The pilot reported that he was practicing touch-and-go landings when the accident occurred. The pilot stated that during the second landing roll, the airplane veered to the right with the tires “skittering” during the landing roll. The pilot applied left rudder to no avail then “tapped” the left brake. The pilot reported that the airplane's heading straightened out, then it veered “hard” to the left, again with the tires “skittering.” The pilot applied right rudder, but the airplane continued off the left side of the runway. The airplane traveled through the grass, the nose gear contacted the raised pavement of a taxiway, and the airplane became airborne. The pilot stated that he applied back pressure on the control yoke and the airplane touched down on all three landing gear. The nose gear collapsed and the airplane nosed over. Postaccident inspection of the airplane did not reveal any preexisting failure/malfunction which would have resulted in the loss of control.