PROBABILISTIC ASSESSMENT OF A 70-YEAR-OLD PIPELINE SUBJECT TO SEISMIC DEFORMATION. Robert W. Warke LeTourneau University Longview, Texas, USA

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1 Proceedings o IPC 006 6th International Pipeline Conerence eptember 5-9, 006, Calgary, Alberta, Canada IPC PROBABILITIC AEMENT OF A 70-YEAR-OLD PIPELINE UBJECT TO EIMIC DEFORMATION Robert W. Warke LeTourneau University Longview, Texas, UA James D. Hart D, Inc. Reno, Nevada, UA Ben H. Thacker outhwest Research Institute an Antonio, Texas, UA ABTRACT This paper presents an assessment case study on several segments o buried natural gas pipeline constructed in 1936 with bell-bell-chill ring (BBCR) style girth weld joints, and currently operating in a seismically active region o North America. mic vulnerability was evaluated in terms o girth weld racture and plastic collapse probabilities or speciied hazards o varying severity and likelihood. Monte Carlo simulations perormed in NEU provided ailure probability estimates rom distributed inputs based on PIPLIN deormation analyses, nondestructive and destructive law sizing, residual stress measurements, weld metal tensile and CTOD tests, and limit state unctions based on published stress intensity and collapse solutions. INTRODUCTION AND BACKGROUND Over the past decade or so, a major owner/operator that chooses to remain unidentiied has been engaged in an ongoing girth weld inspection and assessment program or a buried gas transmission pipeline o pre-world War II construction. Their previous work had been ocused on developing critical law height vs. length curves as acceptance criteria or nondestructive inspection. These were initially developed or a series o assumed seismic loading magnitudes in various combinations with other sources o loading, but the criteria ultimately applied were simply based on an assumed maximum tensile stress o 30 ksi. Despite this and several other conservatisms that were adopted, ewer than 3% o the irst ~50 arc-welded BBCR joints inspected were considered rejectable. Given these results, coupled with the high cost o girth weld inspection, the owner/operator entertained a proposal to reassess the pipeline on a probabilistic basis. egments o this pipeline in regions subject to large-scale ground ailure (liqueaction, ault rupture, etc.) were already replaced or designated or such, and thereore outside the scope o this work. At the opposite end o the soil response spectrum were regions subject only to elastic shaking strains due to traveling waves, or which acceleration-strain relationships based on maximum ground particle and apparent shear wave propagation velocities have been established [1,]. It is not overly conservative in the latter case to assume perectly eicient soil-to-pipe strain transer. Annualized probability density unctions or pipeline strain can thereore be estimated directly rom available peak ground acceleration (PGA) hazard curves. Compared to the uncertainty o event occurrence itsel, the uncertainties o soil and pipe response due to elastic shaking alone are relatively small, and the likelihood o pipeline ailure is negligible [3,4]. The present study was to address the middle ground between these two extremes, where reasonably postulated seismic events could induce a limited but signiicant degree o permanent ground strain (landslide, lurching, etc.). Hazards o this kind were reportedly conceivable, i not probable, in regions comprising more than 90% o the pipeline s total length. Pipe-soil interaction was thereore a major contributor to the overall uncertainty o its seismic itness. The present assessment addressed ive separate segments o old pipeline operating in such areas. OBJECTIVE The primary objectives o this study were to: 1. Deine relevant ailure criteria or BBCR girth welds in ive segments o a pre-world War II vintage pipeline subject to various levels o deormation during potential seismic events.. Incorporate available BBCR girth weld properties data and the results o PIPLIN-based seismic deormation analyses into suitable probability density unctions. 3. Compute the overall girth weld ailure probability within each segment or the range o postulated seismic events represented by the deormation analyses. 4. Interpret the results to enable an inormed itness-or-service (FF) decision by the owner/operator or each segment. PROCEDURE AND REULT The ollowing sections describe the tasks undertaken and results obtained to achieve the stated objectives. Deining Failure Criteria As in a deterministic FF assessment, a probabilistic assessment requires a mathematical description o the criterion by which each o

2 the potential ailure modes is deined. For sake o convenience in probabilistic calculations, this is generally expressed as a limit state unction o the orm: [ g( X, X,, X ) 0] P K (1) = P 1 n where X i are the random variables that determine structural perormance, e.g., low strength, racture toughness, applied stress and law size. Failure is predicted or all combinations o these variables satisying g(x i ) 0, so the assessment calculations seek to determine the raction o their joint probability density alling outside the limit state. This raction represents the probability o ailure (P ). The two ailure modes typically considered in the assessment o lawed girth welds are unstable racture and plastic collapse. The Level Failure Assessment Diagram (FAD) method o B 7910 [5] (ormerly PD 6493) combines both o these into a single graphical ormat, which had been the basis o the owner/operator s previous acceptance criteria. However, experience has shown that limit state unctions based on FAD expressions are oten problematic or the algorithms employed by probabilistic analysis codes. These problems are generally not intractable, but can be time-consuming to debug. Under the time and budget constraints o this project, it was decided that the probabilities o racture and collapse would be calculated separately. Fracture. Using the racture assessment parameter K r given by B 7910, ormulated in terms o crack-tip opening displacement (CTOD), evaluations o the probability o ailure due to unstable racture were based on an expanded version o the expression: App Q Frac δe + δ e P = P 1 + ρ δ 0 () mat The driving orce or racture was deined as the elastic App Q component o the applied CTOD, denoted as δ e and δ e or the respective contributions o the applied (seismic) and residual stresses. δ represents the measured racture resistance (critical CTOD) o mat the girth weld metal, and ρ is a plasticity correction actor. It has been shown [4] that secondary bending induced by a bell geometry essentially the same as that o the BBCR joints in the subject pipeline has negligible eect on the stress intensity (or applied CTOD) associated with a girth weld law. A stress intensity solution developed by Wang et. al [6] or laws o inite length in straight joints was thereore adopted as the basis or crack driving orce due to applied (seismic) stresses: K App I = where : F b D 3 or β η t π and where : 4 α = D t β β = + m1 + m α α 1. πaf b β + m 3 α (3) 1 m = η 3 and where: F = F ( η η ) m = exp at 4 3 η π D t or 3 m = 39.1η η 4169.η η b b D 3 β > η t π is the applied seismic stress, a is the law height, parameter η is law height expressed as a raction o pipe wall thickness (t = in.), and parameter β is law length expressed as a raction o pipe circumerence (πd, where D = in.). In addition to externally-applied stresses, welding-induced residual stresses can also contribute to the unstable racture driving orce. Girth weld residual stresses in large D/t pipes are governed primarily by an axisymmetric bending moment induced by shrinkage in the hoop direction, causing tension at the root and compression at the cap. According to Michaleris et al [7], the total stress intensity due to weld residual stresses acting on a circumerential, internal surace Q I crack ( K ) is best estimated by combining the solution o Gordon, et al [8] with the series solution o Buchalet [9], giving: K Q I = where: Q πa b c [ 1.1+ A( 6η + η )] 3 Q πa [ η η η ] D A = t b = ( ) 0. D c = t D 0 t and where Q is the maximum (root surace) tension value. The irst (Gordon) hal o the equation establishes the stress intensity the crack tip would experience i the root surace tension value existed over the ull wall thickness. The second (Buchalet) hal eectively reduces this value to account or the through-thickness stress gradient that is actually present. The use o Equations (3) and (4) with CTOD as the deinition o crack driving orce due to applied and residual stresses ( δ and required a conversion rom K I, which in the present case was: δ e = d n where : d and : J e J n e Y 1 = n K = E I ( 1 ν ) n App e (4) Q δ e ) (5)

3 where J e is the elastic component o the plane-strain J-integral value, Y is the material yield strength, n is the strain hardening exponent, E is the modulus o elasticity and ν is Poisson s ratio [6,10]. Plastic apse. Evaluations o the probability o ailure due to plastic collapse were based on an expanded version o the expression: P P 0 (6) [ ] = C Computational and experimental work reported by Wang et al [6,10] has shown the Miller solution to be the most accurate o the several available or girth weld plastic collapse prediction. However, experience has again shown that the cyclic (sine and cosine) unctions in the Miller solution tend to be problematic or the algorithms employed by probabilistic analysis codes. The second most accurate (only 7% less so, and in the conservative direction), is one given by Wilkowski and Eiber [11]. It was adopted as the basis or plastic collapse assessment: C where: N = = F 1 η η 1 N β + 47β 3 59β and where F is the low strength, typically deined as the average o yield and ultimate tensile. Characterizing Input Parameters As dictated by the two limit state unctions deined above, the input parameters adopted as random variables or the probabilistic assessment were: Relative law height and length (η and β) Applied (seismic) stresses ( ) Residual stresses ( Q ) Fracture resistance in terms o critical CTOD ( δ mat ) Weld metal low strength ( F ) Deterministic (singular), conservative values were adopted or a number o other variables: Modulus o elasticity Poisson s ratio Yield strength (only or K I to δ e conversion) train hardening exponent ρ (plasticity correction actor) Pipe diameter and wall thickness In preparation or this assessment, the owner/operator had contracted with a reputable laboratory to conduct a airly comprehensive characterization o our girth welds taken rom straight joints in the subject pipeline, three o them BBCR and one having a chill ring without belled pipe ends. Their evaluation included macroexamination o weld cross-sections, hardness tests, residual stress measurements, analyses o chemical composition, cross-weld tensile strength o both standard and wide-plate specimens, additional breakage o specimens to reveal weld law geometries, and racture toughness tests [1]. Following are descriptions o the work undertaken to characterize and incorporate these and other available data into the assessment ramework. (7) Flaw Dimensions. Nondestructively-measured height and length data rom 84 BBCR girth weld laws ound in the subject pipeline were provided to this project by the owner/operator. To simpliy the limit state unction or the racture assessment, as well as App Q to ensure that in terms o δ e and δ e the combined eects o height and length o each law were accurately represented, two new random variables F App and F Q were created, as: and F Q = a F App = af b c [( 1.1+ A[ 6η + η ]) ( η η η )] 3 Values o F App and F Q were computed or each law, then their maximum values were extracted rom each girth weld. Unstable racture is a weakest link ailure mode, in that the single law representing the largest value o δ e determines the nominal stress or racture initiation. The resulting data were then processed and examined to determine their mean values (µ), standard deviations (σ) and distribution types, using a combination o statistical tests (method o moments, Kolmogorov-mirnov and Chi-square), prior irsthand experience [e.g., 4,13], knowledge o other investigators indings [e.g., 14], and engineering judgment. Figures 1 and show the probability density unctions (PDF) and cumulative distribution unctions (CDF) that were established or F App and F Q. Both were modeled as Type I Extreme Value (EVD I), which represents distributions o maxima. The correlation coeicient between F App and F Q indicated a rather high value o 0.8, not surprising given that both parameters are strongly dependent on law height, and especially since most o their respective maxima were due to the very same law. This eect was included in the probabilistic analysis. A comparison o law heights made visible on racture suraces by the wide plate tests with those measured ultrasonically by the owner/operator indicated generally close agreement, within 0.01 inch in all but one case. In that particular case, the exposed law was 0.04 inch taller than any o the measured values or that weld. imilar comparisons between other racture suraces produced intentionally or the purpose o comparison with ultrasonic data showed close agreement. For the plastic collapse assessment, law height and length were again combined into a single random variable, this time as the strength reduction actor enclosed in square brackets in Equation (7). However, since the distribution o that quantity was o a nonstandard shape and ound to be problematic, its inverse was instead deined as a new parameter F or purposes o distribution itting: b 1 (8) 1 η F = (9) η 1 N with the plastic collapse limit state modiied accordingly as: F P = P 0 (10) F

4 Values o β or calculating values o F were based on the total law length or each weld, accompanied by a length-weighted average law height, calculated as: η avg = n i= 1 β η i β i tot (11) where n is the total number o laws ound in a given weld. The resulting values o F were processed and examined to determine mean (µ), standard deviation (σ) and distribution type, again using a combination o statistical tests and engineering judgment. Figure 3 shows the PDF and CDF that were established. As with F App and F Q, it was ound that F was best modeled as a Type I EVD. Applied (mic) tresses. Using PIPLIN [15], a computational deormation analysis was perormed on each o the ive pipeline segments. A series o ground movement proile sequences was applied to each segment, with each sequence representing one combination rom a matrix o various soil displacement amplitudes and three dierent along-the-ground-contour block proile widths. Each displacement proile was traversed across each segment in 100- t. position increments to comprise each sequence (Figure 4). Eight to thirteen dierent displacement amplitudes were applied in this manner, with the upper-bound amplitude or each segment based on guidelines provided by the owner/operator s geotechnical sta. The results provided various demand eects (axial orce, bending moment, maximum axial tension and compression stresses) at the node corresponding to the maximum pipeline curvature location or each position o the proile. It was most convenient rom the standpoint o the orm o both limit state unctions, as well as most relevant to the ailure modes o interest, to use tensile stress as the input parameter. ince it was not computationally easible to record and store the peak stress at each weld location, it was decided to extract the largest value rom each series o proile positions, and assume that any weld within the region could experience that value. Instructions given by the owner/operator s geotechnical sta were to assess P separately or each o the three dierent proile widths (100, 550 and 1000 eet), without attempting to rank their relative probabilities. Based on urther discussions, a simple but reasonable distribution-itting approach was ormulated or the range o maximum applied tensile stresses predicted by PIPLIN or each permutation o segment and proile width. The mean value was calculated in the usual way, then the applied stress resulting rom the upper-bound soil displacement was assigned a cumulative probability o Assuming a normal (Gaussian) distribution, ixing the mean and 99 th percentile values determined the standard deviation. Fiteen dierent distributions were thus identiied, o which two representative examples are given in Figures 5 and 6. Given the highly stochastic nature o seismic ground motion, demand eects are perhaps the most uncertain o all relevant assessment inputs. It should thereore be noted that all o the estimated displacements and proile widths were based on a single, 10% in 50-year (500-year return period) postulated seismic event. As such, this assessment did not address the ull spectrum o possible events and their associated likelihoods. It was essentially an assessment o a single design case event with all o its possible pipeline demand outcomes, in terms o their probability o producing one or more girth weld ailures. It should also be noted that the much smaller stresses induced by the Poisson eect were justiiably omitted, since the overall peak stresses would occur at a moment when pipe and soil were essentially decoupled. Residual tresses. It has been shown that in large (>~40) D/t pipes, the magnitude o the tensile residual stress at the root o a girth weld is approximately equal to that o the compressive value measured on the weld cap surace at the same circumerential position [7]. Measurements o this kind had been perormed by the aorementioned laboratory using the blind hole drilling (BHD) method at our locations, 90 degrees apart, on each o the our girth welds removed rom the pipeline (Figure 7) [1]. Their data indicated at least one location in each weld where the sign o the through-thickness residual stress proile was reversed; these values were conservatively omitted. The remaining 1 data were processed to obtain the normal distribution o Q shown in Figure 8. It should be noted that while residual stresses can play a signiicant role in the initiation o unstable racture, they generally do not contribute to plastic collapse events. In the present assessment they were treated as such. Fracture Resistance (CTOD). The laboratory conducted tests on 16 specimens taken rom the our welds to provide CTOD data or racture assessment [1]. Elevated loading rates such as those resulting rom seismic events typically increase the ductile-to-brittle transition temperature (DBTT) or structural steels. The temperature shit recommended by Barsom [16] was employed to account or this, and the resulting test temperatures ranged rom 14 to 19 F. Even at these low temperatures, all but one o the specimens exhibited limit load behavior. The resulting data were processed to obtain the Weibull distribution o δ mat shown in Figure 9. Flow trength. Also perormed were 16 cross-weld tensile tests to provide yield and ultimate tensile strength data. Flow strength ( F ), the resistance variable in the plastic collapse assessment, was conservatively deined as the stress midway between yield and ultimate tensile. The resulting data, most o which were corrected to account or the presence o laws, were processed to obtain the normal distribution o F shown in Figure 10. Miscellaneous Constants. As mentioned previously, several input parameters were applied deterministically, i.e., as single values. Table 1 summarizes these, most o which were used only to convert crack driving orce rom K I to δ e. The assumed value o yield strength ( Y ) was two standard deviations below the mean value (µ σ) o the available data. The use o deterministic variables or ρ, D and t was motivated primarily by time and budget constraints, although typical variations in D and t have been shown to have negligible inluence on P or both o the limit states being considered [13]. TABLE 1. Deterministic Input Values Constant Value Purpose Modulus o elasticity (E) 30,000 ksi K I to δ e conversion Poisson s ratio (ν) 0.3 K I to δ e conversion Yield strength ( Y ) 36 ksi K I to δ e conversion train hardening exponent (n) 8.5 K I to δ e conversion Plasticity correction actor (ρ) Frac P calculation Pipe diameter (D) in. β calculation Pipe wall thickness (t) in. η calculation

5 Calculating Failure Probabilities Using Equations () and (10) and the various probabilistic and deterministic parameters given above, calculations o P or both racture and plastic collapse were perormed using the Monte Carlo imulation (MC) algorithm in NEU [17]. To ensure adequate accuracy or the P values that were computed or each ailure mode, 3.5 million MC trials were conducted or each racture case, and 100,000 or each plastic collapse case. 95% conidence intervals due to MC sampling error indicated maximum possible errors ranging rom ±16.5% to ±54.5% or the various racture cases. Due to the signiicantly higher values o P, 95% conidence intervals on computed collapse probabilities ranged rom ±1.8% to ±9.%. For both ailure modes, and as was expected, the largest conidence intervals were associated with the smallest values o P. To estimate the total ailure probability o each segment or both racture and collapse, the pipeline was treated as a system o elements (girth welds) in series. I ailures o the individual elements in a series system are perectly correlated to one another, P or the system can be deined simply as: P = max P i (1) ys i where P is the ailure probability o any single weld in the segment i o interest. ince all o the girth welds in each segment were assumed to have the same chance o ailure, Equation (1) reverted to P = P as deined by Equations () or (10). I individual ailures are statistically independent rom one another (i.e., perectly uncorrelated), P or the system can be deined as: ys n P = 1 1 P (13) ys i= 1 i where n is the total number o girth welds in any segment o interest. Again, since all girth welds within each segment were assumed to have an equal chance o ailure, Equation (13) reverted to: n P = 1 P 1 (14) ys i First-order bounds were thereby placed on the girth weld reliability or each segment. ome degree o ailure correlation among the girth welds throughout the line can be expected, since a particular seismic event may apply similar stresses to all o them. On the other hand, the material properties and law sizes luctuate more or less randomly rom one weld to another. The actual girth weld P or the system (pipeline segment) can be taken to lie somewhere between these two extremes. Calculations based on Equation (14) assumed that girth welds occur at 30-t. intervals over the entire length o each segment. For both racture and plastic collapse, Table provides lower- and upperbound values o P or the segment associated with each segment and ground movement proile width. DICUION In evaluating the various ailure probabilities given in Table, the reader is reminded that they were based on a postulated design case seismic event having a 10% in 50-year probability o occurrence (500-year return period). Their overall likelihoods are thereore ar less than those shown. Bearing that reality in mind, two general conclusions can be drawn: irst, that unstable racture is highly unlikely, regardless o model region or ground motion proile width, and second, that plastic collapse is likely to occur in several cases. This was essentially inevitable, given the range o applied stresses predicted or those cases, and has less to do with law sizes than with the sheer magnitude o the stresses. Nonetheless, the lack o appreciable weld metal strength overmatching in older pipelines [4,1] does contribute to this problem, since it precludes the usual assumption that plastic strain will distribute more or less uniormly across the joint, rather than localize at laws in the weld metal. However, the latter is not necessarily a reason or grave concern, since plastic collapse indicates imminent ailure only in load- or stresscontrolled, not strain- or displacement-controlled events. Much like the onset o necking in a standard uniaxial tensile test specimen, which deines the engineering property known as ultimate tensile strength, plastic collapse indicates the ar-ield (nominal) stress at which the load-carrying capacity o a girth weld begins to decline. It does not deine the strain level at which separation occurs. When assessing the structural itness o a pipeline that may experience signiicant ground movement, strain (rather than load) capacity is typically the relevant parameter, since a pipeline is generally not required to resist such motion, merely to accommodate it. All but one o the cross-weld wide plate test results rom samples containing laws at the upper end o the size range ound in this pipeline indicated crosshead displacements o 0.5 to over 0.4 in. prior to separation [1]. The lone exception contained an unusually large law. Beore identiying the present P results as problematic, it would be useul to revisit the PIPLIN model output to determine whether per-unit-length displacements o similar magnitude would be expected in the most severe cases. The owner/operator did not make the necessary FF decisions or each segment solely on the basis o the results presented here. These were incorporated into a system-wide risk management and GI program or allocating maintenance resources according to various potential causes and consequences o ailure. As such, it is not possible to identiy which o the P values given in Table 1 were considered acceptable and which were not. It must suice to say that no immediate action was required. Finally, it should also be noted that the results presented here are speciic to a particular (and airly unusual) pipeline operating under a speciic set o conditions, thus have very limited applicabilty to other situations. However, the assessment methodology can be adapted and applied to most situations. CONCLUION AND RECOMMENDATION 1. Given the occurrence o a 500-year seismic event, the predicted maximum probability o girth weld unstable racture within any particular segment was less than 0.1% in over hal o the cases evaluated, and less than 1% in all cases.. Also given the occurrence o a 500-year seismic event, the predicted maximum probability o girth weld plastic collapse within any particular segment was moderately to very high in several cases. However, this was not necessarily cause or immediate action, since pipeline loading is essentially strain- or displacement-controlled, which lessens the relevance o plastic collapse as a limit state. 3. The PIPLIN analysis results should be revisited to compare predicted axial strain levels to the maximum per-unit-length crosshead displacements measured in cross-weld wide-plate tests.

6 4. mic events representing various other return periods should be modeled in order to construct a complete hazard curve or each segment. This would enable the ull spectrum o event likelihood to be incorporated into calculations o ailure probability or these and other limit states, thus providing a more realistic assessment o seismic itness. ACKNOWLEDGEMENT This work was perormed under Gas Research Institute Contract , and the helpul oversight o GRI program manager Mr. Chuck French is grateully acknowledged. It could not have been completed without the invaluable guidance o the owner/operator s pipeline engineering and geotechnical sta. The timely assistance o Mr. David Riha o outhwest Research Institute was also most appreciated. REFERENCE [1] Litehiser, J. J., Abrahamson, N. A. and Arango, I., Wave- Induced Axial train o Buried Pipes, Columbian Geotechnical ociety, date unknown. [] Newmark, N. M., Problems in Wave Propagation in oil and Rock, Proceedings o the International ymposium on Wave Propagation and Dynamic Properties o Earth Materials, August 3-5, University o New Mexico Press, pp [3] Honegger, D. G. and Nyman, D. J., Guidelines or the mic Design and Assessment o Natural Gas and Liquid Hydrocarbon Pipelines, Final Report, PRCI Contract PR , PRC International, October 004. [4] Warke, R. W., Koppenhoeer, K. C. and Amend, W. E., mic Fitness o Girth Welds in an Early-1930s Vintage Gas Transmission Line, Proceedings o the 1997 Pipeline Risk Management & Reliability Conerence, Houston, 1997, Clarion Technical Conerences and cientiic urveys Ltd. [5] B 7910:1999, Guide on Methods or Assessing the Acceptability o Flaws in Metallic tructures, British tandards Institution, [6] Wang Y.-Y., Rudland, D., and Horsley, D., Development o a FAD-Based Girth Weld ECA Procedure: Part I Theoretical Framework, Paper IPC , Proceedings o the 4th International Pipeline Conerence, Calgary, Alberta, Canada, ep. 9 Oct. 3, 00. [7] Michaleris, P., Kirk, M. T. and Laverty, K., Incorporation o Residual tresses into Fracture Assessment Models, Final Report, EWI Project 0136IRP, December [8] Gordon, J. R., Wang, Y-Y. and Dong, P., "The Development o Fitness-or-Purpose Flaw Acceptance Criteria or leeve Connections," 8th ymposium on Line Pipe Research, PRC International, eptember [9] Buchalet, C. B. and Bamord, W. H., tress Intensity Factor olutions or Continuous urace Flaws in Reactor Pressure Vessels, in Mechanics o Crack Growth, ATM TP 590, pp , ATM, [10] Wang Y.-Y., Rudland, D., and Horsley, D., Development o a FAD-Based Girth Weld ECA Procedure: Part II Experimental Veriication, Paper IPC , Proceedings o the 4th International Pipeline Conerence, Calgary, Alberta, Canada, ep. 9 Oct. 3, 00. [11] Wilkowski, G. M. and Eiber, R. J., Evaluation o Tensile Failure o Girth Weld Repair Grooves in Pipe ubjected to Oshore Laying tresses, J. Energy Resources Technology, vol. 103, pp , [1] Orth, F., Material Properties o [ ] Gas Transmission Line No. [ ] Girth Weld amples, Final Report, EWI Project 4398CAP, August 003. [13] Warke, R. W. and Ferregut, C. M., Reliability-Based Fitnessor-ervice Assessment o Pipeline Girth Welds, Final Report, PRCI Contract PR , PRC International, August [14] Gianetto, J. A., hen, G., Tyson, W. R., and Glover, A. G., Assessment o the Fracture Toughness o Pipeline Girth Welds, Proceedings o the 5 th International Conerence on Trends in Welding Research, pp , AM International, [15] D, Inc., PIPLIN: Computer Program or tress and Deormation Analysis o Pipelines, Version 4.54, User Reerence and Theoretical Manual, Reno, Nevada, March 006. [16] Barsom, J. M., Eect o Temperature and Rate o Loading on the Fracture Behaviour o Various teels, Paper 31 in Dynamic Fracture Toughness: Proceedings o the International Conerence, July 1976, pp , The Welding Institute, [17] Riha, D., Thacker, B. H., Enright, M. P., Huyse, L. and Fitch,. H. K., Recent Advances o the NEU Probabilistic Analysis otware or Engineering Applications, Proceedings 4nd AIAA/AME/ACE/AH/AC tructures, tructural Dynamics, and Materials (DM) Conerence, AIAA , Denver, Colorado, April 00.

7 TABLE. Predicted Probabilities o Fracture and Plastic apse egment 1 tress Input and Result Type Proile Width (t.) µ (ksi) σ egment Frac P Min Max egment Min P Max µ (ksi) σ egment Frac P egment P Min Max Min Max ~1.0 ~1.0 µ (ksi) σ egment Min P Max Frac egment P Min Max µ (ksi) σ egment Frac P egment P Min Max Min Max µ (ksi) σ egment Min P Max Frac egment Min P Max ~

8 FIGURE 1. PDF and CDF o parameter F App (µ = 0.353; σ = ) FIGURE. PDF and CDF o parameter F Q (µ = 0.357; σ = )

9 FIGURE 3. PDF and CDF o parameter F (µ = 1.037; σ = ) FIGURE 4. Example o Ground Movement Proile Application to Pipeline egment

10 FIGURE 5. PDF and CDF o parameter or egment with a proile width o 1000 t. (µ = ksi; σ = 3.7 ksi) FIGURE 6. PDF and CDF o parameter or egment 4 with a proile width o 550 t. (µ = 36.8 ksi; σ = 1.55 ksi)

11 PIPE WALL CHILL RING FIGURE 7. Example o ection through Girth Weld howing Location o BHD Residual tress Measurement FIGURE 8. PDF and CDF o parameter Q (µ = ksi; σ = 8.53 ksi)

12 FIGURE 9. PDF and CDF o parameter δ mat (µ = 0.0 in.; σ = in.) FIGURE 10. PDF and CDF o parameter F (µ = 58.8 ksi; σ = 6.0 ksi)