Looking at the commentary for this section (the pages with gray trim), equation I6-6 seems to show the equation for circular area by coincidence.
The engaged perimeter is assumed to be one-quarter of the circumference (0.25 pi D) assuming the member giving load to the filled steel member frames in from only one side. The engaged transfer length of load is assumed to be twice the diameter in each direction (above and/or below) (Cin D)
Therefore the surface area engaged in load transfer is shown as (0.25 pi D)(Cin D) = 0.25 pi D^2 Cin.
The commentary states that you are allowed to increase the amount of the circumference engaged in load transfer when the applied load comes in from multiple sides or some configuration other than the basic assumed one.
For a micropile, I believe you could use the full circumference, and a value of 2 for Cin (the pile is only below the point of load application, not above).
Hope this helps! It's always good to visualize the load path for your structure.
------------------------------
Walter Kaniecki A.M.ASCE
Transportation Engineer
Penfield NY
------------------------------