What sensors are commonly used for vehicle detection?
"Vehicle detection loops, called inductive-loop traffic detectors" are one pretty common method. A groove is cut in the pavement, wire is layed in the groove, the groove is filled in with a sealant, and the wires go to a processor which makes the wire act like a metal detector - the vehicle interacts with the e-mag field, and the processor detects that.

Are you allowed to sawcut the area in question? If not, then a different method should be selected.  Maybe just tubes across the road as one finds leading into or out of a town so the local municipality can count how many cars are using a road.  I imagine they just detect change in air pressure as cars drive over the tubes.