Strain-Based Design of Pipelines


9
Strain-Based Design of Pipelines


Nader Yoosef-Ghodsi


Enbridge Pipelines, Edmonton, Alberta, Canada


9.1 Introduction and Basic Concepts


9.1.1 Overview of Strain-Based Design


Historically, stress-based methods have been used for designing pipelines. In a traditional stress-based pipeline design, the applied stress is kept below a prescribed limiting stress, typically the specified minimum yield stress (SMYS), by an amount dictated by the adopted safety factor. Since the SMYS for a line pipe is typically defined as the stress measured at 0.5% total strain, stress-based design generally limits the longitudinal strain to a value less than 0.5%. In contrast, strain-based design of pipelines aims at maintaining pipeline integrity and serviceability under larger longitudinal strain levels (typically greater than 0.5%), by recognizing and taking advantage of the steel’s ability to deform plastically without loss of integrity. Large longitudinal strain levels can result from installation practices or from deformations induced by ground movement. For onshore pipelines, high strain levels generally arise when the line is in service due to seismic activity (including fault movement and slope liquefaction1), slope instability, frost heave,2 thaw settlement,3 or mine subsidence.4 For offshore pipelines, high strain levels more commonly arise during pipe laying, but in service events such as ice scour5 can also produce high strain levels.


Strain-based design involves the consideration of both strain demand (the strain applied to the pipe by its surrounding environment) and strain capacity (the strain limit beyond which the pipe would experience a drop in its load-carrying ability and/or material failure). The two basic limiting conditions for strain-based design are tensile rupture and compressive local buckling. In this context, a strain-based approach requires that both tensile and compressive strain demands be kept below the tensile and compressive strain capacities, respectively.


Strain-based methods may be applied in two different situations: first, at the design stage where displacement-controlled loading events are anticipated, and second, when an existing pipeline is subjected to (or anticipated to be subjected to) displacement-controlled loading not expected or accounted for at the design stage. Strain-based assessment of an existing pipeline can serve to demonstrate continued safety of the pipeline in operation or inform decisions on integrity maintenance measures required to meet safety criteria.6 There have been recent industry initiatives to create a framework for the management of geotechnical hazards based on the principles of strain-based design and assessment [2, 3].


Several pipeline codes including DNV-ST-F101, CSA Z662, ASME B31.8, ABS, API RP 1111, BS 8010 Parts 1 and 3, ISO 16708:2006, and the Dutch standard NEN 3650 recognize strain-based design as an alternative to stress-based design. While some of these codes such as the DNV and CSA codes set out detailed requirements and provisions for the use of strain-based methods, other codes such as B31.8 do not provide explicit provisions related to strain-based design.


9.1.2 Deterministic Versus Probabilistic Design Methods


The primary goal of structural design and assessment procedures is to achieve an economical design with an adequate level of safety. Modern structural design and assessment methods can be categorized as either deterministic or probabilistic. Deterministic methods generally employ design checks containing one or more explicit safety factors and a number of implicit measures to achieve the intended level of safety.7 The implicit measures typically include the use of conservative estimates of material strength parameters and analysis methods that give lower-bound estimates of failure loads. The probabilistic (or reliability-based8) methods treat the load effects and structural resistances as uncertain quantities, which are explicitly characterized by probability distributions. Probabilistic methods generally yield an estimate of the probability of component failure, and the design and/or assessment approach involves ensuring that the calculated probability levels do not exceed a prescribed threshold.9


By explicitly considering analysis uncertainties on a case-by-case basis, probabilistic methods have the potential to achieve greater consistency in operating safety levels. It is noted, however, that probabilistic analysis methods can and have been used to assess and calibrate the safety factors for deterministic methods in some design codes. In this way, some of the advantages of a probabilistic approach are reflected in some deterministic methods.


9.1.3 Limit States


A limit state can be defined as a state beyond which a structure no longer satisfies a particular design requirement. There are two basic limit state categories that are typically addressed in civil engineering codes:



  1. Ultimate limit states (ULS) pertain to loss of the primary structural function. They often refer to loss of strength or stability and may have adverse safety and environmental consequences. Burst and tensile rupture are prime examples of ultimate limit states for pipelines.
  2. Serviceability limit states (SLS) pertain to the ability of the system to meet its functional requirements. They usually refer to excessive deformations that affect functionality without jeopardizing the structural integrity and thus do not lead to safety or environmental impacts. Ovalization and local buckling are two examples of serviceability limit states for pipelines.

Some pipeline codes define other limit state categories that overlap the ULS category. For instance, DNV [5] and ISO [6] define fatigue limit states (FLS) and accidental limit states (ALS) as separate categories. Fatigue limit states relate to failures resulting from cyclic loading, and accidental limit states address severe, rare accidental loading events such as fires or falling objects. Furthermore, Annex O of CSA Z662 [4] defines leakage limit states (LLS) as small leaks that do not lead to significant safety consequences and reserve the ULS category for rupture failures only.


Local buckling is typically considered to be a serviceability limit state. However, if local buckling progresses to the extent that it results in almost full blockage of the flow or excessive axial or hoop tensile strains, or if the buckle is subject to significant cyclic axial loading (i.e., ratcheting), it should be reclassified as an ultimate limit state.


A comprehensive design and/or assessment approach involves the consideration of all applicable limit states. Using a deterministic approach, separate checks are required for each limit state. Using a probabilistic approach, the probability of failure due to each applicable limit state within each limit state category is evaluated, and the total combined probability of failure is compared with the prescribed threshold value for that category.


9.1.4 Displacement Control Versus Load Control


Load-controlled loading is through direct application of loads that are not relieved (or affected in any way) as the pipe deforms. In contrast, displacement-controlled loading can be relieved with the deformation of the pipe. Pipeline loadings are often a combination of displacement- and load-controlled components. Pressure (be it internal or external) is load-controlled, whereas ground movement is usually displacement-controlled.10 Thermally induced loads and loads induced by Poisson’s effects are displacement-controlled in most situations. Pipe laying tension is typically caused by a combination of displacement- and load-controlled loadings.


A wide variety of intermediate conditions are possible between displacement-controlled and load-controlled situations. Strains resulting from load-controlled loading can often be readily calculated. When they occur under displacement-controlled loading, or are intermediate in type, they may require nonlinear elastic–plastic analysis.


The resistance of a pipeline to load- and displacement-controlled loads is governed by the strength and deformation capacity of the pipe, respectively. Therefore, stress-based and strain-based criteria are typically used for load-controlled and displacement-controlled limit states, respectively. However, strain-based design or assessment can also be applied in predominantly load-controlled conditions if the occurrence of plastic strains is to be accommodated.


9.1.5 Strain-Based Design Applications


The development of plastic strains during the installation of offshore pipelines has been a reality for many years since reeling11 of small diameter steel pipes was first practiced in the 1940s [7]. Cold bending of pipes before installation12 has also been successfully practiced for many years. These installation techniques have over time been extended to higher-strength and larger-diameter pipes. To adequately deal with high-strain installation processes and displacement-controlled loadings during operation, especially ground movement, many pipeline projects have utilized strain-based design in recent years. Table 9.1 presents a sample of recent worldwide projects that have used strain-based design. Cases of in-service plastic strain have also been observed in pipelines as a result of ground movement (e.g., slope movement, mining subsidence, and seismic loadings). The resistance of steel pipelines to these loadings and better understanding of pipe behavior have led pipeline designers to employ strain-based methods to address in-service plastic strains.


Table 9.1 Examples of Pipelines Utilizing Strain-Based Design


Source: Reference [7]/Edison Welding Institute.
































































Pipeline Application
Northstar for BP Shallow subsea in Alaskan Arctic
Haltenpipe for Statoil Design strain limits near 0.5%, mostly for spanning on an uneven seabed
Norman Wells for Enbridge Onshore pipeline across permafrost, strain-based acceptance of on-slope design
Badami for BP River crossings in Alaskan Arctic
Nova Gas Transmission Line in Alberta Strain-based acceptance for discontinuous permafrost
TAPS fuel gas pipeline Strain-based acceptance of upheaval buckling in permafrost
Ekofisk II pipelines for ConocoPhillips Limit state design over a subsiding seabed
Malampaya for Shell Limit state design for seismic events and seabed movement
Erskine replacement line for Texaco Limit state design for HP/HT (high-pressure/high-temperature) pipe-in-pipe replacement
Elgin/Franklin flowlines and gas export line Limit state design for pipeline bundles
Mallard in North Sea Limit state design for pipe-in-pipe
Sakhalin Island for ExxonMobil Onshore pipelines in seismic area
Liberty in offshore Alaska for BP Shallow water Arctic pipeline
Thunder Horse for BP Limit state design for HP/HT flow lines
Mackenzie Gas Project for Imperial Oil, ConocoPhillips Canada, Shell Canada, and ExxonMobil Canada Strain-based design for frost heave and thaw settlement in discontinuous permafrost
Alaska Pipeline Project for TransCanada and ExxonMobil Strain-based design for frost heave and thaw settlement in discontinuous permafrost
China’s West-East Pipelines Extensive use of strain-based design
China-Russia Crude Oil Pipelines Extensive use of strain-based design
Burma-China Oil and Gas Pipelines Extensive use of strain-based design

9.2 Strain Demand


9.2.1 Overview


A variety of installation and operating conditions can produce loads sufficient to induce large, potentially inelastic strain levels in a pipeline. The magnitude of these strains is defined as the strain demand. The following outlines some of the conditions leading to high strain levels and provides some guidance for determining the strain demand for different loading conditions.


9.2.2 Challenging Environments and Strain Demand


Increasingly challenging environments such as Arctic and offshore regions must be accommodated to facilitate the development of new oil and gas fields. For pipelines in Arctic and sub-Arctic regions, designers are required to deal with ice scour, permafrost thaw, frost heave, and installation techniques. Also, an increasing number of onshore pipelines traverse mountainous regions and earthquake-prone areas, which expose the pipelines to geohazards such as landslides, progressive slope movements, and soil liquefaction. Offshore pipelines can experience significant longitudinal strains if they are reeled prior to laying, are laid in deep water, or operate at high temperatures and high pressures.


Global buckling of offshore pipelines can be caused or assisted by high temperature and pressure, wave and current loading, and trawling interference. Onshore pipelines could also experience upheaval buckling due to significant temperature differentials and reduced support from the surrounding soil. Global buckling can lead to failure modes such as local buckling, fracture, and fatigue.13 Complete failures of offshore pipelines have occurred due to cyclic thermal fatigue of global buckles within relatively short periods after start-up. The cyclic strain range of unplanned, upheaval, or lateral thermal buckles can exceed 1%, which may lead to pipeline section collapse or high strain–low cycle fatigue and failure by either leakage or rupture [8].


9.2.3 Strain Levels and Analysis Considerations


9.2.3.1 Installation Strains


Field cold bends typically have a curvature of 1–3° per diameter,14 which translates into the maximum longitudinal strains of approximately 1.5–3.2% as the pipe is bent with a mandrel inside to prevent significant wrinkling and ovalization. Minor wrinkling (rippling) of the pipe wall may occur on the compression side to varying sizes in different cold bending instances of pipes from the same heat.15 This problem is generally more severe for higher-grade, high-Y/T (yield-to-tensile strength ratio) materials [7]. Furthermore, cold bends in older pipelines are more likely to contain wrinkles than newer pipelines mainly due to lack of or less effective wrinkling prevention measures in the older cold bending processes. While cold bend ripples have little effect on burst pressure, they may grow fatigue cracks through cycling, or in extreme cases, the wrinkles may impede pigging (thus exceeding a serviceability limit). The presence of cold bends can be accounted for in strain demand analysis by incorporating the residual stresses and strains due to the cold bending process. Cold bends typically do not include girth welds, which are usually the weak link in terms of tensile strain capacity, as pipeline codes specify a certain straight length as the buffer between the cold-bent segment and the ends of the joint. However, girth welds and pipelines in general could be subjected to construction strains of up to 0.25% (and sometimes more) when the pipeline has to undergo a certain amount of deformation to conform to the trench geometry [11].


Strains during installation of offshore pipelines can typically be put in one of the three categories: strains before the pipe is released (i.e., reeling strains), strains as the pipe is released (i.e., overbend in S-lay), and strains in the area of laying (i.e., sagbend in J-lay and S-lay). A close examination of these situations indicates that the loading condition at various stages of offshore pipeline installations is typically a combination of load- and displacement-controlled conditions [7]. While longitudinal strains of up to 2% can be generated by S-lay and J-lay processes [12], strains on the order of 2–4% can develop in a coiled pipe on a reel [13]. Pipe sections that include items other than standard pipe such as buckle arrestors or cathodic protection anodes may need a special treatment in the assessment of the laying process as strain concentrations may occur at the transitions.


9.2.4 Strains due to Ground Movement


Pipelines can be subjected to high longitudinal strains due to movement of the surrounding or underlying soil. Ground movement can result from slope movement (triggered by rainstorms, snow-melt, earthquakes, and various human activities), fault displacement and soil liquefaction (mainly due to earthquakes), ground subsidence (caused by mining or natural sinkholes due to solution of bedrock), thaw settlement, and frost heave. Slope movement, which is typically the most common geohazard for onshore pipelines outside Arctic regions, can be either progressive (i.e., creep) or sudden (i.e., slip). Permafrost thaw settlement and frost heave are usually the most common geohazards for onshore pipelines in Arctic regions. Ground movements can lead to pipeline failure due to excessive tensile and/or compressive longitudinal strains depending on the orientation of the pipeline with respect to the ground movement.


Seismic events can impact a pipeline through transient or permanent ground movement effects. Transient ground movements include near-surface ground deformations caused by ground waves that propagate from a seismic source. Shell and beam buckling are typical failure modes for buried pipelines when exposed to strong ground shaking as a result of excessive compressive axial load [14]. Permanent ground movements associated with earthquakes include landslides (i.e., failing slopes during or shortly after an earthquake due to additional inertial forces or increased pore water pressure), liquefaction (due to the weakening effect of increased pore water pressure in a saturated cohesionless soil), and fault displacement. Since estimates of ground motion in any particular geological setting may be subject to large uncertainties, standards are normally used to define the maximum expected values for general design. Japanese standards have addressed both temporary ground deformation such as seismic wave motion during an earthquake and permanent ground motion, including soil liquefaction [15, 16]. The pipe axial strains due to temporary ground deformation have been found to be limited to ±0.41%. The Japanese standards provide two levels of ground motion for permanent ground deformation: level 1 soil motion occurs once or twice during the pipeline lifetime with pipe axial strains within ±1%, and level 2 constitutes very strong seismic motion with a low probability of occurrence, resulting in pipe axial strains within ±3%, which may also apply to liquefaction cases.16


There are both analytical and numerical (finite element analysis [FEA]) methods for modeling a pipeline’s response to ground movement. Analytical models are typically based on solutions to differential equations for a “beam on elastic foundation” as developed for specific pipe layouts (usually straight) and ground motions relative to the pipeline. Newmark and Hall [17], Kennedy et al. [18], and Wang and Yeh [19] developed approximate methods for predicting pipeline response to large fault displacements.17 Miyajima et al. [22] and O’Rourke [23] developed simple analytical models for pipeline response to spatially distributed transverse ground movement, where a finite length of soil is assumed to move perpendicular to the pipe direction.18 Rajani et al. [24] developed an analytical model for pipelines subject to longitudinal soil movements,19 which was later improved by Yoosef-Ghodsi et al. [25]. The use of analytical methods for pipe–soil interaction is best suited for preliminary design or the screening of an existing pipeline and determination of the need for more detailed calculations.


Finite element analysis is the preferred method to assess pipeline response to imposed ground movements as it allows for realistic modeling of the pipe and ground geometry and can account for nonlinearities in both the behavior of the pipe and soil material. The expanded use of FEA for analyzing pipelines in recent years is due to the widespread availability of high-speed, desktop computers and relatively inexpensive, user-friendly FEA software.


The common approach in pipe–soil interaction analysis is to model the pipeline with beam elements and to represent the soil loading on the pipeline using discrete spring or pipe-soil interaction elements. The beam elements should be capable of accounting for the biaxial state of stress due to the presence of internal pressure in addition to axial loading, as the hoop stresses from internal pressure can reduce the axial stress at yield. The finite element formulation should also be able to accommodate large displacements and strains, nonlinear soil springs, and nonlinear stress–strain curves for the pipe material. Beam elements can adequately represent the pipe response up to the point of peak moment prior to wrinkling of the pipe. Thus, in order to determine the valid range for an FEA using beam elements, the analysis should be performed in conjunction with evaluating compressive strain capacity, which is typically defined at peak moment (see Section 9.3.2). The soil springs are defined such that the spring forces act in the axial, horizontal, and vertical directions relative to the pipeline. Comprehensive guidelines and recommendations for pipe–soil interaction analysis can be found in Refs. [26–28].


Three-dimensional (3D) continuum models, where pipe and soil are, respectively, represented by 3D shell and continuum elements, have also been developed for computing pipeline response to large ground displacements. While these models can explicitly address many of the limitations inherent in the simplified pipe–soil interaction using beam elements and soil springs, several significant obstacles remain to be overcome before continuum models can be considered superior to beam element and soil spring representations for routine engineering applications [27]. Some of these obstacles are (1) large size of the continuum models, which makes them computationally intensive (typically requiring significant effort to create as well); (2) inability of the continuum models to capture noncontinuum behavior including flow and fracture behavior with slip planes developing within the soil mass; (3) the continuum modeling requirement for more detailed characterization of soil properties than is required for the simple soil spring analogy and is typically available in the industry; and (4) limited validation of the continuum models. To overcome some of the shortcomings of the continuum soil modeling, 3D particle-based finite element soil models such as SPH (smooth particle hydrodynamic) and DEM (discrete element method) have been developed and successfully applied to industry applications [29, 30].20


9.3 Strain Capacity


9.3.1 Overview


This section discusses the pipe strain capacity with respect to the main failure modes or limit states that are typically associated with strain-based design.21 These are local buckling on the compression side and tensile fracture on the tension side of a pipeline, which are serviceability and ultimate limit states, respectively. Load-controlled failure modes such as burst, collapse, and fatigue are more commonly addressed by stress-based criteria. Similarly, dent and ovalization failure modes (mainly serviceability limit states) are addressed by pipeline codes through limiting the cross-sectional deformation to maintain piggability and unhindered fluid flow as well as eliminating the potential for fatigue failure rather than through strain capacity analysis.


9.3.2 Compressive Strain Capacity


During installation or in service, pipelines may experience strains high enough to precipitate local buckling (or wrinkling), in which the pipe wall buckles under axial compressive stresses. The formation of a local buckle can lead to severe cross-sectional deformation and ovalization that could obstruct the passage of pigs through the pipeline (i.e., a serviceability limit state). Continued bending of the pipe following the initiation of local buckling can lead to excessive tensile strains on the tension side of the pipe or at the wrinkle on the compression side, resulting in pipe rupture and loss of containment (i.e., an ultimate limit state). Cyclic ratcheting of the wrinkle and a shortened fatigue life due to the wrinkle may also pose integrity threats.


It is current practice to define compressive strain capacity as the average compressive strain over a gauge length of 1D to 2D (more commonly 1D, where D is the pipe outer diameter) at the peak bending moment at the wrinkle location. Even though strain localization on the compression side starts typically before the peak bending moment is attained, visible wrinkle and major ovalization generally do not occur until after the peak moment has been reached. Compressive strain capacity is primarily influenced by the pipe D/t ratio (where t is the pipe wall thickness), with higher D/t ratios resulting in lower strain capacities. Compressive strain capacity is generally increased by the presence of internal pressure and decreased by the following: higher misalignment values at the girth weld, larger pipe body imperfections, higher yield strengths, and lower strain hardening slopes (including the presence of a Lüder’s yield plateau in the pipe body stress–strain curve).


The preferred approach to the determination of compressive strain capacity for a given pipeline is to use a combination of full-scale testing and supporting FEA. However, it is recognized that this can be impractical (e.g., due to lack of a representative pipe for test), prohibitively expensive, or simply not warranted if compressive strain capacity is not likely to be the governing limit state. The alternative is the use of semiempirical models.


Early versions of compressive strain capacity models were developed based on elastic shell buckling theory, small-scale tests, and a limited number of full-scale tests. Since the early 1990s, various research organizations have developed compressive strain capacity equations based on significant number of full-scale tests in combination with supporting nonlinear finite element analyses. Selected compressive strain capacity models are presented below, followed by a general discussion of these models.


9.3.2.1 CSA Z662-11


CSA Z662-11 [4] incorporates a modified version of the compressive strain capacity equations developed by Gresnigt [33].22 The CSA equations differ from those of Gresnigt by leaving out the ovalization effects present in Gresnigt’s equations and introducing a cutoff on the strain limit for internal pressure values greater than 40% of the yield pressure.23 Moreover, while Gresnigt’s equations are based on the average (i.e., mid-wall) pipe diameter, the CSA equations are based on the outside diameter of the pipe. The CSA and Gresnigt’s equations produce very close strain capacity predictions for internal pressure values up to 40% of the yield pressure, especially at higher D/t values.


The CSA strain capacity equations show an explicit dependence on the inverse of the D/t ratio and a correction term for pressure. However, the CSA equations do not explicitly account for yield strength or the strain-hardening characteristics of the pipe material and do not distinguish between plain and girth-welded pipes. Furthermore, the CSA equations do not directly account for geometric imperfections (i.e., pipe body imperfection and misalignment at girth weld), and they do not explicitly account for the effect of axial force. Finally, no particular gauge length is assigned to the predicted strain limits.


9.3.2.2 DNV-ST-F101


The offshore pipelines standard DNV-ST-F101 [5] contains a compressive strain capacity model for pipelines subjected to bending moment, axial force, and internal overpressure (i.e., internal pressure > external pressure) in a displacement-controlled loading condition that is valid for D/t ≤ 45. Based on work by Yoosef-Ghodsi et al. [34], the DNV standard acknowledges the significant impact of girth welds on compressive strain capacity by applying a reduction factor for D/t > 20. The basic form of the equation has similarities to Gresnigt’s equation, where there is a dependence of strain capacity on the inverse of the D/t ratio and a correction term for pressure. There is a second correction term to account for the shape of the stress–strain curve, as represented by the Y/T ratio. The DNV model also makes a distinction between plain and girth-welded pipes, even though it does not directly account for the magnitude of geometric imperfections. Furthermore, the effect of axial force is not explicitly accounted for in the DNV equation. Finally, no particular gauge length is associated with the predicted strain limits.


9.3.2.3 Dorey’s Model


Dorey [35] developed a compressive strain capacity model based on parametric FEA that was validated by a series of full-scale bend tests performed under a variety of internal pressure and axial force levels based on practical operating conditions. Dorey defined the critical buckling strain over a 1D gauge length at the initiation of compressive strain localization. Dorey’s model distinguishes between plain and girth-welded pipes also between pipe materials represented by a rounded stress–strain curve at yield or a distinct yield plateau. Dorey’s compressive strain capacity model was the first to account for the magnitude of geometric imperfections. While Dorey’s model does not account for the degree of strain hardening,24 it recognizes the reduction in capacity due to the presence of a Lüder’s yield plateau. Finally, although the effect of axial force is not explicitly accounted for in Dorey’s equations, the parametric FEA used to derive the model incorporated a temperature increase of 45 °C and the Poisson’s effect due to pressurization (always resulting in a net compressive axial force).


9.3.2.4 CRES CSC Model


The Center for Reliable Energy Systems (CRES) [36–38] developed a compressive strain capacity model based on parametric finite element analysis calibrated to experimental data from 40 tests carried out in North America, Europe, and Japan. The model defines the critical buckling strain over a 2D gauge length at the initiation of softening. Like other models, the CRES model accounts for the effects of D/t and internal pressure. Like the DNV and Dorey’s models, it accounts for the strain-hardening characteristic of the steel, as represented by the Y/T ratio. Also similar to Dorey’s model, it incorporates a term to differentiate between the pipe exhibiting a rounded stress–strain curve and a distinct yield plateau. The CRES model accounts for the impact of geometric imperfections only through the peak-to-valley amplitude of pipe surface undulations. Unlike other models, the CRES model accounts for the effect of net axial force, increasing the capacity if the net force is tensile and decreasing the capacity if compressive.


9.3.2.5 Discussion on Compressive Strain Capacity Models


As discussed earlier, most existing models do not explicitly account for influential variables other than D/t and internal pressure, those being gauge length, geometric imperfection levels, axial forces, and post-yield (i.e., strain-hardening) stiffness. The existing models generally produce conservative predictions of compressive strain capacity. However, it should be noted that these models can produce nonconservative predictions for high-pressure, high-strength pipes, and the DNV equation can lead to nonconservative predictions for unpressurized pipes.


Furthermore, since the available compressive strain capacity models do not explicitly account for cold bends, caution is advised when applying these models to cold bend pipe segments. Cold bends can negatively impact the compressive strain capacity, particularly in the closing mode where the cold bend curvature is subject to increase. Cold bending processes result in both altered material properties and amplification of pipe body imperfections. Although some studies have been carried out on this topic, more work needs to be done to incorporate the effect of cold bends in strain limit equations.


Finally, the bending of a pipeline under relatively high external pressures can lead to a collapse (i.e., flattening of the cross-section) failure mode [39]. The above compressive strain capacity equations are only valid for the local buckling failure mode and not the collapse failure mode, which may be a concern for offshore pipelines.


9.3.3 Tensile Strain Capacity


Defect-free steel pipes, constructed using arc welded butt joints (i.e., girth welds), are normally very ductile and can carry large axial tensile strains typically exceeding 4% [21]. The Guideline for the Seismic Design of Oil and Gas Pipelines [20] suggests that maximum tensile strain limits on the order of 2–5% may be reasonable for a well-designed and constructed pipeline.25 In contrast, older steel pipelines constructed using gas-welded joints often cannot carry large tensile strains before rupture, and welded slip joints also do not perform as well as butt-welded joints. In addition, it is noted that the tensile strain capacity can be significantly reduced due to the presence of weld flaws.


In conventional stress-based design, girth-weld flaws are implicitly addressed through workmanship criteria. For a flaw outside the workmanship limits, welding standards may allow the acceptance of the rejected flaw when an engineering critical assessment (ECA) is performed based on fitness-for-service acceptance criteria. The acceptance criteria used in an ECA are typically based on stress-based fracture mechanics considerations and a plastic collapse criterion.26 Note, however, that such ECA methods generally produce conservative estimates, provided relevant material property data are available. This conservatism is even more pronounced for flaws in overmatched27 welds [40]. Furthermore, since stress-based ECA methods do not provide any information on the degree of conservatism, such assessments do not necessarily lead to the most economical solutions.


Tensile strain capacity is primarily influenced by the dimensions of the flaw that is present in the girth weld or the heat-affected zone (HAZ) relative to the pipe wall thickness and the weld/HAZ material toughness. In addition, tensile strain capacity is negatively impacted by lower levels of weld strength overmatch [41], higher internal pressure values,28 higher misalignment values at the girth weld [43], and lower strain hardening slopes (typically represented by higher Y/T ratios) [41].


A number of research programs have been carried out in recent years to characterize the tensile strain capacity of pipeline girth welds and to develop strain-based ECA methods. A selection of these methods is described below,29 followed by a discussion on the role of full-scale and curved wide plate testing.


9.3.3.1 CSA Z662-11


A strain-based ECA method was first introduced in Annex C of the 2007 edition of the Canadian pipeline code CSA Z662 [47], which was also included in the 2011 edition of the code [48], but not in the later editions of the code [4]. The CSA standard offers two different equations to calculate the tensile strain capacity for surface breaking and embedded flaws. The input parameters for these equations include the pipe diameter and wall thickness, the flaw dimensions (flaw depth and length, also the embedment depth in the case of embedded flaws), the weld/HAZ apparent toughness,30 and the Y/T ratio for the parent pipe material. The CSA approach has the advantage of not requiring the so-called crack resistance curve31 (i.e., J or CTOD R-curve) as an input, which is not readily available for most in-service pipelines. The CSA method does not allow for weld strength undermatching (i.e., where the weld strength is less than that of the parent pipe), but it does not take advantage of potential gains in tensile strain capacity due to weld strength overmatching.


Similar to stress-based ECA methods, the CSA strain-based ECA method does not explicitly account for the effects of pressure-induced biaxial loading in a pipeline. The effect was implicitly considered by setting a hard limit on the maximum value of the apparent toughness (0.3 mm) to prevent nonconservative TSC predictions. Several studies in recent years have shown that although the material resistance to fracture appears to be similar under uniaxial and biaxial loading, the tensile strain capacity of girth welds can be significantly reduced under biaxial loading due to an increase in the crack driving force.32 This implies that the CSA strain-based ECA method results in different levels of conservatism for different pressure values (i.e., less conservative tensile strain capacities at higher pressure values).


9.3.3.2 DNV-RP-F108


The focus of DNV-RP-F108 [49] is assessing the acceptability of girth weld flaws in pipelines and risers. Welds satisfying certain requirements are acceptable without further analysis if the maximum longitudinal strain is below 0.4%. The defect acceptance requirements are more restrictive than the typical girth weld workmanship limits. In addition, the welds have to satisfy the same Charpy energy requirements as for the parent material. The defect assessment for strains above 0.4% is based on BS 7910 [50] where the primary membrane stress is derived from the material stress–strain curve at the strain of interest. Other deviations from the basic BS 7910 requirements are the use of a Neuber notch plasticity analysis to determine the primary bending stress due to weld misalignment and the non-inclusion of the Mk weld geometry factor at strains over 0.4%. The standard requires resistance curve testing to determine the fracture toughness and does now allow the use of correlations between Charpy energy and fracture toughness.


DNV-RP-F108 requires the use of finite element fracture mechanics analysis for girth weld flaw assessment primarily when the strain demand or internal pressure levels exceed certain limits or when the material properties (e.g. fracture toughness and Y/T ratio) fall outside prescribed ranges. It is recommended to use general solid 3D FE fracture mechanics analyses, but utilizing other dedicated software programs is also acceptable if the geometry and flaw sizes assessed are benchmarked against dedicated solid 3D FE fracture mechanics analyses that fulfill the requirements specified in the standard. This assessment requires a crack resistance curve (J or CTOD, R-curve) for the weld/HAZ and the stress–strain curve of the weld metal in addition to that of the parent pipe. The capacity assessment can be based on either of the following two analysis options:



  1. Multiple stationary flaw analyses, where a minimum of three FE analyses of stationary flaws with different heights but equal length are performed, and the resulting crack driving force is plotted versus flaw height. The instability point may be determined as the tangency point between the crack driving force curve based on the FE predictions and the crack resistance curve established by testing of the relevant material condition.
  2. One FE analysis capable of simulating crack growth, for instance, is the Gurson–Tvergaard–Needleman formulation crack growth model. However, the crack growth model must be calibrated and validated against relevant experimental results.

9.3.3.3 ExxonMobil ECA Framework


ExxonMobil recently developed a three-tier approach to calculate the tensile strain capacity of pipeline girth welds containing flaws, which explicitly accounts for the pressure-induced biaxial loading [51, 52]. The capacity assessment is done using either simplified closed-form parametric equations or detailed FEA based on the limiting condition defined as the point where the crack driving force curve becomes tangential to the R-curve. The common input parameters for all assessment levels include the pipe diameter and wall thickness, flaw dimensions, weld overmatch ratio, and internal pressure.


An increase in the ECA level (from 1 to 3) implies an increase in complexity and accuracy of the assessment procedure and a decrease in conservatism. Level 1 and 2 procedures have some limitations in terms of the range of input parameters. For example, both procedures cover only pipe grades from X60 to X80 and are based on an assumed Y/T ratio of 0.9 for level 1 and 0.92 for level 2.33 Furthermore, in the interest of simplicity and conservatism, the level 1 procedure has these additional fixed inputs: weld misalignment = 3 mm, uniform elongation strain (UEL) = 6%, and a lower bound CTOD R-curve, which is the lowest of the three specified R-curves available for the level 2 procedure. In addition to detailed FEA, the level 3 procedure requires project-specific testing. Level 3 appears to be most suitable for cases involving high strain demand, higher-strength pipe (X80+), or other step out factors. Levels 1 and 2 would be suitable for evaluating preliminary designs and conducting strain-based ECA for cases involving relatively routine strain capacities and conventional pipe grades.34


9.3.3.4 CRES ECA Framework


The Center for Reliable Energy Systems (CRES) has developed a four-level ECA approach that can be adapted to the scale of the project and its design and maintenance requirements [37, 38, 55–58]. The common input parameters for all assessment levels include the pipe diameter and wall thickness, flaw dimensions, weld misalignment, yield and tensile strength and uniform elongation of the pipe material, tensile strength of the weld material, and internal pressure.


The CRES approach allows the use of a wide variety of material toughness test options and explicitly accounts for the pressure-induced biaxial loading. The level 1 procedure provides estimated tensile strain capacity in a tabulated form for quick initial assessment, where the apparent toughness is estimated from upper shelf Charpy impact energy. The level 2 procedure includes parametric equations, where the apparent toughness is obtained from either upper shelf Charpy energy or upper shelf toughness of standard CTOD test specimens. The level 3 procedure uses the same equations as in level 2 with the distinction that the toughness values are obtained from low-constraint tests (e.g., single-edge-notched tension or SENT test). In the level 3 procedure, two limit state options are available. Level 3a is based on the initiation control limit state, which implies the use of apparent toughness as the toughness parameter, and level 3b is based on the ductile instability limit state (or tangency method) using the resistance curve as the toughness parameter. The level 4 procedure is based on direct FEA to develop crack driving force relations using the same limit state options as those in level 3. The level 4 procedures are recommended to be used by experts only and in special circumstances where lower-level procedures are judged inappropriate or inadequate.


9.4 Role Of Full-Scale and Curved Wide Plate Testing


Full-scale tension (FST) testing of pipes containing flaws in their girth welds is the preferred experimental method to determine the tensile strain capacity, as FST testing realistically accounts for the biaxial effects of pressure loading. Thus, major projects often use FST testing to validate/calibrate project-specific tensile strain capacity models. In fact, full-scale verification of any tensile strain capacity model should be considered for any given project to ensure its applicability.


Curved wide plate35 (CWP) testing can more economically address variability through repeated testing at the expense of requiring adjustments for pressure effects. Denys et al. [40] suggest that for welds having a strength comparable to that of the parent pipe (i.e., even-matched), the strain capacity as determined from CWP tests needs to be reduced by a factor of 2 to account for the adverse biaxial stress effects that would exist in a pipeline operating at pressure.36


9.5 Summary


The following summarizes the key aspects of the strain-based design and assessment of pipelines:



  • Strain-based design is the preferred way to design new or assess existing pipelines subject to very high (inelastic) longitudinal strains resulting from extreme service and/or installation environments, particularly where the loads are displacement-controlled.
  • The primary limit states (or failure conditions) addressed by strain-based design are tensile rupture and compressive local buckling.
  • Assessment involves comparing the strain demand resulting from applied loads with the strain capacity, as affected by pipe geometry, material properties, and the presence of defects.
  • Two design and assessment philosophies exist, deterministic and probabilistic, which differ in how the analysis uncertainties are handled (i.e., implicitly through safety factors or explicitly through calculation of probability of failure and comparison with probability limits). Probabilistic methods, while more difficult to implement, have the potential of achieving more consistent safety levels by more accurately accounting for analysis uncertainties.
  • The compressive strain capacity is better understood and better addressed by existing models than tensile strain capacity, and tensile strain capacity models are limited in their range of applicability due to reliance on validation by tests.

References



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  25. 25 Yoosef-Ghodsi, N., Zhou, J., and Murray, D.W. (2008) A simplified model for evaluating strain demand in a pipeline subjected to longitudinal ground movement. International Pipeline Conference, September 28–October 3, ASME, Calgary, Alberta.
  26. 26 American Lifelines Alliance (2005) Guidelines for the design of buried steel pipe, ASCE.
  27. 27 C-CORE, D.G Honegger Consulting, and SSD, Inc. (2009) Guidelines for Constructing Natural Gas and Liquid Hydrocarbon Pipelines Through Areas Prone to Landslide and Subsidence Hazards. Final Report, Pipeline Research Council International Inc., No. L52292.
  28. 28 Honegger, D.G. and Nyman, D.J. (2017) Pipeline Seismic Design and Assessment Guideline. Final Report, Pipeline Research Council International Inc., No. PR-268-134501-R01.
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  30. 30 Fredj, A., Dinovitzer, A., and Sen, M. (2016) Application of the Discrete Element Method (DEM) to Evaluate Pipeline Response to Slope Movement. International Pipeline Conference, September 26–30, ASME, Calgary, Alberta.
  31. 31 Yu, D., Wang, Y.Y., Liu, B., and Chen, X. (2020) A review of pipe-soil interaction models for strain demand estimation. Proceedings of the 13th ASME International Pipeline Conference, Calgary, Alberta, Canada, Paper IPC2020-9678.
  32. 32 Andrews, R., Stephens, M., Carr, M., and Brückner, J. (2018) A review of strain capacity assessment methods for transmission pipelines. Journal of Pipeline Engineering, 17, 29.
  33. 33 Gresnigt, A.M. (1986) Plastic design of buried steel pipelines in settlement areas. Heron, 31(4), 1–113.
  34. 34 Yoosef-Ghodsi, N., Kulak, G.L., and Murray, D.W. (1994) Behaviour of Girth Welded Line-pipe. Structural Engineering Report No. 23, Department of Civil Engineering, University of Alberta.
  35. 35 Dorey, A. (2001) Critical buckling strains in energy pipelines. Ph.D. thesis, Department of Civil and Environmental Engineering, University of Alberta, Edmonton, Alberta, Canada.
  36. 36 Liu, M., Wang, Y.-Y., Zhang, F., Wu, X., and Nanney, S. (2013) Refined compressive strain capacity models. Proceedings of the 6th International Pipeline Technology Conference, October 6–9, Ostend, Belgium.
  37. 37 Wang, Y.-Y. and Liu, M. (2013) Real world considerations for strain-based design and assessment. Proceedings of the 6th International Pipeline Technology Conference, October 6–9, Ostend, Belgium.
  38. 38 Liu, M., Wang, Y.-Y., Zhang, F. and Kotian, K. (2013) Realistic Strain Capacity Models for Pipeline Construction and Maintenance. Final Report on PHMSA Contract No. DTPH56-10-T-000016. CRES-2010-J03-01. CRES, Dublin, OH. https://primis.phmsa.dot.gov/matrix/PrjHome.rdm?prj=361 (last accessed December 9, 2013).
  39. 39 Gresnigt, A.M. and van Foeken, R.J. (1996) Experiences with strain based limit state design in the Netherlands. Advances in Subsea Pipeline Engineering and Technology (Aspect ’96), November 27–28, Aberdeen, UK, Paper No. ASPECT-96-111.
  40. 40 Denys, R.M., Hertelé, S., and Lefevre, A.A. (2013) Use of curved-wide-plate (CWP) data for the prediction of girth-weld integrity. Journal of Pipeline Engineering, 12(3), 245.
  41. 41 Denys, R.M., Lefevre, A.A., and De Baets, P. (2002) A rational approach to weld and pipe material requirements for a strain based pipeline design. Proceedings of the International Conference on Application and Evaluation of High-Grade Linepipes in Hostile Environments, Pacifico Yokohama, Japan, pp. 121–158.
  42. 42 Gordon, J.R., Zettlemoyer, N., and Mohr, W.C. (2007) Crack driving force in pipelines subjected to large strain and biaxial stress conditions. Proceedings of the 17th International Offshore and Polar Engineering Conference, Lisbon, Portugal, pp. 3130–3140.
  43. 43 Kibey, S., Minnaar, A.K., Issa, J.A., and Gioielli, P.C. (2008) Effect of misalignment on the tensile strain capacity of welded pipelines. Proceedings of the 18th International Offshore and Polar Engineering Conference, Vancouver, British Columbia, Canada, pp. 90–95.
  44. 44 Østby, E. (2005) Fracture control—offshore pipelines: new strain-based fracture mechanics equations including the effects of biaxial loading, mismatch and misalignment. Proceedings of the International Conference on Ocean, Offshore and Arctic Engineering, Halkidiki, Greece, Paper No. OMAE2005-67518.
  45. 45 Andrews, R.M., Denys, R., Knauf, G., and Zarea, M. (2014) EPRG Guidelines on the Assessment of Defects in Transmission Pipeline Girth Welds—Revision 2014. European Pipeline Research Group e.V. www.eprg.net.
  46. 46 Denys, R., Hertelé, S., and De Waele, W. (2013) Strain capacity prediction for strain-based pipeline designs. Proceedings of the Internal Workshop on Welding of High Strength Pipeline Steels, CBMM and TMS, Araxá, Brazil.
  47. 47 Canadian Standards Association (CSA) (2007) CSA Standard Z662-07: Oil and Gas Pipeline Systems. Canadian Standards Association, Mississauga, Ontario, Canada.
  48. 48 Canadian Standards Association (CSA) (2011) CSA Standard Z662-11: Oil and Gas Pipeline Systems. Canadian Standards Association, Mississauga, Ontario, Canada.
  49. 49 DNVGL (2021) Recommended Practice RP-F108: Assessment of Flaws in Pipeline and Riser Girth Welds. Det Norske Veritas Classification A/S.
  50. 50 BSI (2019) BS 7910:2019: Guide to Methods for Assessing the Acceptability of Flaws in Metallic Structures. British Standards Institution (BSI), London, UK.
  51. 51 Fairchild, D.P., Kibey, S.A., Tang, H.S., Krishnan, V.R., Wang, X., Macia, M.L., and Cheng, W. (2012) Continued advancements regarding capacity prediction of strain-based pipelines. Proceedings of the 9th ASME International Pipeline Conference, Calgary, Alberta, Canada, Paper IPC2012-90471.
  52. 52 Fairchild, D.P., Macia, M.L., Kibey, S., Wang, X., Krishnan, V.R., Bardi, F., Tang, H., and Cheng, W. (2011) A multi-tiered procedure for engineering critical assessment of strain-based pipelines. Proceedings of the 21st International Offshore and Polar Engineering Conference (ISOPE), June 19–24, Maui, HI.
  53. 53 Tang, H., Fairchild, D., Panico, M., Crapps, J., and Cheng, W. (2014) Strain capacity prediction of strain-based pipelines. Proceedings of the 10th ASME International Pipeline Conference, Calgary, Alberta, Canada, Paper IPC2014-33749.
  54. 54 Fairchild, D.P., Tang, H., Shafrova, S., Crapps, J., and Cheng, W. (2016) Full-scale pipe strain test quality and safety factor determination for strain-based engineering critical assessment. 11th International Pipeline Conference, IPC 2016. Calgary, AB. Paper IPC2016-64191.
  55. 55 Wang, Y.-Y., Liu, M., and Song, Y. (2011) Second Generation Models for Strain Based Design, Contract PR-ABD-1, Project 2, Final Report to Pipeline Research Council International, Prepared for U.S. Department of Transportation Pipeline and Hazardous Materials Safety Administration (PHMSA).
  56. 56 Wang, Y.-Y. and Liu, M. (2013) Status and applications of tensile strain capacity models. Proceedings of the 6th International Pipeline Technology Conference, October 6–9, Ostend, Belgium.
  57. 57 Liu, M., Wang, Y.Y., Song, Y., Horsley, D., and Nanney, S. (2012) Multi-tier tensile strain models for strain-based design. Part 2. Development and formulation of tensile strain capacity models. Proceedings of the 9th ASME International Pipeline Conference, Calgary, Alberta, Canada, Paper IPC2012-90659.
  58. 58 Wang, B., Liu, B., Wang, Y.Y., and Huising, O.J. (2020) Estimation of tensile strain capacity of vintage girth welds. Proceedings of the 13th ASME International Pipeline Conference, Calgary, Alberta, Canada, Paper IPC2020-9664.
  59. 59 Verstraete, M. (2013) Experimental–numerical evaluation of ductile tearing resistance and tensile strain capacity of biaxially loaded pipelines. Ph.D. thesis, Ghent University.

Notes



  1. 1 Liquefaction is the loss of soil strength and stiffness under an applied stress, which is mainly caused by seismic activity.
  2. 2 Frost heave is an upward ground movement due to the growth of ice lenses around the pipeline. This freezing process is caused by sufficiently low temperatures of the transported oil or gas.
  3. 3 Thaw settlement is a downward ground movement due to the melting of the ice-rich soil near the pipeline. This melting process is caused by sufficiently high temperatures of the transported oil or gas.
  4. 4 Mining subsidence is a ground movement caused by collapse of underlying mines.
  5. 5 Ice scour is the impact of a pipeline by the passage of keels of floating ice.
  6. 6 The term “strain-based analysis” has been suggested by Law [1] as an alternative to “strain-based design and assessment.”
  7. 7 Working stress design (WSD), also known as allowable stress design (ASD), involves the use of design checks with a single safety factor intended to account for all uncertainties associated with the applied loads and the component resistance capacity. Load and resistance factor design (LRFD) involves the use of design checks with separate partial factors for the applied load and component resistance.
  8. 8 In this context, reliability is defined as one minus the probability of failure.
  9. 9 An example of probabilistic design included the reliability-based design and assessment (RBDA) method as set out in Annex O of CSA Z662 [4].
  10. 10 Some ground movements that can cause severe integrity concerns are not purely displacement-controlled. For example, the sudden failure of a slope or mine subsidence may not be purely displacement-controlled.
  11. 11 Reeling is a part of a pipeline (typically offshore) installation process where the pipe is fabricated into a long segment, wrapped around a circular reel, transported to the installation site, and then unwound from the reel.
  12. 12 Cold bends (or field bends) serve to adapt the pipeline profile to that of the terrain or accommodate the deviations required in the pipeline route plan.
  13. 13 Note that according to DNV-ST-F101 [5], global buckling may be allowed provided that (1) the global buckling is not entirely load-controlled; (2) pipeline integrity is maintained in post-buckling configurations (against failure modes such as local buckling, fracture, and fatigue); and (3) displacement of the pipeline is acceptable.
  14. 14 Note that while B31.8 [9] and API RP 1111 [8] set a variable cold bend curvature of approximately 1.9°/D to 3.2°/D as a function of the pipe outer diameter (D), CSA Z662-11 [4] prescribes a cold bend curvature limit of 1.5°/D unless the effects of further bending on the mechanical properties of the pipe are determined to be within acceptable limits.
  15. 15 The reader may refer to the work by Bilston and Murray [10] for a method to determine the critical wrinkling (which they term buckling) stress.
  16. 16 More guidance on seismic loading and analysis of pipelines subjected to seismic events can be found in PRCI seismic guidelines [13] and Japanese seismic codes [15, 16].
  17. 17 Detailed discussions of these models can be found in the Guideline for the Seismic Design of Oil and Gas Pipelines [20, 21].
  18. 18 Detailed discussions of these models can be found in Ref. [21].
  19. 19 The authors also developed an analytical model for transverse soil movements in the same reference; however, the model is based on elastic pipe behavior and was primarily used for evaluating pipe stresses, not strains.
  20. 20 For a more detailed review and comparison of various strain demand models, see Ref. [31].
  21. 21 For a more detailed review and comparison of various strain capacity models, see Ref. [32].
  22. 22 Gresnigt developed a semi-analytical model based on an elastic–plastic pipe material to represent the behavior of pipes subjected to internal pressure, axial force, and bending. The compressive strain capacity was defined at the peak bending moment and incorporated the ovalization of the pipe cross-section due to bending.
  23. 23 The yield pressure is an internal pressure corresponding to a nominal hoop stress equal to the pipe SMYS.
  24. 24 The parameters n (i.e., the strain hardening exponent in Ramberg-Osgood equation) and Y/T used by some models can be considered as indicators of the strain hardening slope.
  25. 25 Note that these statements apply to high strain-hardening pipes made of quenched and tempered materials. Some modern microalloyed TMCP steels can have uniform elongation strains less than 4–5%.
  26. 26 The combination of ductile fracture and plastic collapse criteria is usually represented by a failure assessment diagram (FAD), which divides the plane of interaction between fracture and plastic collapse resistances into safe and unsafe zones.
  27. 27 Overmatched welds are those with an overmatch ratio of greater than 1. The weld overmatch ratio is the ratio of the weld tensile strength to that of the parent pipe material.
  28. 28 Tensile strain capacity decreases by about 50% as internal pressure increases from 0 up to a certain (high) level of internal pressure, where the strain capacity has its minimum. Higher pressure levels typically result in a small increase of the strain capacity [42].
  29. 29 The reader can also refer to the tensile strain capacity models developed by SINTEF [44], EPRG [45], and University of Ghent [12, 46], which are not further described in this chapter.
  30. 30 The term “apparent” implies that the traditional single-parameter-based fracture mechanics does not strictly apply to large crack tip plasticity. The apparent toughness represents the combined effects of the material toughness and structural response. For large-scale test specimens, the CTOD values associated with final failure are generally well above 0.5 mm, sometimes much larger at 1.0–1.5 mm. These values are much greater than the single-parameter “valid” CTOD value (0.1 mm or less) for a tension CTOD specimen [39].
  31. 31 Crack resistance curve, or R-curve, is a plot of crack driving force (J or CTOD) versus crack extension.
  32. 32 Crack driving force is defined as either the applied J-integral or crack tip opening displacement (CTOD).
  33. 33 These choices for the Y/T ratio are on the conservative side.
  34. 34 The reader can also refer to the recent tensile strain capacity model developed by ExxonMobil [53, 54], which is not further described in this chapter.
  35. 35 The CWP test involves a curved (i.e., unflattened) girth-welded pipe segment containing a surface-breaking circumferentially oriented crack-like notch (or possibly a real flaw) in the weld or HAZ at mid-length of the specimen, which is axially loaded in tension to failure.
  36. 36 Denys et al. suggest that a lower reduction factor would be appropriate for overmatched welds [40]. Other pressure correction factors have recently been developed in independent studies with similar outcomes [51, 58, 59].

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