I am not a pipeline person by any definition, but I have personally bent hydraulic tubing up to 2" OD.
To make a bend anywhere in the range of '10D', meaning centerline radius is ten times the pipe OD, you generally need some kind of tooling, comprising minimally a curved shoe that supports the inside radius and keeps the 'inner side' walls from ballooning out where the material is being compressed in cold bending, plus a hook of sorts to grab the stationary tangent, and a sliding shoe that moves around outside the shoe and forces the moving tangent to be, er, tangent to, the shoe while applying compression to the 'outer side' walls. Such a bender can be as simple as the 'conduit hickey' you find at Home Depot, up through 'compression benders' as awkwardly described above, to 'mandrel benders' that support the inside of the tube while the outside is being bent.
All of those tools will leave scars in a coating on the pipe OD, and they're big and expensive and heavy and require power, so they're normally used in a shop, and any coatings are applied after bending.
I get the impression you are not asking about shop bending, but field bending, e.g. establishing some minimum radius for the trench into which the pipe will be laid.
That is off the edge of my experience, but I would take a run at it as follows:
Take a guess at an arbitrary radius to which the pipe must conform (via three bulldozers and fabric straps for instance), and calculate the strain in the pipe's outer 'fiber' at that radius. First compare it to the yield strain for the pipe material. Then compare it with the allowed elongation of the coating. Or even try a test bend in the shop to see what the coating can take, if you can't get a usable number from the coating supplier.
Or take a look at photos of similar pipe being entrenched. The pipe, being flexible on a large scale, assumes an S sort of shape as it is being lowered. Take a guess at the radius in a vertical plane, and infer that you can safely bend it to the same radius in a horizontal plane. There's your trench radius.
Or restate your question with a little more detail, Juan. Thanks.
Mike Halloran
Pembroke Pines, FL, USA