I am new to the forum so I hope this is not too late to be of use. Generally speaking minimum covers are not for load carrying capabilities, for RCP pipe the worst load is the three-edge load which is directly related to pipe class. In the field, regardless of how shallow the cover, the backfill offers some lateral support and the bedding some foundation load distribution. The pipe should withstand the design load without negative consequence.
Minimum cover is necessary to prevent excessive settlement of the backfill around the pipe and subsequent exposure of the pipe. There are two basic methods:
1) Since the soil will settle adjacent to the pipe more than over the pipe, there needs to be cover to dampen this effect.
2) There must be sufficient cover opposite a moving vehicle to resist the lateral component of the tire pressure. Even minute movement of the pipe will lead to soil settlement an exposure of the pipe.
2" in nowhere near enough. Generally speaking 9" of cover for non-traffic bearing situations is sufficient. For traffic installations a minimum of 12" should be provided.
Hope this helps
regards,
KEW
Hope this is helpfull.