gravel force

huangyhg

gravel force
i have a 14" od pipe that is buried under 18" of gravel.  along this 14" pipe there are several branch connection, each branch consisting of a 3" pipe sticking up through the gravel approx. 5'.  the 14" pipe will be exposed to a temperature causing thermal expansion.  
my question is how to calcualate the drag force that the gravel will exert on the 3" branch pipes, due to the thermal expansion of the 14" line.  does anybody have any ideas?
estimate the longitudinal movement of the 14" pipe for the span between 3" pipes.  assume the gravel is compacted and "immoveable" along the axis of the 14" pipe. this will result in a cantilever beam condition of the 3" pipe, fixed at the 14" pipe, uniformly loaded for the 18" of gravel with the load equivalent to the deformation created by the longitudinal displacement of the 14" pipe.
in actuality, the gravel will compress and displace so that your load on the 3" pipe will be less than estimated.
one other method is to insulate the 3" pipe with compressible insulation, with its thickness equal to twice the anticipated longitudinal displacement of the 14" pipe spanning between the 3" pipes.  this will allow free movement of the 3" pipe with no ensuing load.
is this a ground flare?
yes, good guess.
i don't have a copy available to check, but does api recommended practice 521 鈥?guide for pressure-
relieving and depressuring systems have any guidance in this area?  if not, then i assume that ansi/asme b31.3 would govern the underground piping design.  
if you have access to caesar ii piping analysis software, it has soil modeling capability for buried piping.  unfornately, this is one area of caesar ii that i personally have no experience with.