SPECIAL REPORT_ New Method Assesses the Risk of Upheaval Buckling for Submerged Pipelines - Print...

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8/18/13 SPECIAL REPORT: New method assesses the risk of upheaval buckling for submerged pipelines - Print this page

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SPECIAL REPORT: New method assesses the

risk of upheaval buckling for submerged

pipelines

Alex Aynbinder

Cronus Technology Inc.

Houston

David Bevil

WorleyParsons Group

Houston

A new methodology assesses the risk of upheaval buckling and determines the required profile of the trench

bottom as a bed for both subsea and onshore pipelines.

The method uses as input data the design operating parameters of the pipeline (internal pressure and temperature

differential) and soil properties. Variable parameters are depth of cover, thickness of concrete coating or

concrete weight for overbend pipeline section, if required, and angle of turn and minimum elastic (free) bend

radius, or the height of any hills to be crossed.

Background

When a pipeline is operated at a temperature higher than tie-in and high internal pressure, the high temperature-

highpressure (HT/HP) pipeline will try to expand. If the line is not free to expand, an axial compressive force

develops in the pipe, potentially causing considerable vertical, lateral, or combined movement.

When the line is buried in a trench, the lateral soil resistance usually exceeds both the vertical uplift resistance

created by the pipe's air or submerged weight and the soil overburden, in which case the pipe will tend to move

upward, and unacceptable large vertical movement (displacements) may occur partly to release the compressive

force. This phenomenon is called upheaval or global buckling.

The primary factors affecting the buckling behavior of buried pipeline include the compressive axial force due to

temperature differential and internal pressure, soil resistance, and pipeline geometry (profile). The stability of the

pipeline in its initial position turns out to depend on the local profile of the pipe in contact with its foundation
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Downward load

Elastic (free) bending. Trenching and laying operations modify the profile of the bottom of the trench

(foundation) on which the pipe rests. The bottom of the trench should support the pipeline. Elastic bending

usually provides changes of the pipeline profile in the vertical plane. Elastic bending of the pipeline in the verticalplane stems from the transverse load q, which is part or full linear weight of pipe, and the restriction of the trench

profile. The solution of the condition of equilibrium (Equation 3) and boundary conditions (Equation 4) therefore

determines the pipeline and design bottom of trench profiles.

From the solution of the differential equation (Equation 3) with consideration boundary conditions (Equation 4),

Equation 5 represents pipeline profile and the distance to connection with straight pipe.

In design practice, minimum allowable bending radius, Rmin, in addition to the angle of turn, describes the

requirements for elastic bending.


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The condition of Equation 6 yields:

The relation between required transverse load and minimum elastic bend radius and angle of turn

(Equation 7).

The relation between distance and minimum elastic bend radius and angle of turn (Equation 8).

Pipeline and bottom trench profiles (Equation 9).

The pipeline profile is a parabola with variable radius from infinite at the connection with straight pipe and a given

minimum radius on the hill. The tangent of this curve is 1.5 times more than the tangent of a circle curve.

Equation 7 is the main equation, describing the relation between minimum elastic bend radius, angle of turn, pipe

flexural rigidity, and required weight for the pipeline profile to be in continuous contact with trench bottom. The

maximum value of load q is the linear weight of the pipe if the pipe is installed in the trench without water or the

submerged weight of pipe during installation. Stress criteria determine the allowable minimum elastic bending

radius Rmin. If the required load is more than the maximum weight of pipe, minimum radius or angle of turn must

be increased.

Profile changing due to short steep-sided hills. Short steep-sided hills as part of the profile introduce a

complication in that the pipeline may form spans on either side. Examples of such local imperfections include the

crossing of foreign pipelines, cables, etc.

Height describes this parameter and is established at design. Analysis of the beam under downward loads

determines the length of each side span. The design profile should also comply with stress criteria. As for the

previous case, the minimum radius along the section will establish these criteria.

Under an assumption that the beginning of a coordinate axis is on the summit of the curve, the unknown lengths

of the spans are l = L/2, and height is denoted by fo. Equation 10 describes boundary conditions in this case.

Solving the differential equation (Equation 3) with consideration of boundary conditions (Equation 10) yields the

pipeline profile and the distance to the connection with straight pipe (Equation 11).


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The curvature describes allowable bending stress, and Equation 12 describes the minimum radius.

Using Equation 12:

Equation 13 presents the relation between required transverse load and minimum elastic bend radius and

initial displacement.

Equation 14 presents the relation between distance and minimum elastic bend radius and initial

displacement.

Equation 13 is the main equation describing the relation between minimum elastic bend radius, initial

displacement, pipe flexural rigidity, and required weight for the trench and pipeline profile (Equation 11) to be in

continuous contact.

Fixed-profile stabilization

Classic beam-column theory for a pipeline under the axial compressive force S and downward load/unit length

w(x) yields an equilibrium condition described by Equation 15.

Load w(x) represents the downward load required to maintain the pipeline in position v(x) described as initially

imperfect due to the elastic bending or the short, steep hills. Equation 2 determines the value of axial compressive

force S, with initial profiles described by Equation 9 or 11 for elastic bending and hills, respectively.

Elastic (free) bending. Substituting profile Equation 9 in the condition of equilibrium, Equation 15, yields the

distribution of the required loads along the section of elastic bend (Equation 16).

The largest required load wmax occurs on the summit of the hill, when x = 0. Equation 17 calculates its value.

Equation 18 determines the critical length that required maximum load. From this condition, Equation 19

calculates the critical length.

Substituting the critical length in Equation 17 causes critical load to be calculated by Equation 20.

Short, steep hills. Substituting the profile Equation 11 in Equation 15 allows distribution of the required loads

along the section of pipeline at a steep-sided hill to be found in Equation 21.

The largest required force wmax occurs on the summit of the hill, when x = 0. Equation 22 calculates its value.

Equation 23 determines the critical length that required maximum load. From this condition, Equation 24

calculates the critical length. Substituting the critical length in Equation 22 causes critical load to be calculated by

Equation 25.

Risk assessment

Equations 7 and 13 therefore calculate required vertical loads for a pipeline to be laid in the design profile for

elastic (free) bending and in the design profile for short steep-sided hills, respectively. Equations 20 and 25

calculate, respectively, the required vertical loads for pipeline stabilization due to internal pressure and

temperature differential for a pipeline to be laid in the design profile for elastic (free) bending and in the design

profile for short steep-sided hills.


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Risk assessment of upheaval buckling may be guided by comparing the required total load presented by

Equation 26 as the sum of the required loads to lay the pipe in the design position (profile) and to stabilize the

pipe during operation (temperature and internal pressure effect) with the total loads calculated by Equation 27 as

sum of the load by the weight of pipe (Equation 28) and uplift soil resistance calculated by Equation 29.

DNV-RP-F110-2007 states the approach should "design a sufficient cover height to prevent upheaval buckling

and keep the pipe in its original position." Equation 30 can calculate the safety factor, or design criteria for

upheaval buckling failure mode. Establishing the value of the safety factor as criteria at 1.1 yields a conservative

approach in determining stabilization loads.

Design approach

The presented example (see table) includes the nomenclature used in the equations box and describes the

process of upheaval buckling risk assessment.

The stress criteria and the load required for installation should establish minimum bending radius and angle of turn

or hill deflection. The load of the pipe during installation should consider submerged weight of bare pipe and

concrete coating. The uplift soil resistance should consider the possible soil properties during operation.

References

1. Palmer, A.C., Ellinas, C.P., Richards, D.M., and Guijt, J., "Design of Submarine Pipelines Against

Upheaval Buckling," Offshore Technology Conference, Houston, May 7-10, 1990.

2. DNV-RP-F110-2007, "Global Buckling of Submarine Pipelines," Det Norske Veritas, 2007.

The authors

Alexander Aynbinder ([email protected]) is a senior technical advisor at

WorleyParsons Group (Houston). He also served as senior principal pipeline engineer at Technip, J.R.

McDermott, Fluor Daniel, and Gulf Interstate Engineering. Before immigrating to the US in 1990, Aynbinder wa

lead research scientist in the Russian State Research Institute for Pipeline Construction (VNIIST). He is a

graduate (1970) of Moscow Civil Engineering University and received a PhD (1977) in civil engineering from theCentral Research Institute of Civil Structures in Moscow. His major research interest is the stability and stress

analysis of offshore-onshore pipeline-piping systems. He is a member of ASME.


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David Bevil ([email protected]) has been a senior principal pipeline engineer at WorleyParsons

Group (Houston) for the past 12 years. He also served in a similar role at LummusCrest Engineering and Gulf

Interstate Engineering over the previous 23 years. He holds a BS in electrical engineering (1975) from Oklahoma

State University. In addition to extensive work in the analysis of stress in pipelines, he is also lead pipeline flow

assurance engineer for WPG and has authored a number of programs for use in specialty pipeline hydraulics,

addressing multiphase, dense phase, and non-Newtonian flow.

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