A FA-10 BLOWS A TIRE AND THE PIC ABORTS AT A HIGH SPD ON THE RWY AT SLN; KS.

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NORMAL TKOF ROLL TILL 120 KTS. AT THIS POINT; HEARD SOUND AND FELT VIBRATION FROM A MAIN GEAR WHEEL. ACCOMPLISHED AN ABORTED TKOF MAINTAINING DIRECTIONAL CTL WITHIN 15 FT L AND R OF THE CTRLINE. CALLED TWR AND RECEIVED PERMISSION TO TAXI OFF THE RWY. TAXIED OFF THE RWY; COMPLETED AND STOPPED WHEN FULLY OFF AND ASKED TWR PERMISSION TO HAVE FO OPEN CABIN DOOR TO SEE IF THERE WAS ANY IMMEDIATE DANGER. THERE WAS NONE. ASKED TWR PERMISSION TO SHUT DOWN ENGS SO PROPER DAMAGE ASSESSMENT COULD BE MADE AND ASKED FOR ESCORT FOR PAX TO THE RAMP. ASKED TWR TO SEE IF ARPT AUTH COULD BEGIN CHKING FOR DEBRIS ON THE RWY. ASSESSED THAT THE 2 L MAIN GEAR TIRES HAD DISINTEGRATED. ASSESSED THAT THE STRUCTURAL INTEGRITY OF THE L MAIN GEAR WAS SUCH THAT A FURTHER TAXI TO THE RAMP WAS WARRANTED. REQUESTED PERMISSION TO START ENGS AND CLRNC TO TAXI TO THE RAMP. THIS WAS DONE SUCCESSFULLY. SHUT DOWN. TALKED LATER WITH TWR AND ASKED IF THEY NEEDED ANY FURTHER INFO FROM US. THEY SAID NO SINCE NO ASSISTANCE HAD BEEN REQUESTED; NO EMER DECLARED; AND THE ARPT AND TXWY HAD NOT HAD TO BE CLOSED. TALKED TO THE ARPT AUTH AND FILLED OUT AN ACFT INCIDENT RPT AND WAS TOLD NOTHING FURTHER NEEDED TO BE DONE. THE ABORTED TKOF WAS HANDLED FLAWLESSLY. COM WAS MAINTAINED CONSTANTLY WITH TWR AND GND. THE OUTCOME WAS GOOD; OTHER THAN SOME DAMAGE TO THE FLAP AND GEAR DOOR AND OF COURSE THE L TIRES. OUR MAINT WAS ON THE SCENE AT XA00 LCL THE NEXT MORNING JUL/XA/03. SUPPLEMENTAL INFO FROM ACN 587829: AT 120 KIAS I FELT AND HEARD A 'BUMP'. I THOUGHT THIS MAY JUST BE AN EXPANSION JOINT IN THE CONCRETE RWY. THE NOISE WAS IMMEDIATELY FOLLOWED BY A VIBRATION THAT WAS INCREASING IN INTENSITY. AS PNF I CALLED 'ABORT; ABORT; ABORT.' WE COULD NOT MOVE THE ACFT BECAUSE THE THRUST REVERSERS WERE STUCK IN PLACE DUE TO THE L MAIN SQUAT SWITCH BEING DAMAGED. UPON GETTING THE THRUST REVERSERS TO STOW; WE STARTED ENGS AND TAXIED TO THE FBO. THE ARPT MAINT CREW DID A RWY CHK AND FOUND RUBBER; A CANNON PLUG; AND TIRE REMNANTS ON THE RWY. THEY PROCEEDED TO MANUALLY PICK UP THE LARGE PIECE. THEY ALSO USED A TRACTOR MOUNTED SWEEPER TO CLEAR THE SMALLER PIECES; AND ENSURE NO DEBRIS REMAINED ON THE RWY.