Summary of experimental, analytical and numerical results.
This chapter investigates buckle propagation of subsea single-walled pipeline and pipe-in-pipe (PIP) systems under hydrostatic pressure, using 2D analytical solutions, hyperbaric chamber tests and 3D FE analyses. Experimental results are presented using hyperbaric chamber tests, and are compared with a modified analytical solution and with numerical results using finite element analysis for single-walled pipelines and PIPs. The experimental investigation is conducted using commercial aluminum tubes with diameter-to-thickness (D/t) ratio in the range 20–48. The comparison indicates that the modified analytical expression presented in this work provides a more accurate lower bound estimate of the propagation buckling pressure of PIPs compared to the existing equations, especially for higher Do/to ratios. A 3D FE model is developed and is validated against the experimental results of the propagation bucking. A parametric FE study is carried out and empirical expressions are provided for buckle propagation pressures of PIPs with (Do/to) ratio in the range 15–25. Moreover, empirical expressions are proposed for the collapse pressure of the inner pipe (Pci), the proposed empirical equation for Pci, is shown to agree well with the experimental results of the tested PIPs.
- collapse pressure
- external pressure
- offshore pipelines
- propagation buckling
1. Propagation buckling of single pipe
Deep and ultra-deep water pipelines are vulnerable to propagation buckling due to the high external pressures. The pipeline may collapse due to the local dents, imperfections and ovalizations in the pipe-wall. This collapse will change the cross-section of the pipeline from a circular shape into a dog-bone or even flat shape. The buckle may then propagate along the pipeline and cause the pipeline to be shut down. A typical propagation buckle scenario is shown in Figure 1, which is triggered by impact on the pipeline from an anchor dropped from a passing vessel.
Different stages of the buckle are shown in Figure 1 in terms of the external pressure versus change in volume of the pipe. The dent caused by the impact can initiate the buckle due to high external pressure. The elastic buckling is followed by a plastic collapse and change in the cross-section of the tube from circular to oval and finally a dog-bone shape. If the pressure is maintained, the buckle will propagate quickly along the length of the pipe. Offshore pipelines normally experience high service external pressure; therefore the buckle will propagate through the length, forcing the flow line to be shut. The lowest pressure that maintains propagation is known as the propagation pressure, and is much smaller than the collapse pressure. To account for the difference between the collapse and the propagation pressures in design, a thick-walled pipeline is required [1, 2].
As shown in Figure 1, the propagation pressure is much less than initiation pressure (peak pressure in Figure 1). The initiation pressure is significantly affected by the size of the local dent. Local dents may also occur during the installation period. The most common types of offshore pipeline installation are S-lay method, J-lay method, Reel-lay method and Towing method. A combination of bending and external pressure happens in the sag bend length of the pipe. Normally high tension is applied to the pipe to maintain its stiffness during installation. If for any reason this tension is released, high bending in the sag bend region may cause local buckling which may be followed by propagation buckling. Apart from the foretold loading sources, manufacturing imperfections in pipe such as non-uniform thickness, varying elastic modulus, local ovalization, and also erosion and corrosion may cause local buckling in pipelines.
Many researchers have investigated various aspects of this problem since it was first presented by Mesloh et al.  and Palmer and Martin . Most notably is the extensive work of Kyriakides [5, 6], Kamalarasa  and Albermani et al. . Recent books by Kyriakides  and Palmer and King  provide comprehensive review of this problem and the associated literature. The work done by Xue et al.  investigates the effect of corrosion in the propagation buckling of subsea pipelines. Buckle arrestors [1, 18], pipe-in-pipe system [10, 11, 12, 13, 14], sandwich pipe system  and ring-stiffened pipelines , are used to confine the propagation buckling in subsea pipelines.
As stated before, a local dent or ovalization in the pipe wall can cause a local collapse as in the pipe-wall. It is well-known that the collapse pressure of a 2D arch (similar to a single pipeline (
1.2 Analytical solution of propagation pressure of single pipe
A typical buckle propagation response is characterized by the pressure at which the snap-through takes place (the initiation pressure
Palmer and Martin  suggested a 2D approximation for propagation buckling of subsea pipelines Eq. (2). Their solution is based on a 2D ring collapse (plane strain) mechanism, and accounts for the circumferential bending effect of the pipe wall (see Figure 2). The Palmer and Martin (PM) solution underestimates the propagation pressure when compared to experimental results. This difference increases as
for a pipe with radius,
Accordingly, a modification to the lower bound PM solution is proposed , by accounting for the circumferential membrane as well as flexural effects in the pipe wall
where is the change in the cross section area, is the change in the circumferential length and is the plastic moment, these are given by:
Experimental observations confirm that the propagation pressure predicted by (Eq. (8)) is 19% higher than the PM prediction Eq. (2), regardless of
1.3 Experiments on propagation buckling of single-walled pipelines
A stiff 4 m long hyperbaric chamber rated for 20 MPa (2000 m water depth) internal pressure was used for testing (Figure 3a). Three meter long aluminum pipes were used in the hyperbaric chamber tests . Ovalization measurements along the pipe samples before testing were carried out that gave an average ovalization ratio
The hyperbaric chamber test procedure is as follows. Thick discs are welded at both ends of 3 m pipeline. The pipeline is then filled with water and inserted inside the chamber (Figure 3b). The bolts at the chamber lid are tightened using a pneumatic torque wrench and the chamber is sealed. Using a control-volume analogy, the water inside the chamber is pressurized at a slow rate, using a hand pump. When the pressure reaches the initiation pressure
The average pressures of the 19 pipes tested in the hyperbaric chamber are represented in Table 1. A typical pressure-volume change response obtained from the hyperbaric chamber tests is shown in Figure 4. In Figure 4, the pressure inside the chamber is normalized by the propagation pressure,
|Sample/material||Coupon tests||Analytical (MPa)||Hyperbaric chamber (MPa)|
|ID||Al-6060||(MPa)||(%)||Eq. (8)||Experiment||Finite element|
The analytical, experimental and numerical pressures are compared in Table 2. The ratio of propagation pressure from the hyperbaric chamber tests
|Sample||Hyperbaric chamber||Finite element|
1.4 Finite element study on propagation buckling of single-walled pipelines
FE models were created in ANSYS  to investigate the response of the pipe to propagation buckling. Thin 4-noded shell elements (181) were used to model the pipe. SHELL181 is suitable for analyzing thin to moderately-thick shell structures. It is a four-noded element with six degrees of freedom at each node: translations in the x, y, and z directions, and rotations about the x, y, and z axes. Hydrostatic pressure can be applied as surface loads on corresponding surface. Pipe wall thickness is defined using section data command. A convergence study was performed and five integration points was found to be adequate for propagation buckling of cylindrical pipes. Frictionless contact and target elements (ANSYS elements 174 and 170) are used to define the contact between the inner surfaces of the pipe wall. These elements are created on the surface of the existing shell elements using ESURF command. The 3D contact surface elements CONTA174 are associated with the 3D target segment elements TARGE170 via a shared real constant set. Contact stiffness can be controlled by normal penalty stiffness factors and tangent penalty stiffness factor. Normal penalty stiffness factor of 0.1 was selected based on a convergence study performed that ensures both real contact behavior and reasonable computational time. Tangent stiffness factor appeared not to affect the results significantly.
A von-Mises elastoplastic material definition with isotropic hardening was adopted based on material properties shown in Table 1. Total of 40 shell-181 elements in circumference were utilized for modeling the pipe. Local ovalizations were introduced to FE model by applying external pressures symmetrically on 8 elements on top of the pipe along a length equal to diameter of the pipe. Geometry is then updated using UPGEOM command and nonlinear geometric and material analysis is carried out. The FE model is 3 m long and is restrained against translation at all nodes at both ends.
The initiation and propagation pressures obtained from FE analysis (
2. Propagation buckling of pipe-in-pipe systems
Pipe-in Pipe (PIP) systems are extensively being used in the design of high pressure and high temperature (HP/HT) flowlines due to their outstanding thermal insulation. A typical PIP system consists of concentric inner and outer pipes, bulk heads and centralizers. The inner pipe (flowline) conveys the production fluids and the outer pipe (carrier pipe) protects the system from external pressure and mechanical damage. The two pipes are isolated by centralizers at joints and connected through bulkheads at the ends of the pipeline. The annulus (space between the tubes) is either empty or filled with non-structural insulation material such as foam or water .
PIP systems are normally divided into two categories, namely, compliant and non-compliant systems. In a compliant system, the inner pipe and the carrier pipe are attached at close intervals; whereas both inner and carrier pipes are only connected through bulkheads at discrete locations in a non-compliant system. The relative movement between the inner and outer pipes is arrested in a compliant system while the two pipes can move relative to each other in a non-compliant system. PIPs are exploited in subsea developments, where the carrier pipe is designed to resist high hydrostatic pressures (water depths up to 3000 m) and the inner pipe is designed to transmit hydrocarbons at temperatures as high as 180°C . The HP/HT flow can cause global upheaval  or lateral buckling  in the system. Furthermore, the high hydrostatic pressure may trigger a local collapse, such as propagation buckling or buckle interaction [13, 14, 25, 26, 27, 28, 29, 33], in the carrier (outer) pipe. Structural integrity of the PIP system under external pressure is an issue of concern, because the collapse of the carrier pipe may result in collapse of the inner pipe.
Despite the extensive investigations performed on integrity of single pipelines, to date, instabilities of PIPs have only been marginally addressed. Kyriakides  conducted a thorough experimental study on propagation buckling of steel PIPs with two-inch diameter carrier tubes with
2.2 Analytical solution of propagation pressure of pipe-in-pipe systems
Numerous analytical solutions have been suggested to estimate the propagation pressure of a single pipe. Unlike propagation pressure, the initiation pressure is very sensitive to initial imperfection such as local dents or ovalizations. The propagation pressure is related to plastic properties of the pipe and is only a fraction of the buckle initiation pressure. Both buckle initiation pressure and buckle propagation pressure are related to the diameter to wall-thickness ratio of the pipe, however previous studies suggest that there is no evident relationship between the two [2, 3]. The simplest propagation pressure model was established by Palmer and Martin , which only considered the initial and final configurations of the cross-section of the pipe. Figure 6 shows the four plastic hinges developed in the pipe at different stages of propagation buckling on subsea pipelines and pipe-in-pipe systems.
By adopting plane strain analogy, Kyriakides and Vogler  proposed the following expression for the propagation pressure of the PIP system. Their formulation accounts for development of four plastic hinges in each of the carrier and the inner pipes (Figure 6d-f).
The analytical lower bound solution to propagation buckling of a single pipe given by (Eq. (8)), can be extended to the pipe-in-pipe systems by accounting for the membrane and flexural effects of the outer and the inner pipes:
2.3 Experiments on propagation buckling of pipe-in-pipe system
The experimental protocol is comprised of end-sealing concentric PIP systems with parameters shown in Table 3 and a length of 1.6 m (
|ID||Carrier pipe||Inner pipe||(MPa)|
Figures 8–10 present the experimental results of the buckle propagation response of PIPs. The pressure inside the chamber is plotted against the normalized change in volume of the carrier pipe (60 × 2 mm) of PIP-2 in Figure 8a. The chamber is gradually pressurized until the initiation pressure
The hyperbaric chamber propagation buckling results of the 80 × 2 mm carrier pipe and the PIP-1 system are shown in Figure 9. A small dent was imposed to the carrier pipe in the single-pipe test, which explains the lower buckle initiation pressure of the carrier pipe compared to that of PIP-2. As shown in Figure 9b, following the collapse of the carrier pipe the pressure inside the chamber drops drastically until the carrier pipe and inner pipe come into contact. Subsequently, a dog-bone buckle shape propagates along the PIP while the pressure is maintained at
Results of the PIP-3 with
2.4 Finite element analysis on propagation buckling of pipe-in-pipe systems
Finite element simulation of 1.6 m long samples of PIPs used in the hyperbaric chamber tests were conducted using ANSYS 16.1 . Thin 4-node shell elements (181) were used to model the carrier pipe and the inner pipe. The contact between the inner and outer pipes, and in between the inner surfaces of the inner pipe were modeled using non-linear frictionless contact and target elements (174 and 170). Symmetry is used and only one half of the pipeline is modeled. The mesh uses shell elements with seven integration points along the wall-thickness. To better facilitate the nonlinear analysis, a small ovalization ratio
The nodes at either end of the PIPs were restrained from translation in all directions. A von Mises elastoplastic (bi-linear) material definition with isotropic hardening was adopted. The modulus of elasticity (
The pressure response and the deformed shape of PIP-1 from the FE analyses are shown in Figure 11b. The pressure is plotted against the normalized ovalization of the carrier and inner pipes (
2.5 Empirical expressions for propagation buckling of PIPs with thin and moderately thin carrier pipes
A comprehensive parametric study is conducted using the validated FE model to find the buckle propagation pressures of PIP systems with various wall thickness
Figure 13 shows the pressure response and the deformed shape of a moderately thin PIP with
The parametric study ascertained the dependency of the propagation pressure of the PIP systems on geometric and material parameters of the outer and inner pipes. Moreover, current FE results proved that the buckle propagation modes of PIPs with large
The coefficients in Eqs. (17) and (18) are determined using the Leven-berg-Marquardt algorithm and correspond to correlation factors (
2.6 Empirical expressions for propagation buckling of PIPs with thick and moderately thick carrier pipes
In PIP systems with thin and moderately thin carrier pipes, expressions (Eqs. (17) and (18)) derived in Section 2.5 can be used to predict the propagation pressures. A total of 254 data points were collected from the raw data reported in [11, 12], and the current FE results for PIPs with
with multiple correlation factor (
2.7 Empirical expression for collapse pressure Pci of PIPs
The hyperbaric chamber results disused in the previous section suggest that, the collapse pressure of the inner pipe of the PIP system, (
The coefficient (0.05) in Eq. (20) is determined using the Levenberg-Marquardt algorithm with a correlation factor (
The normalized collapse pressures obtained from the proposed empirical expression (Eq. (20)) and those acquired from the hyperbaric chamber for the tested PIPs are represented in Table 5. The differences are less than 5%. As represented in the last column of Table 5, the empirical expression predicts the experimental results with good accuracy.
Buckling propagation mechanisms of subsea single-walled pipelines and pipe-in-pipe (PIP) systems under external pressure in quasi-static steady-state conditions were investigated using 2D analytical solutions, hyperbaric chamber and 3D FE analyses considering non-linear material and geometric behavior. In general, reasonable agreement is obtained between analytical, numerical and experimental results. The modified analytical solution suggested in this chapter accounts for the
The comprehensive FE study suggested the existence of two major buckle modes in PIPs with thin and moderately thin carrier pipes. In mode
Kyriakides S, Corona E. Mechanics of Offshore Pipelines: Volume 1 Buckling and Collapse. Vol. 1. Oxford, UK: Elsevier; 2007
Albermani F, Khalilpasha H, Karampour H. Propagation buckling in deep sub-sea pipelines. Engineering Structures. 2011; 33(9):2547-2553
Mesloh RE, Sorenson JE, Atterbury TJ. Buckling and offshore pipelines. Gas. 1973; 49(7):40-43
Palmer AC, Martin JH. Buckle propagation in submarine pipelines. Nature. 1975; 254(5495):46
Kyriakides S, Babcock CD. Experimental determination of the propagation pressure of circular pipes. Journal of Pressure Vessel Technology. 1981; 103(4):328-336
Kyriakides S, Netto TA. On the dynamics of propagating buckles in pipelines. International Journal of Solids and Structures. 2000; 37:6843-6867
Kamalarasa S, Calladine CR. Buckle propagation in submarine pipelines. International Journal of Mechanical Sciences. 1988; 30(3–4):217-228
Palmer AC, King RA. Subsea pipeline engineering. Oklahoma, USA: PennWell Books; 2004
Xue J, Fatt MH. Buckling of a non-uniform, long cylindrical shell subjected to external hydrostatic pressure. Engineering Structures. 2002; 24(8):1027-1034
Kyriakides S. Buckle propagation in pipe-in-pipe systems: Part I. Experiments. International Journal of Solids and Structures. 2002; 39(2):351-366
Kyriakides S, Vogler TJ. Buckle propagation in pipe-in-pipe systems: Part II. Analysis. International Journal of Solids and Structures. 2002; 39(2):367-392
Gong S, Li G. Buckle propagation of pipe-in-pipe systems under external pressure. Engineering Structures. 2015; 84:207-222
Karampour H, Alrsai M, Albermani F, Guan H, Jeng DS. Propagation buckling in subsea pipe-in-pipe systems. Journal of Engineering Mechanics. 2017; 143(9):04017113
Alrsai M, Karampour H, Albermani F. Numerical study and parametric analysis of the propagation buckling behaviour of subsea pipe-in-pipe systems. Thin-Walled Structures. 2018; 125:119-128
Estefen SF, Netto TA, Pasqualino IP. Strength analyses of sandwich pipes for ultra deepwaters. Journal of Applied Mechanics. 2005; 72(4):599-608
Showkati H, Shahandeh R. Experiments on the buckling behavior of ring-stiffened pipelines under hydrostatic pressure. Journal of Engineering Mechanics. 2009; 136(4):464-471
Timoshenko SP, Gere JM. Theory of Elastic Stability. NewYork, USA: McGraw-Hill; 1961
Kyriakides S, Babcock CD. On the dynamics and the arrest of the propagating buckle in offshore pipelines. In: Offshore Technology Conference. 1979;(1):45-57
Mesloh R, Johns TG, Sorenson JE. The propagating buckle. Boss. Proceedings. 1976; 76:787–797
ANSYS 16.1 Release, A. I. 275 Technology Drive, Canonsburg, PA 15317
Bai Y, Bai Q, editors. Subsea Pipelines and Risers. Oxford, UK: Elsevier; 2005
Jukes P, Eltaher A, Sun J, Harrison G. Extra high-pressure high-temperature (XHPHT) flowlines: Design considerations and challenges. In: Proceedings of the ASME 2009 28th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers. 2009. pp. 469-478
Wang Z, Chen Z, Liu H. Numerical study on upheaval buckling of pipe-in-pipe systems with full contact imperfections. Engineering Structures. 2015; 99:264-271
Vaz MA, Patel MH. Lateral buckling of bundled pipe systems. Marine Structures. 1999; 12(1):21-40
Karampour H, Albermani F. Experimental and numerical investigations of buckle interaction in subsea pipelines. Engineering Structures. 2014; 66:81-88
Karampour H, Albermani F. Buckle interaction in textured deep subsea pipelines. Ships and Offshore Structures. 2016; 11(6):625-635
Karampour H, Albermani F, Gross J. On lateral and upheaval buckling of subsea pipelines. Engineering Structures. 2013; 52:317-330
Karampour H, Albermani F, Major P. Interaction between lateral buckling and propagation buckling in textured deep subsea pipelines. In: Proceedings of the ASME 34th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers; 2015. pp. V003T02A079-V003T02A079
Karampour H, Albermani F, Veidt M. Buckle interaction in deep subsea pipelines. Thin-Walled Structures. 2013; 72:113-120
Zheng J, Palmer A, Brunning P, Gan CT. Indentation and external pressure on subsea single wall pipe and pipe-in-pipe. Ocean Engineering. 2014; 83:125-132
Lee LH, Kyriakides S. On the arresting efficiency of slip-on buckle arrestors for offshore pipelines. International Journal of Mechanical Sciences. 2004; 46(7):1035-1055
Stephan P, Love C, Albermani F, Karampour H. Experimental study on confined buckle propagation. Advanced Steel Construction. 2016; 12(1):44-54
Alrsai M, Karampour H, Albermani F. On collapse of the inner pipe of a pipe-in-pipe system under external pressure. Engineering Structures. 2018; 172:614-628