AN A310 CARGO ACFT DAMAGED AFTER HITTING TUG WHEN THE PARKING BRAKE FAILS TO MAINTAIN PRESSURE AFTER ENG SHUTDOWN ON RAMP AT ZZZ; US.

Narrative

AFTER PARKING ACFT; PARKING BRAKE WAS SET AND I CONTINUED WITH ROUTINE SHUTDOWN FLOW. ENGS WERE SHUT DOWN; PRESSURIZATION PAGE WAS CHKED ON ECAM AS WELL AS DOOR PAGE PRIOR TO FO LEAVING COCKPIT TO DISARM EXIT DOORS. THE AFOREMENTIONED TOOK ABOUT 10 SECONDS AND AT THIS POINT I REACHED FOR THE BEACON SWITCH AND IMMEDIATELY NOTICED THAT THE ACFT WAS MOVING FORWARD. PARKING BRAKE LEVER WAS RELEASED AS I SIMULTANEOUSLY APPLIED TOE BRAKES BRINGING THE ACFT TO AN ABRUPT STOP. ACFT HAD MOVED FORWARD APPROX 25 FT UNNOTICED AND STRIKING A TUG WHICH WAS ATTACHED TO AIR STAIRS. ACFT #2 ENG ANTI-ICE LIP COWLING STRUCK TUG JUST AS ACFT WAS ABRUPTLY STOPPED CAUSING SUFFICIENT DAMAGE TO REQUIRE REPLACEMENT. GND CREW CAME ON INTERCOM AT THIS TIME ASKING IF PARKING BRAKE HAD BEEN SET. RESPONSE FROM CAPT WAS 'YES; IT WAS.' I DID NOT RELEASE TOE BRAKES UNTIL TUG AND TOW BAR WERE ATTACHED FOR PUSHBACK TO PARKING. AFTER PARKING; AND CHOCKS WERE IN PLACE; 3 CHKS OF THE PARKING BRAKE SYS INDICATED SOME TYPE OF PARKING BRAKE SYS MALFUNCTION. PARKING BRAKE SYS PRESSURE NOW WOULD DECREASE TO ZERO WITHIN SECONDS. NO PERSONNEL WERE INJURED. SUSPECT PARKING BRAKE FAILURE MOMENTS AFTER PARKING BRAKE WAS INITIALLY SET. MAINT FOUND PARKING BRAKE LEVER HAD FAILED AND WOULD NOT ACTUATE PARKING BRAKE HYD VALVE.