Falcon 2000
Flight Crew Air Transport Pilot (ATP)
Fatigue; Distraction
Inflight Event / Encounter CFTT / CFIT
Air Traffic Control Issued Advisory / Alert; Flight Crew Became Reoriented; Flight Crew FLC complied w / Automation / Advisory
Human Factors; Procedure
Cleared for the Visual Approach to Runway 33 at KBTV. Weather was 10+ visibility and clear skies. Approximately 3-4 miles on a straight in final we got the 'terrain pull up' warning. I was the flying pilot in the left seat and was visual. I immediately climbed until the warning subsided. At approximately the same time; the Tower advised they were getting a low altitude warning. I was hand flying the plane due to a rapid descent and a later than normal decent from altitude from ATC. At all; times I was in visual conditions and felt I was in a proper position to land; we had the ILS loaded and displayed but I obviously was below the ILS Glideslope. Distracted for a moment by the last minute steep descent from ATC and the resulting visual approach. We landed normally and without incident.I was tired after several long days and was considering using the Fatigue call but failed to do so. Also; I should have paid more attention to the ILS but I was visual and felt the terrain was well below us. Obviously it wasn't.  This was my first time in 17 years that the Terrain warning activated. It was an eye opening experience on many levels.
While descending out of altitude in we received an extremely late descent out of the flight levels even after we ask multiple times for lower. Pilot Flying had to put the airplane in a descent with the air brakes out in a high rate of descent. This put us behind the approach segment of the visual approach. Despite this the Pilot Flying was able to establish a normal rate of decent several miles out but with the mountains in Burlington and the unusual visual clues in the hills it put us in a lower than normal approach position. Just as I was about to warn him his air brakes where still out and we were getting low the GPWS went off and the tower gave us a warning of an upcoming mountain. We immediately corrected and told the tower we were correcting. Climbed up; established a normal stabilized approach; and landed with no incident.Should have not been so distracted and [should have] warned Pilot Flying earlier in the approach phase. We also could have taken vectors in order to make a more normal descent. Air brakes usage could have been monitored better. Following the glide path would have helped as well. Taking the visual approach for granted in the mountains also contributed to this unusual situation. ATC could have been much more helpful as well.
DA-2000 pilot reported low altitude alert while on visual approach; by both the aircraft systems and control tower.