ORIGINAL ARTICLE

Comparison of computational and analytical methodsfor evaluation of failure pressure of subsea pipelines containinginternal and external corrosions

Kwang-Ho Choi1 • Chi-Seung Lee1 • Dong-Man Ryu1 • Bon-Yong Koo2 •

Myung-Hyun Kim1• Jae-Myung Lee1

Received: 2 June 2015 / Accepted: 29 November 2015 / Published online: 15 December 2015

� JASNAOE 2015

Abstract In the designing stage of subsea pipelines, the

design parameters, such as pipe materials, thickness and

diameters, are carefully determined to guarantee flow

assurance and structural safety. However, once corrosion

occurs in pipelines, the operating pressure should be

decreased to prevent the failure of pipelines. Otherwise, an

abrupt burst can occur in the corroded region of the pipe-

line, and it leads to serious disasters in the environment and

financial loss. Accordingly, the relationship between the

corrosion amount and failure pressure of the pipeline, i.e.,

the maximum operating pressure, should be investigated,

and then, the assessment guideline considering the failure

pressure should be identified. There are several explicit

type codes that regulate the structural safety for corroded

subsea pipelines, such as ASME B31G, DNV RF 101, ABS

Building and Classing Subsea Pipeline Systems, and API

579. These rules are well defined; however, there are some

limitations associated with describing precise failure pres-

sure. Briefly, all of the existing rules cannot consider the

material nonlinearity, such as elastoplasticity effect of the

pipeline, as well as the actual three-dimensional corrosion

shape. Therefore, the primary aim of this study is to sug-

gest a modified formula parameter considering the above-

mentioned pipeline and corrosion characteristics. As a

result, the material nonlinearity as well as the corrosion

configuration, i.e., axial/circumferential corrosion length,

width and depth, is reflected in a set of finite element

models and a series of finite element analysis considering

the operation conditions are followed. Based on the com-

parative study between the simulation and analytical

results, which can be obtained from the classification

society rules, the modified formulae for failure pressure

calculation are proposed.

Keywords Subsea pipeline � Corrosion � Finite element

analysis � Failure pressure � Classification society rules

1 Introduction

Recently, the installation and operation of onshore and

offshore pipelines have been increasing rapidly because of

the increased demand for fossil fuel energy, such as crude

oil and gas. According to the energy resources-related

report, approximately 60,000 km of onshore and offshore

pipelines will be installed worldwide between 2014 and

2016 to transport the fossil fuel. The length of subsea

pipelines is expected to be at least 18,000 km [1].

However, according to the Pipeline and Hazardous

Materials Safety Administration (PHMSA), more than 600

pipeline accidents occurred during the past decade [2].

There are many causes of pipeline accidents. As corrosion

and construction defects were found to be main causes of

some catastrophic disasters, corrosion was deemed very

critical for onshore and offshore pipelines (Figs. 1, 2).

Subsea pipelines, specifically, are more significantly

affected by corrosion from seawater. In particular, various

seawater characteristics, such as seawater temperature,

salinity, water velocity and surface roughness, can affect

the corrosion state of the pipeline [3, 4].

With a view to ensuring the structural safety of the

pipelines during the operation, the relationship between the

& Jae-Myung Lee

jaemlee@pusan.ac.kr

1 Department of Naval Architecture and Ocean Engineering,

Pusan National University, Busan 46241, Republic of Korea

2 Korea Energy Technology Center, American Bureau of

Shipping, Busan 47300, Republic of Korea

123

J Mar Sci Technol (2016) 21:369–384

DOI 10.1007/s00773-015-0359-5

corrosion amount and failure pressure of the pipeline

should be investigated. In addition, the assessment guide-

line considering the failure pressure should be identified.

There are several explicit type codes that regulate the

structural safety for corroded subsea pipelines such as

ASME B31G, DNV RF 101, ABS Building and Classing

Subsea Pipeline Systems and API 579. These codes have

been widely adopted in onshore and offshore engineering

fields since 1960s and have been updated from time to

time. Nevertheless, there are some limitations to describe

the precise failure pressure, i.e., all the existing rules can-

not consider the material nonlinearity, such as elastoplas-

ticity effect of the pipeline, as well as the actual three-

dimensional (3D) corrosion shape. Because of these limi-

tations, two types of mechanical problems cannot be rec-

ognized. First, the failure pressure is underestimated/

overestimated since the pipe material is postulated as an

elastic media. Second, the precise failure pressure is not

calculated since the circumferential corrosion length is not

considered in the pipeline assessment formulae.

In order to overcome the above-mentioned limitations,

many pipeline engineers and researchers have improved

the pipe assessment formulae used in field, and proposed a

new assessment code. Netto et al. [5] recognized that the

existing criteria for evaluating the residual strength of the

corroded pipeline could have some limitations, and the

numerical tool that utilized the 3D model was not simple

enough for the field engineer. Therefore, Netto et al. pro-

posed the improved explicit formulae. To do this, they

performed laboratory experiments to evaluate failure

pressure of externally corroded pipes and conducted non-

linear numerical analysis to identify the failure pressure of

pipelines with local metal loss. Explicit failure pressure

formulae which based on their experimental results were

proposed and that were a function of corrosion depth and

length and pipe diameter. However, the improved explicit

formulae also have some limitations in applying geomet-

rical range.

Fekete and Varga [6] also mentioned causes of the

limitations of the guides and rules, especially; they ana-

lyzed the geometrical limitations of the existing guides and

rules. For this, they studied the effect of the corrosion

width on mechanical capacity changes of steel pipes.

Various corrosion factors related to the pipe dimensions

that can yield geometrical nonlinearity were considered

during the computational stress analyses, such as the cor-

rosion width and corrosion length. The results were com-

pared to some of the classification rules, such as DNV,

ASME and Advantica.

Moreover, some researchers focused on the material

characteristics of the pipelines. Xu and Cheng [7] investi-

gated the failure pressure changes for various grades of

pipeline steel with corrosion defects, i.e., they focused as

material aspects. They confirmed that as the corrosion

Fig. 1 Internal and external corroded pipeline in subsea environment

Fig. 2 Causes of structural failure for onshore and offshore pipelines

[2]

370 J Mar Sci Technol (2016) 21:369–384

123

depth is increased and the steel grade is decreased, the

failure pressure of a pipe is reduced. In addition, they

validated the computational analysis results by comparing

with as-is codes, such as ASME B31G and DNV Recom-

mendation Practice (RP) F101.

Besides, Ma et al. [8] also focused on the material

characteristics, especially the hardening behavior of

materials. They proposed a method for prediction failure

pressure of corroded pipelines that were fabricated by

various high-grade steel. To determine the structures’

failure state, the von Mises strength failure criterion cou-

pled with the Ramberg–Osgood hardening stress–strain

relationship was adopted. Furthermore, extensive finite

element simulations with respect to eight grades of pipeline

were carried out.

In addition to the above-mentioned parametric study

methods, some researchers tried to use another method,

which is related to the reliability analysis of the pipelines.

Valor et al. [9] investigated the relationship between cor-

rosion depth and the reliability of buried pipeline. Several

types of corrosion rate models were introduced to describe

the real pit depth distribution of corrosion empirically, e.g.,

the linear growth model, Markov model, time-independent

generalized extreme value distribution (GEVD) model and

time-dependent GEVD model. Corrosion data measured

from 1996 to 2005 were used in this study. They focused at

the explicit formulae type.

In the context of aforementioned, various analysis

methods were introduced for stress or failure analysis of

corroded pipes, such as statistical and parametrical studies.

The nonlinearity is one of the most essential pipeline

assessment factors to be considered for a robust assessment

and has been examined by many researchers. However, it is

still difficult to apply these previous research results to

solve the actual corrosion problem of a subsea pipeline.

Some of the physical factors that are induced by the subsea

environment, such as the correlation between internal or

external pressures of pipeline and three-dimensional cor-

rosion geometries, cannot be considered in as-is codes.

Hence, the present study used finite element analysis (FEA)

reflecting the material nonlinearity to analyze the structural

behavior and failure aspects of subsea pipelines according

to corrosion geometry and location. Furthermore, various

internal and external pressures were applied to the subsea

pipeline finite element (FE) model during analysis to

deliberate the subsea environment and oil or gas transport

conditions.

Based on the aforementioned corrosion configurations,

i.e., corrosion length, width and depth, a number of anal-

ysis scenarios were established and a series of computa-

tional analyses were carried out. From the results, the

relationship between failure pressures and corrosion

geometries was estimated quantitatively. In addition, the

analysis results of failure pressure were compared to

classification society’s codes, such as the API, ASME,

DNV and ABS, to investigate the limitations of the

aforementioned codes.

2 Codes for estimating of failure stressof corroded pipelines

It takes much time and cost to install or to replace large-

scale industrial structures. In addition, catastrophic disas-

ters could occur if these structures fail. Therefore, the

industry has established guidance for robust pipeline

assessment of subsea pipelines such as the ASME, DNV,

ABS and API. The equations for failure pressure, charac-

teristics and limitations regarding four kinds of pipeline

assessment codes are discussed below.

2.1 ASME B31G

ASME B31G is one of the most widely used codes for

assessment of failure pressure in corroded pipelines. This

rule was developed in the early 1960s based on experi-

mental fracture mechanism in the early 1960s and

introduces the effective area for the calculation of failure

pressure. The failure pressure is specified as follows

[10]:

pf ¼2t

Drh ð1Þ

rh ¼ rf1� AC

A0

1� 1M

AC

A0

" #ð2Þ

M ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ 0:8 � l2

Dt

rð3Þ

where pf is the failure pressure, rh the hoop stress, rf thepipeline material’s flow stress, AC the projected cross-

sectional area with corrosion, the represented area of the

corroded region, which can be calculated by length times

thickness of the corrosion region, M the stress concentra-

tion factor (or Folias factor), l the length of the corrosion

region, D the pipeline’s outside diameter, and t the pipe-

line’s thickness. In the ASME B31G code, the flow stress

was defined as 1.1 times the yield stress. The expression

between the brackets in Eq. 2 is a section reduction factor,

which is a function of the corroded pipeline area and can be

considered as an effective pipeline region.

2.2 DNV-RP-F101

DNV-RP-F101 is similar to ASME B31G with two dif-

ferences: (1) A safety factor is implemented into the failure

J Mar Sci Technol (2016) 21:369–384 371

123

stress formulae and (2) the tensile (not a yield) stress is

adopted in the rules. The failure pressure is specified as

follows [11]:

pf ¼ cm2t � fuD� tð Þ

1� cdðd=tÞ�ð Þ

1� cdðd=tÞ�Q

� � ð4Þ

Q ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ 0:31

lffiffiffiffiffiDt

p� �2

sð5Þ

where cm is the partial safety factor for the prediction

longitudinal corrosion, cd the partial safety factor for the

corrosion depth, fu the material’s tensile strength, D the

nominal outside diameter, l the longitudinal length of the

corroded region, and t the uncorroded pipeline’s wall

thickness.

2.3 ABS guide for building and classing subsea

pipeline systems

The ABS code ‘‘Guide for Building and Classing Subsea

Pipeline Systems’’ is also similar to ASME B31G. How-

ever, the flow stress is calculated by as the average of yield

and tensile strengths. The failure pressure is specified as

follows [12]:

pf ¼ 0:5 SMYSþ SMTSð Þ 2t

D

� �1� d

t

1� d

t

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ0:8 Lffiffiffi

Dtp

� �2r ð6Þ

where D is the average diameter, t the wall thickness

measurement, d the depth of the corrosion defect (should

not exceed 0.8 9 t), L the measured length of the corrosion

depth, and SMYS and SMTS the specified minimum yield

strength and specified minimum tensile strength, respec-

tively, in the hoop direction.

2.4 API 579

The concept of ‘‘Fitness-For-Service (FFS)’’ was intro-

duced by the API to determine the time and location of

inspection and/or repair. It contains many comments rela-

ted to inspection and repair, the decision-making proce-

dure, and cost-effective inspection and repair methods. API

579, which is part of FFS in the API code, is one of the

most widely adopted FFS codes for industrial structures,

particularly pressure vessels, offshore structures and

equipments. The general FFS assessment procedure of API

579 is shown in Fig. 3.

One of the most distinctive characteristics of API 579

assessment methods is categorized into three levels

depending on the accuracy of calculation and the required

calculation complexity.

1. Level 1 is the most conservative level; however, it is

easy to apply and calculations require least amount

data.

2. Level 2 is similar to Level 1; however, a detailed

calculation process is required. It can estimate struc-

tural behavior more accurately than Level 1.

3. Level 3 is the most accurate and the analysis requires

more complex computation and expertise.

Level 2 uses an explicit formula and requires only

geometric information to calculate the critical stress value.

However, there are some limitations to estimate the precise

failure stress of corroded pipelines. Because the given

parameters in formulae were not reflected perfectly for the

reality of corrosion phenomenon.

A Level 3 assessment cannot be easily adopted in the

actual field owing to the complex analysis procedure

required (nonlinear FEA). However, it provides more

precise analysis results than the other assessment levels.

For this reason, the present study used Level 3 as an FFS

assessment method for subsea pipelines. Calculation results

from a Level 2 assessment were also used in the validation

of the current comparative study.

2.5 API 579 remaining strength factor

API 579 introduced the remaining strength factor (RSF) as

the ratio of strength of a pipeline with corrosion over that

of the intact condition. The assessment methods with

respect to the corrosion are demonstrated in Parts 4–6.

Parts 4, 5, 6 of API 579 describe the assessment techniques

for general metal loss, localized metal loss and pitting

corrosion, respectively. The present study postulated a

pipeline corrosion as a local metal loss which falls in the

scope of Part 5 of API 579.

Some differences exist between the API 579 and FEA

calculations. In the API 579 calculation, only the internal

pressure was considered. On the other hand, in the FEA

calculation, both the internal and external pressures were

considered. Additionally, axial force, weld joint efficiency,

thermal load and other parameters were not considered

during FEA. Hence, these terms were not considered dur-

ing the API 579 calculations.

Level 2 of API 579 Part 5 specified formulae for the

circumferential and longitudinal stresses, and longitudinal

shear stress. The maximum values of the calculated

equivalent stress need to be calculated and are compared to

failure criterion.

Figure 4 shows API 579 definition of internal and

external corrosions. The circumferential stress ðrcmÞ, lon-gitudinal stress at point A ðrAlmÞ, longitudinal stress at pointB ðrBlmÞ and longitudinal shear stress (s) are calculated

using Eqs. 7–10, according to API 579 [13].

372 J Mar Sci Technol (2016) 21:369–384

123

rcm ¼ MAWP

RSF � cos aD

D0 � Dþ 0:6

� �ð7Þ

rAlm ¼ MCs

Ec

Aw

Am � Af

MAWPð Þ þ F

Am � Af

�

þ yA

IXFyþ yþ bð Þ MAWPð ÞAw þMx½ � þ xA

IYMy

�ð8Þ

rBlm ¼ MCs

Ec � cos aAw

Am � Af

MAWPð Þ þ F

Am � Af

�

þ yB

I �XF�yþ yþ bð Þ MAWPð ÞAw þMx½ � þ xB

I �YMy

�ð9Þ

s ¼ MT

2 At þ Atfð Þ tmm � FCAð Þ þV

Am � Af

ð10Þ

MCs ¼

1� 1MC

t

� �dtc

� �1� d

tc

� � ð11Þ

MCt ¼ 1:0þ 0:1401ðkcÞ2 þ 0:002046ðkcÞ4

1:0þ 0:09556ðkcÞ2 þ 0:00025024ðkcÞ4ð12Þ

kc ¼1:285cffiffiffiffiffiffiffi

Dtcp ð13Þ

whereMAWP is the maximum allowable working pressure;

RSF remaining strength factor computed based on the flaw

Flaw & Damage Mechanism Identification

Applicability and Limitations of the FFSAssessment Procedures

Data Requirements

Assessment Techniques and AcceptanceCriteria

Remaining Life Evaluation

Remediation

In-Service Monitoring

Documentation

Damage Classes :Corrosion, Crack-like flaw, Brittle fracture, Creep,

Cover components in the pressure boundary of PV,Piping and Tanks

Design pressure & temperature, Past inspection records,NDE

Assessment LevelLevel 1 : Inspector/Plant Engineer

Level 2 : Plant EngineerLevel 3 : Expert EngineerAcceptance Criteria

Allowable stress (shell distortion)Remaining Strength Factor (metal Loss)

Failure Assessment Diagram (crack-like flaw)

To set an inspection interval

May used when a flaw is not acceptable in its currentcondition

In-service monitoring is one method whereby futuredamage or conditions leading to future damage can beassessed or confidence in the remaining life estimate can

be increased

A general rule A practitioner should be able to repeatthe analysis from documentation without consulting an

individual originally involved in the FFS assessment

STEP DETAIL

Fig. 3 General FFS assessment procedure of API 579 [13]

J Mar Sci Technol (2016) 21:369–384 373

123

and damage mechanism in the component; a the cone half-

apex angle in conical type pipe, which is 0 for a cylindrical

pipe; D the cylinder’s inside diameter: cone (at the location

of the flaw), sphere or formed head; D0 the cylinder’s

outside diameter, corrected for LOSS and FCA as appli-

cable; Ec the circumferential weld joint efficiency; Aw the

effective area on which pressure acts; Am the metal area of

the cylinder’s cross section; Af the cross-sectional area of

the region of local metal loss; yA the distance from the x–x

axis measured along the y-axis to Point A on the cross

section; yB the distance from the x–x axis measured along

the y-axis to Point B on the cross section; IX the cylinder’s

moment of inertia about the x–x axis; IX the moment of

inertia of the cross section with the region of local metal

loss about the x-axis; IY the moment of inertia of the cross

section with the region of local metal loss about the y-axis;

F the applied net-section axial force for the weight or

weight plus thermal load case; �y the location of the neutral

axis; b the location of the centroid of area, Aw, measured

from the x–x axis; Mx the applied section bending moment

yx

x

y,yMetal Loss

tmm

x

x

A

Df

2

Do

2

B

D2

yLx

tc

My

c

FMx

MT

P

(a)

y, y Metal Loss

xx

x

Do

2

D2

x

tmm

Df

2

AB

yLx

y

tc

(b)

Fig. 4 Parameters used in API

579 for defining a internal

corrosion and b external

corrosion [13]

374 J Mar Sci Technol (2016) 21:369–384

123

for the weight or weight plus thermal load case about the x-

axis;My the applied section bending moment for the weight

or weight plus thermal load case about the y-axis; xA the

distance along the x-axis to Point A on the cross section; xBthe distance along the x-axis to Point B on the cross sec-

tion; MT the applied net-section torsion for the weight or

weight plus thermal load; At the mean area to compute

torsion stress for the region of the cross section without

metal loss; Atf the mean area to compute torsion stress for

the region of the cross section with metal loss; tmm the

minimum remaining thickness determined at the time of

the assessment; FCA the future corrosion allowance

applied to the region of local metal loss; and V the applied

net-section shear force for the weight or weight plus ther-

mal load case; MCs ;M

Ct Folias factor or the bulging cor-

rection factor; c the circumferential extent or length of the

region of local metal loss.

The equivalent stress is defined as

rAe ¼ rcmð Þ2� rcmð Þ rAlm

þ rAlm 2þ3s2

h i0:5ð14Þ

rBe ¼ rcmð Þ2� rcmð Þ rBlm

þ rBlm 2þ3s2

h i0:5ð15Þ

where rAe and rBe are the equivalent stresses at point A and

B, respectively. The maximum stress in the corroded pipe

was chosen by one of the larger values in these two:

re ¼ max rAe ; rBe

� �ð16Þ

3 Sample pipelines and computational analysisprocedures

3.1 Sample pipeline and case studies

A series of computational analyses were conducted to

predict the structural behavior and failure pressure. The

targeted subsea pipeline experiences both internal and

external pressures. The computational analysis was carried

out using the commercial FEA software tool ABAQUS.

Corrosion was defined in accordance with Fig. 5. This

approach had already been verified by several researchers,

e.g., Netto et al. [5]. Netto et al. introduced two corrosion

idealized models in the FEA: the exact defect-shape model

(EDSM) and the simplified defect-shape model (SDSM). As

shown in Fig. 1, the EDSM is elliptical, which reflects the

actual corrosion shape. In contrast, the SDSM is rectangu-

lar, which provides efficiency for modeling the corrosion

shape. An analysis was conducted, and the results were

compared with those from an actual failure pressure test.

The failure pressure of the EDSM and SDSM models had

acceptable average errors of 10 and 15 %, respectively. The

failure pressures of the EDSM and SDSM were slightly

overestimated and underestimated, respectively. The SDSM

has limitations such as the stress concentration because of

its rectangular shape. However, the underestimation ten-

dency could be an advantage for safety assessment.

Therefore, the SDSM was adopted in this study. It was

postulated that the corrosion had taken place at the center of

the pipe, away from the boundaries of the FEM model.

Table 1 presents the 43 analysis cases to investigate

effects of both external and internal corrosions with vary-

ing depth, width and length corrosion. The corrosion depth

and length are expressed as ratios over the initial pipe

thickness and diameter, respectively. The degree of cor-

rosion width denotes an arc length of the corroded region in

the pipe’s cross section.

3.2 Material properties and dimensions of pipeline

The subsea pipeline used in this study was made of carbon

manganese steel grade API 5L X65. Figure 6 is an example

of the strain–stress curves of this material. Table 2 shows

its material properties and dimensions. A piecewise linear

material model was used to represent the nonlinear material

behavior.

Fig. 5 Configuration of internal

and external corrosion in a

subsea pipeline

J Mar Sci Technol (2016) 21:369–384 375

123

3.3 Finite element model loading and boundary

conditions

Figure 7 shows the FE model. The number of FE is

approximately 17,600. The selected element was

reduced integration 20-node hexahedral element

(C3D20R in ABAQUS). To reduce the computation

time, only a half in cross section and a half in lengths

were modeled and symmetric boundary conditions were

applied. Moreover, to avoid rigid body motion during

Table 1 Analysis casesAnalysis case Corrosion location Depth (%) Width (�) Length (%)

E-D1 External 10 30 50

E-D2 20

E-D3 25

E-D4 30

E-D5 40

E-D6 50

E-D7 60

E-D8 75

E-W1 30 15 50

E-W2 30

E-W3 45

E-W4 60

E-W5 50 15 50

E-W6 30

E-W7 45

E-W8 60

E-W9 70 15 50

E-W10 30

E-W11 45

E-W12 60

E-L1 30 30 25

E-L2 50

E-L3 75

E-L4 100

E-L5 50 30 25

E-L6 50

E-L7 75

E-L8 100

E-L9 70 30 25

E-L10 50

E-L11 75

E-L12 100

I-D1 Internal 25 30 50

I-D2 50

I-D3 75

I-W1 50 15 50

I-W2 30

I-W3 45

I-W4 60

I-L1 50 30 25

I-L2 50

I-L3 75

I-L4 100

376 J Mar Sci Technol (2016) 21:369–384

123

analysis, one point at the center of the pipe was totally

fixed [15].

The symmetric condition of the pipe was checked in

order to reduce the series-analysis time. Figure 8 shows the

FEA results of the full-scale and the symmetric FE models

under a 12 MPa inner pressure.

There was no significant difference in the von Mises

stress contours between those two FEM models. Hence, the

quarter FE model with symmetric boundary condition was

acceptable.

The analysis started with applying external pressure of

300 bar or 30 MPa, because it was assumed that the target

subsea pipeline operated approximately 3000 m below the

sea level.

Then, the internal pressure is applied and increased until

reaching the maximum tensile strength of pipe material.

Then, the failure pressure is postulated as the maximum

internal pressure that leads to the burst of the pipeline, i.e.,

the maximum internal pressure can be considered as the

failure pressure when themaximum stress reaches the tensile

strength of the pipe materials. The stress-judging point,

which determined the failure of pipe, is not at the specific

point, but at the thin part induced by the local metal loss,

because if the stress anywhere in this part reaches the tensile

strength of the pipeline, a failure can occur.

4 Computational analysis results and discussion

4.1 Responses at corroded pipeline subject

to internal and external pressures

Figure 9 shows the stress contour for the E-D3, E-D6 and

E-D8 analysis cases at 43 MPa, which is the failure pressure

for the E-D8 case. Table 3 shows the predicted failure pres-

sure. Figure 10 shows the relationship between failure pres-

sure and corrosion depth, and corrosion width and length.

Major observation, as seen from Table 3 and Fig. 10, is

as follows:

1. There were no apparent differences in failure pressure

between the external and internal corrosion locations.

2. As the corrosion depth increased, the failure pressure

decreasedproportionally.Specifically, the failure pressure

dropped significantly in the 50–60 % range of corrosion

depth and the slope rapidly decreased above 60 %.

3. Corrosion length or width does not exhibit strong

influences on failure pressure.

4. The wall thickness is the most sensitive parame-

ter. Therefore, proper wall thickness must be assessed

to ensure sufficient safe in operating or to determine

the necessity of maintenance.

4.2 Comparison between existing codes

and simulation results

The simulation results regarding the location of external

corrosion were compared with the calculation results of

Fig. 6 Stress–strain curve of API 5L X65 steel and the idealized

piecewise linear material model [14]

Table 2 Material properties and dimensions of the target pipeline

Items Values

Density (kg/m3) 7850

Young’s modulus (GPa) 206.7

Poisson’s ratio 0.3

Yield stress (MPa) (Minimum) 449

Tensile stress (MPa) (Minimum) 531

Out diameter (mm) 508

Length (mm) 5080

Thickness (mm) 17.5

Fig. 7 A quarter finite element model for a subsea pipeline with the

20 node hexahedral elements

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123

Fig. 8 von Mises stress contours of a full model and b quarter model

Fig. 9 von Mises stress contours of pipe at an internal pressure of 43 MPa with corrosion depths of a 25 %, b 50 % and c 75 %

378 J Mar Sci Technol (2016) 21:369–384

123

existing codes such as ASME, DNV and ABS. See Table 4

and Fig. 11. In this case, the corrosion width and length

conditions were 30� and 50 %, respectively.

An external pressure of 30 MPa was applied in FEM

analysis. However, no external pressure was considered in

the codes. To compare the FEA results with the calcula-

tion results of the codes, the FEA results need to be

calibrated. Hence, in the FEA results, the equivalent

pressure was the difference between predicted failure

pressure and 30 MPa.

Table 3 Computational

analysis resultsAnalysis case Corrosion location Depth (%) Width (�) Length (%) Failure pressure (MPa)

E-D1 External 10 30 50 73

E-D2 20 69

E-D3 25 67

E-D4 30 66

E-D5 40 61

E-D6 50 56

E-D7 60 45

E-D8 75 43

E-W1 30 15 50 65

E-W2 30 66

E-W3 45 66

E-W4 60 66

E-W5 50 15 50 58

E-W6 30 56

E-W7 45 56

E-W8 60 56

E-W9 70 15 50 49

E-W10 30 45

E-W11 45 45

E-W12 60 45

E-L1 30 30 25 68

E-L2 50 66

E-L3 75 64

E-L4 100 64

E-L5 50 30 25 61

E-L6 50 56

E-L7 75 55

E-L8 100 56

E-L9 70 30 25 49

E-L10 50 45

E-L11 75 45

E-L12 100 45

I-D1 Internal 25 30 50 67

I-D2 50 55

I-D3 75 49

I-W1 50 15 50 59

I-W2 30 55

I-W3 45 54

I-W4 60 54

I-L1 50 30 25 61

I-L2 50 55

I-L3 75 54

I-L4 100 54

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The failure pressure of FEA was larger than the average

of ASME, DNV and ABS until the corrosion depth reached

50 %. After 50 % corrosion depth, the failure pressure of

FEA with calibration was smaller than the average of code

calculations.

In brief, the slope of the failure pressure curve estimated

using the FEA with the calibration changed excessively,

while the slope of the curve calculated using the codes was

close to linear. Because of this phenomenon, the assess-

ment codes of the failure pressure could lead to underes-

timations/overestimations. This is because the nonlinear

effect of the material, e.g., plasticity, was not considered in

the codes. There were proposals for considering material

nonlinearity in the analysis of failure pressure of the

pipelines, such as Cronin [16], Lee and Kim [17], Chauhan

and Sloterdijk [18], Smith et al. [19] and Xu and Cheng [7].

Therefore, a precise evaluation cannot be accomplished

using these codes. It should be improved to reflect the

material nonlinear property in the codes.

4.3 Investigation of material nonlinearity effect

To investigate the material’s nonlinearity, the stress–strain

relationship of the API 5L X65 (Fig. 6) was implemented

into ABAQUS [14]. Figure 12 shows the relationship

between the equivalent pressure and stress to illustrate the

effect of material nonlinearity. The linear FEM shows a

linear relationship between equivalent pressure and von

Mises stress. The elastoplastic analysis shows a more

complex pattern. The first phase is characterized by a

Fig. 10 Relationship between failure pressure and corrosion in a depth, b width and c length

380 J Mar Sci Technol (2016) 21:369–384

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linear elastic pattern until the von Mises stress reached

the elastic proportional limit at a certain points in the

structure.

In the second phase (plastic deformation), as the equiva-

lent pressure increased the equivalent stress increased very

slowly, because the plasticity spreads through the ligament

and the constraint of the surrounding pipeline wall. In the

third phase, the whole ligament deformed plastically but

failure did not occur due to hardening. A failure could

eventually take place with the internal pressure increases

when the maximum von Mises stress through the ligament

reaches the ultimate tensile strength of the material.

5 Potential improvement to API 579 codeand other code

5.1 Comparison between results calculated

with API code and computed by FEA

The assessment codes did not agree with the FEA results,

i.e., the failure pressure values from the FEA apparently

changed their slope at certain corrosion depths. One cause

may be that the assessment codes do not reflect the non-

linear material properties.

Therefore, the fitness-for-service (FFS) code API 579,

which consists of several geometrical terms of the pipe and

Table 4 Comparison of failure

pressure among ASME, DNV,

ABS and FEA

Corrosion depth (%) Calculated result (MPa) Relative error (%)b

ASME B31G DNV-RP-F101 ABS FEAb

10 32.7 33.7 34.7 43 27.6

20 31.2 31.3 32.1 39 23.7

25 30.4 30.0 30.7 37 21.8

30 29.5 28.6 29.3 36 23.6

40 27.9 25.3 26.3 31 17.0

50 26.1 21.4 22.9 26 10.8

60 24.2 16.7 19.3 15 -25.2

75 21.1 10.7 15.2 13 -17.0

Corrosion width: 30�, corrosion length: 50 %a Equivalent pressure, which is predicted failure pressure—30 MPab Relative error = (FEAc-AVG)*100/AVG where FEAc = FEA with calibration, AVG = (AS-

ME?DNV?ABS)/3

Fig. 11 Comparison of predicted failure pressure between FEM and

design codes of ASME, ABS, DNV (corrosion width: 30�, corrosionlength: 50 %)

Fig. 12 Relationship between equivalent pressure and von Mises

stress predicted assuming elastic and elastoplastic material

characteristics

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corrosion, was used to investigate the geometrical effect

and compare with the FEA results. To distinguish dominant

factors, aforementioned process was carried out. As shown

in Eqs. 7–10, Level 2 of Part 5 in the API 579 code has

terms of geometrical information, such as the neutral axis,

the moment of inertia of the pipe and corrosion. Because

the calculation results of API 579 were represented as

equivalent stress values, not failure pressure, the FEA

results were adopted as von Mises stress values and com-

pared with the calculation results of the API 579 code. The

internal pressure condition of the FEA was fixed to only

12 MPa, which is a subsea pipeline’s operating pressure

[20]. Other conditions were the same as those of the con-

ducted FEA. To calculate the API 579 code, the maximum

allowable working pressure (MAWP) value was required,

which is the value of the internal pressure load. However,

because the FEA results considered both the external and

internal pressure load, MAWP should be changed to the

equivalent pressure load that indicates the same as loading

condition of FEA. As described above, the internal pressure

load was 12 MPa and the external pressure load was

30 MPa, which is the hydrostatic load at 3,000 m water

depth. Then, the equivalent pressure load was 18 MPa.

Each direction of pressure is in the opposite way.

However, when the magnitude of the equivalent pressure

load was the same, the direction of the equivalent pressure

did not affect structure behavior in the pipe significantly.

Additional analysis, which only had a difference of load

direction for corrosion depths of 25 and 50 %, was per-

formed and its results were 374.1 and 434.92 MPa,

respectively. The results had a 5 and 6 % error, respec-

tively, compared with the corresponding results in Table 5.

Because there was no significant difference between them,

18 MPa was adopted as MAWP. The calculation results

were represented in accordance with the procedures of the

API 579 code (Table 5; Fig. 13).

Apparently, stresses based on API 579 are much lower

than those of FEM. The same trend was found in other

investigated codes. In addition, the calculation results of

API 579 show a gradually rising slope, while the nonlinear

FEM shows a more complex pattern. Differences were

considered to be due to the material’s nonlinearity, which

is not explicitly considered in API 579 code or other codes.

5.2 Suggestion of including material nonlinearity

in API 579 code

A RSF factor may be introduced as a dimension less

measure of strength of corroded pipe. RSF was defined as

the ratio of the non-damage to the damage value. The

failure pressure could be predicted using RSF, if the failure

pressure of the intact pipe was known. The failure pressure

of the intact pipe was determined by FEA, taking into

account the material’s nonlinearity. Equations 17–20 show

the RSF calculations, which were provided in the API 579

code.

RSF ¼1� A

A0

1� 1Mt

AA0

ð17Þ

A0 ¼ s � tc ð18Þ

Mt ¼ 1:0010� 0:014195kþ 0:29090k2 � 0:096420k3

þ 1:4656 10�10

k10 þ 0:020890k4

� 0:0030540k5 þ 2:950 10�4

k6 � 1:8462 10�5

k7

þ 7:1533 10�7

k8 � 1:5631 10�8

k9 ð19Þ

k ¼ 1:285sffiffiffiffiffiffiffiDtc

p ð20Þ

where A is the allowable remaining strength factor, A0 the

original metal area based on s, tc the corroded wall thick-

ness away from the region of local metal loss,Mt the Folias

Table 5 Results of API 579 and FEA

Corrosion depth (%) Calculated result

RSF MAWPra (MPa) API 579b (MPa) FEAc (MPa) Failure pressure using RSF (MPa)

10 0.94 18.81 234.44 272.26 76.17

20 0.88 17.50 252.36 339.11 70.88

25 0.84 16.80 263.19 395.62 68.04

30 0.80 16.07 275.64 421.33 65.07

40 0.72 14.48 307.10 440.91 58.66

50 0.64 12.73 351.84 463.06 51.55

60 0.54 10.77 420.11 526.15 43.62

65 0.49 8.57 469.53 626.36 39.30

a Reduced permissible maximum allowable working pressure of the damaged componentb Equivalent stress of pipe calculated in accordance with the API 579 proceduresc Maximum von Mises stress

382 J Mar Sci Technol (2016) 21:369–384

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factor or bulging correction factor based on the longitudi-

nal extent of the local thin area (LTA) for a through-wall

flaw, and k the longitudinal or meridional flaw length

parameter. The FEA’s failure pressure for the intact pipe

was 81 MPa. The failure pressure calculated using this

value and the RSF value are presented in Table 5 and

Fig. 14.

Up to a 60 % corrosion depth, the results had a high

degree of comparison, with an error between 1 and 9 %.

The RSF equations (Eqs. 17–20) resemble the hoop stress

equation. However, there was a distinct difference between

the calculation results. Therefore, corrosion assessment

that used the RSF and failure pressure values of the intact

pipe, which reflect the material’s nonlinearity, could be

more accurate than the existing assessment codes.

6 Conclusions

This paper summarizes a study on the strength of a cor-

roded pipe under inflow-induced (internal) as well as

hydraulic pressure (external). Extent of corrosion pipe was

defined by corrosion depth (radius), width (angle) and

length (height). The corrosion location (internal and

external) was also investigated.

A series of linear and nonlinear FEM analyses was

performed to investigate the failure of corroded pipeline

and the influences of corrosion and material properties on

the failure pressures. These FEA results were compared

with various assessment codes.

The following conclusions could be drawn:

• Whether corrosion takes place on divided external or

internal surface, the behavior of the pipeline remains

same.

• Corrosion depth was the most significant factor for

safety of subsea pipes. With the increase in corrosion

depth, the maximum von Mises stress on the corroded

pipe increased drastically and the failure pressure

decreased rapidly.

• Effect of material nonlinearity becomes more pro-

nounced when corrosion depth is high. However, this

effect was not explicitly considered in the existing

codes of ASME, DNV, ABS and API. A suggestion

was made to adjust the API 579 prediction of failure

pressure using a calibrated factor to take into account

the effects of material nonlinearity.

Acknowledgments This work was supported by the National

Research Foundation of Korea (NRF) Grant funded by the Korea

government (MSIP) through GCRC-SOP (No. 2011-0030013). This

research was supported by Basic Science Research Program through

the National Research Foundation of Korea (NRF) funded by the

Ministry of Education (NRF-2013R1A1A2A10011206).

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