What is the name of the part of a culvert that projects above the top slab?

The part of a culvert that projects above the top slab is known as the headwall. The headwall serves multiple functions, including providing structural support to the culvert, preventing soil erosion around the inlet and outlet, and facilitating the transition of water flow from the culvert to surrounding areas. It is designed to manage water flow, reduce turbulence, and protect the integrity of the culvert structure.

While parapets are typically associated with bridge structures for safety and to provide a barrier, they do not serve the same structural or functional role as the headwall in a culvert system. The deck refers to the surface or top area of a bridge, and the endwall, while a part of culverts, typically serves to close the ends rather than projecting above the top slab. Thus, the headwall is the accurate term for the feature described in the question.