What is the service? What is the piping material (and coating, if involved)? What kind and consolidation of "clay", depth of cover, etc. is involved? Is this application underwater/submerged (as one would think for post on this forum)?
Friction and cohesion combine to make axial resistance of soil. Friction is more prominate in sand. Cohesion in clays. Cohesion is likely to be quite high, if there is little to no sand. Have a measurement of the remolded cohesion value of this clay taken. You may be able to find various estimates for clays on the internet somewhere, but there is typically a lot of scattering of the values even in a specific sample, so its best to measure it at your locations when possible.
These assume the clay returns to a nice goo-ey mass soon after backfilling. For a soft clay (basically fish poo and other marine detritus) this may be somewhat true, but for stiffer clays the backfill may resemble more of a ploughed field with the backfill clay being in clumps and behaving more like low density rock dump material.
It is my experience that trenches are typically left open for natural backfill from washed in materials to occur, in which case it would probably behave more like a remolded clay. If the trench is backfilled mechanically, as Darren notes, the values could be a lot different.
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