On March 23, 1999, at 1913 central standard time, a Piper PA-31-350, N812TB, operated by an airline transport pilot sustained substantial damage when it exited runway 30 (8,400' X 150' dry/asphalt), at Waterloo Municipal Airport, near Waterloo, Iowa. The pilot reported no injuries. He told authorities that he was conducting touch and go landings and the accident occurred on the second landing. He said that when the nosewheel touched down the airplane veered to the left and exited the runway. The personal 14 CFR Part 91 flight was operating in visual meteorological conditions. No flight plan was on file. The local flight departed at 1845. When asked to make a written statement by Federal Aviation Administration (FAA) inspectors, the pilot said he needed time to think the events over. In the written statement signed by the pilot, he indicated that directional control was lost when the nosewheel touched down. During a telephone interview with the pilot, he stated that he did not know why he lost control of the airplane on touchdown. He said that he did not know of any mechanical problem with the airplane. An inspection of the airplane after the accident failed to reveal any pre-existing anomalies.