1. A Computational Study of Pipelines Subjected to
External and Internal Pressures
Raj Kiran
Motilal Nehru National Institute of Technology Allahabad
me123025@mnnit.ac.in
Abstract: Earthquakes, landslides and other seismic events can cause severe damage to
underground structures such as fiber-optic cables, electric cables and the pipelines used to
transport natural gas and oil. Therefore, it is important to understand the response of these
structures due to sudden ground motion in order to better design the structures.
The present study examines the behaviour of a buried pipeline caused by the external
pressure exerted by the surrounding soil and the internal pressure exerted by the gas carried
by the pipeline. The finite element method has been selected as the tool for examining the
response of the buried pipeline. For the present work, the soil medium is replaced by the
external pressure that it exerts on the pipe. In the analyses, first, the pipeline with only
the external pressure is considered. Following this, the pipe response due to the presence
of both internal and external pressures is considered. The pipeline is assumed to be made
of APIX65 grade steel. The material behaviour is assumed to be governed by J2, rate-
independent plasticity theory with strain-hardening included.
A three-dimensional finite element model of the pipeline has been developed using the
commercial finite element software ABAQUS 6.11-3. The pipeline is discretized using shell
elements and the analyses are carried out as quasi static problems. In the present study shell
mode of buckling is observed and purpose is to set criteria for onset of local buckling. For
determining the onset of buckling two parameters have been taken into account: 1) Total
Energy 2) Axial Strain. It has been observed that the total energy plot starts fluctuating
and the plots of axial strain go down when buckling starts.
1 Introduction
It has always been assumed that underground structures suffer less damage than those
present on ground. But the recent earthquakes and, landslides and other seismic events
have led to severe damage to underground structures. Now-a-days pipeline structures are
used for transporting variety of commodities ranging from oil,natural gas etc. to the electric
cables.So any severe damage to the pipelines can bring the human life to halt.
The failure of offshore pipelines due to seismic events and propagating collapse and its
catastrophic effects were brought to light by researchers in 1975.Since then many scientists
and researchers have investigated behavior of underground pipelines in different ways.(1)
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2. The objective of this study is to analyse the response of the pipeline subjected to the
external pressure exerted by the soil and internal pressure exerted by the gases carried by
pipeline during the seismic activities.Here the purpose is to understand the buckling mode
of deformation as the loads are applied on the pipe.Commercial finite element software
ABAQUS/Explicit 6.11-3 has been used for analysis and MATLAB as mathematical tool.
2 3-D Finite Element Modelling
The pipeline was modelled as a 3D deformable shell model due to less thickness of the
pipeline. The diameter and thickness of the pipeline were taken as 0.914 m and 0.0126 m
respectively. The length of the pipe is 60 metres.
Figure 1: Pipe Model
2.1 Material Properties
For the present study, pipelines made of APIX65 grade steel were chosen. Tensile properties
of APIX65 grade steel are as below:
1. Young’s Modulus : 210 GPa
2. Poisson’s Ration : 0.3
3. Yield Strength : 464.5 MPa
True stress-strain data at room temperature was taken from a graph in Figure 2.(2)
Assumptions Following assumptions have been take while performing the analysis :
1. The welding between pipeline segments is not considered.
2. The pipeline is deformable and isotropic.
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3. Figure 2: True stress Vs strain curve for APIX65 steel
2.2 Steps
In the analysis all the loads have been applied in a single of type Dynamic Explicit to
study the transient response of the pipeline subjected to certain loads.Dynamic Explicit is
an effective tool for solving non-linear problems.It is employed where large deformations and
inertial effects are taken into consideration. It requires a small step time increment which
depends upon the highest natural frequency of the model.(3)
2.3 Types of Loads and Boundary Conditions
In general, several loads and load combinations affect buried structures. The buried pipeline
is no exception.So, the effect of these different loads has to be considered in pipeline structure
design and analysis.Here, only two loads have been taken into account:
1. External pressure applied by the soil
2. Internal pressure applied by the gas carried by the pipeline
Two different analyses have been performed.First analysis only considers external pres-
sure exerted on pipeline while second takes care of internal pressure also. The pipeline was
divided into two equal halves axially and transversely and an external pressure of 25 kPa
was applied and gas pressure is taken as 916 kPa. External pressure was applied on the two
quarter surfaces on opposite sides.
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4. The pipeline was encastred on one of its ends i.e. rotation and translation in all directions
were restricted.Loading and boundary conditions for both the analyses are shown in Figure
3.
[a]
[b]
Figure 3: Loads and boundary conditions for: [a] External pressure analysis [b] Internal
pressure analysis.
2.4 Meshing Techniques
The pipeline was divided into 3 portions for meshing.We have used dense mesh in the areas
from where the pipeline locally buckles.Since the pipeline is assumed to be a thin walled
structure the best suited elements are shell elements so S4R element was chosen.These ele-
ments are four noded element with reduced integration.Meshed pipeline has been shown in
Figure 4.
3 Results and Discussion
In the analysis purpose is to understand shell mode of buckling.In general, buckling is a
process in which a structure on application of critical load switches from straight and stiff
configuration to the bent one where the stiffness of the structure is very less.
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5. [a]
[b]
Figure 4: An example of :[a] mesh used for pipe [b] its closer view
In the present study shell mode of buckling is observed and purpose is to set criteria
for onset of local buckling.Shell mode or local buckling results in large deformations in pipe
wall.The shell elements have been oriented in such a way that LE22 and SE22 represent axial
strain and stress respectively.
For determining the onset of buckling we have taken two parameters:
1. Total Energy: The statement of energy balance says that total energy of the system
should remain constant.A constant energy balance is an indication that the solution
is stable and a non-constant energy balance strongly suggests that the solution is
unstable(4) So for determining the step time at which system becomes unstable Total
Energy of the system has been plotted against time.
In the Figure(number) the total energy of the system remains constant at zero. But
energy imbalance can be observed at time near 0.32 seconds in analysis 1 while it is
observed near 0.44 seconds in analysis 2.So this imbalance in energy can be interpreted
as onset of local buckling in the pipeline.
2. Axial Strain: It has been observed that local buckling can be characterised by three
events :
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6. [a]
[b]
Figure 5: An example of :Total energy of the system for : [a] external pressure analysis [b]
internal pressure analysis
(a) Initially, the axial compression increases and wavy structured contours can be
observed in Figure 6. These contours depict wrinkles in actual structure.
[a]
[b]
Figure 6: Strain contours representing wavy structure in : [a] external pressure analysis [b]
internal pressure analysis
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7. (b) Then the pipeline structure bulges out and wrinkle formation takes place as shown
in Figure 7.At this stage the maximum strain can be observed to be in wrinkled
area and the surrounding areas can be seen to be in compression.
[a]
[b]
[b]
Figure 7: Strain contours representing bulging portion in pipeline and maximum strain in
critical areas in : [a] external pressure analysis [b],[c] internal pressure analysis
(c) As the compressive strain increases in the critical areas kink formation takes place
and finally the structure becomes unstable as can be seen in Figure 8.
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8. [a]
[b]
Figure 8: Strain contours depicting kink formation and local buckling in : [a] external
pressure analysis [b],[c] internal pressure analysis
Strain changes suddenly so it is not possible to capture the exact moment at which
structure buckles.But still it is quite evident from the strain contours that in external pressure
analysis the pipeline structures buckles locally in between 0.30 and 0.35 second while in the
other case it happens in between 0.40 and 0.45 second.
Figure 9 shows how the evolution of strain with time in the buckling zone.X axis represents
length of the pipeline for which strain has been plotted while Y axis tells about the axial
strain.In both the analysis the compressive axial strain near the buckling area increases
with time and leads to wrinkling,kink formation and eventually buckles.So the two graphs
of axial strain versus length at different times are in close accordance with Figure 6,7,8.It is
also evident that the compressive strain increases as the structure starts buckling.
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9. [a]
[b]
Figure 9: Axial strain curves
4 Conclusion
The present study tries to come up with a criterion for onset of local buckling in pipeline
structures subjected to external pressure and internal pressure.So,two criteria : a) Total
Energy b) Axial Strain have been studied to determine the time at which structure buckles.
It has been observed that the plot of total energy starts fluctuating after some time as the
load increases and eventually the structure becomes unstable.The axial strain also increases
in the critical region and drops down significantly as the formation takes place and pipeline
structure buckles.It is also evident that the structure in internal pressure analysis buckles
later than that buckles in external pressure analysis.So, it can also be concluded that if the
internal pressure is increased then the local buckling can be avoided upto some extent.
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10. References
[1] Mechanics of Offshore Pipelines Vol I Buckling and Collapse by Stelios Kyriakides.
[2] A phenomenological model of ductile fracture of API 65 steel: International Journal of
Mechanical Sciences Vol. 49, Issue 12, December 2007.
[3] Getting started with ABAQUS Explicit
[4] Getting started with ABAQUS Explicit
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