The solo airline transport pilot reported he was landing a twin-engine airplane on a gravel-covered airstrip, at the conclusion of a Title 14, Code of Federal Regulations Part 91 positioning flight. He reported that while on final approach, the airplane "encountered a sinker" and it began to descend below his anticipated approach path. He added full engine power to stop the descent, but the airplane continued to descend, and it landed hard on the right side of the runway. During touchdown, the airplane’s landing gear collapsed, and it continued to slide for about 150 yards, resulting in substantial damage to the fuselage. The pilot reported that there were no preaccident mechanical problems with the airplane. A weather reporting station 14 miles south of the accident site reported wind from 110 degrees at 24 knots, gusting to 35 knots 12 minutes before the accident.