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Pipeline Dent Strain Assessment Using ASME B31.8

David D. MACKINTOSH

Acuren Inc., Edmonton, Alberta, Canada

[email protected]

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 over-

sensitive 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 Why calculate dent strain? .................................................................................................... 2

2 What is in ASME B31.8R? ....................................................................................................... 2

3 How is surface curvature determined? ................................................................................. 4

4 Do the different methods usually agree? ............................................................................ 10

5 Should the strain be calculated over the whole dent surface? ........................................... 11

6 What are the accept-reject criteria for dent strain in code? ............................................... 11

7 When should ASME B31.8R not be used? ........................................................................... 12

8 What is the strain in very shallow dents? ............................................................................ 12

9 What’s the final word on ASME B31.8R? ............................................................................. 13

10 Appendix: Theory ................................................................................................................. 16

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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).

3

Figure 1a: Sample dent with corrosion, crack, and gouging. (See also Figure 1b.)

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.

Crack Gouging Corrosion

Flow

Flow

Brush

marks

4

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).

L

5

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 noise-

sensitive, 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 over-

react 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.

6

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.

Figure 4: A dent profile obtained from laser scanning showing correct and incorrect circle-fitting

for dent strain assessment. (Back wall profile is estimated.)

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.)

Radius too small

Radius correct

Radius too large

approximate points of inflection

selected segment

7

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.

8

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.

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.

Straight edge

Dent

Profile measurement

Ring spacer

9

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)

10

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 technician-

dependent. 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 high-

resolution 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.

11

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).

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

Straight-edge #1

Straight-edge #2

12

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].

13

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)

14

Figure 12: Laser analysis of a dent that has a point of maximum strain away from the apex. See

also Figure 13.

(a) External dent surface as

seen in 3D laser scan data.

(b) Depth contours showing

position of apex.

(c) Strain contours showing

area of maximum strain.

Apex (deepest point)

Point of highest strain,

(away from apex)

15

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?

(a) Radius of curvature is

smaller at point of maximum

strain.

(b) Radius of curvature is

larger (lower strain) at

apex.

100 mm

16

10 Appendix: Theory

10.1 What are the ASME B31.8R equations?

Table A1: Notation

Wall thickness t

Measured dent depth d

Measured dent length L

Pipe nominal radius R0

Measured dent curvature in circumferential direction R1

Measured dent curvature in longitudinal direction R2

Bending strain in circumferential direction ε1

Bending strain in longitudinal direction ε2

Extensional strain in longitudinal direction ε3

Effective strain at inside surface of pipe εi

Effective strain at outside surface of pipe εo

Maximum effective strain εeff

Based on the notation in Table A1 and Figure 3, the ASME B31.8R-2018 equations are:

�� = �2 � 1

− 1

�� (A1)

�� = �2�

(A2)

�� = 12 ��

��

(A3)

�� = 2√3 � �� + ��(�� + ��) + (�� + ��)� ��/� (A4)

�� = 2√3 � �� − ��(−�� + ��) + (−�� + ��)� ��/� (A5)

�� = max ��, �� (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 inside-

surface 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).

17

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:

�� = 9.532 � 1

254 − 1−300� = 0.0346 = 3.46% (A7)

�� = 9.532 × 200 = 0.0238 = 2.38% (A8)

�� = 12 � 10

250��

= 0.0008 = 0.08% (A9)

The effective strains are:

�� = 1.155 × �0.001200 + 0.000853 + 0.000606 ��/� = 0.0595 = 5.95% (A10)

�� = 1.155 × �0.001200 − (−0.000798) + 0.000530��/� = 0.0581 = 5.81% (A11)

The reported maximum effective strain εeff is the maximum of the results from A10 and A11,

which is 5.95% strain.

18

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:

�� = 0.3752 � 1

10 − 1−12� = 0.0344 = 3.34% (A7b)

�� = 0.3752 × 8 = 0.0234 = 2.34% (A8b)

�� = 12 �0.375

10 ��

= 0.0008 = 0.08% (A9b)

The effective strains are:

�� = 1.155 × �0.001182 + 0.000833 + 0.000587 ��/� = 0.0589 = 5.89% (A10b)

�� = 1.155 × �0.001182 − (−0.000778) + 0.000512��/� = 0.0574 = 5.74% (A11b)

The reported maximum effective strain εeff is the maximum of the results from A10b and A11b,

which is 5.89% strain.

19

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 = �

2 = �� (strain) (312)

(same as Equation A2).

(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).

R

L

neutral t

20

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.)

21

Endnotes

1 Escoe, A. Keith (2006). Piping and Pipeline Assessment Guide, 1st ed., Gulf Professional

Publishing, Burlington, MA. Page 179.

2 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.

3 Escoe (2006). Page 180.

4 Rosenfeld et al. (2002a). Page 649.

5 ASME B31.8 (2018), Gas Transmission and Distribution Piping Systems. American Society

of Mechanical Engineers, New York, NY.

6 API 579-1 / ASME FFS-1, Fitness-For-Service, 3rd ed (2016). American Petroleum Institute,

Washington, DC.

7 BS 7608:2014+A1:2015, Guide to fatigue design and assessment of steel products. BSI

Group, London, UK.


9 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.

10 ASME B31.8-2018. Para R-1.

11 ASME B31.8-2018. Para 851.4.1.

12 CSA Z662 (2019), Oil and Gas Pipeline Systems. Canadian Standards Association, Ottawa,

Canada. Para 10.10.4.1.

13 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.

14 Creaform, Inc (2020). Contextual Help for Pipecheck 6.0.0 (2020.06.29). Lévis, QC, Canada.

15 Okoloekwe et al. (2018). Page 3.

16 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.

17 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.

18 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.

19 Creaform, Inc (2020). Pipecheck software version 6.0.0 (2020.06.29). Lévis, QC, Canada.

20 Rosenfeld, M., Porter, P., and Cox, J. (1998), “Strain estimation using Vetco deformation

tool data”. ASME 2nd International Pipeline Conference, Calgary.

21 Lukasiewicz et al. Page 5.

22 Lukasiewicz et al. Page 2.

22

23 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.

24 Noronha et al. (2005).


26 API Std 1163 (R2018) In-line Inspection Systems Qualification Standard, 2nd ed (2013,

reaffirmed 2018). American Petroleum Institute, Washington, DC. Para 9.3.


28 ASME B31.8-2018. Para R-1.

29 Rosenfield et al. (2002). Page 648

30 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).

31 ASME B31.8-2018. Para 841.2.4(c)(1).

32 CSA Z662-2019. Para 10.10.4.1.

33 Rafi et al. (2012). Page 1.

34 ASME B31.8-2018. Para R-1.


36 ASME B31.8-2018. Para. 851.4.1.

37 CSA Z662-2019. Para. 10.10.4.2.

38 Rosenfeld, M.J. (2002b). “Factors to Consider When Evaluating Damage on Pipelines.” Oil

and Gas Journal, September 9, 2002.



41 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.

42 Young, W. and Budynas, R. (2001). Roark’s Formulas for Stress and Strain, 7th ed.

McGraw-Hill Education, New York. Page 589.

43 Okoloekwe et al. (2018).

44 ASME B31.8-2018. Para R-1.

45 Gao et al. (2008). Page 5.

46 Hibbeler, R. C. (2003), Mechanics of Materials, SI Edition. Prentice-Hall, Inc., Upper Saddle

River, NJ. Page 571.


48 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.

49 Lukasiewicz et al. (2006).


51 API 579-2016. Para 8.4.4.3(c).

52 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.


23

54 ASME B31.8-2018. Para R-1.


56 Gao et al. (2008). Page 4.

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