue Design Criteria for Offshore Structures Considering the Effect of Inspection and Repair, Proc. 25 th Offshore Technology Conference, Houston, 993 [2] Burns, D.J., Lambert, S.B.and Mohaupt, U.H., Crack Growth Behaviour and Fracture Mechanics Approach, Proc. of Conference on Steel in Marine Structures: Paper PS 6, Delft: Delft University of Technology,987 [3] Madsen, H.O. and Sorensen, J.D., Probability-based optimization of fatigue design, inspection and maintenance, Proc. 4th Integrity of Offshore Structures, London: Elsevier Applied Science [4] Olesen, R., PROBAN General Purpose Probabilistic Analysis Program User s Manual. Veritas Sesam Systems, Report No ,Høvik, Norway,992 [3] Larsen, T. J., How 2 HAWC2, the user's manual, Ver. 3-7, Risø National Laboratory, Technical University of Denmark, 29 [4] USFOS A/S, User's Manuals, [5] Moan, T., Reliability-based management of inspection, maintenance and repair of offshore structures, Journal of Structure and Infrastructure engineering, 25,(), 33-62