I think you need to provide actual diagram of box culvert to understand how it is placed. If the height of soil cover is much bigger than box culvert is subjected to soil load on the top slab and earth pressures on the side walls which may be partially submerged.

Thank you Sir, What are the other geotechnical parameters that affect the performance of the box culvert for the Rod Under Bridge (RUB) design?

Not perform well when subjected to significant differential settlement due to subgrade reaction.