When buried piping is subjected to mine subsidence, the soil around the pipe drops vertically down and also moves axially and laterally in the horizontal plane.

Forcing the pipeline to match the horizontal soil displacements does not account for the slipping / flow of soil that would occur around the pipe. Do you use the soil spring restraint between the pipe and a cnoded displacement as the only "flow" effect or some other method?

I am interested to know how others model these horizontal soil movements in Caesar.

Mike,

I do not have an answer but I offer the following observation.

In Western Pennsylvania the mining companies collapse the mine tunnels as the mineral vein is depleted. This causes the earth subsidence that you describe. Prior to the intentional "cave-ins" the mining company notifies the owners of all the neighboring pipelines. The pipeline owners uncover the pipelines and leave them uncovered until the dust settles. In some cases, typically when the pipeline follows rolling hills with an even overburden just below the frost-line, it becomes necessary to either shorten the pipe (by cutting and rewelding) or arrange it in the bottom of the trench in a "snake-like" way to accommodate the "extra" pipe length.

This kind of cooperation controls the problem you describe and helps keep the peace between the mining companies and the pipeline owners.

Regards, John.

This is not really a phenomenon suitable for modeling. If you leave the burden above the pipeline and collapse the tunnel below, you are going to have a problem everywhere the burden is "stiffer than elsewhere." Don't ask for a definition of the term in quotes! If this happens to an existing pipeline, survival of the pipeline will be a matter of luck, not engineering design. You can figure all you want, but a few poorly placed rocks in or near the overburden will overcome all the engineering you can muster!

The safest plan is as John describes, with a few added bells & whistles. Remove the overburden, instrument the pipeline periodically with strain gauges, take before and after readings, and replace the burden after any issues revealed by the strain gauges are resolved. For really long runs, you might want a surveyor to establish TOP elevations from a benchmark outside the subsidence area. "Periodically" is probably on the order of every few hundred meters of straight run (calculate a minimum unsupported span length that will result in yielding, and instrument in increments 1/2 that span), and both sides of any elbows or bends. A good map of the proposed collapse area might lead you to choose other locations, too. In cases of extreme deformations, major surgery may be necessary on the pipe.

As John notes, this may require some modification to the pipeline routing, although in general you would have to have Western PA or Rocky Mountain type terrain for this to matter. (I've lived in both places, one quite a bit longer than the other.)