THE PLT PERFORMED 1 NORMAL TOUCH & GO OPERATION, & TOUCHED DOWN NORMALLY ON THE SECOND PLANED TOUCH & GO WHICH WAS TO TERMINATE WITH A RIGHT DEP OUT OF THE PATTERN. AFTER TOUCHDOWN, WITNESSES OBSERVED THE ACFT ROLL STRAIGHT ALONG THE RWY CENTERLINE FOR ABOUT 800 FT THEN BEGIN A GRADUAL DIVERGENCE FROM THE RWY WHICH SEEMED TO STABILIZE AT ABOUT A 30 DEGREE ANGLE. AFTER DEPARTING THE RWY EDGE, THE ACFT ROLLED AT A CONSTANT RATE OF SPEED FOR AN ADDITIONAL 900 FT THROUGH THE DIRT AREA BETWEEN THE RWY & ADJACENT TAXIWAY BEFORE COLLIDING WITH A CONCRETE DRAINAGE ABUTMENT. THE WITNESSES SAW THE WINGS OF THE ACFT ROCK BACK & FOURTH DURING THE GND ROLL THROUGH THE DIRT. EXAMINATION OF THE ACFT TRACKS CONFIRMED THAT THE ACFT DID OSCILLATE ABOUT THE ROLL AXIS & SHIFT WEIGHT FROM SIDE OT SIDE DURING THE GND ROLL. THE PLT HAD ACCRUED ONLY 8 DUAL HOURS TO THE FIRST UNSUPERVISED SOLO. THE ACCIDENT FLIGHT WAS THE SECOND SOLO FLIGHT WITHOUT SUPERVISION. NO PREIMPACT FAILURES OR MALFUNCTIONS WERE FOUND.