As we all know, CAESAR only considers displacement in the form of beam elements, and simplifies the stress calculation due to the beam displacement.

If the soil vibrations are capable of causing the soil to compact and slump, then if you have the displacements, you could apply the displacements to the pipe, and still have the soil restraints be flexible.

You would have to cnode all the restraints to otherwise unused node numbers, and the apply a displacement on the element with the restraints and cnodes to the otherwise unused node number. I.E. if your pipe was 10-20-30 before burial, and then becomes 10,11,12,13,14...30 after burial, you'd then use 1010, 1011, 1012, 1013, 1014... 1030 as cnode numbers.

However, if the proximity and severity of the vibration equipment are close and large, the failure mode could be localized. The soil would be "flowing" away and towards the source of the vibrations, which I speculate could exert a localized pressure on one side of the pipe, causing rapid ovalization. CAESAR doesn't address this. The energy placed into the pipe will be a function of the soil material and the pipe material, I'm sure, but there's not a large amount of experimental data to design to.