# How can I calculate the stresses and limits for the physical lowering of in-service pipelines?

Sometimes underground pipelines are exposed due to vertical scour or lateral migration of streams (or other erosion). One option is to lower the (in-service) pipeline to a new depth that provides sufficient ground cover.

How can I determine the mechanical stresses on the pipe, and determine how much the line can be lowered? Also required is determining what length of trench will be required to accommodate the lowering. What are the relevant codes or standards?

This question is in relation to steel pipelines for both gas and liquids.

• This is a neat question. How do they go about lowering a pipe? Do they just remove the supporting soil underneath and let it bend itself...?
– Rick
Commented Jan 21, 2015 at 15:49
• Do the dots in the diagram represent connections of pipe segments? Commented Jan 21, 2015 at 16:28
• Yes, Rick. Gravity does the bending. The pipeline is temporarily supported while soil is removed. The pipeline is then gradually lowered onto the new trench bottom. Commented Jan 21, 2015 at 18:02
• The dots are just representative points along the profile to show depth values. The pipeline is connected by welding and does not need to be represented in this analysis. Commented Jan 21, 2015 at 18:04

This is something that I've looked at with tunnels, rather than pipes, and arguably with smaller deflections. Hopefully it'll be some help, however.

If you can satisfy yourself that the rate of curvature is relatively small- then you can approximate the stress generated by the lowering using simple beam theory:

$$\sigma=\frac{Ey}{R}$$

Where:

• E is the Youngs Modulus
• y is the distance from the neutral axis you are measure the stress at (i.e. the radius of the pipe itself)
• R is the radius of curvature.

Mechanically, you'll need to check that the stresses in the pipe along the parabaola that defines your curve never exceed the limiting stress of the pipe material, and (probably more critcally) the capacity of the connections.

This is a bit of a simplification, and depending on the type of pipe, the joints themselves will have some play.

• Thanks for the input but it is a bit more complicated than this. The limiting factor will be the total longitudinal stress on the pipeline due to existing conditions such as internal pressure, as well as imposed stresses from bending and elongation of the pipeline. Commented Jan 21, 2015 at 18:14
• The stress above would be the longitudinal stressed caused by the elongation from bending though? I imagine internal pressure is primarily a ring force, so doesn't contribute? Commented Jan 22, 2015 at 8:32
• Simple beam theory works pretty well as long as the deflections and slopes are kept relatively small as a proportion of the length of the beam. When these conditions can no longer be obtained, then a more sophisticated large-defection beam theory may have to be employed, and I believe the laying of subsea pipelines is one of those areas where you typically see such analyses employed. The analysis is complicated, because things are no longer linear as in standard beam theory. Because the analysis is so complicated, typically non-linear FEM programs are used instead of hand calculations. Commented Jun 4, 2016 at 3:20