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Structural and containment failure analysis of ductile steel
pipes
Ali Rajabipour1, Robert E. Melchers2
ABSTRACT: Many pipe failures are the result of localized pipe wall damage. The paper report results of
numerical modelling of the behaviour of pipes under increasing axial load and constant internal pressure when
there are corrosion pits on the exterior surface of the pipe. The pipe is assumed to have ideal elastic-plastic
material properties. As the axial load increases the region around the pit takes on an increasingly more
complex plastic zone, commencing originally at the bottom of a pit. This is described and formulated. It is
shown that the shape and volume of the plastic field depend on pit depth and its geometry. Pipe wall fracture
around a pit, important for estimating loss of pipe flow, can be associated with a critical plastic section. The
results reported herein should be relevant for estimating of the risk of perforation and of loss of contents for
steel pipes under seismic and other loading. To facilitate this, herein a damage index is proposed for pitting
corroded pipes.
KEYWORDS: Pitting corrosion, Damage index, Steel pipes
1
Ali Rajabipour, The Centre for Infrastructure Performance and Reliability, The University of Newcastle. Email:
[email protected]
2
Robert E. Melchers, The Centre for Infrastructure Performance and Reliability, The University of Newcastle. Email:
[email protected]
1 INTRODUCTION
This paper is concerned with the estimation of the
structural damage and hence the serviceability
performance of buried, already corroded steel
pipelines. The pipelines are subject both to internal
pressure and to axial stresses such as resulting from
earthquake ground shaking and hence earthquake
loading.
The failure of buried steel pipes used for critical
services such as water and gas can have significant
social and economic impact. This is particularly the
case if multiple failure events occur such as is
possible under earthquake conditions. Indeed a
large number of cases of earthquake damage to
pipelines have been reviewed [1, 2]. Multiple
failures, small breaks and leaks have been reported
for uncoated steel water pipes, attributed to both
corrosion damage and stresses, particularly axial
stresses, generated by earthquake induced ground
displacement [3]. The losses caused by failure of
water and gas pipelines in metropolitan areas can
be very high. It can amount to millions of dollars,
particularly for earthquake scenarios. A simulation
carried out in 2009 for earthquakes in Tokyo with a
probability of occurrence of about 70% in 30 years,
estimated that losses in lifeline systems exceed 11.4
trillion yen (about $US 145.6 billion in 2012). This
comprised almost 10% of the total economic losses
for that event [4]. Indeed a large number of cases of
earthquake damage to pipelines have been
summarized [1], including: 1906 San Francisco,
1933 Long Beach, 1952 Kern County, 1964
Alaska, 1964 Niigata, 1971 San Fernando, 1976
Guatemala, 1976 Tangshan, 1979 Imperial Valley,
1983 Coalinga, 1983 Nihonkai-Chubu, 1987
Whitlier, 1989 Loma Prieta, 1991 Costa Rica, 1993
Kushora-Oki and 1994 Northridge. In 1994
Northridge earthquake three major transmission
systems, providing more than 75% of the water for
the City of Los Angeles, were disrupted [5].
One practically important issue for lifeline systems
such as buried pipes is that they are prone to
corrosion, despite the presence, in many cases, of
external and/or internal protective coatings or
linings. Corrosion causes the strength of the
pipeline to decline with age, decreasing the
capacity of the pipe to sustain exterior loads such
as those resulting from traffic loading, thermal
loading, soil subsidence, etc. and also internal
pressure. This issue has been a matter of serious
concern for the oil and gas industry for many years.
Guidance for the design of pipelines, taking some
accounts of corrosion losses, is available in
engineering manuals [6, 7]. However these do not
deal specifically with the details of the corrosion
damage under applied stresses, such as axial stress.
That is why approximations often are made for
assessing the capacity of pressure pipelines, as
recently reviewed [8, 9].
Apart from the effect of so-called general or
„uniform‟ corrosion on structural capacity, there is
also the possibility that corrosion pits may
perforate the pipe wall or lead to reduction in local
wall thickness sufficient to cause local structural
failure and hence leakage [10]. In addition, pitting
may cause local stress concentrations that then may
cause structural cracking or tearing of the wall
under external loadings[11, 12].
Design criteria for seismic design of buildings and
their performance levels have been defined in
engineering guidelines for many years [13]. In the
case of pipelines, two general levels of damage
including leakage and break are defined, for
example, in HAZUS, a multi-hazard loss estimation
methodology developed by FEMA [14]. Its
methodology is based on the very general
assumption that damage due to seismic waves
causes 80% leaks and 20% breaks. However, in this
document, as well as others in this area, clear
criteria for these two failure scenarios are not
defined. In addition, there is no clear methodology
to distinguish breaks from leaks. At present, lack of
practical methods for evaluating pipes performance
is concurrent with progressive need of urban
lifeline management. In fact, models for lifeline
management such as optimum maintenance models
usually assume a probability of pipes failure. In this
regard, pipes performance usually is limited to two
conditions of “intact” and “failed”. In many cases
of a pipe damage the pipe is neither intact nor
failed, but a situation between these two extremes.
For example the damage might be just a small hole
(an opening) on the pipe body – which is
sometimes undetectable. This condition is not
intact condition from environmental and safety
point of view when oil or gas is conveyed by the
pipe. It also is not a complete failure as the pipe is
still able to carry fluid. In this sense, damage needs
to have some levels so be able to reflect the reality
more precisely. Ideally pipe damage can be a
continuous variable covering a range of pipe
performance.
It is impossible (or too time consuming) to take
into account the damage of every element of a
structure when its seismic performance is
considered [15]. Instead, damage indices may be
employed. Damage indices represent the overall
condition of a structure based on some of its
responses. These indicators of damage usually vary
between zero and one, representing no damage and
collapse conditions respectively. Four approaches
can be distinguished in the developing of seismic
damage indices for buildings, strength demand,
ductility demand, energy dissipation and stiffness
degradation[16]. Many seismic damage indices
have been developed in this regard such as ductility
ratio, flexural damage ratio [17], inter-story drift
[18, 19], normalized cumulative dissipated energy
[20] and maximum softening [21].
For estimating the structural capacity of pipes in
corrosive soils one approach is to use fragility
curves. These curves relate the number of pipes
break with a ground motion parameter such as Peak
Ground Acceleration (PGA). However, typically
there is no clear indication or classification of
corrosion: “Engineering judgment says that a
small-diameter cast iron pipe in corrosive soil is
about 40% more susceptible to damage than the
best fit curve from the empirical database, and that
cast iron pipe in non-corrosive soils is about 30%
less susceptible to damage than the best fit curve
from the empirical database.” [22]. In the case of
seismic loads fragility relations have been
developed since mid-1970s based on the data
gathered in various earthquakes [23]. The ground
motion characteristics which are more considered
in fragility relations are: Peak Ground Acceleration
(PGA), Peak Ground Velocity (PGV), Peak Ground
Displacement (PGD) and Modified Mercalli
Intensity (MMI). Fragility relations developed for
transient ground displacement are usually based on
PGV.
The present paper concerns the structural damage
around a pre-existing corrosion pit on the exterior
surface of a steel pipe under internal pressure and
subject to earthquake induced axial stress. Of
particular interest is the possibility of loss of pipe
wall in the immediate area of the pit as a result of
the plasticity developed by the combination of
internal pressure and increasing axial stress. The
next section reviews the concepts of material
rupture around a pit and introduces a criterion for
wall failure. A suitable damage index also is
introduced. This is followed by an example
illustrating how the proposed damage index is
calculated. Criteria for acceptable performance and
for acceptable damage levels of pipes are beyond
the scope of the paper.
2 Definition of damage in pitting
corroded straight steel pipe
The primary purpose of a pipe is to convey fluid
from one point to another. Its performance
therefore can be defined as the degree of success in
achieving this purpose. One way of defining this is
a limit state, for example, the loss of fluid between
two points, such as resulting from pipe damage or
pipe fracture. For a given hydrostatic pressure in
the pipe, the amount of fluid loss depends largely
on the area of the hole that forms in the pipe wall.
The possible size of opening around corrosion pits
is considered herein as the core parameter of
damage in ductile straight pipes. The openings
from pits can account for occurrence of holes on
the pipe wall. The parameter APZ is introduced in
this sense as the possible opening from an
individual pit. Estimation of this parameter is
discussed in detail in this section. A suitable
damage index for a pipe may then be proposed as
the ratio of total area of the openings from the pits
to the pipe section area. Equation (1) shows this
ratio:
∑
In which:
Damage index for a pitting corroded pipe,
∑
Total area of openings on the pipe wall
because of individual openings around pits,
Area of the pipe section
As Equation (1) shows it is assumed that the pipe is
totally failed when the total probable opening on
the pipes reaches its cross section area.
2.1 Estimation of Apz
The area of the hole can be considered to consist of
the pit plus some part of the immediately adjacent
pipe wall that is removed by the pressure of the
fluid. It also may be simply the area of pipe wall
removed by internal pressure at a location
sufficiently weakened by the presence of the pit.
Figure 1 shows the two scenarios.
The scenarios in Figure 1 show schematically the
region of plasticized material around or near the pit
that could be removed by the high internal pressure
in the pipe. The plasticity results from both the
internal pressure in the pipe and axial stress along
the pipe wall. The latter can be compressive or
tensile. It is clear that the material at or around the
pit must be at a high stress state for rupture to
occur. In principle other failure modes of slightly
different geometries are possible. All require the
computation of the state of stress around the pit,
including the gradual increase in plastic flow of the
material in the neighbourhood of the pit as the
stress levels increase. It is assumed herein that an
indication (but not necessarily the actual) size of
the hole that will be possible because of the plastic
flow in the neighbourhood of the pit is given by the
minimum cross-section of the plastic volume that
has been created at any particular stress state.
It is assumed also that rupture of the material to
form the hole can be approximated by the yield
strength of the steel. This then permits the use of
ideal elastic-plastic theory [24]. It is assumed also
that the material is isotropic, an assumption
consistent with the mild and low alloy steels
commonly used for steel pipes. In view of the
strain-hardening behaviour of mild steel and also
its ductile behaviour after damage initiation, these
assumptions are conservative and will underestimate the loads at which failure can be expected
to occur. In reality, the area of the hole cannot be
calculated unless criteria both for damage initiation
and for damage evolution are known. In many
(1)
cases in practice, the structural characteristics of
old pipes are not known. For these pipes
experimental tests are expensive, if not impossible.
For this reason the von Mises yield criterion [24] is
assumed as failure criterion herein (Figure 2).
Although conservative, this assumption is widely
accepted and employed in assessing the failure of
pipes [6, 12, 25].
Likely location of
plasticity region that
may be removed to
form a hole
Pit
formulated in a damage index based approach,
generally similar to that used in other performance
based assessments [13, 26]. Herein the index is
defined as the minimum plastic cross-section along
the pipe wall of the local plastic flow zone, termed
APZ or „Minimum Section Area in Plastic Zone‟. It
should be clear that APZ will be a function of the
applied stress state and also of the geometry of the
Pit
Plastic
region
Plastic
region
is is
minimum
in this
minimum
in this
level
level
PlasticPlastic
region region
is
is
minimum
here here
minimum
Plastic
region
Plastic
Plastic
region
region
Pipe
Likely location of
plasticity region that may
be removed to form a
hole
Pit
Pit
Plastic
region
Pipe
Plastic
region
Plastic
region
Plastic
Plastic
region
region
(a)
(b)
Figure 1: Two scenarios of forming a potential opening around a pit, (a): effective area of potential opening hole
including the pit, (b): effective area of hole caused by wall weakening perhaps including that resulting from the
presence of the pit
Pipe wall
Pipe wall
Pipe int ernal pressure
Pipe wall
Pipe int ernal pressure
s3
Von Mises yield surface
s2
s1
Figure 2: Indication of hole based on plasticity around a pit. The minimum area of the empty space in the metal is the
available area for the fluid to scape
Figure 2 shows the area available for the fluid to
escape. It is the minimum area of the empty space
in the pipe wall. Thus, all sections parallel to the
pipe wall must be examined, as shown in Figure 3.
The approach outlined above for the approximate
estimation of the size of the hole also may be
pit. The dependence of APZ on these influences is
discussed in detail in [27].
almost uniformly around the pit. The second, phase
two, begins when the development of plastic
volume is focused near the pit mouth. In this case X
has a significant role in development of APZ / A0.
6
APZ / A0
5
Phase
one
4
Phase
two
3
2
Figure 3: Pit cross-sections to calculate opening
(hole) size. Area of plastic region is calculated on
each layer.
2.2 Changes of Apz with pit shape
1
0
0.5
0.6
0.7
0.8
0.9
Figure 5: APZ changes with axial stress (X =0.56
and Y=0.66)
Employing the method proposed in the previous
section changes of Apz with pit shape is reviewed in
this section. Results presented in here have been
adopted from [27]. Figure 4 shows the shape
parameters considered in estimating Apz.
Pi
t
Figure 6: Development of APZ with different X
values
Figure 4: Shape parameters of a modelled pit. A0=
Are of pit mouth and b= Pipe wall thickness
The minimum section area at any level in the
plastic zone developed around the pit (APZ) changes
as 1 increases after plasticity has reached the inner
pipe wall (initiation). Let APZ be nondimensionalized by dividing it by the area of the pit
at the outer pipe surface (A0 in Figure 4).
Observation of the numerical analyses shows that
the development of the plastic region around the
pit, measured by APZ / A0, has the non-uniform
functional form as a function of applied axial stress
1. An example is shown in Figure 5 for selected
values of Y and X. For this case it is seen that two
different phases can be distinguished. The first,
phase one, shows that the plastic volume grows
The numerical data for phase one in Figure 5 can
be fitted reasonably well (R2 > 0.9 for all the cases)
by a second order polynomial, while the data for
phase two can be fitted reasonably well (R2 = 0.9
for all the cases) by a third order polynomial.
Figure 6 shows that the pit area aspect ratio X has a
significant role in development of APZ / A0, with
trends shown for several values of X and two
values of non-dimensional pit depth Y.
3 An example of calculation of the
proposed damage index
In this section the proposed damage index is
calculated for a simple water network. The
calculated damage indices then are used to estimate
the expected water loss. All values are calculated
deterministically in this example. However,
probabilistic approach can be employed to estimate
seismic loading and spatial distribution of pits.
Figure 7 shows how the proposed damage index is
calculated in this example.
10000
D/th=0.9
D/th=0.8
D/th=1.1
1000
Apz
(mm2)
100
Estimating
seismic axial
loads on pipes
Calculating
Apz
Calculating
Damage Index
10
Estimating
pits shape and
density
Axial Stress/Yield Stress
1
0.4
0.6
0.8
1
Figure 9: Apz versus normalized axial stress
Figure 7: General Process of calculating the
(W/D=0.5)
proposed damage index
Axial stress on pipes can be estimated using the
methods described in [1, 2] There are two
categories of seismic loads in this regard, axial load
caused by seismic wave propagation and that
resulting from Peak Ground Displacement (PGD).
The strain due to the former rarely exceeds 0.3%.
That is why Apz is zero for usual pit shapes under
this amount of strain [27]. The strains resulting
from PGD, however, can reach 2% under which Apz
become six times bigger than the pit mouth area
[27]. Figure 8 shows shape parameters of the
elliptical pits considered in this example. Density
of pits on pipe walls can be estimated using spatial
analysis on corrosion data [28-31]. Applied stress
on pipes and density of pits are assumed to be
known in this example.
W
Pit
Table 1 shows the value of the damage index for
three pipes subject to axial load. Pit density which
is the ratio of number of pits to unit of area of pipe
wall is show by r in this table. Apz is obtained from
the numerical values of Figure 9. The ratio of W to
D is 0.5 for all pits in this example and the ratio of
D to th is 0.8, 0.9 and 1.1 for pit1, pit2 and pit3
respectively in Table 1.
Table 1: Calculation of the proposed damage
index for pipe in the example
r
(Pit/m2)(10-3)
Apz (mm2)
D
L sMax /
Pipe (mm) (km) sy Pit1 Pit2 Pit3 Pit1 Pit2 Pit3
DI
1
500
10
0.77 10
50
05
0
15.6
63.9 0.09
2
400
12
0.85 12
20
2
36.6
54.9
152.6 0.22
3
300
15
0.9
15
1
279.9 104.8 297.8 0.88
9
Based on Equation (1), Damage index (DI) for ith
pipe is (summation convention is implied):
(2)
D
th
4 Conclusion
Figure 8: Shape parameters of pits in the
example
Using the method described in [27] Figure 9 shows
how Apz changes for three states of D/th=0.8, 0.9
and 1.1 when W/D=0.5. In the case of D/th=1.1 an
open hole exists on the pipe wall before loading.
A damage index reflecting the range of
serviceability or service performance of steel water
pipes is useful in performance-based design and
assessment of pipelines, as shown herein. For
pitting corroded straight pipes subject to axial loads
this index can be defined based on the probable
size of the opening that develops around corrosion
pits when the pipe is subject to applied loads. It is
shown that the loss of local pipe wall around a
corrosion pit through plastic flow deformation can
be estimated from the amount of plasticity that
forms in the pipe wall under the applied stress state.
To make this operational a critical minimum
section of plasticity was associated with pipe wall
failure, and this was assumed to lead to local pipe
bursting. This was proposed as a suitable Damage
Index. As shown, the damage index is a function of
pit depth, pit aspect ratio and applied axial stress.
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