The 3D solver Freebird in iRIC has been enhanced to allow the configuration of obstacle walls that include culverts.
https://www.youtube.com/watch?v=EVUraIi3bz4
This video shows a 3D simulation in which a vertical wall with a culvert is installed in the middle of a channel, and the discharge is gradually increased. Initially, the flow passes only through the culvert, but as the discharge increases, the simulation captures the transition to full overflow across the entire wall.