More info about this article: http://www.ndt.net/?id=25447 Pipeline Dent Strain Assessment Using ASME B31.8 David D. MACKINTOSH Acuren Inc., Edmonton, Alberta, Canada david.mackintosh@acuren.com Abstract ASME B31.8-2018 Appendix R provides a method for assessing strain in pipeline dents based mainly on measured surface curvature. Strain is one indicator of whether a dent may develop a leak or rupture. In practice, there can be some confusion when different technologies – for example manual assessment, laser scanning, and inline inspection – appear to produce different strain results. With any method, it can be a challenge to find the curvature that actually represents local wall bending without being oversensitive to small surface variations or under-sensitive to short, sharply-bent areas. This paper summarizes the rationale and theory behind ASME B31.8-2018 Appendix R and suggests some practical tips for accurate and consistent results. This paper discusses strain but does not cover pressure-cycle fatigue. Keywords: pipeline, ASME B31.8, dent, strain, direct assessment, laser scanning, inline inspection. Contents 1 2 3 4 5 6 7 8 9 10 Why calculate dent strain? .................................................................................................... 2 What is in ASME B31.8R?....................................................................................................... 2 How is surface curvature determined? ................................................................................. 4 Do the different methods usually agree? ............................................................................ 10 Should the strain be calculated over the whole dent surface? ........................................... 11 What are the accept-reject criteria for dent strain in code?............................................... 11 When should ASME B31.8R not be used? ........................................................................... 12 What is the strain in very shallow dents? ............................................................................ 12 What’s the final word on ASME B31.8R?............................................................................. 13 Appendix: Theory ................................................................................................................. 16 Copyright © 2020 Acuren, licensed to NDT.net. 1 1 Why calculate dent strain? As part of the ongoing battle to keep steel pipelines operating safely, operators face the challenge of determining which dents need repair and which can be left in safe operation. Although enshrined in code, depth measurement is not a great help since plain dents (those without stress concentrators such as cracks, welds, corrosion, or gouging) often have minimal effect on burst pressure [1, 2]. Dents with cracks (Figures 1a and 1b) are generally dangerous and require expedited repair [3]. Dent strain – local elongation or compression – is one indicator of whether a dent may develop cracking or other material damage that could cause a leak or rupture [4]. This paper outlines some methods and practical considerations for estimating dent strain according to ASME B31.8R, which is an abbreviation for ASME B31.8-2018 – Gas Transmission and Distribution Piping Systems, Nonmandatory Appendix R, Estimating Strain In Dents [5]. This paper does not cover pressure-cycle fatigue. For pressure-cycle fatigue, see other standards such as API 579 [6], BS 7608 [7], or API 1183 (still only in draft form when this article was published). ASME B31.8R strain is mainly determined from dent curvature: the sharper the dent, the higher the strain (Figure 2). Curvature is mainly affected by the shape of the indenter: a sharp rock makes a sharp dent. Rosenfeld et al. state that “there is almost no relationship between dent depth and strain...” [8], which was confirmed in a study by Rafi et al. [9]. 2 What is in ASME B31.8R? Besides general guidance, ASME B31.8R gives bending strain equations based on longitudinal and circumferential curvatures (Figure 3). Another equation based on the depth-to-length ratio of the dent gives the longitudinal extensional strain component, which is usually small compared to the bending strains. A final equation is used to combine the components and estimate the effective strain on the inside and outside surfaces of the pipe. See the Appendix of this paper for the equations and theory. Note that ASME B31.8 does not “preclude the use of other strain estimating techniques” [10] and allows strain to be calculated using “other engineering methodology” [11] (as does Canadian CSA Z662 code [12], which references ASME B31.8). 2 Corrosion Crack Gouging Flow Figure 1a: Sample dent with corrosion, crack, and gouging. (See also Figure 1b.) Brush marks Flow Figure 1b: The dent from Figure 1a viewed from the inside of the pipe showing the crack. Surface brush marks from inline tools can also be seen. 3 L Figure 2: Visual comparison of low- and high-strain dents. Note that in the high-strain dent, the sharpest part of the bend covers only a short length L (see Section 3.3). Figure 3: Surface curvatures and sign conventions for ASME B31.8R strain calculations (adapted from ASME B31.8-2018). 3 How is surface curvature determined? 3.1 What are the overall objectives? Dent curvature can be difficult to determine [13], partly because on a deformed surface it can be hard to determine which area or size of area to select for the calculation. The analyst needs to: • find the curvature that corresponds to local pipe wall bending; • ignore small surface variations unrelated to bending; • be sure not to filter out sharply-bent areas; and • avoid reporting strain where features such as corrosion or gouges make ASME B31.8R strain calculations inapplicable (see Section 7). 4 3.2 What software and mathematical methods are used? One simple strategy to determine curvature is to plot a circle at the point of interest and use visual judgment to select the correct radius (Figure 4). If this task is performed using software, caution is strongly recommended if viewing the data with a zoom much greater than 1:1 scale, since small surface blemishes can begin to look like major deformations. Another strategy is, instead of selecting a radius, to select the length of the segment to which the circle will be mathematically fit (Figure 5). Too short a segment can be overly noisesensitive, and too long a segment can smooth over a sharp dent. To obtain the right balance, one manufacturer suggests selecting a segment length that covers an area of similar curvature at the point of interest [14]. This segment would also lie within the points of inflection at each end of the profile. Our experience suggests that this strategy may be less user-dependent than simply selecting the radius visually. For inline inspection (ILI) tool data, which requires mass processing, a host of techniques have been developed which we will not attempt to review here. One example technique is to interpolate between data points using B-splines,* from which curvatures can be mathematically extracted [15]. 3.3 What are the potential pitfalls? One pitfall to avoid is not visually checking if the strain calculation looks reasonable. For example, the software might calculate a high strain at corrosion or a weld, whereas the surface curvature at those features has nothing to do with bending strain. For accurate results, the measurement grid needs to be fine enough to capture the sharpest curvature in a dent. Based on a study of dent assessment by laser, for reliable and repeatable results Arumugam et al. recommend a grid resolution of 2 mm or finer [16]. Figure 6 shows a laser profile plotted with manual depth readings, which were spaced too widely for this dent at 10 mm (0.4 inch), leading to an under-call of strain. This assessment might be improved by aligning the grid to the point of interest but preferably by using a finer grid. Note that for many smoother dents, a 10 mm grid could be quite adequate. Filtering, smoothing, or averaging out noise and surface roughness is usually essential, as Lukasiewicz et al. observed in processing ILI data [17]. For example, an algorithm that uses only three neighboring data points to calculate curvature, without smoothing, would tend to overreact to noise [18]. In Figure 7, the hypothetical ‘noise-sensitive’ algorithm under-calls the radius and over-calls strain. ASME B31.8R states that suitable smoothing techniques should be used to minimize noise. * A spline is a mathematical function that behaves similarly to a flexible strip of wood that is used to draw smooth curves between defined points. 5 Because some software (or software settings) may incorrectly flag small surface variations as high strain, it could be tempting to simply screen out all short variations. However, Figure 2 illustrates that a sharply-bent area may also be short. It is therefore important not to ignore short areas where the dent profile can be seen to converge to a sharp bend. Radius too small Radius correct Radius too large Figure 4: A dent profile obtained from laser scanning showing correct and incorrect circle-fitting for dent strain assessment. (Back wall profile is estimated.) approximate points of inflection selected segment Figure 5: Example of a method where the user selects the length of segment to which the circle will be fit, over an area of similar curvature. (Same dent profile as in Figure 4.) 6 Figure 6: Comparison of manual and laser dent longitudinal profiles. The manual data points are shown joined by straight lines because in this case no interpolation was used. Figure 7: Sketch of results that might be obtained using different circle-fitting algorithms. The data are from a laser-generated dent profile with simulated noise added. 3.4 How is curvature found manually? Profile gauges (Figure 8) are often used to obtain the axial and circumferential profiles of dents. The profiles can be traced onto paper and matched with reference circles printed on a clear plastic sheet, similar to the curve matching shown in Figure 4. The dent dimensions and curvatures can then be entered into a spreadsheet or software to calculate strain. 7 Another manual measurement method is to use a straight-edge placed on ring spacers (Figure 9), which help to maintain a constant offset if there is nearby corrosion or distortion. Depth measurements can be taken on a 2D grid, which allows strain calculations both at the apex and at other points on the dent. Figure 8: A profile gauge can be used to obtain a dent profile. Straight edge Profile measurement Ring spacer Dent Figure 9: A straight edge with ring spacers can be used to obtain a dent profile or grid. 3.5 How is curvature found by laser scanning? Laser scan data can be fed into pipeline integrity software to determine strain. A typical grid resolution is 1.0 to 1.5 mm (0.039 to 0.059 inch). With one software package (Pipecheck by Creaform [19]), the analyst adjusts the length of the segment that is used to fit the circle, as described in Section 3.2. Figure 10 shows an example of a laser-generated strain plot. Note that this dent has curvatures that are sharp in the longitudinal direction and smoother in the circumferential direction. 8 Figure 10: A dent strain plot calculated from laser data. 3.6 How is curvature found by ILI? High-resolution ILI tools [20] designed for dents commonly use caliper arms with contact or proximity sensors to map the inside surface of the pipeline. Closely-spaced, narrow sensors tend to be best for strain calculations [21]. Before analysis, the data are smoothed to remove noise, which is typically caused by surface irregularities [22]. The dent curvatures and ASME B31.8R strain are then calculated by custom algorithms. Depending on the ILI tool, it may be necessary to interpolate between sensors to estimate the dent profile [23], a process that could be prone to inaccuracy on sharper dents. Some studies make the favourable assumption that a sensor always passes over the deepest point of the dent [24, 25]. API STD 1163 for ILI systems recommends that “a quality process should be employed in order to ensure the accuracy of ... strain calculations” [26] – advice that would be well-heeded for any method. (continued on next page) 9 3.7 What are the strengths and limitations of each method? Table 1 summarises three common methods for determining dent strain along with their strengths and weaknesses. Table 1: Comparison of three methods to determine dent strain Method of strain measurement Strengths Weaknesses Manual Manual methods tend to be simpler and more intuitive. Direct examination can reveal stress concentrators such as cracks and gouges that may make strain analysis not applicable. Manual methods may be more techniciandependent. Accuracy can be affected by applying a measurement device at the wrong position or out of alignment with the pipe axis, or by careless tracing of the dent profile to paper. Measuring a depth grid manually can be time-consuming. Laser Provides accurate and highresolution measurements. Provides a strain map over the entire dent surface. Analysis is software-intensive and requires training and experience. The laser can detect small changes in the wall surface profile, leading to a temptation to over-call strain on small, irrelevant surface variations. In-line inspection Can easily record profiles of hundreds of dents for assessment in one inspection run. Sensor noise needs to be filtered out. Interpolation may be necessary to estimate the dent profile between sensors. For some tools it can be difficult to characterize flaws on dents [27], which can affect strain assessment. 4 Do the different methods usually agree? ILI, manual, and laser methods agree closely very often, but not always. Some sources of disagreement are discussed below. 4.1 External and internal curvatures The external, indented profile of a dent (as measured by manual and laser in the field) would tend to be sharper than the internal surface (as measured by ILI) and hence would give a higher estimated strain – more so when the wall thickness is not negligible compared to the dent curvature. For a discussion on how to compensate see Section 10.4. 10 4.2 Changes with pressure Dent shapes may change with operating pressure, which can cause discrepancies if the different measurement methods were applied at different times [28]. Also, excavating a dent for direct assessment can cause a dent to reround (spring back) to a shallower depth [29] due to the removal of the indenter or load on the pipe. 4.3 Measurement of depth and length There is minimal guidance in ASME B31.8 (and Canadian CSA Z662) on how specifically to measure dent depth and length [30], which adds a small uncertainty to dent strain calculations. Dent depth and length are used to calculate longitudinal extensional strain, which is admittedly usually a very small component of overall strain in the ASME B31.8R equations. The ‘original contour’ of the pipe required by the codes for measurement reference [31, 32] would presumably be the pipe contour without the dent – but is that simply a cylinder, or should overall bending or ovality be preserved? Another common source of variation is that straight edges of different lengths can give different depths (Figure 11). Straight-edge #1 Straight-edge #2 Figure 11: Two straight-edges of different lengths measure different depths, as shown on a laser depth profile. 5 Should the strain be calculated over the whole dent surface? Traditionally strain was calculated just at the dent apex [33]. ASME B31.8-2018R seems to allow strain to be calculated over the whole dent surface “where detailed profile measurement methods are used” [34]. In our experience as inspection vendors, some pipeline operators are interested in the dent strain at the apex but not at the point of maximum strain. The point of maximum strain is often found away from the apex [35]; see the example in Figures 12 and 13. 6 What are the accept-reject criteria for dent strain in code? We encourage the reader to develop their own interpretation of the applicable code. Our simplified suggestions are below. 6.1 ASME B31.8 According to our reading, ASME B31.8 allows a plain dent rejected by depth to be rendered acceptable if its strain is below 6% (in the absence of other strain thresholds based on 11 elongation data), although safe passage of inline devices is also a requirement for acceptance [36]. A dent affecting a ductile pipe weld, rejected by depth, can be rendered acceptable by engineering analysis, but not if its strain exceeds 4%. 6.2 CSA Z662 Canadian CSA Z662 pipeline code does not reject dents solely based on strain. This code does allow a plain dent to be ‘rescued’ from rejection if its strain is below 6%, or 4% if the dent interacts with a defect-free weld [37]. 6.3 What is the basis for the accept-reject criteria? According to Rosenfeld et al. (in 2002), the manufacturing codes permit field bends with strain up to 3%. Various coatings tend to fail when the pipe strain is in the 2% to 7% range [38]. And since cracking “seems to increase” when the strain exceeds around 12%, 6% was selected as a reasonable strain threshold [39]. 7 When should ASME B31.8R not be used? ASME B31.8R strain analysis would not apply to dents with additional damage such as corrosion or gouging, since the code does not deal with wall thickness variations and stress concentrators. Caution is strongly recommended when estimating dent strain with the damage ‘smoothed out’, or in other words answering the question, ‘What would the dent strain have been without the additional damage?’ Relying on such a hypothetical strain value could be a liability exposure for inspector or operator. The ASME B31.8R model assumes a simple, well-behaved, symmetrical dent geometry with axes aligned with the pipe [40]. Gao et al. recommend that “For dents with complex geometry, critically located in high consequence areas ... FEA [finite element analysis] methods should be used” to calculate strain [41]. Based on this recommendation, the operator can take the appropriate action if a complex dent (for example multi-apex) is reported. 8 What is the strain in very shallow dents? Figure 14 helps visualize the question: when is a dent too small to cause appreciable strain? If a sharp rock impinges on a pipe wall as in Figure 14 Case A, the strain would likely be high. In case B the dent is not as deep, but the radius of curvature and hence strain would likely be similar to case A. In case C the same sharp rock has impinged on the pipe, but the dent is so shallow that intuitively we might expect it to have lower strain. Research is needed, likely involving theory or finite element analysis, to determine a reasonable limit on dent size where a strain assessment would not apply. The theory is not simple. Young and Budynas describe a similar problem of calculating stress where a liquid-filled pipe sits on supports: ‘... the stress analysis is difficult and the results are rendered uncertain by doubtful boundary conditions’ [42]. 12 9 What’s the final word on ASME B31.8R? Although there is ongoing discussion on the accuracy of ASME B31.8R equations compared to other methods [43], according to Okoloekwe et al. the ASME B31.8R equations provide a ‘reasonable estimate’ [44], and Gao et al. state that on the whole ASME B31.8R gives a simple, easy, and useful method for determining dent strain [45]. Acknowledgement The author would like to thank Ted Hamre and Kelly Cisar for their valuable input. Any errors or omissions are solely the author’s. (continued on next page) 13 (a) External dent surface as seen in 3D laser scan data. (b) Depth contours showing position of apex. Apex (deepest point) (c) Strain contours showing area of maximum strain. Point of highest strain, (away from apex) Figure 12: Laser analysis of a dent that has a point of maximum strain away from the apex. See also Figure 13. 14 (a) Radius of curvature is smaller at point of maximum strain. (b) Radius of curvature is larger (lower strain) at apex. 100 mm Figure 13: In the dent from Figure 12, dent contours are shown (a) through point of maximum strain and (b) through dent apex. The superimposed circles indicate why, in this dent, the strain is higher (smaller radius of curvature) away from the apex. Figure 14: Three scenarios where a sharp rock creates dents of different depths – but are the strains the same? 15 10 Appendix: Theory 10.1 What are the ASME B31.8R equations? Table A1: Notation Wall thickness Measured dent depth Measured dent length Pipe nominal radius Measured dent curvature in circumferential direction Measured dent curvature in longitudinal direction Bending strain in circumferential direction Bending strain in longitudinal direction Extensional strain in longitudinal direction Effective strain at inside surface of pipe Effective strain at outside surface of pipe Maximum effective strain t d L R0 R1 R2 ε1 ε2 ε3 εi εo εeff Based on the notation in Table A1 and Figure 3, the ASME B31.8R-2018 equations are: = = = = = 2 1 − 1 (A1) (A2) 2 1 2 2 √3 2 √3 = max (A3) + ( − (− , + + ) / ) + (− + ) )+ ( + (A4) / (A5) (A6) Note that in Equations A1 and A2 a heavier wall (t) is the worst-case scenario and yields a higher strain. Equations A4 and A5 combine the component strains to give the effective insidesurface and outside-surface strains, εi and εo. The maximum effective strain (A6) is the maximum of εi and εo at the point of interest (sometimes misunderstood to mean the maximum strain in the entire dent). 16 10.2 What is an example of dent strain calculation? Below are sample metric calculations for a dent in an NPS 20 pipe per ASME B31.8R-2018. Calculations in inch units are on the next page. Nominal OD D0 508 mm Wall thickness t 9.53 Measured dent depth d 10 Measured dent length L 250 Pipe nominal radius R0 254 Measured dent curvature in circumferential direction* R1 -300 Measured dent curvature in longitudinal direction R2 200 * In this example we assume that the circumferential profile is convex (indented), as in Figure 3(b); therefore R1 is set negative. In the 2018 code, for a longitudinal profile that is convex, the radius of curvature R2 is set positive. The three component strains are: = 9.53 1 1 − = 0.0346 = 3.46% 2 254 −300 (A7) = 9.53 = 0.0238 = 2.38% 2 × 200 (A8) = 1 10 2 250 (A9) = 0.0008 = 0.08% The effective strains are: = 1.155 × 0.001200 + 0.000853 + 0.000606 / = 1.155 × 0.001200 − (−0.000798) + 0.000530 = 0.0595 = 5.95% / = 0.0581 = 5.81% (A10) (A11) The reported maximum effective strain εeff is the maximum of the results from A10 and A11, which is 5.95% strain. 17 The calculations on the previous page are repeated here using inch units with some slightly different input values. Nominal OD D0 20 inch Wall thickness t 0.375 Measured dent depth d 0.400 Measured dent length L 10 Pipe nominal radius R0 10 Measured dent curvature in circumferential direction* R1 -12 Measured dent curvature in longitudinal direction R2 8 In this example we assume that the circumferential profile is convex (indented), as in Figure 3(b); therefore R1 is set negative. In the 2018 code, for a longitudinal profile that is convex (i.e. a dent), the radius of curvature R2 is set positive. The three component strains are: = 0.375 1 1 − = 0.0344 = 3.34% 2 10 −12 (A7b) = 0.375 = 0.0234 = 2.34% 2×8 (A8b) = 1 0.375 2 10 (A9b) = 0.0008 = 0.08% The effective strains are: = 1.155 × 0.001182 + 0.000833 + 0.000587 / = 1.155 × 0.001182 − (−0.000778) + 0.000512 = 0.0589 = 5.89% / = 0.0574 = 5.74% (A10b) (A11b) The reported maximum effective strain εeff is the maximum of the results from A10b and A11b, which is 5.89% strain. 18 L neutral t R Figure A1: Linear bending strain model. Top: original plate. Bottom: bent plate. 10.3 What is the basic theory behind the B31.8R strain equations? Using a simplistic, linear model, the strain of a bent plate can be estimated from its radius of curvature [46]. Figure A1 shows a straight segment of plate which is then bent to a radius R, which could represent the longitudinal profile of a pipeline dent. The neutral (unchanged) axis is assumed to be mid-wall. With a linear model the length of an arc is proportional to the radius [47], so at a radius of R + t/2 the increase in length ΔL is given by: ∆ = ∆ /2 (strain) = 2 (same as Equation A2). = = (312) (Applying Equation A12 at a radius of R - t/2, the ‘indented’ surface, the plate is in compression and ε2 is negative.) In the circumferential direction the nominal (unstrained) pipe has a radius of R0 = OD/2, so the strain in Equation A12 is adjusted by t/2R0 as follows: = 2 − 2 = 2 1 − 1 (313) (same as Equation A1). 19 Equation A3 — the formula for extensional strain (stretching rather than bending) in the longitudinal direction — was developed empirically from finite element simulations [48]. Equations A4 and A5 were developed by Lukasiewicz and Czyz et. al. [49] based on plastic strain theory where an incompressibility requirement implicitly includes the radial strain in the results [50]. 10.4 How can we compensate for the difference in external and internal curvatures? As mentioned in Section 4.1, the curvatures on the inside and outside surface of a dent are different and would yield different calculated strains. In the linear model (Figure A1) the curvatures of the convex and concave surfaces are R+t/2 and R-t/2 respectively, whereas the strain indicator is the radius of curvature of the neutral axis, R. To improve consistency between methods operating on the inside and outside surfaces of a pipe (and subject to engineering approval by the pipeline operator), it would seem reasonable to adjust curvatures by ±t/2 to obtain R. Remember that R is the dent curvature, not the pipe radius, so t is not necessarily very small compared to R. 10.5 What are the limitations of the ASME B31.8R strain equations? For sharp dents, it appears that the ASME B31.8R equations produce a severity indicator rather the true strain. For sharp or kinked deformations, API 579 tells us that ‘traditional shell theory’ gives inaccurate results and that advanced evaluation methods are needed [51]. API 579 defines a ‘sharp’ deformation as R < 5t, where R is the local radius of curvature (which Cosham and Hopkins note is an approximate definition [52]). Note that plugging R = 5t into equation A2 gives a longitudinal bending strain of 10%. The ASME B31.8R equations do not take shear strain, circumferential extensional strain, and the pressure at the time of dent formation into account, all of which can have significant effects on dent strain [53, 54]. These unaccounted-for components could lead to inaccuracy in estimating actual dent strain. 10.6 Why have the B31.8R equations changed over the years? The ASME B31.8R strain equations have been updated twice with a view to improving accuracy. • The 2003 version had “t” instead of “t/2” in equations A1 and A2, leading to a 2× overcall of strain. • The above problem was fixed in the 2007 version by replacing “t” with “t/2” in the equations [55], which reduced the calculated strain by a factor of 2. • The 2018 version introduced the equations for combined strain of Lukasiewicz and Czyz (Equations A4 and A5), which moved the calculated strain back up again by a factor of around 2 [56]. (Note: the 2018 version also changed the sign convention to make the longitudinal curvature of a dent a positive number (Figure 3), with a corresponding change in sign in Equation A2 to keep ε2 positive for dents.) 20 Endnotes 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Escoe, A. Keith (2006). Piping and Pipeline Assessment Guide, 1st ed., Gulf Professional Publishing, Burlington, MA. Page 179. Rosenfeld, M., Pepper, J., and Leewis, K. (2002a). ‘Basis of the New Criteria in ASME B31.8 for Prioritization and Repair of Mechanical Damage,’ 4th International Pipeline Conference, Calgary, Canada, paper no. IPC2002-27122. Pages 649 and 652. Escoe (2006). Page 180. Rosenfeld et al. (2002a). Page 649. ASME B31.8 (2018), Gas Transmission and Distribution Piping Systems. American Society of Mechanical Engineers, New York, NY. API 579-1 / ASME FFS-1, Fitness-For-Service, 3rd ed (2016). American Petroleum Institute, Washington, DC. BS 7608:2014+A1:2015, Guide to fatigue design and assessment of steel products. BSI Group, London, UK. Rosenfeld et al. (2002a). Page 649. Rafi, A., Das, S., Ghaednia, H., Silva, J., Kania, R., and Wang, R. (2012). ‘Revisiting ASME Strain-Based Dent Evaluation Criterion,’ Journal of Pressure Vessel Technology 134 (4). Page 5. ASME B31.8-2018. Para R-1. ASME B31.8-2018. Para 851.4.1. CSA Z662 (2019), Oil and Gas Pipeline Systems. Canadian Standards Association, Ottawa, Canada. Para 10.10.4.1. Okoloekwe, C., Aranas, N., Cheng, J., Adeeb, S., Kainat, M., Langer, D., Hassanien, S. (2018). 'Improvements to the ASME B31. 8 Dent Strain Equations'. Journal of Pressure Vessel Technology, 140(4):041101. Page 2. Creaform, Inc (2020). Contextual Help for Pipecheck 6.0.0 (2020.06.29). Lévis, QC, Canada. Okoloekwe et al. (2018). Page 3. Arumugam, U., Tinacos, K., Gao, M., Wang, R., and Kania, R. (2014). "Parameters Affecting Dent Strain Using 3D Laser Scan Profile." Proceedings of the 10th International Pipeline Conference, Volume 2: Pipeline Integrity Management. Calgary, Alberta, Canada. Lukasiewicz, S. A., Czyz, J. A., Sun, C., Adeeb, S. (2006). ‘Calculation of Strains in Dents Based on High Resolution In-Line Caliper Survey’, 6th International Pipeline Conference, Calgary, Canada, paper no. IPC2006-10101. Page 5. Umbach, D, and Jones, K. (2003). "A Few Methods for Fitting Circles to Data," IEEE Transactions on Instrumentation and Measurement. vol. 52, no. 6, p. 1881–1885, Dec. 2003. Creaform, Inc (2020). Pipecheck software version 6.0.0 (2020.06.29). Lévis, QC, Canada. Rosenfeld, M., Porter, P., and Cox, J. (1998), “Strain estimation using Vetco deformation tool data”. ASME 2nd International Pipeline Conference, Calgary. Lukasiewicz et al. Page 5. Lukasiewicz et al. Page 2. 21 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 Noronha, D. Jr, Martins, R., Jacob, B., and Souza, E. (2005). “The Use of B-Splines in the Assessment of Strain Levels Associated with Plain Dents,” Rio Pipeline Conference & Exposition 2005, paper no. IBP 1245_05. Page 3. Noronha et al. (2005). Okoloekwe et al. (2018). Page 8. API Std 1163 (R2018) In-line Inspection Systems Qualification Standard, 2nd ed (2013, reaffirmed 2018). American Petroleum Institute, Washington, DC. Para 9.3. Rosenfeld et al. (2002a). Page 649. ASME B31.8-2018. Para R-1. Rosenfield et al. (2002). Page 648 Noronha, D., Martins, R., Jacob, B., and Souza, E. (2010), “Procedures for the Strain Based Assessment of Pipeline Dents,” Int. J. Pressure Vessels Piping, 87, pp. 254–269. Cited in Rafi et al. (2012). ASME B31.8-2018. Para 841.2.4(c)(1). CSA Z662-2019. Para 10.10.4.1. Rafi et al. (2012). Page 1. ASME B31.8-2018. Para R-1. Rafi et al. (2012). Page 5. ASME B31.8-2018. Para. 851.4.1. CSA Z662-2019. Para. 10.10.4.2. Rosenfeld, M.J. (2002b). “Factors to Consider When Evaluating Damage on Pipelines.” Oil and Gas Journal, September 9, 2002. Rosenfeld et al. (2002a). Page 650. Okoloekwe et al. (2018). Page 2. Gao, M., McNealy, R., Krishnamurthy, R., Colquhoun, I. (2008) 'Strain-Based Models For Dent Assessment – A Review', 7th International Pipeline Conference, Calgary, Canada, paper no. IPC2008-64565. Page 4. Young, W. and Budynas, R. (2001). Roark’s Formulas for Stress and Strain, 7th ed. McGraw-Hill Education, New York. Page 589. Okoloekwe et al. (2018). ASME B31.8-2018. Para R-1. Gao et al. (2008). Page 5. Hibbeler, R. C. (2003), Mechanics of Materials, SI Edition. Prentice-Hall, Inc., Upper Saddle River, NJ. Page 571. Rafi et al. (2012). Page 2. Baker, Michael Jr (2004). Dent Study, OPS TTO10, Delivery Order DTRS56-02-D-70036, Department of Transportation, Office of Pipeline Safety, Washington, DC. Page 9. Lukasiewicz et al. (2006). Okoloekwe et al. (2018). Page 2. API 579-2016. Para 8.4.4.3(c). Cosham, A. and Hopkins, P., 2003. The Effect of Dents in Pipelines – Guidance in the Pipeline Defect Assessment Manual, Proceedings of ICPVT-10 International Council for Pressure Vessel Technology, Vienna, Austria, 7-10 July 2003. Page 2. Rafi et al. (2012). Page 6. 22 54 55 56 ASME B31.8-2018. Para R-1. Rafi et al. (2012). Page 2. Gao et al. (2008). Page 4. 23