TXWY EXCURSION. BRAKING ACTION NIL.

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FLEW COUPLED ILS TO 500 FT -- LANDED VISUALLY ON RWY 03. WX 600 BROKEN 1100 OVCST 2L-F 40/39 WIND 350/6. LAND; AUTO BRAKE TURN OFF AT TXWY D NORMAL. STOPPED ON TXWY D AWAITING TAXI CLRNC. CLRED TO GATE -- PROCEEDED W ON TXWY D -- MADE 45 L NORMAL; ENTERED SECOND 45 AT NORMAL AND APPROPRIATE TAXI SPD. AFTER APPROX 15 DEGS OF TURN; IT FELT LIKE THE NOSEWHEEL WENT HARD OVER L. LOSS OF NOSEWHEEL TRACTION WAS INSTANT --ANXIOUS AND ACFT WENT TANGENT TO THE TURN ARC. I RELEASED NOSEWHEEL STEERING AND APPLIED BRAKES WITH NO EFFECT. ACFT SHUDDERED ALMOST VIOLENTLY; BRAKES SEEMED TO CHATTER; BUT THE SHUDDER/CHATTER MAY HAVE BEEN THE NOSEWHEEL HOPPING. FLT OFFICER JOINED ME ON THE BRAKES. DECELERATION WAS ABSOLUTELY NIL. I MODULATED NOSEWHEEL STEERING AND BRAKES ATTEMPTING TO REGAIN CTL BUT NOTHING TOOK EFFECT. AS IT BECAME OBVIOUS THAT WE WERE GOING IN THE DIRT I APPLIED REVERSE THRUST AND CTRED THE NOSEWHEEL STEERING. THE REVERSE WAS IN DESPERATION; BUT I WANTED THE NOSEWHEEL STEERING STRAIGHT SO THAT WE WOULD NOT SHEAR OFF THE NOSE GEAR. SKID MARKS SHOW THAT I HAD THE NOSEWHEEL STRAIGHT; NOT LOCKED L FOR A MAJORITY OF THE LAST FEW FT ALTHOUGH THE NOSE GEAR PLOWED SIDEWAYS INTO THE MUD. I AM AWARE OF THE S80 NOSE GEAR TIRE PATCH IN A TURN AND WAS MODULATING THE STEERING TILLER AND BRAKES TRY. ACFT STOPPED IN SOFT GRASS COVERED SOIL IN A RIGHT LIST. I MADE A PA -- KEEP YOUR SEATS -- REPEATED 3 TIMES. THIS WAS IN CONJUNCTION WITH THE FORMAL CREW BRIEFING THAT I HELD WITH ALL FA CREW PRIOR TO DFW DEP IN WHICH I BRIEFED EVACUATION PROCS. WE SHUT DOWN ENGS IAW CHKLIST AND PUT ACFT ON APU PWR. WE MADE THE REQUISITE CALLS TO GND; OPS; ET AL. I MADE SEVERAL PA'S TO PAX TO KEEP THEM INFORMED AND ADVISED. SAT SENT VEHICLES TO COLLECT PAX AND CREW; I WAS LAST TO EXIT ACFT. ALL EXITED OUT THE AFT AIRSTAIRS. I INSTRUCTED ALL CREW TO STAY OUT OF THE PUBLIC AREAS AND TO AVOID THE ASSEMBLED NEWS CREWS. CREW GATHERED IN SAT OPS FOR DEBRIEF. NO PAX RPTED INJURY; FLT ATTENDANTS SAW NONE.