Transactions on the Built Environment vol 17, 1996 WIT Press, ISSN

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1 Reliability based integrity assessment of offshore platforms S. Dharmavasan NDE Centre, University College London, Torrington Place, London WC1E 7JE, UK Abstract Fatigue crack growth is one of the main deterioration processes in offshore structures. The fatigue life of welded connections in offshore structures is therefore an important design criterion as well as a governing factor for the planning of inspection and maintenance actions. Due to the considerable costs associated with inspection and maintenance of offshore structures it is necessary to optimise the inspection and maintenance plans such that the costs are minimised and at the same time the risk kept within acceptable limits. This implies that the estimation of fatigue crack growth as well as the effect of inspection and maintenance actions must be modelled accurately. This paper will describe the development of a reliability based structural integrity assessment tool based on fracture mechanics models. 1 Introduction The offshore industry currently requires that the structural integrity of fixed offshore platforms is ensured by inspecting periodically. In the past, decisions on inspection, repair and maintenance (IRM) have been made by experienced engineers applying their judgement in the form of rules-of-thumb together with appropriate deterministic analyses. However, it is now expected that, by employing recently developed techniques based on structuralreliabilitymethods considering the effects of uncertainties, inspection and maintenance scheduling can be made more rational. In order to be able to applyreliabilitytheory, it is vital to be able to model the failure criteria as well as the uncertainties involved in the process. In the case of fixed offshore structures in areas such as the North Sea, the major problem is that of the deterioration of the welded joints due to fatigue. Furthermore, in-

2 292 Engineering Integrity service inspection data and its interpretation play a major role in the whole process. Thus for fixed offshore structures it is necessary to have accurate fatigue fracture mechanics modelling validated databases for all the modelling parameters, such as material properties # information on NDT reliability such as accuracy and sensitivity This paper describes the development of a fracture mechanics based limit state function which can be used to provide reliability based structural integrity assessment for fixed offshore platforms. 2 Reliability Techniques 2.1 Overview Within the last decade,reliabilitybased methods have become recognised tools in offshore engineering. This is most significantly reflected through the increasing role played by reliability methods in the formulation of codes, classification notes and also recently in the formulation of "safety cases". For offshore structures in the North Sea, the dominant deterioration process is fatigue crack growth. The fatigue life of welded connections in offshore structures is therefore an important design criterion and a governing factor for the planning of inspection repair and maintenance actions. Due to the considerable costs associated with IRM of offshore structures, it is desirable to optimise maintenance planning such that costs are minimized whilst ensuring that risks are kept within acceptable limits. This implies that the estimation of fatigue crack growth, as well as the effect of IRM actions, must be accurate. Unfortunately the fatigue life of a welded connection such as a tubular joint is influenced by a large number of uncertainties, such as wave loading, stress concentration factors, material properties and the size and number of initial defects. Furthermore, inspections and repair actions of joints are subject to significant uncertainties mainly due to the difficult conditions under which they are performed. Deterministic analysis methods in combination with, e.g., the partial safety factor code formats have proven their usefulness in assuring safe structural designs. However one area where probabilistic analysis methods provide better information is when the task is to identify which parameters are dominant. For this it is necessary to take into account all the involved uncertainties and to correctly model the mutual dependencies between the uncertainties. Modern reliability methods serve as a tool for the consistent handling of uncertainties and, when combined with state-of-the-art models of fatigue crack growth, can provide a powerful tool forreliability-basedirm planning of offshore structures.

3 Engineering Integrity 293 In order to ensure and maintain the safe operation of offshore structures inspection and maintenance actions are performed with adequate intervals. The costs associated with inspection and maintenance of offshore structures are very considerable mostly due to the difficult conditions under which inspection and maintenance must be performed. Inspection and maintenance actions should therefore be optimised with respect to inspection intervals, inspection techniques and potential repair actions. 2.2 Description of limit state It is usually possible to describe whether a structural component is in a safe or failed condition with the use of a deterministic function (the so called state function). Component reliability analysis is used in the calculation of the probability of this function being in the failure state, under the influence of uncertainties in the input values. This probability is usually known as the probability of failure (POP). The idea of structural reliability can be demonstrated by considering a simple situation where loading, L, interacts with strength, 5 (Figure 1). Here the state function (g), also known as the safety margin, could be formulated as, g = S-L (1) When g > 0, the structural component is said to be in the safe state. Failure occurs when g < 0. In the limiting case where g = 0, g is usually known as the limit state function. P,. Probability ot Filiurs Figure.1: Component reliability analysis - Interaction between Strength and Loading In order to estimate the reliabilities and the expected costs several probabilities must be estimated. To this end modern reliability methods such asfirstorder reliability method (FORM) and second orderreliabilitymethod (SORM) (Faber et al, 1992) are adequate. These methods are based on the concept of a limit state function.

4 294 Engineering Integrity When fatigue crack growth events are considered the limit state functions are formulated as where a^ is the critical crack size and a(tjc) is the actual crack size at time f. Alternatively and often more appropriately, the limit state function can be formulated as *(,)= - ^ W where N is the anticipated lifetime and N(a^,T^) is the time before a crack of size a^j. is obtained. The theory used to predict the crack growth in tubular welded joints is fracture mechanics. 2.3 Reliability analysis results Several proposals for IRM planning can be found in the literature, see for example a review in (Faber et al, 1992). Some strategies are purely reliabilitybased (Pedersen et al, 1992), whereas others combine costs with reliability (Sorenson et al, 1992). The necessary input for IRM planning is: joint and weld geometry stress history material characteristics initial defects previous inspection results inspection reliability costs of failure, inspection and repair The output for each joint and over a period of time, will be: expected remaining life probability of failure and reliability measures expected costs of for maintenance plans reliability sensitivity measures An example of a reliability-based IRM plan is illustrated in Figure 2. Inspections are planned whenever thereliabilityindex decreases to a certain code specified value. At the planned inspections it is assumed that no damage is detected and thereliabilityis updated using this assimption. This approach assures that a minimumreliabilityis maintained throughout the lifetime of the structure. Using a costs based approach only the next inspection time is planned but the costs associated with failure, repair and inspection are taken into account

5 Engineering Integrity 295 (Figure 3). After an inspection is performed the inspection results are taken into account when planning the next inspection. This scheme is often referred to as the adaptive scheme and is described in detail in Faber et al (1994). Figure 2: \ \ \\ s * \! V \ i s» Ti T2 T3 Lifetime Reliability-based IRM planning > Total Costs Failure Costs Repair Costs Inspection Costs Time to Next Inspection Figure 3: Costs-based IRM planning 3 Fracture mechanics modelling 3.1 General Fatigue crack growth models for welded structures, based on linear elastic fracture mechanics have been described recently by several authors (Straalen and Dijkstra, 1991, Dharmavasan et al, 1991). In general, the crack growth model gives the relationship between the crack growth rate (da/dn) and the fatigue loading parameter (AK) (stress intensity factor range). = /(A/0 dn ^ ' (4) This relation has in general a sigmoidal shape as given in figure 4, with a threshold value AK* at the lower AK values and an unstable crack growth part at high AK values.

6 296 Engineering Integrity Kmax=Kc Figure 4: AKth logak Crack growth relationship The stress intensity factor range is the difference between the maximum SIF and the minimum SIFduring a load cycle. The SIF is a measure for the magnitude of the stresses near the crack tip and depending on the geometry, the load level and the crack dimension. where: K = YoJw (5) o = remotely applied stress Y = correction factor depending on geometry and loading conditions a = crack depth Integration of the crack growth relation (equation 5) from an intial defect a. to the final size a, gives the lifetime N of the detail. A fracture mechanics module called the Component Fatigue Analyses (CFA) was developed by combining the FACTS program developed at University College London (Dharmavasan et al, 1991) and the FAFRAM program of TNO (Dijkstra and Straalen, 1991). A brief description of the basis of the CFA is given below. A more detailed description can be found in a paper on the CFA (Dijkstra et al, 1994). 3.2 Application to tubular joints The general purpose fracture mechanics model has to be modified to suit offshore tubular structures (Straalen and Dijkstra, 1991).

7 Engineering Integrity 297 Figure 5: Fracture mechanics model for tubular joints Fatigue cracks in tubular joints generally start at the weld toe and grow in the depth and width direction into the tube wall. Therefore, the CFA assumes a semi-elliptical crack at a weld toe and the real geometry is translated to a simplified model as shown in figure 5. With the crack growing into both depth and width direction, crack extension rules for both directions are needed. In the CFA this can be done in two different ways, namely: 1. Crack growth model for both crack depth and width direction. In this model equation 2 is used in both directions with the appropriate SIF range (AA:,, for the depth direction and ^ for the width direction). 2. Forcing function for crack width direction. In this model the following equation (7) is used only in the depth direction and the crack width is defined as a function of the crack depth. Both methods have their own advantages and disadvantages. The first approach is more correct from a theoretical point of view. However, the problem here is how to deal with multi initiation and crack coalescence. The latter approach needs a forcing function of the type shown in equation 7. However all the available forcing functions are based on experimental observations. One of the questions requiring further investigation is whether the forcing functions are applicable for situations different from the situations on which the formulae are based. The crack growth model mostly used is the Paris-Erdogan relation (equation 8), which represents the linear part of the crack growth curve of figure 4. where: da dn C = crack growth coefficient m = crack growth exponent The material constants C and m are dependent on the material and the environmental conditions (seawater). (8)

8 298 Engineering Integrity The CFA has a number of crack growth relations available and the most appropriate method used in the analysis. 3.3 Stress intensity factor solutions The stress intensity factors implemented within the CFA main categories: system fall into two empirical equations derived from fatigue crack growth data obtained from tubular joints. analytical and empirical solutions dervied for flat plates with semi-elliptical cracks modified by other factors to model crack growth in tubular joints. 3.4 Modelling of multi-segment crack growth curve The behaviour of steels in a corrosive environment leads to a multi-segment Paris curve as shown in Figure 6. da/dn Stress Corrosion Cracking plateau Onset of Stress Cracking,p\ (B) Figure 6: V AK A multi-segment crack growth curve The corrosion crack growth modelling is complicated by random loading experienced by offshore structures in service. Assuming that there is no load interaction, a calculation procedure was developed by Kam and Dover (1989) which adequately predicted the mean values of the experimental data. The procedure involves calculating the mean crack growth rate by summing all the crack growth rates (using the relevant C and m material properties for the segment), each caused by a particular stress range, and weighted by the probability of that stress range occurring in the loading history. This procedure is described by the equation below: (9) Once the average growth rate is determined, the crack growth curve is determined by numerical integration.

9 4 Implementation of software Engineering Integrity 299 The reliability analysis was implemented as a set of FORTRAN modules. The overall framework is shown in Figure 7. In order to enable the analysis module to be embedded within other analysis modules including a knowledge based system, the communication with the analysis modules is by text files. The results are also output to text files in a specific format. The program takes as input probabilistic models for the initial crack geometry, joint geometry, material characteristics and inspection reliability in addition to the long term statistics of the stress processes which are specific to the hot-spot. The latter is stored in a hot-spot specificfileand includes analysis options such as stress intensity factor solution, inspection method etc. The output consists of updated reliabilities, expected cost estimates and crack growth estimates. More detailed results such as partial derivatives, algorithm monitoring, are also possible. A graphical user interface has also been developed to aid with creating input files and to display results. Joint Geometry Material Property Stress History I Inspection 1 [Results J Inspection Costs Reiabiity INPUT DATA i f RISC-RELIABILITY ANALYSIS MODULE 1 RESULTS Reiabiity (Expected Index J Coets 1 Sensitivity 1 Figure 7: Structure of Reliability Analysis Module 5 Conclusions This paper has described how afracturemechanics based model developed for crack growth predictions in tubular welded joints has been modified so that it can be used for reliability based structural integrity assessment. One of the main problems in applying reliability based methods is in the availability of good statistical databases especially for material properties, geometric variations, inspectionreliabilityetc. The methods developed here underwent substantial validation as part of a European Community funded research project.

10 300 Engineering Integrity References Dharmavasan, S., Reynolds, A.G. and Topp, D.A., The Development of a PC-Based Integrated Fatigue Analysis Software Package for Offshore Structures, Proc. Offshore Mechanics and Arctic Engineering, ASME, Stavanger. Dijkstra, O.D., Foeken, R. Van., Dharmavasan, S., Fracture Mechanics Limit States for Reassessment and Maintenance Planning of Offshore Structures, Proc Symp. Offshore Mechanics and Arctic Eng., ASME, Houston. Dijkstra, O.D., Straalen IJJ. Van, Fatigue Crack Growth Program FAFRAM (FAtigue FRActure Mechanics), TNO Building and Construction Research, Report B Faber, M.H., Dharmavasan, S., Dijkstra, O., Integrated Analysis Methodology for Reassessment and Maintenance of Offshore Structures, Proc Symp. Offshore Mechanics and Arctic Eng., ASME, Houston. Faber, M.H., Sorensen, J.D. and Kroon, I.E., Optimal Inspection Strategies for Offshore Structural Systems, Proc Symp. Offshore Mechanics and Arctic Eng., ASME, Calgary. Kam, J.C.P. and Dover, W.D.: Corrosion Fatigue of Welded Tubular Joints: Fracture Mechanics Modelling and Data Interpretation, Proc. 8th Int Offshore Mechanics and Arctic Eng. Symp., ASME, The Hague, Pederson, C, Nielsen J.A., Riber, J.P., Madsen, H.O. and Krenk, S Reliability based Inspection Planning for the TYRA Field, Proc Symp. Offshore Mechanics and Arctic Eng., ASME, Calgary. Sorenson, J.D., Faber, M.H., Thoft-Christensen, P. and Rackwitz, R Modelling in Optimal Inspection and Repair,Proc Symp. Offshore Mechanics and Arctic Eng., ASME, Stavanger. Straalen IJJ. Van., Dijkstra, O.D., Application of the Fracture Mechanics Approach to the Fatigue Behaviour of Welded Tubular Steel Structures. International Symposium on Tubular Structures.