Pilot reported a GPWS terrain warnings on final approach twice; with no published approaches but recent runway construction. After conducting terrain escape maneuvers twice; pilot landed after third approach.

Narrative

Flight was inbound to F82 from the southwest. Weather was VMC. Winds from the south-southwest ceiling scattered at ~5k ft. Mission planning notes; and NOTAMS; indicated that the airport had recently undergone runway construction to lengthen the runway. NOTAMS; and company products; stated that the construction was finished; declared distances were provided; but no approaches existed for the new runway yet. There was also no VGSI. We briefed arriving from the southeast to receive a vectors for the visual approach to step down through the scattered layer and intercept a left downwind for runway 17 at a 45 degree entry to pattern altitude. Descent and arrival went as briefed. Downwind; base; and early final turn were uneventful. On short final we experienced a TAWS Warning pull-up". We executed the proper terrain escape procedure. Warning went away once we established a positive rate. We noticed there was no significant terrain around us as we climbed back into the pattern. A second pattern and approach was conducted with a similar result. As a crew; we determined the approach path was safe and we attributed the warning to a database issue. It seemed to us as if the GPWS data did not account for the runway construction; and it warned us as if we were flying to the ground. Of note; the aircraft's FS database had a valid coordinate for runway 17; and the SVS (synthetic vision system) also showed the runway appropriately. We conducted a third approach; on a slightly steeper profile in an abundance of caution. TAWS was inhibited for the third approach. Third approach to landing was uneventful. Once on the ground we noted that we were in the "yellow" zone for the TAWS further indicating that the system thought we were in the dirt. Taxi and turnaround were uneventful. We received a TAWS caution once airborne. Suggestions: It is recommended for the software to be updated. In the meantime; there should be an analysis of a three degree glide path to the runway to ensure proper obstacle clearance. There should be a NOTAM published for operations at this airfield with respects to the database. Furthermore; pilots should be aware of the country road that is perpendicular to the approach end of 17. There is a power line that was buried to facilitate landings; and any vehicular traffic on that road will be awfully close to aircraft crossing the threshold; specially if the aircraft is low on final."