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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
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
J Mar Sci Technol (2016) 21:369–384 377
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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123
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
123
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
J Mar Sci Technol (2016) 21:369–384 381
123
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
123
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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