Okay after further research on the topic, it is possible to jack a box culvert. However, most contractor's prefer a round pipe to a box culvert, because... as the pipes are jacked they have a tendancy to roll. Obviously a square box culvert which rotates is rather a big deal, so extreme care must be taken to prevent this roll.
CNA Engineering Inc. provided me this free insight.
Rough costs associated with this operation can be upwards to $1000 per foot. It is an interesting opertation, and if your roadways cannot be shut down, it is a reasonable approach.
Thanks for all of your insight.
Sincerely
BLMSOCCER