No idea if C3D can export this or not. *never tried*
Only thought to mention that I used to work for a civil contractor that used Trimble site control, and I'd just take their vanilla CAD/DTM and import it into
Terramodel (optional software with GPS site control purchase?), or
AGTEK _then_ Earthwork 3D, and spit out the files we needed for heavy equipment data cards (i.e., bulldozers, graders, excavators, etc.).
HTH