Report No.
SL/WEM/R/M8663/5/01/C
Date
21 August 2001
Classification
OPEN
Methods, Applications and Software for Structural Reliability Assessment
Corus UK Limited Swinden Technology Centre Moorgate Rotherham S60 3AR Telephone: (01709) 820166 Fax:
(01709) 825337
SL/WEM/R/M8663/5/01/C CONTENTS Page SUMMARY
1
1. 1.1 1.2 1.3
INTRODUCTION Background Historical Development of Methods Scope of Review
3 3 4 4
2. 2.1 2.2
BASIC CONCEPTS Definitions and Acceptance of Risk Failure Modes
4 4 5
3. 3.1 3.2 3.3 3.4
QUANTIFICATION OF RELIABILITY Hierarchy of Structural Reliability Methods Limit States and Definitions Types of Uncertainties Types of Analysis
6 6 7 7 8
4. 4.1 4.2 4.3 4.4 4.5 4.6 4.7
REVIEW OF APPLICATIONS IN DIFFERENT INDUSTRIES Overview Nuclear Offshore Structures Transport Bridges and Buildings Power, Process and Chemical Plant Pipelines
10 10 10 12 14 16 17 17
5. 5.1 5.2 5.3 5.4 5.5
PROBABILISTIC TREATMENT OF FRACTURE AND COLLAPSE Description of Failure Assessment Diagram Status of Current FAD-Based Approaches Inherent Safety Level of FAD Approach and Use of Partial Safety Factors Model Uncertainty in the Failure Assessment Diagram Probabilistic Treatment of Failure Assessment Diagram
20 20 20 21 22 22
6. 6.1 6.2 6.3 6.4
TARGET RELIABILITY LEVELS IN DIFFERENT CODES AND INDUSTRIES Overview Quantifying Societal Consequence Treatment of Consequence in Three Major Codes Comparison of Target Reliability Levels in Different Industries
23 23 23 24 27
7. 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 7.10 7.11
SOFTWARE FOR RELIABILITY ANALYSIS Scope STRUREL ProSINTAP CALREL PROBAN COMPASS NESSUS ISPUD AND COSSAN STAR 6 UMFRAP FORM and MONTE
28 28 28 29 30 30 30 30 30 30 31 31
8. 8.1 8.2 8.3 8.4
FURTHER DEVELOPMENT OF PROBABILISTIC METHODS Generic Methods Failure Assessment Diagrams Distributions of Material Properties Reduction of Data Uncertainty
31 31 31 32 32
9.
CONCLUSIONS
32
REFERENCES
34
TABLES
41
FIGURES
F1
APPENDIX 1
STRUCTURE OF VARIOUS RELIABILITY SOFTWARE PACKAGES
C2
A1/1
Corus UK Limited Swinden Technology Centre
SL/WEM/R/M8663/5/01/C
21 August 2001 OPEN
SUMMARY METHODS, APPLICATIONS ASSESSMENT
AND
SOFTWARE
FOR
STRUCTURAL
RELIABILITY
S.E. Webster and A.C. Bannister Changes in legislation, the trend to life extension and increasing computing power have led to an increase in the use of reliability methods in many industrial sectors. The advantages of these approaches are that overdesign can be avoided, uncertainties can be handled in a logical way, sensitivity to variables assessed and a more rational basis for decision making followed. The methods have been extensively applied in the Nuclear, offshore, rail, shipping, aerospace, bridge, building, process plant and pipeline industries. Failure processes that can be addressed include fracture, collapse, fatigue, creep, corrosion, bursting, buckling, third party damage, stress corrosion and seismic damage. In this report, basic concepts of risk, reliability and consequences are first introduced. The types of failure modes that can be addressed probabilistically are then described with reference to global and local effects and time-dependency. Types of calculation methods are covered, with emphasis on Monte-Carlo Simulation and First Order Reliability Method, and the sources and treatment of uncertainty described. A review of codes providing guidance on target reliability levels related to consequence of failure, and industry practice in defining acceptable failure probability is then presented. The levels generally depend on the reliability of the input data, the consequences of failure and the cost of reducing the risk. The capabilities of various commercial and development software are assessed; A range of reliability analysis software is available for general applications, covering any failure mode, and also for fracture specific applications. Current trends include refinement of calculations of risk throughout a structure's lifetime: 'Reliability updating' coupled with structural health monitoring with sensors enables real-time reliability status to be defined. Risk consideration as a primary input in component/structure design is becoming more widespread and the use of the methods for optimisation of materials selection, design and cost is increasing. Future developments include design and material selection optimisation through reliability methods, interaction of failure modes to more accurately reflect real materials' behaviour, standardisation of consequence scenarios, increased use of time-dependent reliability analysis and benchmarking of methods and software.
Corus UK Limited Swinden Technology Centre Moorgate Rotherham S60 3AR Telephone: (01709) 820166 Fax: (01709) 825337
Cover Pages: Text/Table Pages: Figure Pages: Appendix Pages:
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METHODS, APPLICATIONS ASSESSMENT 1.
INTRODUCTION
1.1
Background
AND
SOFTWARE
FOR
STRUCTURAL
RELIABILITY
There are numerous sources of uncertainty in structural design and the absolute safety of a structure cannot be guaranteed due to unpredictability of future loading, variations of material properties as they exist in the structure, simplifications to analysis methods for predicting behaviour and human factors. However, the risk of a failure with unacceptable consequences can be reduced to an acceptably low number; estimation of this level of risk is the subject of this report. The advantages of a reliability approach are twofold: it enables uncertainties to be handled in a rational and logical way in design and assessment, in particular it enables the sensitivity of uncertainty to various design variables to be determined. Secondly, while decisions are seldom clear cut and are never perfect, it provides a more rational basis for decision making than with a purely deterministic analysis. The fundamental concept for reliability analysis is that resistance and load factors are statistical quantities with a central tendency (mean), dispersion about the mean (variance) and some form of distribution (probability density function, e.g. Normal). When combined together via an expression to describe the limit state (such as fracture or collapse) there will be a finite probability that the load will exceed the resistance; this defines the probability of failure (Pf ) and since reliability is equal to 1-Pf , the inherent reliability of the component against a particular failure mode, and with given resistance properties, is defined. The basic definition of this is shown in Fig. 1. The use of probabilistic methods in structural design and analysis has grown rapidly in the past five years, in parallel with increasing computing power. There is now a general agreement on the philosophy behind the use of probabilistic methods in decision making, methods of uncertainty modelling are accepted and being unified, and numerical techniques have been developed to compute failure probabilities and sensitivity factors efficiently(1). Probabilistic methods were originally used for calibration of safety factors in structural codes and technical standards. One of the first calibrations was for the 1974 Canadian Standards Association offshore code, and since then almost all major codes for land based and offshore structures have been developed through a formal calibration process involving some element of probabilistic analysis. In recent years probabilistic methods have also been used directly in design to account for various failure modes for which there was little previous experience, very costly structures or those with very large failure consequences. These methods are now being extended to cover time-dependent failure modes and to link component reliability with system reliability. Recently, probabilistic methods have been further developed to account for new information becoming available after the design stage, a process known as reliability updating. Such information may be from fabrication, such as control of materials and welding, or from service experience, where inspection and monitoring provide important additional information. With the additional information much of the uncertainty present at the design stage is removed and improved decisions on repair, strengthening, inspection planning and change in use can be made in a quantitative manner which would not be possible if based only on deterministic design information. This has particular relevance in fatigue loaded structures such as bridges and offshore structures. 1.2
Historical Development of Methods
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While probabilistic methods can be applied to any aspect of structural design or operation, it is their use in failure prevention and safety analyses which is the subject of this review. Initial concepts in this area of probabilistic fracture mechanics were developed in the nuclear and offshore industries in the 1980s, applications which have associated with them a very high consequence of failure. More recently these methods have begun to be used in more conventional structures and guidance now exists in many design and integrity analysis codes. This may be either in the form of a direct reference to such methods, their use to derive partial safety factors or their application to maintenance and inspection. Public perception and understanding of risk, the associated role of regulatory bodies and the necessity for a common basis on policy where safety is an issue have further strengthened the move to reliability based methods(2). The advantage of such methods in integrity analyses is that the use of pessimistic assumptions for data inputs is avoided, and the compounding effects of such assumptions can be minimised. This compound effect makes the results of deterministic analyses often very conservative leading to a lack of credibility in their results. The methods can be applied to any mode of failure (e.g. fracture, collapse, fatigue, corrosion, creep and buckling) providing that the limit state can be described by an equation(s) and that one or more of the variables in the equation is statistically distributed. 1.3
Scope of Review
Basic concepts of risk, reliability and consequences are first introduced. The types of failure modes that can be addressed probabilistically are then described with reference to global and local effects and time-dependency. Types of calculation methods are covered, with emphasis on Monte-Carlo Simulation and First Order Reliability Method, and the source and treatment of uncertainty described. General treatment in various industries of fracture, fatigue, corrosion and high temperature failure are then covered. Probabilistic definition of the failure assessment diagram (FAD) is addressed in some detail and a review of codes providing guidance on target reliability levels related to consequence of failure summarised. Finally, the capabilities of various commercial and development software is presented, followed by a view on future developments and conclusions. 2.
BASIC CONCEPTS
2.1
Definitions and Acceptance of Risk
For structural applications, the probability of failure is assessed in the context of 'consequence of failure' such that 'risk' can be defined where:Risk = Probability x consequence A high probability of failure can be accepted where the consequences of that failure are low: conversely, a high consequence of failure must be allied to a low probability of occurrence. Societal and governmental acceptance of risk dictates that different industries and structures will have different combinations of probability of failure and consequence of failure, Fig. 2. There are also governmental targets of what is considered to be negligible risk, unacceptable risk and a region in between where risk is treated in terms of 'ALARP' (As Low As Reasonably Practical). High risk can be treated in terms of mitigating either the frequency of occurrence or reduction of consequence.
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The interpretation of failure probability must be made in the context of the type of structure or component(3). Mass produced components (pumps, valves, electrical devices) can be assessed in terms of failure frequency, or time to failure, due to the numbers involved and the fact that they generally comprise parts which wear out, rather than fail by some unexpected or complex mechanism which may involve human factors. In contrast, engineering structures tend to be unique in their structural form and location and are subjected to a range of operating conditions which can cause failure by one failure mode or a combination of many. The concept used for structures is therefore to sample from the input distributions many times and theoretically create similar structures under the full range of operating conditions. For the case of an existing structure, information can be gained on its behaviour and this can be used to refine the calculations of risk, a form of reliability updating which is not possible with newly designed structures. The assessed reliability is not solely a function of the structure itself but is also dependent on the amount and quality of information available for the structure(4). The perception and acceptance of risk depends on the level of understanding of the particular activity or structure, the level of confidence in the source of information and the freedom of choice that an individual has; it would normally be expected that if a definite choice was made, then a higher level of risk would be tolerated. A summary of certain societal risks and broad indicators of what is considered tolerable are given in Tables 1 and 2(5). Failure rates for populations of buildings and bridges(5) are given in Table 3 for comparison. 2.2
Failure Modes
The general concept behind all probabilistic methods is that some or all of the inputs contain inherent uncertainty and these can combine to give an uncertainty rating for structural performance. For general structural assessment purposes it is standard practice to assess safety by comparison of load and resistance effects using established design rules to predict the likelihood of failure. Where there are uncertainties in the input variables, or scatter in the material properties, reliability-based methods can be employed to determine the probability that the load effects will exceed the resistance effects. Inherent scatter in a material property will affect the failure probability and it is therefore not only the mean value of a property which is important, as in deterministic analysis, but also its variance and the type of distribution used to represent the dataset. Depending on the failure mode, material properties, temperature, geometry and loading will influence the reliability of the component. It is more usual to assess failure modes which contribute to the ultimate limit states rather than serviceability limit states. These include yielding, fracture, fatigue, creep, corrosion, stress-corrosion cracking, bursting and buckling. These can be divided firstly into those which act only at a crack tip as compared to those which act globally. Secondly, those which have a time element associated with them (time-variant) and those which are time-invariant can also be defined. This leads to a 2 x 2 matrix, Fig. 3. However, since human factors also play a major role in risk, structural reliability should also acknowledge, if not quantify, those factors which are not directly incorporated in the calculation procedure but will affect risk, this adds a third dimension to the matrix; an example of the complex interrelationship between these different factors is shown in Fig. 4(6). A schematic of a reliability analysis for failure of a corroded pipe is shown in Fig. 5(7). This shows the interaction of materials and operating data, together with inspection data and model uncertainties, and illustrates the range of inputs needed for a typical reliability analysis. 3.
QUANTIFICATION OF RELIABILITY
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3.1
Hierarchy of Structural Reliability Methods
The underlying principles for reliability analysis were defined in the 1950s by Pugsley and Freudenthal(8,9). The subsequent evolution of methods was initially slow, first order methods being developed in the 1970s and only in the 1980/90s were the methods extended to structural systems. The reasons for this include(3): Ÿ
The traditional approach of overdesign, which carries relatively low cost penalties at the design stage.
Ÿ
The priority for understanding modes of failure rather than risk of failure.
Ÿ
Probabilistic methods were not considered relevant in traditional engineering.
The increased use of risk-based approaches is thought to be due to: Ÿ
Change in legislation to safety leading to the need to quantify risk.
Ÿ
The trend of life extension of existing plant and structures, many of which do not meet the requirements of current codes.
Ÿ
Increased experience with probabilistic approaches and increased computing power.
Ÿ
The potential cost savings which can be made when applying risk-based methods.
It is generally accepted that reliability methods can be characterised into one of 4 levels: Ÿ
Level 1 uses partial safety factors to imply reliability and is used in simple codes.
Ÿ
Level 2 is known as second moment, First Order Reliability, Method (FORM). The random variables are defined in terms of means and variances and are considered to be Normally distributed. The measure of reliability is based on the reliability index β. In Advanced level 2 methods the design variables can have any form of probability distributions.
Ÿ
Level 3 have multi-dimensional joint probability distributions. System effects and time-variance may be incorporated. They include numerical integration and simulation techniques.
Ÿ
Level 4 includes any of the above, together with economic data for prediction of maximum benefit or minimum cost.
All methods are approximate and the problems become more difficult as the number of random variables and the complexity of the limit state function increase and when statistical dependence between random variables is present. The asymptotic approximate methods such as FORM are the most suitable for a large variety of structural reliability problems, although simulation methods are useful as complementary methods. A summary of this hierarchy is given in Table 4, although in the present report, most attention is given to the methods of Monte-Carlo Simulation (MCS) and advanced First Order Reliability Method (FORM). 3.2
Limit States and Definitions
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The fundamental notion is the limit state function which gives a discretised assessment of the state of a structure or structural element as being either failed or safe(10). The limit state function is obtained from traditional deterministic analysis, but uncertain input parameters are identified and quantified, as shown for a pipeline analysis in Table 5(17). Interpretation of what is considered to be an acceptable failure probability is made with consideration of the consequences of failure, which can be societal, environmental or financial. The general case of reliability, shown in Fig. 6, enables definition of the following parameters: Ÿ
Safety Margin.
Ÿ
Limit state.
Ÿ
Probability of Failure (Pf ).
Ÿ
Reliability.
Ÿ
Reliability index (β).
The limit state, M, is a function of material properties, loads and dimensions; M>0 represents safety, M<0 represents failure and M=0 represents attainment of the limit state. The probability of failure is given by P(M<0) and therefore the reliability index is related to probability of failure via a unique relationship, Fig. 7. 3.3
Types of Uncertainties
Formal uncertainties can be classified into three categories: Physical, knowledge based and human: The first represents natural randomness intrinsic to a variable and is known as objective uncertainty, such as wind loading. The second, subjective uncertainties, can be reduced at a cost by collecting more data or adopting more realistic models while the third category is hardest to quantify and modify. Knowledge based uncertainty can be further subdivided into statistical, model and phenomenological uncertainties. Statistical uncertainty arises due to a limited number of observations being used to make up a sample which is then taken to represent a population. Generally, a sample does not perfectly represent the full population but the degree of imperfection is never known, although it can be estimated. Modelling uncertainty is caused by the use of simplified relationships between variables to represent real behaviour. Methods use to simplify loads and structural responses as limit state equations are examples of modelling uncertainties. Typical levels of modelling uncertainties are given in Table 6(11). Phenomenological uncertainty arises because unimaginable phenomena occur which affect structural failure. Examples include wind-induced resonant effects and frequencies of earthquake loading and since such phenomenon have not been previously encountered they are particularly important for novel structures or those which attempt to extend the state-of-the-art. Human uncertainty accounts for well over 50% of all structural failures and ranges from variability in task performance to gross errors but they are not covered in any more detail in this report. The difference between 'real' experienced risk of structural failure and the modelled or predicted failure probability (which is lower) is usually referred to as the adjunct probability of failure(11). It is mainly attributable to human error and modelling uncertainty; as long as these remain there will
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always be a gap between predicted and experienced risks, this gap is generally 1 to 3 orders of magnitude(11), although accounting for modelling uncertainty alone in fracture analyses gives a difference of one order of magnitude(12) and for these reasons, predicted reliability levels are best referred to as notional, rather than absolute, levels and are better suited to comparison purposes. 3.4
Types of Analysis
3.4.1
Simulation v Transformation Methods
In simulation methods, a number of random samples are made and the probability determined by simple ratios; in transformation methods, the integrand is transformed into a standard type of distribution which can then be analysed using the particular properties of the distribution. Decision of relevant failure modes and their limit states are common to both classes of analysis, as is interpretation of the consequences of failure. The methods differ in the middle step of determination of failure probability from distributions of applied and resistance factors. 3.4.2
Monte-Carlo Simulation (MCS)
MCS is a relatively simple method which uses the fact that failure probability can be expressed as a mean value of the result of a large number of random combinations of input data. An estimate is therefore given by averaging a suitably large number of independent outcomes (simulations) of this experiment. The basic building block of this sampling is the generation of random numbers from a uniform distribution. Simple algorithms repeat themselves after approximately 2 x 103 to 2 x 109 simulations and are therefore not suitable to calculate medium to small failure probabilities. Once a random number u, between 0 and 1, has been generated, it can be used to generate a value of the desired random variable with a given distribution. A common method is the inverse transform method. To calculate the failure probability, one performs N deterministic simulations and for every simulation checks if the component analysed has failed. The number of failures is NF, and an estimate of the mean probability of failure is the ratio of NF to N. A schematic of the MCS method is shown in Fig. 8. An advantage with MCS, is that it is robust and easy to implement into a computer program, and for a sample size tending to infinity, the estimated probability converges to the exact result. Another advantage is that MCS works with any distribution of the random variables and there are no restrictions on the limit state functions. However, MCS is rather inefficient, when calculating failure probabilities, since most of the contribution to Pf is in a limited part of the integration interval. In addition, for very low failure probabilities, a large number of simulations is required for the result to converge to the actual value; in these case FORM is preferred or the method of Importance sampling (MCS-IS) can be used. 3.4.3
Monte-Carlo Simulation with Importance Sampling (MCS-IS)
MCS-IS is an algorithm that concentrates the samples in the most important part of the integration interval. Instead of sampling around the mean values, as in MCS, sampling is made around the most probable point of failure. This point, called MPP, is generally evaluated using information from a FORM/SORM analysis and as such the MCS-IS has limited application except for cases where convergence in FORM cannot be achieved due to complexity of the limit state.
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3.4.4
First Order Reliability Method (FORM)
FORM uses a combination of analytical and approximation methods and comprises three stages: Firstly, independent of whether each parameter has been defined as a Normal, Log-Normal or Weibull distribution, all variables are first transformed into equivalent Normal space with zero mean and unit variance. The original limit state surface is then mapped onto the new limit state surface. Secondly, the shortest distance between the origin and the limit state surface, termed the reliability index β, is evaluated; this is termed the design point, or point of maximum likelihood, and gives the most likely combination of basic variables to cause failure. Finally, the failure probability associated with this point is then calculated via the relationship between β and Pf . This is shown schematically for the case of a linear safety margin in Fig. 9. For non-linear limit states, the failure surface is linearised at the design point, Fig. 10, the error in β depending on the non-linearity of the function at this point. By transforming the variables into equivalent Normal variables in standard Normal space (mean = 0 and standard deviation = 1). This gives the joint probability density function as the standardised multivariate Normal which has many useful properties; This is known as the Hasofer-Lind Transformation(14) and by its application the original limit state surface g (x) = 0 then becomes mapped onto the new limit state surface gU (u) = 0. Calculation of the shortest distance between the origin and the limit state surface, β, requires an appropriate non-linear optimisation algorithm. A modified Rackwitz and Fiessler(15) algorithm is used as the default algorithm in most reliability analyses, which works by damping the gradient contribution of the limit state function, is a robust algorithm and converges quite quickly for most cases. Finally, the failure probability is calculated using an approximation of the limit state surface at the most probable point of failure, and the relationship shown in Fig. 7 is used for this. FORM is more efficient than MCS in terms of computing time and accurate results can be obtained even when the failure probability is low. All the random parameters must however be continuous and large errors can also result if there are local minima in the limit state or high non-linearity at the design point(16). Despite these limitations, FORM is the most popular reliability analysis method, can be easily extended to non-linear limit states and has a reasonable balance between ease of use and accuracy. 3.4.5
Second Order Reliability Method (SORM)
The approximation of the limit state at the design point as a straight line is a step which leads to errors in FORM analyses, the magnitude of which depends on the degree of non-linearity of the limit state equation. In SORM, a parabolic, quadratic or high order polynomial is used to describe the limit state surface, centred on the design point. This leads to higher accuracy but is not generally considered necessary for the majority of engineering applications. Examples of calculations made using MCS, FORM and SORM for one analysis case are presented in Reference (17). 4.
REVIEW OF APPLICATION IN DIFFERENT INDUSTRIES
4.1
Overview
In the following sections the application of reliability methods in a number of different industries is reviewed. This is limited to those industries in which the method forms an integral part of design, construction and operation and covers predominantly fracture, fatigue and corrosion failure
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processes. Examples of application to inspection scheduling, life extension, design and change in operating conditions are described. 4.2
Nuclear
4.2.1
General Characteristics
The application of reliability-based methods in the nuclear industry is widely documented and only a selection of representative literature is reviewed here. The R5(18) and R6(19) methodologies are the most widely applied for high and low temperature failure assessments respectively, and both can be treated probabilistically. R5 reliability analysis is currently at the development stage while examples of R6 application in reliability are well documented. Examples of the application of each in a reliability context are given in Reference (20). The use of the R6 method in support of safety cases, and determination of acceptable levels of reserve factors, has however demonstrated that it is usually the lack of high quality input data, particularly defect size distributions, that limits the usefulness of the approaches rather than any inherent limitation of the methods themselves(21). Similar approaches for AGRs(22) emphasise the application of the Nuclear Safety Principles (NSPs) of prevention, protection and mitigation to initiating events in various combinations depending on the acceptable probability of occurrence, which in turn is inversely related to the severity of consequences of the event. In order of increasing consequence, the failure probabilities (Pf ) and protection against the event(22) are: v
Frequent: Pf >10-3 per year, protection and mitigation with two lines of protection.
v
Infrequent: 10-3>Pf >10-5 per year, protection and mitigation with one line of protection with redundancy.
v
High Integrity: 10-5>Pf >10-7 per year, Demonstrate that all reasonably practical steps have been taken to provide a line of protection.
v
Incredibility of Failure (IoF): Pf <10-7 per year, need to demonstrate IoF.
An IoF approach, as is used for ultimate limit state events such as fracture, comprises a number of steps: Ÿ
Build Quality (Materials, welding, pressure testing, inspection, operational history).
Ÿ
Design Assessment (Code used, operational loads).
Ÿ
Defect Tolerance (R6, BS 7910).
Ÿ
Failure Modes (Fatigue, creep, fracture, stress corrosion).
Ÿ
Degradation (corrosion, radiation embrittlement).
Ÿ
Forewarning of Failure (Leak detection, observable events prior to total failure).
These steps form the basis of a safety case, with consideration of fault loadings and inspection strategies added as the final stage.
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4.2.2
Creep Analysis
The R5 method enables analysis of creep crack growth; The material properties describing creep crack growth and creep strain responses are usually treated probabilistically, while all other parameters are handled as deterministic quantities. Monte-Carlo simulation is generally used due to the complexities of the equation describing the limit state. An example of the application of this is given in Reference (20): MCS was used with the creep crack growth properties and the creep strain being defined as probability density functions and all other inputs as deterministic. The example showed how an initial distribution of defects would change by creep crack growth in 1 year increments over a ten year period. Conditional probabilities were also addressed since ductile materials tend to have higher creep strains and lower crack growth rates; by accounting for this interrelationship of material properties the failure probability at the end of the ten year period was reduced by an order of magnitude. 4.2.3
Fracture and Collapse Analysis
The R6 method uses the well-known Failure Assessment Diagram (FAD) which enables simultaneous analysis of fracture and collapse for a component with a flaw, Fig. 11. Material properties and flaw sizes are usually treated probabilistically, while applied and residual stress is deterministic. MCS is relatively straightforward with the R6 method and other codes using the FAD, although FORM analysis can also be applied but with some limitations to ensure convergence of solutions. The FAD approach and its treatment from a reliability aspect is covered in more detail in Section 5. Ideally, full conditional probabilities for materials properties should be established since strength and toughness are related but alternatively realistic lower tails can be imposed on the distributions to reduce the level of pessimism. This approach is also described in the context of corrosion performance in relation to steel composition(23): By using the actual composition from a test certificate, and based on knowledge of the performance of different compositions, a more realistic estimate of failure probability can be obtained than if the minimum or maximum allowable limits of each element had been assumed. Dependence of failure probability on quality of flaw and fracture toughness data is emphasised in detail in many publications(15), and an example of effect of quality of NDE data on resultant failure probability is shown in Fig. 12(13), while in Fig. 13 the effect of increasing scatter of fracture toughness on resultant Pf is highlighted(24), an increase in COV in toughness from 8 to 10% leading to an increase in Pf of two orders of magnitude. Time dependence is also relevant since irradiation embrittlement over time can lead to reduced toughness and hence increased failure probability; A schematic of the effect of this is shown in Fig. 14 for the case of reducing toughness (e.g. due to irradiation) and increasing stress (e.g. due to loss of area by corrosion) with time.
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4.2.4
Sensitivity and Benchmark Studies
A further issue in most safety assessments, and in nuclear components in particular, is that there is high reliability and a relatively small number (in statistical terms) of components or plant. The concept of actual failure probabilities is therefore better interpreted as relative, or notional, failure probability(25). Round robin analyses have been carried out to investigate the reproducibility of these approaches(25,26). The study in Japan(26) indicated that while seven different computer programmes gave failure probabilities which were within a factor of 2-5 of each other, the sensitivity of the result to assumed fracture toughness was such that the degree of neutron irradiation greatly influences the judgement on plant life extension. Such sensitivities are further studied in Reference (25) where FORM (First Order Reliability Method), SORM (Second Order Reliability Method) and a round robin MCS (Monte-Carlo Simulation) were compared, Fig. 15. The treatment of failure probabilities as relative values, indicating where greatest sensitivity to inputs lies, and the fact that only 'orders of magnitude' of Pf values are of interest seem to be the main conclusions of comparative studies. The US Heavy Section Steel Technology (HSST) Programme (27) concentrated on the effects of materials and flaw data distributions on calculated failure probabilities. The input flaw size distribution has a dominant influence on Pf , a detailed analysis of inspection capabilities(28) shows that the probability of detection (POD) and probability of correct sizing (POS) vary significantly with inspection method and quality, and type and size of flaw, Fig. 16. The advantages of applying constraint corrections for the cases of shallow cracks have also been identified(27). Inclusion of ductile tearing prior to cleavage fracture was seen as a mode that should be treated probabilistically and the possibility of including both constraint and tearing analysis has been demonstrated based on the Weibull Stress concept(28). As well as the influence of the actual flaw distribution on failure probability, the effects of using varying qualities of inspection on resultant failure have been demonstrated probabilistically and specific use of reliability-based methods for definition of inspection and maintenance schedules are also widely documented. It is predicted(30) that reliability approaches will play an increasing part in structural integrity safety cases. 4.3
Offshore Structures
4.3.1
General Characteristics
Probabilistic methods have also been applied for many years in the offshore industry, although due to the loading regimes there is more emphasis on linking fatigue and fracture than in the nuclear industry. Safety cases are now required for offshore structures in the North sea, and inspection plans are linked to these. The ALARP principle is a cornerstone of reliability analysis of offshore structures, most analyses are linked to the optimisation of inspection plans in terms of location, frequency and reliability of detection methods. Floating Production, Storage and Offloading (FPSO) structures are covered under Section 4.4 of this report. 4.3.2
System Reliability
Due to the nature of welded jacket structures one of the key issues is to link individual member failure to overall system failure(31): The degree of redundancy, consequences of failure, warning time of impending collapse, accessibility of joint for inspection and limits of the probabilistic model are usually linked to define the potential probability of failure by different paths. Redundancy must also be defined in terms of ultimate strength, fracture and fatigue limit states. These interrelationships inevitably lead to complex analysis with the number of failure paths increasing factorially with the numbers of members and joints: Methods for assessing this complexity are described in Reference (32).
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4.3.2
Reliability Updating and Inspection Scheduling
Since fatigue is the dominant damage mechanism in offshore jacket structures, there have been numerous examples of reliability assessments linking crack growth with inspection requirements. Most approaches involve a reliability-based interpretation of the S-N curve in conjunction with Miner's Rule. This method can be used to define the required inspection interval to maintain a specific level of reliability(31), Fig. 17, or for reliability updating to refine the original crack growth calculations based on knowledge obtained by inspection of the actual, or similar, joints. An example of this second application(33), shows the potential advantages for carrying out remnant life assessments of existing structures and applies the following steps: (a)
Estimate of fatigue reliability, β, for each joint.
(b)
Identification of critical joints where β is less than the target value (Pf higher).
(c)
Identification of a subset of critical joints to be inspected.
(d)
Carry out inspections.
(e)
Reliability updating for all joints.
(f)
Planning of following inspection surveys.
Activity (c) requires a correlation to be established between joints so that the results of the inspection can be extended to the non-inspected joints; this is achieved by the following; Ÿ
A reliability model based on S-N to account for fatigue failure and crack detection during inspection.
Ÿ
A rational correlation between joints based on type, geometry and response to loads.
Ÿ
A Bayesian updating of the reliability estimates for all joints, based on the results of the inspected joints. This enables system reliability updating using FORM/MCS in real time and uses all information made available by the surveys.
Ÿ
A method for accounting for inspection uncertainty by modifying the PDFs for crack sizes.
This method has proved successful for life extension, significant improvements in reliability being obtained due to the updating method, Fig. 18. Reliability approaches have also been used to demonstrate the suitability of inspection techniques. Flooded Member Detection (FMD) uses the presence of water in a normally air-filled structural member to indicate through-wall damage. In order for this method to be viable the structure must tolerate the damage without an increase in the overall probability of failure and risk-based methods have been used to demonstrate this(34). The required size of an inspection sample needed to update reliability based on the original safety index of an uninspected joint(33) can also be determined, Fig. 19.
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4.3.3
Application of LEFM Crack Growth Methods
Although the above methods apply mainly S-N approaches for fatigue, LEFM-based crack growth methods have also been applied: In Reference (35) the da/dN approach was used mainly to calibrate S-N design lines which were not available for the particular joint configuration, and environmental effects were also incorporated. In Reference (36) the crack growth law was treated deterministically but with local ’hot-spot' stress ranges determined from FE, factored by probabilistically defined wave exceedance data, giving a Weibull distribution for the hot-spot stress range. The method used is summarised in Fig. 20, the mean fatigue life of each joint was characterised as one of four states: Ÿ
Time to first detectable crack growth.
Ÿ
Time to 20% through-thickness cracking.
Ÿ
Time to through-thickness cracking.
Ÿ
Time to joint failure, defined as when joint stiffness is reduced to 50% intact value.
4.3.4
Other Failure Modes
Although fatigue crack growth parameters show inherent scatter, the loading and characterisation of realistic load spectra dominate most fatigue analyses and this is where most probabilistic effort tends to be focused in structures where fatigue is the dominant limit state. Hence, this review has been concentrated on these effects. probabilistic methods have also been applied to offshore corrosion problems, fire and blast and sea state modelling but these are not addressed here. 4.4
Transport
4.4.1
General Characteristics
In most transport applications the variable which is most difficult to define with any level of certainty is the loading and most reliability work is focused on fatigue rather than fracture. In many applications reliability methods are used to set inspection regimes optimised for safety and cost, but unlike nuclear and offshore structures, many transport applications directly involve public use and the aim target reliabilities reflect the duty of care that this entails. 4.4.2
Aircraft
Aircraft structures are subjected to a wide variety of live loadings and the principal issue is one of fatigue life estimation and the linking of this to inspection schedules. Consequently, the loading spectrum forms the largest single parameter to be treated probabilistically in aircraft applications(37). The approach used for fatigue estimation often involves full scale testing of components which, coupled with reliability analysis enables optimum inspection scheduling to be made. The issue of engine reliability is beyond the scope of this review.
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4.4.3
Rail
In rail applications, probabilistic methods are being increasingly used to set track and vehicle inspection intervals. The former tend to be based on traffic composition (axle load and speed), the fatigue crack growth characteristics of the rail and the interaction with other degradation modes such as wear and corrosion. The identification of factors that increase the risk of failure, coupled with the definition of high risk joints enables rail NDE to be applied where it is most needed(38). The optimisation of inspection strategies for safety critical rail vehicles has also been made based on fatigue analysis, but linked to a fracture approach for defining critical flaw size. One approach(39) is to use MCS with the fatigue crack growth parameters in the Paris Law, the threshold stress intensity factor and the loadings defined as probability density functions and all other parameters defined deterministically. A risk-cost benefit analysis is then used to set optimum inspection intervals as a function of mileage. 4.4.4
Ships
In ships, the issue again is complexity and unpredictability of loading, coupled with the presence of huge distances of weld runs, largely uninspectable regions and failure mode interaction. Loading spectra in ships are dependent on factors such as trading patterns, cargo loading arrangements, speed, heading angles and time at port. A recommended method for estimation of wave loadings, frequencies and structural response from a fatigue perspective is given in Reference (40), while estimation methods for statistical characteristics of random load variables in ships(41) provides guidance on treating wave-induced bending loads and provides recommendations on COVs for these, Table 7. A prototype code for probability-based design requirements for fatigue of ship structures has been developed(42), in which the S-N curve is described probabilistically. The strength modelling error, in this case the uncertainty in Miner's Rule, is quantified by letting the damage at failure being a log-Normally distributed random variable with median 1.0 and a COV of 30%. Four levels of sophistication of calculation are presented, with target safety levels defined according to a three-level ranking based on consequence of fatigue cracking. 4.4.5
Floating Production, Storage and Offloading Vessels
The use of converted tankers or new-build vessels as Floating Production Storage and Offloading (FPSO) units offshore is an increasing trend. The integrity of such units is usually assessed on a case-by-case basis as the environmental loadings are site-specific. Rules for tankers involved in world trade were previously used for this although reliability-based codes for FPSO assessment has been published by both Lloyd's Register and ABS. A Probability of Exceedance (POE) approach is often used for quantifying wave-induced dynamic loads(44,45) which are then applied in probabilistic fatigue analysis. Reliability analyses for assessment of safety levels of FPSO hulls involve five failure modes(44): hull girder collapse, hull girder yield, failure of unstiffened panels, failure of stiffened panels and fatigue. FORM analyses have been used(44) taking all inputs (dimensions, flaw sizes, material properties, loadings) as random variables with specific distributions and coefficients of variation from various studies(41). Deterministic analysis was first carried out to identify the most critical regions and then a probabilistic analysis carried out on the failure mode with the lowest reliability index. The resulting reliability indices were compared with Recommended target reliability indices for ships and FPSOs and indicated that current codes have adequate, but not excessive, safety margins.
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4.5
Bridges and Buildings
4.5.1
Fatigue Loading
Reliability methods applied to bridges usually address fatigue issues and life extension, but increase in failure probability throughout life due, for example to increased traffic load and loss of load bearing area through corrosion, must also be considered. A comprehensive description of the development of a method for assessing the risk of fatigue failure in highway bridges is given in Reference (46). Initial crack shape, fatigue crack growth data and fracture toughness were treated as statistical distributions. Over 100 stress range histograms were obtained from 40 bridges and equivalent constant amplitude stress ranges determined. An MCS approach was used with Variance Reduction Technique (similar to importance sampling) to reduce the required number of simulations when the risk of failure is small. The simulation output gave the risk of fatigue failure for specific bridge details, the total system failure probability then being calculated by the total number of details in the system and the correlation coefficients between them. The model enabled definition of maximum length of service life extension, specified inspection intervals and maximum fatigue failure risk at which the bridge must be inspected, Fig. 23. Methods for incorporating random variable amplitude traffic loading with data from inspection have been combined into a probabilistic fatigue analysis to identify the statistical properties of damage contribution(47). The fatigue lifetime of each critical detail was then assessed, the method has potential for assessing future damage due to increased traffic growth and truck weights. The methods have also been applied to general bridge management programmes(48), and bridge deterioration(49). 4.5.2
Seismic Loading
Assessment of structural failure due to seismic activity, both for bridges(50) and buildings(51,52) has been carried out probabilistically. In Reference (50) a force based seismic code with dynamic reliability theory was applied and showed the complex nature of the problem of integrating structural response with seismic response, although probability of failure generally increased as period between the vibration peaks increased, Fig. 24. The effect of variability of material ductility was studied from the viewpoint of vertical deflection capacity of a cantilever beam, as would occur in an earthquake(51). Probabilistic models for yield stress and hardening capacity (as indicated by the inverse of the yield/tensile ratio) were introduced into a FORM analysis and studied for a wide range of steel beam and column geometries. The results can be applied in design by the definition of generalised parameters involving cross-sectional properties and material uncertainty coefficients. A FORM method has also been used for determining the required fracture toughness of columns used in direct-welded moment connections in seismic areas(53). The aim target reliability was that quoted in the design code for a severe earthquake with low return period, stresses were determined from a finite element analysis and fracture toughness requirements evaluated using a FORM analysis of the Failure Assessment Diagram. 4.5.3
Static Strength Modelling
Methods have been applied to the static strength modelling of structures which are highly sensitive to geometrical variation. The dominant failure mode in these cases is buckling and a variety of stiffened steel structures have been analysed(54,55). The application is however not limited to steel, concrete structures have also been assessed from the aspect of material property variations and the effect of loading cases on the buckling of GFRP cylinders has also been analysed(56).
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4.6
Power, Process and Chemical Plant
The main application of reliability methods in fossil power, process and chemical plant appears to be in the area of risk-based maintenance and inspection (RBMI). The types of plant to which RBMI is applied is vast but the majority of failures are associated with pressure equipment(57) such as tanks, storage vessels, pumps, towers, heat exchangers and boilers, Fig. 25. Formal approaches detailing such methods have been, or are soon to be, adopted in the USA(58,59,60). An extensive review of industries applying RBMI was carried out in the preparation of the RIMAP proposal(61), which aims to provide a unified approach for a probabilistic lifetime and consequence analysis method, Fig. 26. One criticism of current quantitative methods for RBMI, and therefore limiting their wider use, is their complexity and the unrealistic nature of such analyses being carried out by plant engineers in short timescales. A complicating factor is the vast number of damage mechanisms (thinning, fatigue, stress corrosion cracking, metallurgical damage, mechanical damage) and the complex interactions between them. Furthermore, while the definition of consequences of failure will always be semi-qualitative and open to individual interpretation, RBMI is an expanding area because of the benefits it confers and current thinking is that computational methods and individual experience should go together to form a workable RBMI strategy(57). A move towards this has already been made with the development of appropriate software to formalise the processes of consequence analysis to target maintenance effectively(62). 4.7
Pipelines
4.7.1
General Characteristics
As for nuclear applications, there is a large amount of literature relating to risk and reliability assessments of pipelines and only a brief overview is given here. Probabilistic analysis of pipelines is introduced in Reference (63), risk analysis approaches for these applications being pioneered by British Gas and now applied widely in this field. Despite there being over 100000 km of pipelines in western europe alone, the failure rate is extremely small. Extensive legislation governs the manufacture, installation, operation and inspection of pipelines and the aim of this regulation is to limit the likelihood and consequences of any failure. Consequently, pipelines are the safest method of transporting energy(64). Where flaws are detected, fitness-for-purpose must be demonstrated and this is the main aspect of pipelines in which risk-based methods are applied. FAD-type approaches (R6, BS 7910) form the backbone of such assessments, although obtaining representative data is usually the limiting factor. The major cause of damage in onshore pipelines is third party interference, although ground movement can also affect some locations and fabrication flaws may be an issue in ageing older pipelines; 70% of pre-1968 pipelines would be classed as unacceptable to current standards, whereas this value reduces to 10% for those fabricated between 1968 and 1972(63). Particular emphasis is placed on consequence analysis, a function of the stored energy in the system and the human population density in the vicinity. The probabilistic methods are applied to the assessment of damage or flaws, the setting and optimisation of inspection frequencies, setting maintenance schedules, life extension and pressure uprating of existing pipelines. Examples of each are described briefly below. It is noted in many of the references cited that the codification of limit states and reliability-based pipeline design in the USA has trailed behind that of Europe. Corporate interest in this issue in the USA varies widely, evidently due to concerns regarding public perception and liability. 4.7.2
Third Party Damage
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Use of the FORM method for estimating pipeline failure frequencies has demonstrated that this method represents a suitable compromise between accuracy and useability(65). The probability of failure, given the presence of third party damage, can be estimated using this method, although the frequency of occurrence of impacts can only be determined through the use of historical data. Interrelationships between dents, gouges and failures are determined from existing 'models'(66,67) and a two-parameter Weibull distribution fitted to damage data. However, the fitting of lines to these distributions is itself subject to confidence limits, and by different fitting methods the failure probabilities were found to change by a factor of 1.5-3, highlighting sensitivity to distribution fitting. A reliability-based limit state approach has also been developed for the design of pipelines to resist third party mechanical damage. This involved statistical quantification of damage, Fig. 27, coupled with strength properties defined as random variables which were then applied to existing puncture models in a probabilistic manner and compared with test results. This enabled sensitivity studies to be made which characterise the failure probability as a function of each input variable. Applied load and excavator tooth contact length were found to be the most significant variables, mainly due to the high COV of the load (45%). Examples of reliability levels for various design factors are shown in Fig. 28. 4.7.3
Pressure Uprating
The effect on reliability of pressure uprating of pipelines has been demonstrated in several studies in order to justify the safe use of higher pressure levels. An extensive study for justification of a pressure uprating of a sub-sea pipeline is reported in Reference (69). This involved a probabilistic treatment of all credible failure modes: these are yielding (serviceability limit state), and, for ultimate limit states, bursting, external corrosion, internal corrosion and fatigue crack growth of weld defects. Using such an approach it was demonstrated that only for the fatigue limit state was the probability of reaching a failure condition greater than 'negligible'. At the time of the study, the pipeline was operating at 100 bar g, uprating to 130 and 135 bar g gave a calculated increase in failure probability of 12 and 156 times respectively, demonstrating the sensitivity of certain limit states to small changes in input values, Fig. 29. Based on experience of the pipeline the uprating to 130 bar g was considered acceptable. The application of limit state reliability methods to pipe operation above 80% SMYS has been demonstrated using FORM analysis with limit state equations to describe rupture of new pipe, from corrosion damage and from dent-gouge damage(70). Yield strength, Charpy impact energy, pipe diameter, wall thickness, operating pressure, flaw/gouge size and corrosion rate were considered to be random variables with all other parameters treated deterministically. This showed that the burst of defect-free pipe was not a credible failure mode and that it is important to consider damage and time-dependent deterioration. The failure rates for corrosion defects were expressed as a time-dependent function, Fig. 30(a), while those for dent-gouge failure were represented as a function of wall thickness, Fig. 30(b). Overall, the suitability of the FORM method for justifying pressure uprating was demonstrated, although the importance of linking this with a pipeline management system for maintaining, monitoring and controlling structural integrity through the full life was highlighted.
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4.7.4
Fracture and Collapse
In a study on reliability of pipeline girth welds, both plastic collapse and unstable fracture limit states were assessed(71) using the Failure Assessment Diagram with respect to specific target reliability levels (β = 1-5), although an industry-wide acceptable target was not thought to be presently feasible. The necessity for accurate flaw sizing and the definition of realistic COVs for material properties is emphasised(71), fracture toughness being treated as a mean and 50% of this value in order to account for variability of CTOD not revealed due to a limited number of test data being available. Once the target reliability levels had been established the FORM method was again used, but with the aim of deriving appropriate partial safety factors for application to the main data inputs (flow stress, toughness, stress, flaw size) in a limit state approach. The dominant overall uncertainty for both limit states was found to be flaw size and a high degree of conservatism was noted in the fracture analysis as a simple LEFM approach was used. Furthermore, the difficulty in predicting the occurrence and magnitude of ground movement meant that the contribution of this to overall failure probability could not be quantified. The analysis is applicable on a 'per-weld' basis, and the concept of system reliability and time-dependency were not addressed. FORM/SORM have also been applied in a study to define the upper limits of yield/tensile ratio for reliable pipeline operation(7). Following review of ultimate and serviceability limit states, and stress and strain controlled cases, the three main failure modes in which Y/T played a major role were defined as pipe burst, local buckling and axial rupture. Models describing each of these failure modes are being assessed probabilistically, with particular emphasis on the definition of flow stress, after first demonstrating suitable model accuracy by comparison with existing test data. FORM and MCS methods based on the failure assessment diagram have been used to justify safe use of pipes containing girth welds with low weld metal fracture toughness(72). A system reliability approach was adopted and the total reliability determined from the product of individual probabilities for a flaw giving a failure prediction, a flaw existing in a tension zone and a flaw existing in the weld, multiplied by the number of welds considered in the pipeline. A similar approach has also been used to investigate the probability of pipe failure during hydrotesting(73), using TWI sofware(74). Although not limited to pipeline applications, a reliability-based approach has also been used to assess HAZ fabrication hydrogen cracking(75). Nomograms for preheat requirements as a function of CEV, heat input, combined thicknesses and hydrogen scales were combined with a probabilistic treatment of HAZ hardness to derive probability of cracking values as a function of heat input. The methodology and typical output are shown in Figs. 32 and 33 respectively. 4.7.6
Inspection Planning
Since third party damage is the principal cause of pipeline failure, reliability-based methods have also been applied to evaluate the effectiveness of different design and maintenance practices used to protect pipelines(76). Mechanical damage assessment statistics were collated from numerous sources and a two-component model based on a fault tree applied. The first component relates to frequency of mechanical interference, the second to probability of puncture when interference occurs. Probability of occurrences were determined from historical statistics, while cost implications of pipeline outage were compared with the costs of mitigation measures to give a cost-benefit analysis for maintenance/repair measures compared to preventative measures. Similar approaches are also used for scheduling inspection for corrosion damage.
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5.
PROBABILISTIC TREATMENT OF FRACTURE AND COLLAPSE
5.1
Description of Failure Assessment Diagram
The Failure Assessment Diagram (FAD) gives a graphical representation of the potential effect of a defect on the integrity of a structure. The FAD is a two dimensional plot and indicates the propensity of the defect to cause failure by plastic collapse and brittle fracture. The basic FAD has two axes, Kr and Lr where: Kr = Applied stress intensity/fracture toughness. Lr = Applied stress/yield stress. Kr is known as the brittle fracture parameter and Lr the plastic collapse parameter. The three principal inputs which are necessary for a basic deterministic calculation to be performed are crack size, stress and fracture toughness. If all three are known the safety of a structure can be evaluated, while if any two are known the critical level of the third parameter can be determined. The brittle fracture parameter can also be defined in terms of J or CTOD-based fracture toughness. Once the co-ordinates of the analysis point has been evaluated and plotted on the FAD further information can be gained depending on the relative position of the analysis point in FAD space. The FAD locus divides this space into 'safe' and 'unsafe' regions, the shape of the locus allowing for the interaction of yielding and fracture. Furthermore, depending on where the analysis point falls the most likely failure mode can be estimated; the regions of 'fracture-dominated', 'collapse-dominated' and 'intermediate' behaviour are divided up according to the ratio of Kr/Lr. Another feature of the FAD is that some element of work hardening is allowed for since the Lr cut-off level of 1.0 represents an allowable maximum stress equal to the mean of yield stress and UTS. 5.2
Status of Current FAD-Based Approaches
The main analysis methods using the FAD are R6(19), BS 7910(77), SINTAP (78) and API579(79). BS 7910 is a new standard which replaces the former BS PD 6493. While changes in the scope of the standard have been made and the treatment of data inputs revised, the basic concept of the FAD remains unchanged. The plastic collapse parameter in the FAD is now defined in terms of yield stress, with a subsequent change to the shape of the FAD and definition of the cut-off in terms of yield stress/ultimate tensile stress ratio. The SINTAP method also applies a FAD method based on yield stress but has alternative options for addressing cases such as weld strength mismatch and the treatment of constraint. Establishing the significance of a result in FAD space can involve one, or a combination of, the following concepts:Ÿ
Sensitivity analysis.
Ÿ
Definition of reserve factors.
Ÿ
Use of partial safety factors.
Ÿ
Probabilistic analysis.
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The definition of reserve factors and sensitivity analysis can be linked by determining how sensitive the final result is to variations in the input data: A higher reserve factor is needed for those situations where the result is very sensitive to realistic variations in these data. Similarly, if a high reserve factor is deemed necessary, this can also be achieved by applying partial safety factors to those variables which are shown to have the greatest sensitivity on the analysis point. 5.3
Inherent Safety Level of FAD Approach and Use of Partial Safety Factors
The results of analyses using the above methods are based on the assumption that failure will occur when an assessed defect gives rise to a point which falls on the failure assessment diagram whereas in practice it is often found that the FAD gives safe predictions, due to its inherent conservatism, rather than critical ones. Data from wide plate test programmes to validate the failure assessment diagram approach were used to investigate the effects of the conservatism inherent to the failure assessment diagram approach and to derive appropriate partial safety factors(80,81), Fig. 34. A relatively high level of safety can be observed in the FAD, indicating that the method is inherently safe. By expressing the distance from the origin to the failure locus as a ratio of the distance from the origin to each data point, the inherent safety factor can be determined for each test result at different angles around the FAD, Fig. 35. The region of the FAD is expressed as the angle Theta where θ = 90° equates to pure brittle fracture (Kr = 1) and θ = 0 corresponds to pure plastic collapse (Sr = 1). The resultant plot, Fig. 36, shows that in all except two cases (R/r 1) the method is safe and that the highest safety factor is obtained in the brittle fracture region of the FAD. In BS 7910 and SINTAP allowance has not been made for the inherent level of conservatism of the FAD, further studies would be needed before this could be included in fitness-for-purpose analyses, discussed in Section 5.4. The resulting recommendations for partial safety factors to be applied to the best estimate (mean) values of maximum tensile stresses and flaw sizes, and to the characteristic (i.e. minimum specified) value of toughness and yield strength, are given in Table 8. It is emphasised that the partial safety factors will not always give the exact target reliability indicated but should not give a probability of failure higher than this target value, although this premis has been questioned(82). Additionally, there is no unique solution for partial safety factors and even when a preliminary separation is made into load and resistance groups there are still many alternative combinations of partial factors which could be applied to the separate input variables to give the same required target reliability. The most appropriate solutions are those for which the partial safety factors remain approximately constant over a wide range of input values. The ratios between the different factors should be primarily dependent on the relative COVs of the input data but, as noted in Reference (80), it was found that there was some effect of the absolute values of the some input variables. It has been suggested that a probabilistic assessment should be used in conjunction with the partial safety factor approach since the latter may not always give the target failure probability and where this is the case the results are likely to be unconservative(82). This is because the relationship between probability of failure and reserve factor depends on standard deviation of the variable and the position of the point in the FAD: Fig. 37 shows how the position of constant failure probability within the FAD varies with standard deviation in flaw size. It should be noted that the partial safety factors on fracture toughness are applicable to mean minus one standard deviation values as an approximate estimate of lowest of three. It is recommended that
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sufficient fracture toughness tests should be carried out to enable the distribution and mean minus one standard deviation to be estimated satisfactorily. 5.4
Model Uncertainty in the Failure Assessment Diagram
The relationship between partial safety factor and overall failure probability is linked directly to the variability and uncertainty of specific random data inputs and was studied in detail in Reference (80). Furthermore, the consequence of failure may also affect both the target reliability and the weighting given to the partial safety factors, given in Table 8 for BS 7910 recommended values without modelling uncertainty, to achieve this target reliability. These conservatisms may arise from a number of effects but under loading conditions similar to the dataset, the inherent conservatism can be considered as a modelling error. Including these modelling uncertainties in the calculations of partial factors leads to a modified set of safety factors where it is desired to remove these uncertainties and where they are known to be represented by conditions of the wide plate tests, given in Table 9(80). Typically, removal of the modelling uncertainty allows a reduction in the general recommended partial safety factors of the order of 0.05 to 0.1 on stress, and 0.2 to 1.0 on fracture toughness. It is noted in Reference (81) that incorporating the modelling uncertainty into such assessments reduced the failure probability by generally less than one order of magnitude and that any improvements are most likely at low failure probabilities and in the elastic-plastic (knee region and higher Lr values) region of the FAD, Table 10. Furthermore, the modelling uncertainty can be characterised by a three parameter Weibull distribution, although where there is confidence regarding the dominant region of the FAD then the appropriate factor for that region can be used. 5.5
Probabilistic Treatment of Failure Assessment Diagram
Probabilistic fracture mechanics is based on the concept that all or some of the input parameters for an FAD analysis contain inherent uncertainty, for example due to lack of detailed information, testing variation or material variability. The uncertainty in the data inputs manifests itself as an uncertainty in the resulting analysis point, and those due to uncertainty in flaw size and material toughness are generally considered to have the greatest effect on uncertainty of the final result. The most likely analysis point on the FAD, its associated statistical distribution and the relationship between these two aspects and the failure/no-failure boundary of the FAD enables the probability of failure to be determined for a given set of inputs and their distributions. MCS and FORM are the two most widely used methods for a reliability-based interpretation of the FAD. Various programs are available for automating the analyses, including TWI's FORM/MONTE program, British Energy's STAR6 program and the SINTAP consortium’s proSINTAP software: Within proSINTAP, the following parameters are treated as random parameters: Ÿ
Fracture toughness.
Ÿ
Yield strength.
Ÿ
Ultimate tensile strength.
Ÿ
Defect size given by NDE.
These random parameters are treated as not being correlated with one another and can follow a Normal, log-Normal, Weibull or exponential distribution. This and other software is covered in more detail in Section 7.
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6.
TARGET RELIABILITY LEVELS IN DIFFERENT CODES AND INDUSTRIES
6.1
Overview
Target reliability levels depend on the consequence and the nature of failure, the economic losses, the social loss or inconvenience, environmental consequence and the amount of expense and effort required to reduce the probability of failure. Target levels are usually calibrated against well-established cases that are known from past experience to have adequate reliability, although novel types of structure require formal approaches to define appropriate levels. The reliability index of a structure is often quoted rather than failure probability since there is a substantial difference between the notional probability of failure in the design procedure and the actual failure probability. Most codes apply the ALARP principle (As Low As Reasonably Practical) which recognises that in reliability the level of return of incremental safety improvement diminishes with increasing reliability. The process is therefore one of optimisation of safety and cost. 6.2
Quantifying Societal Consequence
One of the more qualitative aspects of reliability analysis is the estimation of consequences. Attempts to formalise this have only been partially successful due to the difficulty in assigning 'typical' scenarios and an unwillingness in some industries to be seen to assign any fatality as being an acceptable condition. The current convention of the HSE(2) is a benchmark value of ~£1m for the 'Value of a Statistical Life' (VOSL): This concept is usually interpreted as that which people are prepared to pay to secure a certain averaged risk reduction and equates to a reduction of individual risk of 1 x 10-5 being worth ~£10, it is not the value assigned to compensation for loss of life. Structural reliability is important first and foremost if people may be killed or injured as a result of collapse. In ISO 3294(83) it is suggested that an acceptable maximum value for the failure probability in those cases might be found from a comparison with risks resulting from other activities. Taking the overall individual lethal accident rate of 10-4 per year as a reference, a value of 10-6 seems reasonable to use. The maximum allowable probability of failure of the structure then depends on the conditional probability of a person being killed, given the failure of the structure(83): P(f | year) P(d | f) <10-6 year-1
. . . (1)
The probability P(d | f) is the probability that a person present in the structure at the time of failure is killed. If a building is seldom visited by human beings, a further reduction factor may be introduced in Equation (1) which gives a minimum requirement for human safety from the individual point of view. Since authorities explicitly want to avoid accidents where large numbers of people may be killed, the additional requirement in Reference (83) is of the type: P(f | year)
. . . (2)
where N is the expected number of fatalities. The number A and α are constants, for instance A = 0,01 or 0,1 and α = 2. Modifications of the numerical values are possible in special cases. A number of alternative methods have been proposed(5) for quantifying acceptable failure probability in the context of consequence, as defined by design life, number of people at risk, social criteria and potential of prior warning of failure. One such expression is given in as(84): Pft=1E-4 (Ks x nd)/nr
. . . (3)
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Where Ks is a social criterion varying from 0.005 for structures which pose a threat to general society to 5 for structures which do not affect the general public, nd is the design lifetime in years and nr is the number of people at risk. Alternatively, one expression has been developed which takes account of activity type (e.g. normal, high exposure) and warning factor(85): Pft= 1E-5 (A/W)nd x n-0.5
. . . (4)
Where A is an activity factor varying from 0.3 to 10 for low and high exposure structures respectively, and W is a warning factor varying from 0.01 for fail-safe conditions to 1.0 for failure modes which have no prior warning. It is however noted in Reference (5) that the use of such expressions is open to wide interpretation, they do not account for many other relevant issues and comparisons are difficult without specific information and the context of the calculation. For loading situations which occur with low frequency, such as earthquakes, the aim reliability level is generally lower. If this was not the case the cost of guaranteeing very low failure probabilities for events which are unlikely to occur would be prohibitively high. It is therefore recognised that the occupancy and functionality of buildings should be considered with the frequency of damaging event when defining safety levels for individual elements of buildings(86). 6.3
Treatment of Consequence in Three Major Codes
6.3.1
ISO 2394: General Principles on Reliability for Structures
ISO 2394(83) is a recently introduced (1998) standard, the remit of which is to provide a common basis for defining design rules relevant to the construction and use of the wide majority of buildings and civil engineering works. It is emphasised in this code that structural reliability is an overall concept comprising models for describing actions, design rules, reliability elements, structural response and resistance, workmanship, quality control procedures and national requirements, all of which are interrelated. The standard provides a full description of methods to be applied including models, limit state designs, probability-based design, partial safety factors approach and the assessment of existing structures. In the context of ultimate limit states, the following points are stated in ISO 2394: Ÿ
Consequences of failure are defined at three levels and incorporate economic, social and environmental consequences.
Ÿ
Failure is considered to occur by four methods:
(i)
an unfavourable combination of circumstances within normal use.
(ii)
exceptional but foreseeable actions (e.g. climatic).
(iii)
consequence of error or misunderstanding.
(iv)
unforeseen influences.
Ÿ
Any foreseeable scope of damage should be limited to an extent not disproportionate to the original cause.
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Ÿ
A consideration is given to durability by classification of the structure into one of four classes which have notional design working lives of 1-5 years, 25 years, 50 years or 100+ years.
Ÿ
The composition, properties and performance of materials, the shape and detailing of members and the quality/control of workmanship (fabrication) are considered key issues from a durability view.
Ÿ
From a probabilistic point of view, an element can be considered to have one single dominating failure mode. A system may have more than one failure mode and/or consist of two elements, each one with a single failure mode.
Probabilistic structural design is primarily applied to element behaviour and limit states (serviceability and ultimate failure). Systems behaviour is of concern because systems failure is usually the most serious consequence of localised component failure. It is therefore of interest to assess the likelihood of systems failure following an initial element failure. In particular, it is necessary to determine the systems characteristics in relation to damage tolerance or structural integrity with respect to accidental events. The element reliability requirements should depend upon the systems characteristics. Properties of materials should be described by measurable physical quantities and should correspond to the properties considered in the calculation model. Generally, material properties and their variability should be determined from tests on appropriate test specimens, based on random samples which are representative of the population under consideration. By means of appropriately specified conversion factors or functions, the properties obtained from test specimens should be converted to properties corresponding to the assumptions made in calculation models, and the uncertainties of the conversion factors should be considered. The recommended target reliability levels are a function of the relative costs of safety measures and the consequences of failure and are summarised in Table 11. For 'great consequences' the maximum acceptable probability of failure for the cases of high, moderate and low costs of implication of safety measures are 10-3, 7 x 10-5 and 10-5 respectively. The middle of these values is comparable with that implied in Eurocode 3. 6.3.2
Eurocode 3
Eurocode 3(87) for steel structures was published in 1993 although it is not yet in widespread use. A review of the partial safety factor and reliability levels associated with the material toughness requirements of this code(80) has demonstrated that a reliability approach has been used although there is disagreement within the EU on the underlying inputs used for this. Partial safety factors for live loads are higher than for permanent loads due to the increased uncertainty of the former. The target reliability index of EC3 Annex C (Fracture Avoidance) is 3.8, corresponding to a failure probability of 7 x 10-5.
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6.3.3
British Standard BS 7910
In BS 7910(77) the consequence of failure are defined as moderate, severe and very severe which, in combination with two levels of structural redundancy this gives six levels of target failure probability, Table 12: All values refer to probability of failure of individual components, the overall objective is to protect the complete structure against failure, accepting that it may be possible to tolerate local damage in some locations of redundant structures. In redundant structures, failure of a single component may be accommodated by alternative load paths and, although undesirable and expensive, it may be possible to make a case for a higher target probability of failure for such a component compared to a critical one which would cause complete failure. 'Moderate' consequences are interpreted as potential financial costs without threat to life. If failure is predicted to be by brittle fracture, which will by its nature occur without warning, the consequences should be interpreted as 'severe' or 'very severe'. In other respects, 'severe' consequences should be interpreted as any potential threat to human life and 'very severe' consequences as a potential threat to multiple lives. If failure is expected to be by plastic collapse and provided that there is no threat to human life, the consequences may be interpreted as 'moderate'. In order to achieve these reliability levels a system of partial safety factors is used in BS 7910 which, when used in combination for the data inputs, are intended to give a specific reliability level in the FAD analysis, Table 8. As scatter in material properties increases, COV increases, and a higher safety factor must be used to maintain the same failure probability. In addition to this type of material variability, the assessed state may be close to a mode change that could drastically alter material properties. In particular, the ductile-brittle transition may induce cleavage in an otherwise ductile process, and higher factors may be required in these conditions. One level of reliability can also be achieved through the use of different levels of partial safety factor and reliability is therefore not a unique value in this respect. There are many other circumstances listed in BS 7910 that might lead to the requirement for increased reserve factors: Ÿ
The true loading system has to be simplified or assumptions have to be made in order to analyse the component.
Ÿ
The non-destructive examination capabilities are indistinct.
Ÿ
Flaw characterisation is difficult or uncertain.
Ÿ
The assessed loading condition is frequently applied or approached.
Ÿ
Little pre-warning of failure is expected, forewarning being likely in cases of ductile failure.
Ÿ
There is a possibility of time dependent effects (fatigue, creep, corrosion).
Ÿ
Changes of operational requirements are possible in the future.
Ÿ
The consequences of failure are unacceptable.
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6.4
Comparison of Target Reliability Levels in Different Industries
In the context of what constitutes an acceptable level of risk, it is accepted(88) that the likelihood of failure due to the coincidence of under strength material, constructional inaccuracies, and overloading is acceptably small, and by 'acceptable' it is meant that the frequency of occurrence should not be greater than it has been in the recent past. The public acceptance of risk over which they have a choice is different to that over which they do not, just as a service which is paid for (e.g. air travel) carries with it a duty of care which voluntary risk taking (car travel, leisure) does not. The definition of appropriate target reliability levels is therefore a difficult area and must be made with consideration of: Ÿ
Level of choice over whether to take risk.
Ÿ
Consequences (societal, environmental, financial).
Ÿ
Structural redundancy level.
Ÿ
Prior warning of failure.
In addition, the appropriate measure of failure probability must be considered, for example, reliability over planned life span, reliability per year, per inspection interval or per operating unit (/km/year in the case of pipelines). The conventional approach to reliability-based code development is to calibrate them against existing practice and implied levels of structural safety. This is summarised in Fig. 38(5), following an iterative procedure to define the required combination of partial safety factors deemed sufficient to achieve a specific target reliability index (β), and hence maximum aim failure probability. However, this approach has limitations in terms of accounting for human factors, and in the past has been subject to a certain amount of fitting (known as the 'gap factor') to ensure consistency with existing codes(88). For new or novel structures, the method may not be appropriate and a more structured analysis addressing all credible failure modes may be needed. An example of this was the move to floating offshore structures where neither existing codes for fixed platforms, nor classification society rules for ships, were considered appropriate(89). Similarly, target reliability can also be re-defined for existing structures in circumstances including: Ÿ
Change of use, including increased load requirements.
Ÿ
Concern about design or construction errors.
Ÿ
Concern over quality of materials and workmanship.
Ÿ
Effects of deterioration.
Ÿ
Damage following and extreme loading event (storm or earthquake).
Ÿ
Concern over serviceability.
In these cases, load factors may have increased but very often the additional information gathered during the life of the structure can be used for reliability updating using Bayes' theorem(90), thus offsetting the effect of increased loadings or decreased resistance on calculated reliability.
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A comparison of target reliability levels and corresponding maximum acceptable failure probabilities defined for various consequences in different structures is given in Table 13, and summarised in Fig. 39. For the three codes ISO 2394, BS 7910 and EC3, there is reasonable agreement that the aim acceptable probability of failure for a structural element is 7 x 10-5 for 'severe' consequence and 1 x 10-5 for 'very severe' consequences. For ships, failure probabilities vary between 10-5 and 10-3 depending on failure mode and consequence, while for FPSO and TLP (Tension Leg Platform) floating structures 10-4 is generally adopted. The UK offshore target is 10-4, and is similar to mean aim values for API and DNV offshore codes. Building codes have variable target levels depending on materials of construction, occupancy and loading modes (dead, live, wind, snow, earthquake loads) but are as low as 5 x 10-2 for survivability in earthquakes. Pipeline reliability depends on nature of medium (gas or oil), whether the line is off- or onshore, and in the latter case on population density. For onshore gas lines, target maxima are typically 10-4 to 10-6 per km per year. The nuclear industry has one of the highest general target reliability levels of any industry (β = 5.2), giving a target maximum probability of 10-7. 7.
SOFTWARE FOR RELIABILITY ANALYSIS
7.1
Scope
Reliability analysis software is available for general applications in which any failure mode can be addressed using the appropriate limit states, and for fracture-specific applications. Validation of such software is usually carried out by benchmark exercises between different programs since it is not feasible to compare results with real failure statistics. A summary of all the software reviewed is given in Table 14, and structure of the different programs where available is given in Appendix 1. 7.2
STRUREL
STRUREL (STRUctural RELiability) is a general purpose reliability software series that has been developed to perform computational tasks in a windows environment and using the most recent theoretical findings. It is owned and developed by Reliability Consulting Programs GmbH, based at the University of Munich (http:www.strurel.de). It comprises several independent but interrelated programs: STATREL: Statistical analysis of data, simulation, distribution fitting and analysis of time series. COMREL:
Time-invariant and time-variant analysis of component reliability.
SYSREL:
Reliability analysis of systems.
NASCOM:
Finite element code for structural analysis.
NASREL:
Module combining COMREL with NASCOM.
STATREL enables appropriate distributions to be derived for datasets input from e.g. spreadsheets. Goodness of fit tests are also included to demonstrate the best fitting method to be used. COMREL comprises 44 models and limit state equations can be input for failure modes not addressed. It includes MCS, FORM and SORM methods, and in the case of the time-variant version includes methods for incorporating random and point-in-time events. SYSREL enables multiple failure criteria
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for parallel and series systems to be evaluated, including conditional events. It links directly with COMREL, making it straightforward to check individual failure criteria before combining them in a system analysis. STRUREL has applications in many fields and many examples of its use for fracture, fatigue, collapse, corrosion and general strength problems exist. A joint industry project is planned for 2001 in which a variety of reliability problems will be assessed using STRUREL as a benchmarking exercise in comparison with other software(97). 7.3
ProSINTAP
ProSINTAP (PRObabilistic Structural INTegrity Assessment Procedure) automates MCS and FORM analysis of the failure assessment diagram and is only applicable to fracture and collapse failure modes(13,98). It consists of five input decks: Ÿ
Geometry.
Ÿ
Loading.
Ÿ
Material.
Ÿ
NDE (Non-Destructive Evaluation).
Ÿ
Analysis.
The Geometry section comprises stress intensity factor solutions for a range of plate and cylinder geometries with surface and through-thickness cracks. The load module enables through-thickness distributions of applied and welding residual stress to be incorporated. In the material module, yield strength, UTS and fracture toughness and their associated statistical distributions are input. This requires the mean and standard deviation of each parameter as defined by the Normal, Log-Normal or Weibull distribution. The NDE module enables defect sizing data to be input, but also allowing for treatment as an exponential distribution. The Analysis module enables the user to select MCS or FORM methods and to apply partial safety factors if required in order to achieve a specified target reliability method. Validation of the software was carried out within the SINTAP project by comparison with software from British Energy (STAR 6 program) and UMIST (UMFRAP program). Pro SINTAP currently has the following limitations: Ÿ
Embedded defects are not included.
Ÿ
Probability Density Functions for input parameters are considered to be independent; i.e. there is no facility for cross-correlating a yield strength distribution and a fracture toughness distribution.
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Ÿ
Only element failure probabilities are calculated: system reliability and the effect of element failure on failure of a subsequent element is not included.
7.4
CALREL
CALREL (CALibration of RELiability) is a general purpose program for structural reliability analysis using MCS, FORM and SORM for components and systems. It was developed and is owned by the University of Berkeley California (http://socrates.berkeley.edu/~otl/CALREL.html). It contains a large library of probability distributions for independent and dependent variables and has facilities for sensitivity analysis, limit state functions are input by a user-defined subroutine. 7.5
PROBAN
PROBAN (PROBabilistic ANalysis) is a general reliability program developed by DNV and forms part of their hydrodynamic and structural analysis software SESAM (http://www.dnv.com/software). FORM, SORM and MCS are included, as is sensitivity analysis and reliability updating. It can be used to analyse several different failure modes simultaneously, to determine conditional probabilities, for cost optimisation and to derive partial safety factors. 7.6
COMPASS
COMPASS (COMPuter Methods for Probabilistic Analysis of Structures and Systems) is a general purpose program developed by Martec Ltd. (Canada). It includes a library of failure modes, data distribution characterisation, component and system analysis and a link to finite element outputs. Limit states not covered can be input as user-defined sub-routines. FORM, SORM, MCS and MCS-IS are included. 7.7
NESSUS
NESSUS (Numerical Evaluation of Stochastic Structures Under Stress) was originally developed for the US defence industry by NASA. It automates FORM, SORM and MCS, but its main strength lies in its ability to interface with finite element and boundary element codes (Including ABAQUS and Patran). It includes a number of 2 and 3 dimensional elements in the geometry library and can account for large non-linearity of material behaviour. Random variables include geometry, loads, material properties and motions such as vibration and oscillation. It is currently being developed by the Southwest Research Institute in Texas (http://www.swri.org) although emphasis is on aerospace applications, particularly creep performance of engine components. 7.8
ISPUD AND COSSAN
ISPUD (Importance Sampling Procedure Using Design Points) is based on importance sampling methods, with time-dependency handled via definition of extreme values. COSSAN (Computational Stochastic Structural ANalysis) uses third-party finite element cases with MCS and MCS-IS. Both are owned and developed by the University of Innsbruck, Austria (http://info.uibk.ac.at). 7.9
STAR 6
STAR 6(99) is British Energy’s reliability software for automating reliability analyses of the fracture and collapse analysis procedure R6(19). It is similar in approach to proSINTAP and includes FORM and MCS, but a more extensive library stress intensity factor solutions for different component geometries is included. proSINTAP has been validated against STAR 6(19).
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7.10
UMFRAP
UMFRAP is an in-house code developed by UMIST (Manchester, UK) for reliability assessment of the failure assessment diagram. It has been used for the determination of partial safety factors for use in BS 7910 but is not used outside UMIST at present. 7.11
FORM and MONTE
FORM and MONTE automate probabilistic level 2 FAD analysis based on the predecessor to BS 7910, using FORM and MCS methods respectively. They were developed as part of a TWI group-sponsored project and were made available to the project sponsors. Both programs are DOS based and have now been largely superseded. Figure 31 was constructed using the MONTE program. 8.
FURTHER DEVELOPMENT OF PROBABILISTIC METHODS
8.1
Generic Methods
Ÿ
Interaction of failure modes to more accurately reflect real materials' behaviour.
Ÿ
Use of methods for optimisation (of material properties, cost etc.) rather than definition of failure probability(100).
Ÿ
Standardisation of consequence scenarios and definitions to enable uniformity of risk analysis in different structures.
Ÿ
More use of time-dependent reliability analysis: e.g. definition of parameters in the fatigue crack growth or stress corrosion crack growth laws as random parameters and probabilistic definition of time to failure.
Ÿ
Use of reliability updating for analysis of service-proven structures throughout life.
Ÿ
Benchmarking of methods, software and industry approaches; Round-robin activities involving different establishments analysing the same set of problems with different methods, distribution fits and software; Industrial networks on reliability analysis such as Asranet(101).
8.2
Failure Assessment Diagrams
Ÿ
Facility to assess embedded flaws.
Ÿ
Facility to account for material degradation with time (e.g. irradiation embrittlement, hydrogen effects).
Ÿ
Realistic defect distributions related to quality and capability of NDE used.
Ÿ
Secondary stresses defined as random variables, accounting for variation in measured values or effects of material properties (e.g. weld metal yield stress) used to estimate them.
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Ÿ
Fracture toughness distributions determined from distributions of Charpy impact energy using the Master-Curve correlation method.
Ÿ
Facility to account for effects of weld strength mismatch as random distribution based on distributions of yield strength of parent plate and weld metal.
Ÿ
Facility for determining significance and relevance of MOTE (minimum of three equivalent) fracture toughness values for datasets of varying size.
8.3
Distributions of Material Properties
Ÿ
Covariance of property distributions, particularly strength and toughness since these usually show a negative correlation and the probability of low toughness occurring simultaneously with low strength for a given material is low.
Ÿ
Facility to use truncated property distributions, which remove the lower tail of e.g. yield stress distributions where a Normal fit would give a yield stress below the minimum specification value for a given grade.
Ÿ
Increasing demand will be placed on materials suppliers to provide information relating to the statistical distributions of mechanical properties.
8.4
Reduction of Data Uncertainty
Ÿ
Linking of structural health monitoring (strain, fatigue, pressure gauges) to provide real-time snapshot of instantaneous reliability rating; over time, the reliability trend can be established showing effects of e.g. increased loading, increased fatigue damage.
Ÿ
Use of so-called 'Smart Techniques' (Neural networks, fuzzy logic, genetic algorithms) to extract structural response profiles from noisy health monitoring data obtained from actual structure.
Ÿ
Risk consideration as a primary input in structure/equipment design will become more widespread and designing for inspectability to assess degradation by many different failure modes will become increasingly important.
9.
CONCLUSIONS
Changes in legislation, the trend to life extension and increasing computing power have led to an increase in the use of reliability methods in many industrial sectors. The advantages of these approaches are that overdesign can be avoided, uncertainties can be handled in a logical way, sensitivity to variables assessed, materials' selection optimised and a more rational basis for decision making followed. Risk is most commonly defined as the product of probability of occurrence and consequence: Probability of failure is usually quantified per year or over the full lifetime, whereas consequence is usually qualitative and defined as societal, environmental or financial. Levels of acceptable risk are defined by safety regulatory bodies and are usually classified as 'tolerable', 'intolerable', or a region in between where risk must be reduced to 'As low as reasonably practical'. The fundamental concept for reliability analysis is that resistance and load factors are statistical quantities with a central tendency (mean), dispersion about the mean (variance) and some form of
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distribution. When combined together via an expression to describe the limit state there will be a finite probability that the load will exceed the resistance; this defines the probability of failure (Pf ) and since reliability is equal to 1-Pf , the inherent reliability of the component against a particular failure mode, and with given resistance properties, is defined. First Order Reliability Method (FORM) and Monte-Carlo Simulation (MCS) are the most common basic techniques and are applicable to all probabilistic problems. Of these, FORM is usually the preferred method as it does not depend on the number of simulations carried out. For complex limit states, FORM may not converge and an answer not be obtained. In these cases MCS is used but a large number of simulations must be made when failure probability is low, thus requiring extended computing time. The methods have been extensively applied in the Nuclear, offshore, rail, shipping, aerospace, bridge, building, process plant and pipeline industries. Failure processes addressed include fracture, collapse, fatigue, creep, corrosion, bursting, buckling, third party damage, stress corrosion and seismic damage. Advantages of a reliability approach have been demonstrated in the areas of life extension of reactor pressure vessels, inspection scheduling of offshore structures, cost-benefit analysis for NDE inspection of rails, design of fatigue sensitive ship structures, definition of inspection intervals for steel bridges, design of buildings and bridges in earthquake zones and pressure uprating of pipelines. The Failure Assessment Diagram (FAD) remains the standard approach for deterministic and probabilistic structural integrity assessment. This method forms the basis of the R6, BS 7910 and SINTAP methods. It contains an inherent safety factor which varies depending on position within the FAD and although this has been quantified it has not yet been incorporated in any procedure. A number of standards provide recommended maximum aim probability of failure levels (i.e. a target reliability). The levels generally depend on the reliability of the input data, the consequences of failure and the cost of reducing the risk. Acceptable maximum failure probabilities in accordance with many different structures, industries and consequences have been reviewed: An aim maximum failure probability of 7 x 10-5 for 'severe' consequences and 1 x 10-5 for 'very severe' consequences seems to be common to several types of structure. Reliability analysis software is available for general applications in which any failure mode can be addressed using the appropriate limit states. STRUREL (STRUctural RELiability) is a general purpose reliability software family that has been developed to perform computational tasks in a user-friendly windows environment and using the most recent theoretical findings. Owned and developed by Reliability Consulting Programs GmbH, STRUREL appears to be the most likely used due to its modular format and balance between cost and functionality. Other general purpose software either forms part of more expensive suites or is developed by academic institutions without considering commercialisation. For fracture-specific applications, ProSINTAP (PRObabilistic Structural INTegrity Assessment Procedure) automates MCS and FORM analysis of the failure assessment diagram and is applicable to fracture and collapse failure modes. It has been fully validated but has limitations in terms of range of geometries and flaw types. Star 6 (British Energy) performs similar calculations but with a more extensive geometry library. Refinement of calculations of risk can be made throughout a structure's lifetime: 'Reliability updating' coupled with structural health monitoring with sensors enables real-time reliability status to be defined. the use of so-called 'Smart Techniques' to extract structural response profiles from noisy health monitoring data obtained from the actual structure will facilitate this.
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Risk consideration as a primary input in component/structure design will become more widespread and designing for inspectability to assess degradation by different failure modes, and repair where necessary, will become increasingly important. Materials suppliers will be increasingly required to provide data on distributions of mechanical properties. Future developments include design and material selection optimisation through reliability methods, interaction of failure modes to more accurately reflect real materials' behaviour, standardisation of consequence scenarios, increased use of time-dependent reliability analysis, benchmarking of methods and software, and more advanced treatment of property distributions (covariance and truncation). Finally, it is noted that by carrying out reliability analyses, the chances of failure are not altered but they are clarified. A.C. Bannister Knowledge Group Leader S.E. Webster Manager Transport Applications Department REFERENCES 1.
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P. Massarelli and T. Barber: 'Fatigue Lifetime Prediction of Steel Bridge Details', Proc. 7th Speciality Conference on 'Probabilistic Mechanics and Structural Reliability', ASCE, Massachusetts, 1996.
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A.C. Bannister: 'Reliability Basis of Toughness Requirements for Sections Under Seismic Loading', Corus UK Limited, Asranet 2nd Annual Collarium, 9 July 2001, RINA, London, 2000.
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M.A. Bonello and M.K. Chryssanthopoulos: 'Buckling Analysis of Plated Structures Using System Reliability Concepts', Proc. 12th Offshore Mechanics and Arctic Engineering Symposium, 1993, Vol. II.
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P.K. Das, D. Faulkner and R.A. Zimmer: 'Efficient Reliability Based Designs of Ring and Stinger Stiffened Cylinders under Combined Loads', Proc. 6th Intl. Conf. on 'Behaviour of Offshore Structures', BBP Technical Services Ltd., London, Vol. 1, pp180-193.
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API Committee on Refinery Equipment: 'Risk-Based Inspection - Base Resource Document', 1996, API 587.
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61.
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P. Hopkins and J. Haswell: 'Practical Assessment Methods for Application to UK Gas Transmission Pipelines', The Institute of materials 2nd Griffifth Conference, 'Mechanisms of Fracture and their Structural Significance', The Institute of Materials, September 1995.
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Anon: 'Interstate Natural Gas Pipelines - Delivering Energy Safely:' Interstate Natural Gas Association of America.
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T.J.E. Zimmerman, A. Cosham, P. Hopkins and N. Sanderson: 'Can Limit States Design be Used to Design a Pipeline Above 80% SMYS', Proceedings Intl. Symp. 'Offshore Mechanics and Arctic Engineering', OMAE 1998, ASME.
71.
R.W. Warke, C. Ferregut, A.G. Glover and D.J. Horsley: 'A Reliability-Based Method for Assessing the Fitness-for-Service of Pipeline Girth Welds', PRCI-EPRG, 11th Biennial Joint Technical Meeting, Arlington, Virginia, 1997.
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41
SL/WEM/R/M8663/5/01/C
TABLE 1 SELECTED RISKS FOR CERTAIN ACTIVITIES IN SOCIETY (5) Approximate Death Ratea Typical Exposureb Typical Risk of Death (x (x 10-9 Deaths/h Exposure) (h/year) 10-6/year) (Rounded)
Activity Alpine Climbing
30000 - 40000
50
1500 - 2000
Boating
1500
80
120
Swimming
3500
50
170
Cigarette Smoking
2500
400
1000
Air Travel
1200
20
24
Car Travel
700
300
200
Train Travel
80
200
15
Coal Mining (UK)
210
1500
300
70 - 200
2200
150 - 440
20
2000
40
1-3
8000
8 - 24
0.02
6000
0.1
Construction Work Manufacturing Building Fires
c c
Structural Failures
a
b
Adapted from Allen (1968) and CIRIA (1977) For those involved in each activity (estimated values) c Exposure for average person (estimated)
TABLE 2 BROAD INDICATORS OF TOLERABLE RISK(5) Risk of Death/person/year
Characteristic Response
10-3
Uncommon accidents; immediate action is taken to reduce the hazard
10-4
People spend money, especially public money to control the hazard (e.g. traffic signs, police, laws)
10-5
People are warned of hazard (e.g. fire, drowning, firearms, poisons) also air travel avoidance
10-6
Not of great concern to average person; aware of hazard, but not of personal nature; act of God
42
SL/WEM/R/M8663/5/01/C
TABLE 3 TYPICAL COLLAPSE FAILURE RATES FOR BUILDINGS AND STRUCTURES(5)
Structure Type
Data Cover
Number of Average Estimated Lifetime Life Structures (Pf ) (Estimated) (Years)
Denmark
5 x 106
30
3 x 10-7
The Netherlands (1967 - 1968)
2.5 x 106
-
5 x 10-4
Australia (New South Wales)
145500
-
10-5
Mixed Housing
Canada
5 x 106
50
10-3
Engineered Structures
Canada
-
-
10-4
USA (<1900)
-
40
10-3
World (1900 - 1960)
55
40
3 x 10-3
Cantilever and Suspended Span Bridge
USA
-
-
1.5 x 10-3
All Bridges
USA
-
-
10-3
All Bridges
Australia
-
-
10-2
Apartment Floors Mixed Housing Controlled Domestic Housing
Steel Railway Bridge Large Suspension Bridge
TABLE 4 HIERARCHY OF RELIABILITY METHODS(5) Level 1: Code Level Methods 2: 'Second Moment Methods'
3: 'Exact Methods'
4: Decision Methods
Calculation Methods
Probability Distributions
Limit State Functions
Uncertainty Data
Calibration to existing code rules using level 2 or 3
Not used
Linear functions (usually)
Arbitrary factors Partial factors
Second moment algebra
Result
Normal Linear, or May be included 'Nominal' distributions approximated as second failure only as linear moment data probability PfN
Related to Transformation Linear, or equivalent May be included numerical approximated normal as random integration and as linear any distributions variables simulation form fully used
Failure probability Pf
Any of the above, plus economic data
Minimum cost, or maximum benefit
43
SL/WEM/R/M8663/5/01/C
TABLE 5 VARIABLES AND DISTRIBUTIONS FOR YIELD/TENSILE RATIO ANALYSIS OF PIPELINES(7) Variable
Nominal Mean/Nominal
COV (%)
Distribution
Yield Stress (MPa)
483-542
1.10
3.5
Normal
Flow Stress (MPa)
527-556
1.17
4.0
Normal
Pipe Diameter (mm)
914
1.00
-
Wall Thickness (mm)
11.8
1.01
1.0
Circumferential Flaw Model Error (Multiplicative)
1.35
1.00
-
Deterministic
Circumferential Flaw Model Error (Additive)
0.34
1.00
71.0
Shifted Lognormal
Axial Flaw Model Error (Multiplicative)
1.13
1.00
14.0
Lognormal
Circumferential Surface Flaw Depth (mm)
1-2
1.00
60.0
Weibull
Circumferential Surface Flaw Length (mm)
100
1.00
60.0
Lognormal
Longitudinal Surface Flaw Depth (mm)
1-2
1.00
60.0
Weibull
Longitudinal Surface Flaw Length (mm)
1-2
1.00
60.0
Lognormal
44
Deterministic Normal
SL/WEM/R/M8663/5/01/C
TABLE 6 TYPICAL MODELLING UNCERTAINTIES(11) Item
Cov VXm (%)
Bias ζ Xm (%)
Factors affecting strength Flat panel collapse - best
10 - 15
-5 to 5
- typical codes
15 - 30
0 to 20
20 - 40
20 to 50(1)
Stiffened cylinders - best
12 - 18(2)
-20 to 40(1)
- typical codes
20 - 40(2)
0 to 30(1,3)
Unstiffened cylinder - codes
Submarine pressure hull - interframe collapse
5 - 10
-5 to 5
- general instability
15 - 20
0 to 20
30 - 70
50 to 150(4)
Fatigue strength
Factors affecting loads Dead loads
5 - 10
Live loads
10 - 20
-10 to -30(5)
Ship extreme bending
Notes:
- initial distribution
5 - 10
- extreme distribution
15 - 25
-30(6) to 0
Fixed offshore platforms
20 - 40
-10 to 10(7)
Compliant offshore platforms
15 - 30
-20 to 50(8)
Fatigue loads
10 - 20
-20 to 0
(1) (2) (3) (4) (5) (6) (7) (8) COV
'lower bound' curves are mainly used for all load combinations there are some much more extreme examples large scatter on life predictions no reliable data available but 'growth factor' essential relates to overprediction of Linear Strip Theory based on Morrison based on diffraction modelling studies Co-efficient variation = standard deviation/mean (%)
45
SL/WEM/R/M8663/5/01/C
TABLE 7 TYPICAL CHARACTERISTICS OF STRENGTH RANDOM VARIABLES FOR SHIP STRUCTURE ANALYSIS(41) Statistical Information
(Bias) or Error Information
Random Variable
Nominal Value
Thickness t
t
0
0.02
normal
Plate Size a
a
0
0.11
normal
Plate Size b
b
0
0.09
normal
Ship Length L
L
0
0.08
normal
Ship Depth D
D
0
0.01
normal
Ship Breadth B
B
0
0.01
normal
Ordinary Strength Fy
Fy
1.11 Fy
0.07
lognormal
(1.11)
High Strength Fy
Fy
1.22 Fy
0.09
lognormal
(1.22)
Fu
Fu
1.05 Fu
0.05
normal
(1.05)
E
E
1.024E
0.02
normal
(1.03)
Poisson Ration v
0.3
0.3
0
Section Modulus Z
Zr
1.04 Zr
0.05
lognormal
(1.04)
My
Fy Z
F yZ
0.15
lognormal
(1.0)
Mp
Fy Zp
F yZ
0.18
lognormal
(1.0)
c
na
0.74
0.2
normal
(na)
Mean
COV
Distribution Standard Distribution Mean Type Deviation Type
(1)
na = not available, Mp = plastic moment, Zp = plastic Z, Zr = rules Z
46
SL/WEM/R/M8663/5/01/C
TABLE 8 RECOMMENDED PARTIAL SAFETY FACTORS FOR DIFFERENT TARGET RELIABILITIES AND VARIABILITY OF INPUT DATA BASED ON FAD(76,80) p(F) 2.3 x 10-1
p(F) 10-3
p(F) 7 x 10-5
p(F) 10-5
β = 0.739
β = 3.09
β = 3.8
β = 4.27
Stress
(COV) s
γσ
γσ
γσ
γσ
Extreme
0.1
1.05
1.20
1.25
1.30
Dead + Res
0.2
1.10
1.25
1.35
1.40
Live
0.3
1.12
1.40
1.50
1.60
(COV) a
γa
γa
γa
γa
0.1
1.00
1.40
1.50
1.70
0.2
1.05
1.45
1.55
1.80
0.3
1.08
1.50
1.65
1.90
0.5
1.15
1.70
1.85
2.10
(COV) K
γΚ
γΚ
γΚ
γΚ
0.1
1.00
1.30
1.50
1.70
0.2
1.00
1.80
2.60
3.20
0.3
1.00
2.85
NP
NP
(COV) d
γδ
γδ
γδ
γδ
0.2
1.00
1.69
2.25
2.89
0.4
1.00
3.20
6.75
10.00
0.6
1.00
8.00
NP
NP
Yield Strength
(COV) M
γΜ
γΜ
γΜ
γΜ
(on min. spec.)
0.1
1.00
1.05
1.10
1.20
Flaw Size
Toughness Κ (min. of 3) Toughness δ (min. of 3)
Notes: γσ is a multiplier to the mean stress of a normal distribution γa is a multiplier to the mean flaw height of a normal distribution γΚ or γδ are dividers to the mean minus one standard deviation value of fracture toughness of a Weibull distribution γΜ is a divider to the mean minus two standard deviation value of yield strength of a log-normal distribution COV = Co-efficient of variation (= standard deviation/mean)
46
SL/WEM/R/M8663/5/01/C
TABLE 9 RECOMMENDED PARTIAL SAFETY FACTORS FOR DIFFERENT TARGET RELIABILITIES AND VARIABILITY OF INPUT DATA BASED ON FAD WITH MODELLING UNCERTAINTY INCLUDED(80) p(F) 2.3 x 10-1
p(F) 10-3
p(F) 7 x 10-5
p(F) 10-5
β = 0.739
β = 3.09
β = 3.8
β = 4.27
Stress
(COV) s
γσ
γσ
γσ
γσ
Extreme
0.1
1.05
1.14
1.20
1.25
Dead + Res
0.2
1.1
1.20
1.28
1.35
Live
0.3
1.12
1.30
1.41
1.50
(COV) a
γa
γa
γa
γa
0.1
1.00
1.4
1.5
1.7
0.2
1.05
1.45
1.55
1.8
0.3
1.08
1.5
1.65
1.9
0.5
1.15
1.7
1.85
2.1
(COV) K
γΚ
γΚ
γΚ
γΚ
0.1
1
1.2
1.4
1.5
0.2
1
1.5
2.2
2.6
0.3
1
2.2
NP
NP
(COV) d
γδ
γδ
γδ
γδ
0.2
1
1.44
1.96
2.25
0.4
1
2.25
4.84
6.76
0.6
1
4.84
NP
NP
Yield Strength
(COV) M
γΜ
γΜ
γΜ
γΜ
(on min. spec.)
0.1
1
1.05
1.1
1.2
Flaw Size
Toughness Κ (min. of 3) Toughness δ (min. of 3)
Notes: γσ is a multiplier to the mean stress of a normal distribution γa is a multiplier to the mean flaw height of a normal distribution γΚ or γδ are dividers to the mean minus one standard deviation value of fracture toughness of a Weibull distribution γΜ is a divider to the mean minus two standard deviation value of yield strength of a log-normal distribution COV = Co-efficient of variation (= standard deviation/mean)
47
SL/WEM/R/M8663/5/01/C
TABLE 10 EFFECT OF MODELLING UNCERTAINTY ON FAILURE PROBABILITY ESTIMATES IN DIFFERENT REGIONS OF FAD(80) Failure Probability (Pf ) FAD Region
No Modelling Uncertainty (Mu = 0)
Region Specific Uncertainty
General Uncertainty
1: (Fracture Dominated)
5.94E-2
1.61E-3
1.53E-2
2: (Elastic-Plastic)
1.06E-2
4.40E-3
2.72E-3
2.35E-2
†
3.73E-3†
3: (Collapse Dominated) †
5.16E-3
Results from MONTE, analysis using FORM did not converge TABLE 11 TARGET RELIABILITY INDICES (β) OF ISO 2394
Relative Costs of Safety Measures High Moderate Low
Consequence of Failure Small 0
Some
0 (10 )
A 1.5
1.3 (10-1) 2.3 (10-2)
Moderate
Great
-2
2.3 (10 )
B 3.1 (10-3)
3.1 (10-3)
C 3.8 (7 x 10-5)
2.3 (10-2) 3.1 (10-3) 3.8 (7 x 10-5)
4.3 (10-5)
( ) = Equivalent failure probability for each β value. Suggestions for Cases A, B, C in ISO 2394 are. A:
For serviceability limit states, use β = 0 for reversible and β = 1.5 for irreversible limit states.
B:
For fatigue limit states, use β = 2.3 to β = 3.1, depending on the possibility of inspection.
C:
For ultimate limit states design, use β = 3.1, 3.8 and 4.3. TABLE 12 MAXIMUM TARGET FAILURE PROBABILITIES FOR DIFFERENT FAILURE CONSEQUENCES IN ACCORDANCE WITH BS 7910 Target Probability of Failure (Events/Year) Failure Consequences Redundant Component Non-Redundant Component Moderate
2.3 x 10-1
10-3
Severe
10-3
7 x 10-5
Very Severe
7 x 10-5
10-5
48
SL/WEM/R/M8663/5/01/C
TABLE 13 TARGET RELIABILITY AND Pf VALUES IN VARIOUS INDUSTRIES Application
Reference
General Structures: ISO2394
(83)
EC3: Bridges and Buildings
(87)
BS7910: Fracture
(77)
Tanker Ships, Ultimate Limit States
(91)
North Sea TLP
(89)
FPSO
(44)
API RP2A
(89)
DNV Rules
(89)
UK Offshore UK Steel Bridges
(92) (93) (89)
USA Building Codes (94)
Tanker ships and Military Ships [Shown as ( )] for Fatigue Limit States
(91)
Pipelines in USA
(70)
Pipelines in Netherlands
(95)
HSE Pipeline Requirements
(71)
Offshore Pipelines
(96)
Nuclear RPVs
(22)
Conditions and Consequences Moderate consequence/low cost of mitigation Great consequence/low cost of mitigation Great consequence/high cost of mitigation Ultimate limit state with major consequences Severe consequence, non-redundant structure Very severe consequence, non-redundant structure Primary structure (hull) Secondary structure (stiffened panels between bulkheads) Tertiary structure (plates) Very serious consequences Secondary structures Primary structures Hull girder strength Mean Min. Mean Min. Overall structural average target Overall structural average target Ordinary buildings Temporary buildings Earthquake design (given earthquake occurs) Earthquake failure (annual) Cat 1: fatigue crack has little effect on safety/crew/environmental Cat 2: fatigue crack not of immediate danger but repair costly Cat 3: fatigue crack compromises safety, severe economic and environmental consequences Hull girder collapse Average North American (oil and gas) Gas pipeline, moderate population density Gas pipeline, remote areas Onshore, gas Dangerous gas leaks Leaks in areas with schools/hospitals
Target Reliability Aim maximum Index (β) Failure Probability 3.8
7 x 10-5
4.3 3.1
1 x 10-5 1 x 10-3
3.8
7 x 10-5
3.8
7 x 10-5
4.3
1 x 10-5
4.0
2 x 10-5
3.0
1 x 10-3
2.5 3.5 3.0 3.7 3.5 3.3 1.9 3.6 2.8 3.7 4.8 3.0 2.5
6 x 10-3 2 x 10-4 1 x 10-3 1 x 10-4 2 x 10-4 3 x 10-4 2 x 10-2 1 x 10-4 2 x 10-3 1 x 10-4 1 x 10-6 1 x 10-3 6 x 10-3
1.8
5 x 10-2 (per event)
4.0
2 x 10-5 (per year)
2.0 (2.5)
2 x 10-2 (6 x 10-3)
2.5 (3)
6 x 10-3 (1 x 10-3)
3.0 (4)
1 x 10-3 (2 x 10-5)
4.0 (5) 3.7 4.3 3.7 4.7 4.7 5.2
2 x 10-5 (2 x 10-7) 1 x 10-4 (/km/yr) 1 x 10-5 (/km/yr) 1 x 10-4 (/km/yr) 1 x 10-6 (death/yr) 1 x 10-6 1 x 10-7 1 x 10-2 - 1 x 10-3 (/km/yr) 1 x 10-5 - 1 x 10-6 (/km/yr) 1 x 10-7 (/yr)
Serviceability limit state
2.3 - 3.1
Ultimate limit state
4.2 - 4.7
Incredibility of Failure event
5.2
49
TABLE 14 SUMMARY OF VARIOUS GENERAL PURPOSE AND FRACTURE SPECIFIC SOFTWARE
47
Owner/Developer
Application
Methods
Main attributes/advantages
STRUREL
RCP/University Munich (Germany)
General + FE
All
Component and system, time-variant and invariant, wide user experience
CALREL
University Berkeley (USA)
General Links to FE
All
Library of probability density functions. Facilities for sensitivity analysis, Interface to FE
PROBAN
DNV (Norway)
General (Offshore/ships)
All
Component and System reliabilities. Reliability updating, multiple simultaneous failure modes, conditional probability, links to SESAM
COMPASS
Martec Ltd. (Canada)
General +FE
All
Library of failure modes. Links to FE
NESSUS
Southwest Research Institute (USA)
General +FE (Aerospace)
All
Includes FE interface. Many random variables. Extensively used for creep analysis
ISPUD
University Innsbruck (Austria)
General
MCS-IS
System reliability. Suitable for high non-linearity where FORM would not converge to a solution
COSSAN
University Innsbruck (Austria)
General +FE
MCS-IS
Specifically aimed at design of structures to meet certain target reliabilities
proSINTAP
DNV (SAQ)/SINTAP Consortium (Sweden/EU)
Fracture/collapse
MCS and FORM
Emphasis on material property and flaw size as random variables. Stresses treated deterministically. Limited SIF Solutions
STAR 6
British Energy (UK)
Fracture/collapse (Nuclear)
All
Wide user base, links with R6 code. Extensive application in nuclear industry
UMFRAP
UMIST (UK)
Fracture/collapse
FORM
Details not available
FORM/MONTE
TWI (UK)
Fracture/collapse FORM/MCS
DOS- based system for PD6493 level 2 FAD. Largely superseded
SL/WEM/R/M8663/5/01/C
Title
SL/WEM/R/M8663/5/01/C
Load (Stress) Frequency
Resistance (Strength)
Area α (Probability of failure)
Value (a)
Generalised Probability Case (2d)
(b)
Generalised Probability Case (3d) (Acknowledgements to Professor M. Chryssanthopoulos, University Surrey)
FIG. 1(a and b) SCHEMATIC REPRESENTATION OF FAILURE (D0271H08) PROBABILITY BASED ON LOAD AND RESISTANCE DISTRIBUTIONS
F1
SL/WEM/R/M8663/5/01/C
Frequency Event (N/YR)
1E-01 Local Tolerability
1E-02 Intolerable
1E-03 Local Scrutiny 1E-04 ALARP Region
1E-05 Negligible
Negligible
1E-06 1
10
100
1000
10000
Deaths (N )
(a)
Definitions of Risk Tolerability
1E+00 1E-01
Public Assemblies
Failure Probability
1E-02 1E-03
Houses/Offices
1E-04 1E-05
Bridges
1E-06 1E-07
Masts/Offshore
1E-08 1E-09 1
10
100
1000
10000
Persons at Risk
(b)
FIG. 2(a and b)
Probability of Failure v Societal Consequence for Common Structures and Events RISK CLASSIFICATION AS A FUNCTION OF CONSEQUENCE (Acknowledgement to Professor F.M. Burdekin, UMIST)
F2
(D0271H08)
SL/WEM/R/M8663/5/01/C
Crack Tip Processes
Net-Section Processes
Fatigue SCC
Fracture
Collapse Buckling Burst
Corrosion Creep
Time Variant Processes
Time Invariant Processes
FIG. 3
DIVISION OF FAILURE PROCESS ACCORDING TO SCALE AND TIME
F3
(D0271H08)
SL/WEM/R/M8663/5/01/C
Political climate
Economic climate Economic constraints
Industrial climate
Social constraints
Time Education
Clients requirements
Research Design guidance
Communication Design
Basis of contract
Structural system
Materials
Analytical method
Metallurgy
Ductility Calculation accuracy
Strength
Component shape
Thicknesses Tolerances
Identification Fabrication
Erection
Workmanship
Scheme
Imperfections
Reliability of components
Design of temporary works
Load data Number of components Load control Structural reliability
Maintenance
Heavily framed boxes indicate matters related to safety factors
FIG. 4
Execution
Indicates control points
FACTORS AFFECTING STRUCTURAL RELIABILITY (6)
F4
SL/WEM/R/M8663/5/01/C
Maximum operating pressure
Measurement uncertainties
Data on pipe properties and dimensions
Inspection Data
Corrosion model and test results
Data from repetitive inspections
pipe properties
corrosion characteristics
model uncertainties
corrosion growth rates
Frequency
Yield stress (MPa)
Prob. density
Test results
Prob. density
Flaw depth (mm)
Growth Rate (mm/yr)
Model results
Failure probability
FIG. 5
SCHEMATIC OF RELIABILITY ANALYSIS FOR FAILURE OF A CORRODED PIPE(7)
(D0271H08)
fR(r), fL(l)
Load ML
Resistance MR SR
SL r,l
R = Random Variable Describing Resistance fR(r) = Probability Density Function for R (Likewise L, fL(l) are for load) ML = Mean of Load, MR = Mean of Resistance SL = Standard Deviation of Load, SR = Standard Deviation of Resistance If L and R are normally distributed and are independent random variables ∴ Reliability index = b =
MR − ML and Pf = 1 - F (b) Å(S 2R − S 2L )
where Φ ( ) is the cumulative distribution function of the Standard Normal Distribution FIG. 6
THE GENERAL RELIABILITY CASE AND ASSOCIATED DEFINITIONS
F5
(D0271H08)
SL/WEM/R/M8663/5/01/C
Probability of Failure (Pf) 1E-1
1E-3
1E-5
1E-7
1E-9
1E-11
1E-13
1E-15 1
2
3
4 5 Reliability Index (BETA)
6
7
8
Pf = Φ (-β) or β = -Φ -1 (Pf)
FIG. 7
Pf
10-1
10-2
10-3
10-4
10-5
10-7
10-9
β
1.3
2.3
3.1
3.7
4.3
5.2
6.0
FAILURE PROBABILITY v GENERALISED RELIABILITY INDEX (β)
F6
(D0271H08)
SL/WEM/R/M8663/5/01/C
X2 Contours of increasing number of simulations
MCS a
b MCS - IS FAIL
c
Limit state Increasing N NO FAIL X1 d Pf =
FIG. 8
No Points in Area abca No Points in Area abcda
SCHEMATIC OF MCS AND MCS-IS METHODS(11)
(D0271H08)
Z2 = N(O,I) Contours of pdf are circles with radius β and centre at point O.
p = Φ(-β) Z2 O
STANDARD NORMAL SPACE
β Z1 = N(O,I)
Z1
FAIL
SAFE Straight line in Z1 - Z2 plane
FIG. 9
FORM ANALYSIS WITH LINEAR LIMIT STATE(11)
F7
(D0271H08)
SL/WEM/R/M8663/5/01/C
Pƒ = Φ(-β)
Major contribution to Pƒ
Standard Normal Space β1
g(x) = 0 tangent
FORM ANALYSIS WITH NON-LINEAR LIMIT STATE(11)
FIG. 10
(D0271H08)
Kr Fail
1
K r = f(L r)
Safe
K r = K 1/K mat L r = P1 /P L(a,σy) max L r = σ/ σy
0.5
Lr 0 FIG. 11
0.5
1
BASIC PRINCIPLE OF THE FAILURE ASSESSMENT DIAGRAM (FAD)
F8
Lr
max
(D0271H08)
SL/WEM/R/M8663/5/01/C
PF 1 0.1
Advan. Proc.
0.01
'True' P F
0.001
Bad Proc.
Note: 'True' Pf = Standard Deviation on flaw size = 0
0.0001 10
-5
10-6 -7
10 10
-8
10-9 10
-10
100
0
200
300 Stress
400
500
EFFECT OF NDE QUALITY ON FAILURE PROBABILITY (13)
FIG. 12
(D0271H08)
Failure Probability
10-2 10-4 10-6
COV =
standard deviation mean
10-8 10
-10
5
10
15
Coefficient of Variation (%)
FIG. 13
EFFECT OF SCATTER IN FRACTURE TOUGHNESS ON RESULTANT FAILURE PROBABILITY FOR A FRACTURE CONTROLLED CASE(24)
F9
(D0271H08)
SL/WEM/R/M8663/5/01/C
Mean resistance trend (e.g. embrittlement) Mean load trend (e.g. increasing stress)
Resultant failure probability
R (Toughness)
R, L
L (Stress)
t0
t1
t2 Time
FIG. 14
Cumulative Failure Probabilities (1/crack)
1E
EFFECT OF TIME DEPENDENCY OF LOAD AND RESISTANCE (D0271H08) FACTORS ON FAILURE PROBABILITY THROUGHOUT SERVICE LIFE -0 6
FORM SORM Round-Robin MCS
1E
-0 7
1E -0 8 0
FIG. 15
5
10
15 20 25 Operation Years
30
35
RESULTS OF BENCHMARK STUDIES ON TIME-DEPENDANT FAILURE PROBABILITY FOR FRACTURE FROM CRACKS GROWING IN A REACTOR PRESSURE VESSEL(25)
F10
40
(D0271H08)
SL/WEM/R/M8663/5/01/C
POD (%) 100 90 80 70 60 50 40 30 20 10 0 0
POD 95% Confidence 5
10
15
20
25
30
35
40
Crack Depth (mm)
(a)
POD (%) 100 90 80 70 60 50 40 30 20 10 0 0
MPI Defect Depth Dependant POD
POD 95% Confidence 5
10
15
20
25
30
35
40
Crack Depth (mm)
(b) FIG. 16(a and b)
ACFM Defect Depth Dependant POD EFFECTS OF INSPECTION METHODS ON PROBABILITY OF FLAW DETECTION (POD)(28)
F11
(D0271H08)
SL/WEM/R/M8663/5/01/C
10 0 Without Inspection Pr = 1
Pƒ
10
-1
Target P ƒ = 0.04
10 -2
10 -3
10 -4 0
10
20 Servicelife (Years)
30
40
FIG. 17
INSPECTION INTERVALS REQUIRED TO RETAIN FAILURE (D0271H08) PROBABILITY UNDER A PREDETERMINED TARGET LEVEL (Pf = 0.04) (ASSUMING SUCCESSFUL INSPECTION) IN AN OFFSHORE JACKET STRUCTURE(31)
5 Original reliability
4.5
Reliability of the sample joints
Safety Index
4
Reliability after first update
3.5
Reliability after second update
3 2.5
Reliability after third update
2
Reliability after fourth update
1.5
Inspection time
1 0.5 0 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 Time (Years)
FIG. 18
RELIABILITY v TIME FOR A NON-INSPECTED JOINT-IN OFFSHORE JACKET FOLLOWING PERIODIC UPDATING FROM INSPECTION OF A SAMPLE OF FIVE JOINTS(33)
F12
(D0271H08)
Original Safety Index of the not Inspected Joint
SL/WEM/R/M8663/5/01/C
2.8 2.6 Inspection Sample Size
2.4
20 - 25 2.2 15 - 20 2 10 - 15 1.8 5 - 10 1.6 0-5 1.4 1.2 1 0.1 0.2
0.3 0.4 0.5
0.6 0.7 0.8
0.9
1
Ti/Ts: Inspection Time/Intended Service Time FIG. 19
REQUIRED SIZE OF INSPECTION SAMPLE REQUIRED TO (D0271H08) UPDATE ORIGINAL RELIABILITY OF AN UNINSPECTED JOINT TO 3.0(33) Beam models of Jackets
Nominal Stress Range in Jacket Braces
Hot Spot Stress Range
Complex Joint Finite Element Analysis
Stress Range as Weibull Distribution
Wave Exceedance Data
Fracture Mechanics Analysis
Distribution of Joint Life
FIG. 20
Probabilistic Fracture Mechanics Analysis
Uncertainty Factors for Probabilistic Analysis
FLOWCHART FOR DETERMINATION OF FATIGUE LIFE PDFS BASED ON LEFM FATIGUE ANALYSIS WITH PROBABILISTIC WAVE AND STRESS DATA(36)
F13
(D0271H08)
SL/WEM/R/M8663/5/01/C
100
Probability of Failure (%)
10 1 0.1 0.01 Best fit 0.001 0.0001 1E+3
1E+4
1E+5
1E+6
Life (miles) FIG. 21
OUTPUT OF MONTE-CARLO SIMULATIONS OF da/dN FATIGUE LIFE OF RAIL BOGEY (39)
(D0271H07
1E+09 Reference
Cost per Life Saved (£)
Reduced inspection cost 1E+08
Reduced detectability Target cost 1E+07
1E+06
1E+05 3000
FIG. 22
Increased detectability
4000
5000 6000 7000 Inspection Interval (Miles)
8000
EFFECT OF CHANGING DETECTABILITY AND INTERVAL ON INSPECTION COST OF RAIL BOGEY (39)
F14
9000
(D0271H08)
SL/WEM/R/M8663/5/01/C
1960
1970
1980
1990
2000
2010
2020
2030 2040
10-1 16
24
33
41
48
56
63
70
76
10-2
-3
10
1988
Risk of Failure (PF )
PF = 2.4%
10-4
10-5 0
10
20
30
40
50
60
70
80
Years After Bridge Opening FIG. 23
RISK ANALYSIS OF YELLOW MILL POND BRIDGE, CONNECTICUT, SHOWING EFFECT OF INSPECTION ON CALCULATED RISK OF FAILURE(46)
(D0271H08)
2.4
2.2
S1 S2
2.0 β
S3
1.8
1.6
1.4 1.2 0
1.0
2.0
3.0
4.0
Period (s) FIG. 24
EFFECT OF EARTHQUAKE VIBRATION PERIOD ON RELIABILITY OF A STEEL BRIDGE IN THREE DIFFERENT LOCATIONS (S1 - 3)(50)
F15
(D0271H08)
SL/WEM/R/M8663/5/01/C
Piping Systems Tanks Reactors Drums Pumps/Compressors Heat Exchangers Towers Heaters/Boilers Others/Unknown 0
5
10
15
20
25
30
35
Percent of Losses
FIG. 25
EQUIPMENT INVOLVED IN MAJOR PROPERTY LOSSES IN THE OIL REFINING AND PETROCHEMICAL PROCESS INDUSTRIES DURING THE PERIOD 1960 TO 1990(57)
(D0271H08)
Maintenance Planning
Corrective maintenance
Preventative maintenance Condition monitoring
Predetermined maintenance
Calendar based
Op. time based
Continuous monitoring
Periodic Inspection
Planned corrective
Unplanned corrective
Predictive maintenance
RBI
FIG. 26
AREAS ADDRESSED IN RIMAP PROJECT(61)
F16
(D0271H08)
SL/WEM/R/M8663/5/01/C
0.02 Data MOM Gamma Probability Density
0.015
0.01
0.005
0 0
FIG. 27
100
200 300 400 Outside Force (kN)
500
STATISTICS OF OUTSIDE FORCE ASSOCIATED WITH THIRD PARTY DAMAGE TO PIPELINES(68)
(D0271H08)
1.E-03
Probability of Failure (/km-yr)
1.E-04
1.E-05
1.E-06
1.E-07
1.E-08 0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Design Factor (v/a)
FIG. 28
PROBABILITY OF FAILURE PER km-YEAR FOR THIRD PARTY DAMAGE TO PIPELINES OPERATING AT DIFFERENT DESIGN FACTORS(68)
F17
Probability of Failure
SL/WEM/R/M8663/5/01/C
90 100 110 120 130 140 150 160 170 Operating Pressure (Barg) Yielding
Probability of Failure
(a)
100
110
120
130
140
150
Operating Pressure (Barg)
Corrosion
Probability of Failure
(b)
100
110
120
130
140
150
Operating Pressure (Barg)
(c)
FIG. 29(a - c)
Fatigue Crack Growth
SENSITIVITY OF FAILURE PROBABILITY TO FAILURE MODE AND PIPELINE OPERATING PRESSURE(69)
F18
(D0271H08)
SL/WEM/R/M8663/5/01/C
Corrosion Depth Growth Rate
Design Factor
Severe
Moderate
Low
0.85
Annual Probability of Failure per Defect
0.72 1.E+00 1.E-01 1.E-02 1.E-03 1.E-04 1.E-05 1.E-06 1.E-07 1.E-08 0
(a)
5
10
15 20 Time (years)
25
30
Annual Failure Probability of Corroded Pipe
Gouge Depth Design Pressure 1.5 mm
0.5 mm
1050 psi
Conditional Probability of Failure per Defect (Given Damage)
1550 psi 1.E+00 1.E-01 1.E-02 1.E-03 1.E-04 1.E-05 1.E-06
Dent depth = 20 mm 1.E-07 1.E-08 0.400 0.500 0.600 0.700 0.800 0.900 Wall Thickness (inches)
(b)
Conditional Failure Probability of Dent/Gouged Pipe
FIG. 30(a and b)
EFFECT OF CORROSION AND DENT/GOUGE DAMAGE ON FAILURE PROBABILITY (70)
F19
(D0271H08)
SL/WEM/R/M8663/5/01/C
1.2 Failure 1.0 0.8 Ådr
0.6 No Failure 0.4 0.2 0 0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
sr
FIG. 31
MONTE-CARLO SIMULATION FOR FAILURE PROBABILITY FROM A 1.5 mm DEEP FLAW DURING EXPANSION OF X60 LINEPIPE (1000 SIMULATIONS)(73)
Inputs: Composition Hydrogen scale Welding conditions
Compare this with distribution of critical hardness for the hydrogen scale specified
(D0271H08)
Calculate: t/5 g Carbon Equivalents
Calculate: Hardness Mean Value - Transform to a normal distribution with this as the mean value and a standard deviation of 28HV
Manual input
Calculate: Area of overlap of hardness distributions to determine the probability of cracking
Process Connector
Display probability of cracking
FIG. 32
FLOWCHART FOR PROBABILISTIC ANALYSIS OF HAZ HYDROGEN CRACKING (75)
F20
(D0271H08)
SL/WEM/R/M8663/5/01/C
`
Numbers indicate number of cracked faces out of six.
1 C
0.9
C = Cracked NC = Not Cracked
C
Probability of Cracking
0.8
C
W
X
Y
Z
0.7 6
0.6 6
C 6 6
0.5
C NC
0 0
0.4
NC
0 0
0.3
6
0.2
62 30
0.1
0
40
Minimum Heat Input (kJ/mm) for avoidance of cracking :
NC
tg/5 1/(R)½ Nomogram W 1.57 1.21 1.70
0
0 0
X 3.49 2.60 2.56
0
0 0
0.5
1
1.5
2
2.5
3
Z 2.47 1.65 1.68
Heat Input (kJ/mm) FIG. 33
Y 3.82 3.86 4.08
PROBABILITY OF HYDROGEN CRACKING DETERMINED BY (D0271H08) STRUREL FOR FOUR CTS SERIES, SELECTED TO HAVE DIFFERENT TRANSITIONS FROM CRACK TO NO CRACK THRESHOLDS(75)
6 5.5 Data Level 2 FAD
5 4.5
dr^0.5
4 3.5 3 2.5 2 1.5 1 0.5 0 0
0.5
1
1.5
2
2.5
3
3.5
4
Sr FIG. 34
COMPARISON OF FULL SCALE TEST RESULTS WITH FAD PREDICTIONS (CTOD - BASED TOUGHNESS)(81)
F21
(D0271H08)
SL/WEM/R/M8663/5/01/C
2 1.8
Modelling uncertainty, Mu
1.6 Mu : R-r 1 Mu : R/r
Kr or √δr
1.4 1.2
A
1 0.8
R
0.6
r
Level 2 FAD
0.4 0.2 0
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Sr FIG. 35
DEFINITION OF SAFETY FACTOR (R/r) AND ANGLE θ IN RELATION TO FAD AND ANALYSIS POINT A(81)
(D0271H08)
10
80
4.5 4 3.5
R/r
3 2.5 2 1.5 1 0.5 0 0
20
30
40
50
60
70
90
h,°
FIG. 36
FAD SAFETY FACTOR AS A FUNCTION OF POSITION IN (D0271H08) FAD (θ = 90° = BRITTLE FRACTURE, θ = 0° = PLASTIC COLLAPSE)(81)
F22
SL/WEM/R/M8663/5/01/C
1.4
Increasing SD on a from 2 to 5 mm (a = Flaw size)
1.2 Pf = 0.2
(δr)
0.5
1.0 0.8
Pf = 0.1
0.6
P f = 5 x 10-2
0.4
P f = 10 -2
0.2 0 0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Sr FIG. 37
CALCULATED FAILURE PROBABILITY FOR VARYING STANDARD DEVIATION ON FLAW DEPTH COMPARED WITH FAD(82) Define scope
Select calibration points [length, loads, properties etc.]
Use existing design code for each Calibration Point to give a member size
Calculate safety index for each member
Select target safety index
Define basic variables
Define limit states (strength models)
Statistical properties for basic variables
Calculate partial factor format implicit in existing mode
Insufficient closeness to Target
Select (or modify) partial factors for new code format
Use new design code for each calibration point to give a member size
Calculate safety index for each member
Test for closeness to target safety index, using weighting factors
Determine usage weighting factors
New code partial factors
FIG. 38
METHOD FOR RELIABILITY-BASED CALIBRATION OF DESIGN CODES(5)
F23
Select new code partial factor format
(D0271H08)
SL/WEM/R/M8663/5/01/C
Target Max. Probability of Lifetime Failure 1E-1 UK warships
1E-2
USA conventional buildings USA Buildings in earthquakes
ISO2394 target Moderate consequences
1E-3 Offshore pipelines (SLS)
1E-4
Tanker-hull collapse FPSO Ultimate Collapse
ISO2394 target Great consequences
1E-5 Offshore Structures (DofE, API, DNV)
UK Bridges
1E-6 Onshore gas pipelines high population density
Nuclear
1E-7 1E-8 Pf=Φ(-β)
1E-9
1
2
3
4
5
6
Target Reliability Index (BETA)
FIG. 39
TARGET RELIABILITY LEVELS FOR DIFFERENT STRUCTURES AND DESIGN CODES
F24
(D0271H08)
SL/WEM/R/M8663/5/01/C
APPENDIX 1 STRUCTURE OF VARIOUS RELIABILITY SOFTWARE PACKAGES
A1/1
SL/WEM/R/M8663/5/01/C
FIG. A1.1
LAYOUT OF STRUREL SOFTWARE
(D0271H10)
FIG. A1.2
ProSINTAP INPUT TAB FOR MATERIAL
(D0271H10)
A1/F1
SL/WEM/R/M8663/5/01/C
FIG. A1.3
ProSINTAP INPUT TAB FOR CALCULATION TYPE Calrel
Interface
Feap
problem definition
program control
(D0271H10)
problem definition
analysis routines
user routines
FORM
UGFUN
TRUSS
SORM
UDGX
BEAM
DIRS
UDD
program control
problem solution
graphic outputs
element library
2D
MONT
3D
SENS
MEMB
BOUN PNET
FIG. A1.4
CALREL SOFTWARE LAYOUT
A1/F2
(D0271H10)
SL/WEM/R/M8663/5/01/C
Manager Preprocessing
Postprocessing Environmental Analysis
Prefem
Installjac
Wadam
general structures
launching of jackets
wave loads on general structures
Preframe frame structures
Wajac
Waveship
wave loads on frame structures
wave loads on ships
Platework plate design
Stofat shell/plate fatigue Framework frame design
Pretube Profast
tubular joints
probabilistic fatigue and inspection
Presel
Sestra
Splice
superelement assembly
linear statics and dynamics
structure pile-soil interaction
Submod
Advance
submodelling
non-linear statics and dynamics
Postresp presentation of statistical response
Cutres
Usfos
presentation of sectional results
progressive collapse
Xtract graphic presentation of results
Mimosa mooring analysis
Associated
Viewer model and results visualisation
Structural Analysis Proban probabilistic risk and sensitivity
FIG. A1.5
Concode BRIDGES TO CAD/CAE
concrete design
RELATIONSHIP BETWEEN DNV SESAM SOFTWARE AND PROBAN PROGRAM
(D0271H10)
FAST PROBABILITY INTEGRATORS & ADVANCED SIMULATION SCHEMES GRAPHICAL USER INTERFACE
FAILURE MODES LIBRARY
COMPONENT/SYSTEM RELIABILITY ANALYSIS
S
C
PROBABILISTIC RISK ASSESSMENT
S
O
A
M
P
EFFICIENT FEA INTERFACE
PROBABILISTIC DATA CHARACTERISATION
PROBABILISTIC SENSITIVITY STUDIES AND PARAMETRIC STUDIES FIG. A1.6
LAYOUT OF COMPASS SOFTWARE
A1/F3
(D0271H10)
SL/WEM/R/M8663/5/01/C
NESSUS 5.0
Primitive random variables
Most probable points
Random variable definitions
User
Reliability model (damage models)
NESSUS risk
Reliability model response
Probability database
Function
Fast Probability Integration module
Frequency
Key
Structural response
CDF
Finite Element Analysis
Response
Variable
Information Risk
FIG. A1.7
LAYOUT OF NESSUS SOFTWARE
Dynamic Analysis
(D0271H10)
Systems Modelling System Identification
Deterministic Finite Elements
Reliability Assessment
Stochastic Finite Elements
TOOLS
Monte Carlo Simulation
Models of Fracture and Fatigue
Nonlinear Programming
Response Surface Method
Damage Analysis
Reliability Based Optimization
FIG. A1.8
STRUCTURE OF COSSAN SOFTWARE
A1/F4
(D0271H10)
