According to the pilot of the tailwheel-equipped airplane, during approach for landing the airplane encountered "slight" turbulence, but the wind was reported as calm. He further reported that there were building cumulus clouds in the area. The pilot reported that about 4 feet above the ground, the airplane encountered wind gusts from left to right, so he added power and right rudder. He reported that the airplane landed on the left main landing gear, immediately veered left, exited the left side of the runway and impacted a drainage culvert. The airplane sustained substantial damage to the fuselage frame and right wing ribs. The pilot reported that there were no mechanical malfunctions or anomalies with any portion of the airplane during the flight that would have prevented normal flight operations. As a recommendation the pilot reported that he should have gone around at the first indication of turbulence and tested the conditions further. He wrote that had the conditions worsened he would have departed the area for a suitable airport.