Section 7 : Hobbs Lateral Buckling Method

Lateral Buckling

Lateral buckling occurs because of the combination of an initial lateral out of straightness, and axial load due to temperature and pressure. The initial out of straightness is often caused during pipe installation, but can also be caused by movement of the pipe due to trawl interaction or environmental effects. When the axial load reaches the initiation load, the pipe will suddenly buckle sideways.

Lateral buckling can occur as one of four modes. modes 1, 2, 3 and 4. The actual mode depends on the initial out of straightness shape. Generally the pipeline should be designed for the mode with the minimum buckling load, or minimum initial out of straightness. Generally it is not possible to predict which lateral buckling mode will occur.

Lateral Buckle Profiles

The lateral buckle profiles for lateral modes 1, 2, 3 and 4 are shown in the figures below.

The pipe profile with no axial load is shown by the black line. The post buckle profile is shown by the red line.

 

 

 

Lateral Buckle Calculations

The lateral buckling initiation conditions are calculated by:

`Li = ( ( Δu * EI ) / ( k4 * μli * W ) )^(1/4)` `Ni = - ( k1 * EI ) / (Li^2)` `BMi = - k5 * μli * W * Li^2` `Nr = Ni - k3 μa * W * Li * ( sqrt(( 1 + ( k2 * EA * W * μli * 2 * Li^5 ) / ( μa * EI^2 ) )) - 1 )`

where:

`Li` = buckle length at initiation `Δu` = initial vertical out of straightness or prop height `EI` = pipe bending stiffness `BMi` = maximum bending moment at initiation `W` = pipe unit weight `Ni` = axial load in the buckle zone at initiation `Nr` = fully restrained axial load away from the buckle zone `EA` = pipe axial stiffness `μa` = pipe soil axial friction coefficient `μli` = pipe soil initial lateral friction coefficient

The k constants have the following values:

Lateral Buckling k Values.

Mode k1 k2 k3 k4 k5

Mode 1 80.76 6.391e-5 0.5 2.407e-3 0.06938

Mode 2 4 π2 1.743e-4 1.0 5.532e-3 0.1088

Mode 3 34.06 1.668e-4 1.294 1.032e-2 0.1434

Mode 4 28.20 2.144e-4 1.608 1.047e-2 0.1483

The lateral buckling post buckle conditions are calculated by solving:

`Np = -(k1 * EI) / (Lp^2)` `Lp = ( ( (-Nr + Np) / (k3 * μa * W * Lp) + 1 )^2 - 1) * (μa * EI^2) / (k2 * EA * W * μlp^2 ) )^(1/5)`

and:

`Δp = (k4 * μlp * W * Lp^4) / (EI)` `BMp = - k5 * μlp * W * Lp^2`

where:

`Np` = axial load in the buckle zone post buckle `Lp` = buckle length post buckle `μlp` = pipe soil post buckle lateral friction coefficient `Δp` = buckle amplitude post buckle `BMp` = maximum bending moment post buckle

Check that the convergence is close to or equal to 1. Note that the lateral friction coefficient can have different values for initiation and post buckle.