The solo student pilot reported that he took off with the intent to remain in the airport traffic pattern, and do touch and go takeoffs and landings. During the landing on the second circuit, the airplane ballooned during the flare. When the pilot continued to attempt the landing, the airplane ballooned a second time and started to veer to the right. Following a third balloon as it veered to the right and touched down, the pilot applied left brake and rudder. The airplane exited the runway to the left and struck a berm and a rock, which resulted in substantial damage to the right wing. The pilot reported no preimpact mechanical malfunctions or failures with the airplane that would have precluded normal operation.