The student pilot was on his third solo flight and planned to do several “touch-and-go landings.” He reported he had completed 5 series of landings without incident. On the sixth landing, he stated that after the main wheels touched the runway, the airplane veered left. The student pilot was unable to correct back to the center of the runway. The airplane then exited the hard surface runway and when the nose gear encountered soft terrain; dug in, and was torn from the airplane. The student pilot added that at the time of the accident the wind was out of the southeast and gusting, but was within the crosswind limit he and his flight instructor had set before the flight.