I am not sure exactly how you define flowable fill. Current mined tunnel
construction typically uses cellular concrete for this purpose (backfilling the
permanent tunnel lining). When using cellular concrete it is typical to design
for a fluid pressure based on the unit weight of the cellular concrete. The
work can be done in multiple lifts if necessary to reduce the loads induced on
the permanent tunnel structure.
Be very careful about flotation of the permanent structure. I have argued with
many contractors about this issue; they never believe that the "heavy" tunnel
structure can float. It's not a pretty site when it happens...
Eric Lindquist, PE