Upheaval Buckling of Pipelines-2016
Upheaval Buckling of Pipelines-2016
Upheaval Buckling of Pipelines-2016
Several models of upheaval buckling have been identified and discussed, such as those based on idealized
or perfect pipelines, which are related to the railway track analysis and those based on imperfections.
The buckle temperatures of the perfect pipelines are proportional to the buckle lengths and axial forces.
With the consideration of imperfections, buckle temperatures become inversely proportional to the
imperfection heights, therefore larger imperfections would require smaller temperatures to propagate
upheaval buckling. Increasing the downward load on the pipelines aids the prevention of upheaval buckling.
Also, relevant methods to mitigate against the occurrence of upheaval buckling have been discussed. The
use of finite-element analysis which considers the seabed profile and plastic deformation of pipe wall
would be suitable for precise analysis.
a) as-laid
c) start-up
d) upheaval
when the pipeline is trenched or buried, and the buckle [ 7]. Different incidences of upheaval buckling occurred
propagates in a vertical deflection. in the 1980s: the first occurrence of upheaval buckling
took place in 1986 in the Danish sector of the North Sea
When the temperature and pressure of an operating associated on Maersk Olie Og Gas A/S Rolf pipeline
pipeline is higher than the ambient, the pipeline tends to [17]. Authors including Hobbs [10], Boer [2], Richards
expands. Due to the inadequate space to allow expansion [21], Taylor et al. [23], Ju et al. [11], Pederson et al. [20],
of a trenched or buried pipeline, the pipeline develops an Palmer et al. [19], and Klever et al. [13] have addressed and
axial compressive force. If the force created by the pipeline contributed to upheaval buckling problem in pipelines.
is higher than the vertical force produced by the soil cover
which prevents against the uplift movement created by the Hobbs [9] emphasized in his research two methods of
pipe, the pipe then tends to move upward causing a vertical buckling propagation in pipelines: lateral and upheaval
displacement of the pipe. The excessive propagation of the buckling. The classical analysis proposed in his research
vertical displacement of the pipeline can eventually result was identical to the one of the vertical stability of railway
in failure of the pipeline [19]. tracks [12], and his paper addressed responses produced
by the compressive force generated on the pipeline, which
Figure 1 shows a diagram of events that initiates is similar to the bending deformation that propagates in
propagation of vertical displacement (upheaval buckling) the elastic buckling of an axially loaded column. He also
in buried pipelines. Figure 1a illustrates the pipeline considered the pipeline to be perfectly elastic and assumed
being laid on the seabed. The pipeline is then trenched pipeline to be straight without considering imperfections
or buried, as shown in Fig.1b. This process therefore or out-of-straightness [10].
modifies the foundation profile where the pipe rests. In
operation, as depicted in Fig.1c, the increased temperature Further research was directed to this topic, and the
and pressure creates a compressive axial force which classical model proposed in Hobbs paper was modified
causes a lift of the pipeline. Continuous increase of the and refined to consider imperfections (out-of-straightness)
temperature and pressure while in operation causes the and the elasto-plastic behaviour of pipelines undergoing
pipeline to push upward against the soil cover, creating buckling.
an upheaval buckling of the pipeline as shown in Fig.1d.
In his paper Boer [2] discusses buckling associated with
In order to prevent impact on pipeline by other marine operating a pipeline at high temperature (using the 15.3-
activities, such as fishing nets or ships anchors, and for the km long, 12-in diameter, Alwyn pipeline in the N Sea as
safety of the pipeline and the environment, the pipelines a case study). He established his research by focusing on
are usually buried and trenched [7]. previous studies developed by Delft Hydraulics Laboratory
(DHL) and Lloyds Register of Shipping (LRS). The
Considerable research has been made into this topic, and research showed in detail the effects of vertical constraint
the first paper on pipeline buckling was published in 1974 force and prop height on upheaval buckling propagation.
3rd Quarter, 2016 159
y x
Ls L Ls
L/2
P
Po
Po -Ls
Taylor and Gan [23] put together an analysis incorporating Daniels in 1971 which described the analysis of vertical
structural imperfection and deformation-dependent axial- buckling of crane rails, agrees with the theory first made
friction resistance; their study concentrated on both the by Matrinet. In 1974 Kerr [12] published an extensive
vertical and the lateral modes of deformation. literature analysis on upheaval buckling of railway tracks.
Pendersen and Jenson [20] also described the vertical
buckling of pipelines due to thermal expansion and The analyses made by these authors are closely related
internal pressure; they observed that the effect of to buckling problems in pipelines, and thus Hobbs [10]
temperature fluctuations in imperfect pipelines could developed the basic models for buckling in pipeline
produce upheaval buckling at a temperature lower than relating his theory to the previous theory of buckling
the design temperature. The paper presented a model in railway track. In this model, the force created by full
which designs against propagation of upheaval buckling restraint of thermal expansion across the pipeline is:
of buried pipelines subject to time-varying temperature
loading. P0 = EAT (1)
Palmer et al. [19] developed a simplified analytical model where P0 is the force, E is the Youngs modulus, is the
focusing on pipeline stability which analysed whether the coefficient of linear thermal expansion, and T is the
downward force (of the soil cover) would be capable or temperature change.
enough to hold the pipeline in its position and prevent
propagation of upheaval buckling. The axial strain across the wall of the pipeline due to the
pressure difference is given by:
This paper focused on three basic models: the theoretical
1 Pr Pr
analysis for upheaval buckling of perfect straight pipelines, = (2)
imperfect pipelines, and simplified Palmers model. E 2t t
where is Poissons ratio, P is the internal pressure, t is the
wall thickness, and r is the radius.
Theoretical analysis for upheaval
buckling of perfectly straight If the axial strain is restrained, the axial compressive force
pipelines P0 to propagate buckling will be:
A Pr
As identified earlier, compressive axial forces are developed P0 = EA = ( 0.5 ) (3)
along a pipeline due to the increased internal temperature t
and pressure during operation. This compressive axial The pipeline is analysed as a beam under uniform lateral
forces along a pipeline can result in upheaval buckling of load, as illustrated in Fig.2. The linear differential equation
the pipeline. of the deflected shape of the buckled area of the pipeline,
assuming the moment of the lift-off point is zero, is given
Similar occurrences of upheaval buckling have occurred as [10]:
in railway track, and a works were published analysing the
m
problem. In 1936, Matrinet first developed a theory to Y "+ n2 Y +
8
( 4 x 2 L2 ) = 0 (4)
analyse the vertical mode of buckling in railway track [9].
Granstroms discussion on behaviour of continuous crane in which m = EI and n2 = P EI , and is the
rails in 1972, and a research paper published by Marek and submerged weight of pipeline per unit length
160 The Journalof Pipeline Engineering
CL
h
Vom
P=0 P=0
D L0 / 2 L0 / 2
trench bottom / seabed
b) Isolated prop
CL
prop
h
sea (void)
Vom
P=0 P=0
D
Li / 2 Li / 2
c) Infilled prop
CL
h
prop
sand infill
Vom
P=0 P=0
D
Li / 2 Li / 2
Figure 2b compares the axial load P in the buckling area The maximum amplitude of the buckle is given as:
with the axial load P0 away from the buckle area. The axial
L4
load P in the buckle area is less than the axial load away Vm = 2.408 10 3 (7)
from the buckle area because of the extra length around EI
buckle area Ls compared to the length of the buckle area L. The maximum bending moment at x = 0 is:
Equation 4 is can be solved and gives the following result M = 0.06938L2 (8)
for the axial loads:
The slipping length Ls, adjacent to the buckle is given as:
EI
P = 80.76 2 (5)
L P P0
Ls = 0.5L (9)
and
1 For a very large coefficient of friction when Ls = 0:
P0 = P + L (1.59 10 5 EAL5 ) 0.25 ( EI )2 2
EI EI 2 AEL6
P0 = 80.76 2 + 1.597 x 10 5
(6) L ( EI )2
(10)
P represent the axial load in buckled region, P0 is the axial Equation 10 is a minimum when:
load away from the buckled area, and is the coefficient of 1.6856 106 ( EI )3
0.125
a) Datum (P = 0)
Level seabed /
Vom trench bottom
void prop
P=0 Li
P=0
b) Pre-upheaval flexure
(Lu < L < Li)
Vm = Vom
void prop
Lu < L < Li
0<P<Pu 0 < P < Pu
Li
c) Upheaval
(L = Lu)
Vm = Vom
void prop
Lu
Pu Pu
Li
Upheaval buckling authors including Taylor and Gan [23], Boer et al. [2], Ju
of imperfect pipelines and Kyriakides [11], Perdersen and Jensen [20], Ballet and
Hobbs [1], Maltby and Calladine [15], Taylor and Tran
Recent research has expanded the classical view of [24], and Croll [5], have published papers analysing the
upheaval buckling thereby making void the engineering upheaval buckling of imperfect pipelines.
practice that the shape of a buried pipeline is straight. This
is due to the presence of initial imperfections during the Initial imperfections in pipelines could occur in three
pipe laying. different forms as shown in Fig.3. These are illustrated
with different parameters such as Vom which represents
Initial imperfection in pipelines can be due to irregularities the amplitude of the initial imperfection, and L0 which
of the seabed profile, or laying the pipeline over a boulder represents the length.
or prop. The presence of the initial imperfection causes
a deformation on the pipeline during the laying process Taylor and Tran [24] developed models describing each
and during operation as the temperature-increased case of the initial imperfections. The first case, in Fig.3a,
propagation of upheaval buckling takes place. illustrates the pipeline lying in contact with the vertical
undulation of the seabed in a straight line. Figure 3b
Many researchers have contributed to the study of shows the isolated-prop scenario where the pipeline is laid
upheaval buckling of imperfect pipelines. A number of on a sharp vertical irregularity or prop. The third scenario,
162 The Journalof Pipeline Engineering
12
1 L
12
12
8H 3L2 2
T = P + EZ Y xdx
2
(12)
EA 1225EI 2
0
3rd Quarter, 2016 163
The pipeline, after laying on the seabed, is deformed due to where EI is the flexural rigidity of the pipeline, o is the
the height of the imperfection, the weight of the pipeline, submerged weight of the pipeline, H is the imperfection
and the flexural stiffness of the pipeline. Therefore, Palmer height, and P is axial force in operation.
et al. proposed a simple sinusoidal profile of the pipeline
after installation considering the height of imperfection The preliminary design formula compares the required
and length of imperfection, given by: download force determined from Equn 28 with the actual
load (which is the sum of the submerged weight and the
x
Y = H cos2 (23) uplift resistance of the cover).
L
where H is the imperfection height, and L is the length of Schaminee et al. [22] did further research on calculating
imperfection and ranging from -0.5L < x < 0.5L. the uplift resistance of a pipeline buried in rock or in
cohesionless soil. The equations to calculate the uplift
To maintain the position of the pipeline profile, the cohesion are:
downward force required is proposed as:
for cohesionless sand, silt and rock:
4 2
2 X
( x ) = 8HEI + 2HP cos
L L L R
q = yRD 1 + f (29)
(24) D
for cohesionless clay and silt:
At the tip of the imperfection when x = 0, the download
R
force is maximum and is given by: q = ycDmin 3 (30)
D
2 4
= 2H 8HEI (25) where q is the uplift resistance, R is the depth of the cover,
L L y is the submerged unit weight of the cover material, D is
where is the downward force per unit length to stabilize the diameter of pipe, c is the shear strength, and f is the
the pipeline at the tip of the pipeline imperfection. uplift coefficient (0.5 for dense materials and 0.1 for loose
materials) [19].
In the paper [19], it was proposed that Equn 25 can be re-
written as a relationship between dimensionless downward
parameters: Methodology
w = Al4 Bl4 (26) In order to be able to evaluate the use of the proposed
upheaval models, an Excel spread sheet was developed for
( )
12
with w = EI HP 2 and l = L P EI . each upheaval-buckling method described above. A typical
sample pipeline with parameters given in Table 1 was used
Constants A and B can be determined numerically by for each of the models.
plotting wl2 against l2 using finite-element software
(UPBUCK) [19]. The authors confirmed the general Theoretical analysis of perfect straight pipeline
profile of pipeline supported by the axial force in the post-
buckling mode to be given by: According to the theoretical analysis of upheaval buckling
of perfect straight pipelines [10], the following would
9.6 343
w = (27) be used to determine the force or temperature change
l2 l4 corresponding to the buckle length:
In the situation where the maximum height of the
imperfection is known and the length is unknown, an considering high coefficient of friction:
estimated imperfection length is assumed for pipeline that
takes a form dependent on the flexural stiffness and the the value of can be computed using Equn 11;
weight of installed pipe before operation [19].
for a range of values of length L from the
Palmer et al. further derived the formula for preliminary computed , determine Po using Equn 10;
design to determine the required download stability
during operation, which is given by: determine the value of T using Equn 1, and the
buckle amplitude Vm using Equn 7.
EI0
12
the natural length of the suspended portion is given as Li imperfection height, and the safe temperature obtained
as shown in Fig.4a above, assuming the out-of-straightness in the imperfect model is smaller than the one calculated
of the pipeline is free of an axial load i.e. P = 0. using the perfect model.
During operation with increasing axial load P, it was The model proposed by Palmer et al. established a
observed that the values of the wavelength (the lift of preliminary design to determine the stability of buried
wavelength LL) begins to reduce when compared to the pipelines following the procedure of the analysis described
initial wavelength Lo as shown in Fig.4b and Table 2. in above. A full calculation can be seen in the Appendix*.
Following the approach described above, and using the Using the sample pipeline with an axial force of 15 MN
sample pipeline in Table 1, Table 2 depicts the relationship and an imperfection height of 0.2 m, when the depth
between the safe temperature (Tmin), initial wavelength cover used was 0.8 m the factor of safety was less than
(Lo), the uplift wavelength (LL), the uplift load (PL), and 1; when a cover depth of 1.4 m was used, the factor of
the maximum buckling load (Pb) for various imperfection safety increased slightly (1.04), and with a cover depth of
heights. 1.7 m, the factor of safety increased to 1.17. This shows
that a cover depth of 1.7 m would be required to keep the
As the initial imperfection height increased the minimum pipeline stable, and could be used for upheaval design.
safe temperature Tmin to propagate vertical buckling
*Editors note: space unfortunately precludes the inclusion of the
decreased and the maximum axial load for buckle authors Appendix which is made up of a considerable amount of tabular
propagation reduced. This is illustrated in Figs 8 and 9. data. A copy can be sent to readers for whom it would be helpful: to
The maximum buckling load is reached with a very small obtain this, please contact the editor, whos details are given on p.142.
166 The Journalof Pipeline Engineering
Table 2.Values of safe temperature, initial wavelength, uplift wavelength, uplift load, and maximum buckling load for various
imperfection heights.
Imperfection height H (m) Required download W (N/m) Total download W0 (N/m) stability
0.05 -7992.225716 8787.611116 TRUE
0.1 -1594.783839 8787.611116 TRUE
0.2 7452.565228 8787.611116 TRUE
0.3 14394.84034 8787.611116 FALSE
0.4 20247.44898 8787.611116 FALSE
0.5 25403.70071 8787.611116 FALSE
0.6 30065.3086 8787.611116 FALSE
0.7 34352.09946 8787.611116 FALSE
0.8 38342.14712 8787.611116 FALSE
0.9 42089.6818 8787.611116 FALSE
1 45634.18824 8787.611116 FALSE
Table 3.Values of required download and pipeline stability level at different imperfection heights.
It was observed that as the imperfection height increased The simplest method is to stabilize pipeline against
the required download and the necessary cover depth that upheaval buckling by burying the pipeline; due to the
would be required to keep the pipeline stable to avoid difficulties and high cost involved in this method, other
upheaval buckling of the buried pipeline, as shown in options have been introduced. One of these is to reduce
the Fig.10 and Table 3. If the pipeline is stable, further the design temperature and pressure and to increase the
action could be ignored; however if, from the analysis, submerged weight of the pipeline, although this method
the pipeline is shown to be unstable, further investigation is impractical because too much weight would be needed
using finite-element analysis would be required. to accomplish this, and reducing the temperature might
necessitate adding a heat exchanger to the system.
encourage the use of longer pipelines operating at higher 11. G.T.Ju and S.Kyriakides, 1988. Thermal buckling of offshore
temperatures and pressures. There might not be a need pipelines. J. of Offshore Mechanics and Arctic Engineering, 110,
for burying or trenching of pipelines (which is a known pp 335-364.
practice associated to shallow waters) due to the high cost 12. A.D.Kerr, 1974. On the Stability of the railroad track in
vertical plane. Rail International, 5, pp 132-142.
and techniques that would be involved. Therefore laying
13. F.Klever, L.van Helvoirt, and A.Sluyterman, 1990. A
the pipeline on the seabed would be a good option. This dedicated finite-element model for analyzing upheaval
option exposes the pipeline to horizontal snaking which is buckling response of submarine pipelines. Offshore
associated to with lateral buckling. Further research into Technology Conference.
lateral buckling would therefore be of necessity for the 14. R.B.Locke and R.Sheen, 1989. The Tern and Rider pipelines.
future of offshore pipelines. European Seminar on Offshore Pipeline Technology,
Amsterdam.
15. T.C.Maltby and C.R.Calladine, 1995. An investigation into
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