Development of limit load solutions for corroded gas pipelines

J.B. Choia, B.K. Gooa, J.C. Kima, Y.J. Kima,*, W.S. Kimb

aSchool of Mechanical Engineering, SAFE Research Center, Sungkyunkwan University, 300 Chunchun-dong, Jangan-gu, Suwon,

Kyonggi-do 440-746, South KoreabKorea Gas Company Research and Development Center, 638-1 Il-dong Ansan Kyonggi-do 425-150, South Korea

Received 1 May 2001; revised 2 January 2003; accepted 2 January 2003

Abstract

Pipelines have the highest capacity and are the safest and the least environmentally disruptive means for gas or oil transmission. Recently,

failures due to corrosion defects have become of major concern in maintaining pipeline integrity. A number of solutions have been developed

for the assessment of remaining strength of corroded pipelines. However, these solutions are known to be dependent on material properties

and pipeline geometries.

In this paper, a fitness-for-purpose (FFP) type limit load solution for corroded gas pipelines made of X65 steel is proposed. For this

purpose, a series of burst tests with various types of machined pits are performed. Finite element simulations are carried out to derive an

appropriate failure criterion. Then, further, extensive finite element analyses are performed to obtain the FFP type limit load solution for

corroded X65 gas pipelines as a function of defect depth, length and pipeline geometry.

q 2003 Elsevier Science Ltd. All rights reserved.

Keywords: Corrosion defects; Limit load; Pipeline; Finite element analysis; Pipe burst test

1. Introduction

Since the 1950’s, pipelines have been used as one of the

most economical and safest ways of transmitting oil and

gas, and a number of pipelines are still under construction

all around the world. However, the number of accidents

have also dramatically increased with the increasing

number of operating pipelines [1,2]. The integrity of

these pipelines is of importance due to the explosive

characteristic of gas and oil. Currently, soil and water

contamination due to the failure of pipelines has been

raised as one of the critical issues affecting preservation of

the environment. For these reasons, intensive research

efforts have been carried out on the assessment of

structural integrity of pipelines.

Corrosion is known to be one of the major reasons

causing pipeline failure. ASME B31G [3] is one of the most

widely accepted solutions for the assessment of corrosion

defects. ASME B31G idealizes the complex geometry of

a corrosion pit as an elliptical shape, and applies a bulging

factor for the consideration of defect geometry. This

solution has been modified by Kiefner and Vieth [4] to

enhance its accuracy. Vieth and Kiefner [5] collected an

extensive series of pipeline burst test results for deriving

improved corrosion defect assessment procedures. The

improvement was achieved by introducing a new bulging

factor and the material flow stress, and a more detailed

consideration of the defect shape using iterative calcu-

lations. This method has been implemented in a program

known as RSTRENG [6].

ASME B31G and RSTRENG have been widely used for

assessing the remaining strength of piping and pressure

vessels due to its conservatism. However, it has been

revealed that these criteria are excessively conservative

when applied to defects in high strength pipelines [7–9]. In

1997, Stephens and Leis [10] observed that the failure of

corroded pipelines was controlled by ultimate strength

rather than flow strength in mid- to high-strength steel

pipelines. On the basis of experimental observations,

Stephens et al. [11] developed a specific finite element

code, which is called PCORRC, and proposed a limit load

0308-0161/03/$ - see front matter q 2003 Elsevier Science Ltd. All rights reserved.

doi:10.1016/S0308-0161(03)00005-X

International Journal of Pressure Vessels and Piping 80 (2003) 121–128

www.elsevier.com/locate/ijpvp

* Corresponding author. Tel.: þ82-31-290-5274; fax: þ82-31-290-5276.

E-mail address: yjkim@yurim.skku.ac.kr (Y.J. Kim).

Abbreviations: API, American Petroleum Institute; ASME, American

Society of Mechanical Engineers; FEA, Finite element analysis; BG/DNV,

British Gas/Det Norske Veritas; KOGAS, Korea Gas Corporation.

solution for moderate- to high-toughness pipe based on

an extensive series of FEA. Recently, the corrosion defect

assessment procedure has become more specific in terms of

pipeline materials and defect geometries [11–13]. There-

fore, it has been necessary to develop a specific solution for

an accurate assessment of corrosion defects especially in

high strength pipeline steels.

In this paper, a specific limit load solution for the

assessment of corrosion defects in API X65 gas pipelines is

developed by comparing experimental data with FEA

results. An extensive series of 3D elastic–plastic FEA was

performed, and as a result, a limit load solution, which

provides the maximum allowable pressure as a function of

corrosion defect geometry, is proposed.

2. Procedures for development of the limit load

solution

The failure mechanism of corrosion defects in mid- to

high-toughness pipeline materials such as API X65

pipeline steel is known to be different from that of low

toughness pipeline materials [7,8]. While the defect in

low toughness pipeline may fail by a fracture-based

mechanism, which is controlled by material flow stress,

the defect in mid- to high-toughness pipeline shows

plastic collapse, which is controlled by material ultimate

stress. Therefore, the limit load solution for the assess-

ment of corrosion defects in high toughness pipelines

should be developed on the basis of the specific material

tensile properties. In this paper, a new failure criterion for

X65 pipeline steel is introduced by conducting a

systematic approach including pipe burst tests and finite

element simulations.

First, a series of burst tests was performed on various

machined defects to investigate the failure mechanism.

Then, the finite element simulation on test pieces was

performed to derive a failure criterion for the prediction of

maximum allowable pressure. The developed failure

criterion was modified to apply for the general elliptical

shape corrosion pits. Finally, an extensive series of FEA on

elliptical pits was conducted, and a limit load solution is

introduced by applying the analysis results. Fig. 1 shows a

schematic of the development procedure.

3. Pipeline burst test

3.1. Experiments

Burst test pipes were prepared from API 5L X65

pipelines from KOGAS, and widely used for natural gas

transmission. A pipeline of total length 12 m was cut into

pieces with 2.3 m length, and both ends were capped by

Nomenclature

a maximum depth of the defect

c transverse extent of the defect

l axial extent of the defect

t; tnom wall thickness of the pipe

Do outside diameter of the pipe

L length of the pipe

Pmax failure pressure prediction based on the

proposed equation

PFEA maximum pressure from the finite element analysis

PTEST burst pressure from the experiment

R;Rnom mean radius of the pipe

sf flow strength

su ultimate strength

sy yield strength

Fig. 1. Schematic of the limit load solution development for X65 pipeline

steel.

J.B. Choi et al. / International Journal of Pressure Vessels and Piping 80 (2003) 121–128122

circumferential welding to accommodate high internal

pressure. The geometrical configuration of the specimen

tested is shown in Fig. 2, and dimensions of test specimens

and resulting maximum pressures are summarized in

Table 1. The corrosion defect was machined in a rectangular

shape as shown in Fig. 2. The defect was machined to keep

the same thickness at the bottom, and corner edges were

rounded to avoid excessive stress concentration. For

categorizing a corrosion defect, the depth ðaÞ; the width

ðcÞ and the length ðlÞ are usually used. The rectangular shape

corrosion pit is accepted since it can be assumed as the most

critical shape with these three characterizing parameters.

The test equipment is shown in Fig. 3.

In order to observe the strain variation during pressur-

ization, six strain gages were attached in each specimen as

shown in Fig. 4. The positions of strain gages are

summarized in Table 2. Two strain gages were used for

the measurement of local strain at the machined pit, and

others were used for the measurement of global strain

variation.

All specimens showed bulging deformation around the

defect area, and the final failure occurred at the bottom of

the defect area with a crack-like penetration in the

longitudinal direction as shown in Fig. 4. Fig. 5 shows the

variation of pressure during the burst test of the specimen.

The burst pressure was observed to be affected by the

variation of defect depth and length as summarized in

Table 3. The defect width, however, had an insignificant

effect on the burst pressure. Since the burst test produces

much higher hoop stress than axial stress, this tendency

seems to be reasonable.

Fig. 2. A schematic illustration of burst test specimen.

Fig. 3. Picture of burst test equipment.

Table 1

Burst test pipe geometries

Pipe no. l (mm) c (mm) a (mm) ða=tÞ Burst pressure (MPa)

DA 200 50 4.4 (25%) 24.11

DB 200 50 8.8 (50%) 21.76

DC 200 50 13.1 (75%) 17.15

LA 100 50 8.8 (50%) 24.30

LC 300 50 8.8 (50%) 19.80

CB 200 100 8.8 (50%) 23.42

CC 200 200 8.8 (50%) 22.64

L ¼ 2:3 m; Do ¼ 762 mm; t ¼ 17:5 mm:

J.B. Choi et al. / International Journal of Pressure Vessels and Piping 80 (2003) 121–128 123

The final failure was preceded by bubbling deformation

around the defect area, which is typical for mid- to high-

toughness pipeline material. The defect area shows a

significant amount of thickness reduction along the

penetration line, probably caused by local necking prior to

final failure. For all specimens, failure was observed to be

controlled by plastic collapse rather than fracture.

4. Finite element simulation of pipeline burst test

4.1. Finite element analysis

In order to derive the failure criterion for corrosion

defects, 3D elastic–plastic FEA simulating pipeline burst

tests were performed using a commercial finite element

program, ABAQUS [14]. Only a quarter of a full pipe was

modeled by considering symmetry. The machined pit was

modeled as a rectangular shape in accordance with the test

specimen shown in Fig. 6. The model is designed with 20-

node isoparametric brick elements, and the numbers of

elements and nodes are 1129 and 5713, respectively. Since

the final failure was observed from the defect area, the

bottom of the defect area was modeled with sufficient

number of elements determined by a preceding convergence

analysis. The hydrostatic pressure was applied at the inner

surface of the model. Since the test specimen was capped at

both ends prior to the burst test, the corresponding axial

stress was applied at the end of finite element model. The

true stress–true strain curve was adopted from tensile test

results which were performed on the same material as the

burst test specimen. The full stress–strain curve is shown in

Fig. 7. Incremental plasticity with large deformation theory

Fig. 4. Pictures of pipe DC before and after test.

Table 2

Strain gage locations

S1 S2 S3 S4 S5 S6

DA (0,0) (50,0) (150,0) (300,0) (0,75) (0,225)

DB (0,0) (50,0) (150,0) (300,0) (0,75) (0,225)

DC (0,0) (50,0) (150,0) (300,0) (0,75) (0,225)

LA (0,0) – (100,0) (250,0) (0,75) (0,225)

LC (0,0) (50,0) (200,0) (350,0) (0,75) (0,225)

CB (0,0) (50,0) (150,0) (300,0) (0,100) (0,250)

CC (0,0) (50,0) (150,0) (300,0) (0,150) (0,300)

S1(0,0) point is the centre of corrosion defect.

Fig. 5. Variation of pressure during the burst test for various corrosion

depths.

J.B. Choi et al. / International Journal of Pressure Vessels and Piping 80 (2003) 121–128124

was applied for the entire FEA to simulate local deformation

at the defect area.

FEA results are summarized in Table 3 along with burst

test results. Since all test specimens showed local failure at

the defect area, a failure criterion is introduced by

considering the local stress of the defect area. The von

Mises stress values at this area were reviewed in comparison

with experimental results. First, reference stresses were set

to yield strength, sy; flow strength, sf ; ultimate strength, su;

80 and 90% of ultimate strength, respectively. The flow

strength is defined as sf ¼ ðsy þ suÞ=2:

Failure was then assumed to occur when the von Mises

stress distribution across the ligament thickness at the defect

area reached the reference stress as shown in Fig. 8.

Table 3

Comparison between FEA results and experimental results

Pipe Burst pressure (MPa) PFEA=Ptest

sy sf 0:8su 0:9su su

DA 24.11 0.81 0.98 0.99 1.01a 1.01a

DB 21.76 0.66 0.93 0.95 1.04 1.10

DC 17.15 0.42 0.84 0.86 0.95 1.05

LA 24.30 0.68 0.94 0.95 1.00 1.01a

LC 19.80 0.61 0.86 0.88 0.98 1.06

CB 23.42 0.57 0.84 0.86 0.93 1.00

CC 22.64 0.59 0.85 0.88 0.95 1.02

sy : yield strength; sf : flow strength; su : ultimate strength.a The analysis stopped before it reached the corresponding criterion.

Fig. 6. A typical finite element mesh for the burst test simulation.

Fig. 7. True stress–strain curve for API X65 steel (tested at room

temperature).

Fig. 8. The variation of von Mises stress at the defect area with increasing

pressure.

Fig. 9. A schematic illustration of corrosion defect idealization.

J.B. Choi et al. / International Journal of Pressure Vessels and Piping 80 (2003) 121–128 125

The corresponding internal pressure was determined as the

failure pressure. Resulting failure pressures are normalized

with corresponding experimental burst pressures, and

summarized in Table 3. The best prediction is achieved

with the reference stress of 90% of ultimate strength, and the

difference is less than 7%.

Predictions obtained from sy or sf showed overly

conservative results and insufficient sensitivity on defect

geometries. Since the failure mechanism is controlled by

plastic collapse as observed from the test, the prediction on

the basis of su provided more accurate results and

reasonable sensitivity on defect geometries.

4.2. Failure criteria for elliptical corrosion pits

In general, a corrosion pit is idealized into a semi-

elliptical shape rather than a rectangular shape [3] as

shown in Fig. 9. Since the shape of a corrosion pit in a

test specimen is rectangular to model the most severe

case, it is necessary to modify the failure criterion for an

elliptical corrosion defect to an arbitrarily shaped

corrosion pit. For this reason, FEA on elliptical corrosion

pits were performed, and results were compared to test

results. Finite element models with an elliptical corrosion

pit were designed by changing l and c in Fig. 9 to the

corresponding elliptical shape, and analyses were per-

formed for DA, DB and DC. A typical finite element

mesh is shown in Fig. 10.

Fig. 11 shows comparisons between test and analysis

results. In the FEA, su was used for the failure criterion

based on the finite element simulation results. Reference

stresses for the failure prediction were set to su and 0:8su;

respectively. While the predictions with su showed 10%

overestimation, those from 0:8su showed good agreement

with test results. The rectangular shape corrosion pit can be

assumed as the most severe one considering the shape

idealization. In order to develop a conservative engineering

solution, 0:8su was chosen to be the reference stress for the

failure prediction of elliptical shape defects.

5. Generation of limit load solution using FEA

In order to derive a general solution for defect assessment

of X65 gas pipelines, extensive FEA on various elliptical

corrosion defects were performed. Only a quarter of a full

pipe was designed, and the corrosion pit was introduced on

the outside surface as shown in Fig. 9. The finite element

model was designed with 20-node isoparametric brick

elements, and the numbers of elements and nodes are 1071

and 5711, respectively. The same material properties and

loading conditions as specified in Section 4.1 were applied.

Three different parameters of R=t; a=t and l=ffiffiffiRt

pwere

considered in the FEA. The values of R=t were set to 21.3

and 30 considering the actual dimensions of a gas pipeline.

The values of a=t were set to 0.4, 0.6 and 0.8. Five different

l=ffiffiffiRt

pvalues ranging from 0.5 to 6 were considered. Thus a

total of 30 cases were analyzed as summarized in Table 4.

The variation of c would not be significant since axial cracks

are more critical than circumferential cracks for pressurized

pipes as observed from the test, and thus, c=pRo was

fixed to 1/10 for the entire analysis matrix. For all cases,

Fig. 11. Comparison of Pmax between burst test and FEA for elliptical shape

defects.

Fig. 10. A typical finite element mesh for an elliptical corrosion pit.

J.B. Choi et al. / International Journal of Pressure Vessels and Piping 80 (2003) 121–128126

the maximum von Mises stress was observed at the deepest

point of defect. The failure, therefore, was assumed to occur

when the von Mises stress in the defect ligament reached

0:8su as determined in Section 4.2. The maximum

allowable pressure, Pmax; was determined as the internal

pressure when the failure criterion was satisfied.

6. Derivation of limit load solution

Figs. 12 and 13 show the resulting maximum allowable

pressure values for R=t ¼ 21:3 and 30, respectively, in

comparison with modified B31G [2], Battelle PCORRC

[10] and BG/DNV [12] solutions. With increasing R=t; the

maximum allowable pressure decreases. For cases of a=t ¼

0:4 and 0.6, the FEA produced approximately 10–20%

higher values than those from modified B31G. For deep

defects of a=t ¼ 0:8; the FEA results showed lower values

than those from modified B31G with increasing defect

length. This implies that the modified B31G solution is

conservative for all shallow defects, but may be non-

conservative for long and deep corrosion defects. This

tendency is consistent for PCORRC and BG/DNV solutions.

While the proposed solution provides similar predictions to

those from PCORRC for short defects, it results in slightly

higher predictions for long defects.

By applying regression analysis on the FEA results, a

limit load solution is proposed as a function of R=t; a=t and

l=ffiffiffiRt

pas follows:

forlffiffiffiRt

p , 6;

Pmax ¼ 0:9 £2t

Di

su C2

lffiffiffiRt

p

� �2

þC1

lffiffiffiRt

p

� �þ C0

" # ð1Þ

C2 ¼ 0:1163a

t

� �2

20:1053a

t

� �þ 0:0292

C1 ¼ 20:6913a

t

� �2

þ0:4548a

t

� �2 0:1447

C0 ¼ 0:06a

t

� �2

20:1035a

t

� �þ 1:0

Table 4

The analysis matrix

c=pRo R=t a=t l=ffiffiffiRt

pR=t a=t l=

ffiffiffiRt

p

0.1 21.3 0.4 0.5 30 0.4 0.5

1 1

2 2

4 4

6 6

0.6 0.5 0.6 0.5

1 1

2 2

4 4

6 6

0.8 0.5 0.8 0.5

1 1

2 2

4 4

6 6

Fig. 13. Comparison of Pmax between PCORRC, BG/DNV, Modified B31G

and FEA ðR=t ¼ 30Þ:

Fig. 12. Comparison of Pmax between PCORRC, BG/DNV, Modified B31G

and FEA ðR=t ¼ 21:3Þ:

J.B. Choi et al. / International Journal of Pressure Vessels and Piping 80 (2003) 121–128 127

forlffiffiffiRt

p $ 6; Pmax ¼2t

Di

su C1

lffiffiffiRt

p

� �þ C0

� �ð2Þ

C1 ¼ 0:0071a

t

� �2 0:0126

C0 ¼ 20:9847a

t

� �þ 1:1101

Fig. 14 shows the comparison between the prediction by Eq.

(1) and experimental burst pressure. The prediction provides

conservative estimates and shows excellent agreement for

all cases. The proposed systematic approach resulted in a

simple equation on the basis of a complete understanding of

pipeline failure behaviour, and seems to provide sound and

reliable failure predictions.

7. Conclusions

In this paper, a systematic approach was followed to

develop a limit load solution for the assessment of corrosion

pits in API X65 gas pipelines, and the resulting conclusions

are as follows:

(1) In order to derive a failure criterion, a series of burst

test were performed and corresponding finite element

simulations were carried out. The failure mechanism

was controlled by plastic collapse for all cases.

(2) Failure was predicted to occur when the von Mises

stress reached a reference stress across the entire

ligament. While the reference stress for rectangular

corrosion pit was determined to be 90% of the ultimate

strength, that of a corresponding elliptical corrosion pit

was 80% of the ultimate strength.

(3) The modified B31G solution provides conservative

predictions for shallow and short corrosion pits, but

those for deep and long corrosion pits were non-

conservative in comparison with FEA results.

(4) A limit load solution for the assessment of corrosion

pits in API X65 gas pipelines is proposed as a function

of R=t; a=t and l=ffiffiffiRt

pon the basis of FEA results, and

shows excellent agreement with burst test results.

Acknowledgements

The authors are grateful for the support provided by a

grant from Korea Gas Corporation (KOGAS) and Safety

and Structural Integrity Research Center (SAFE) at the

Sungkyunkwan university.

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Fig. 14. Comparison between actual burst pressure and the prediction by

Eq. (1).

J.B. Choi et al. / International Journal of Pressure Vessels and Piping 80 (2003) 121–128128