I would question why road traffic is driving very fast in “heavy rainfall”, but the solution is the same: truncate the gutter before the intersection, so that the intersection itself drains conventionally, into the center gutters on all approaches to the intersection. Alternatively, where it makes sense, use a center drained roundabout.

having a hollow space beneath the part of the road that needs to support the most weight of vehicles

My understanding is that there is only one storm drain pipe underneath a street, somewhere near the center, and each side of the road has laterals that connect to this pipe. There are not two pipes, one for each side of the street directly under the edges of the paved surface. See amwua.org/…/only-rain-should-go-down-the-storm-dr… (relevant image only shows up on desktop mode)