INFLT ENG SHUTDOWN PERFORMED AFTER IT WAS DETERMINED THAT A MAJOR FUEL LEAK HAD OCCURRED BY OR IN #1 ENG.

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FUEL LEAK/ENG DAMAGE. REMARKS: AT FL310; 30 MINS N OF MIA ON AR-1; XA06L; THE #1 FUEL GAUGE STARTED DECREASING. A TEST OF THE FUEL GAUGES WAS DONE AND INDICATIONS WERE NORMAL FOR THE TEST. THE YOKE WAS 10-15 DEGS L INDICATING A HVY R WING. AUTOPLT WAS DISENGAGED AND THE OUT OF BAL CONDITION WAS VERIFIED. FE WAS SENT TO THE CABIN TO VISUALLY CHK THE WINGS; L PRIMARILY; FOR ANY FUEL LEAKS. NO LEAKS COULD BE SEEN. THERE WAS APPROX A 5000 LB SPLIT BTWN THE #1 AND #3 TANKS. #1 BEING LOWER. EXECUTED THE 'FUEL QUANTITY DECREASING' PROC. SHUT DOWN THE #1 ENG. CONTACTED ATC; ZMA; AND DECLARED AN EMER. NEAREST SUITABLE FIELD WAS MIA RELATIVE TO PLANNED FLT PROFILE. EXECUTED ALL APPROPRIATE CHKLISTS FOR A 2 ENG APCH. NOTIFIED THE #1 FLT ATTENDANT TO PREPARE THE CABIN FOR A POSSIBLE EVAC. UPON LNDG RWY 9L MIA; I WAS INFORMED THAT WE HAD A MAJOR FUEL LEAK FROM THE #1 ENG POD. WITH THAT CONFIRMATION; I COMMANDED AN EVAC OF THE ACFT WITH INSTRUCTIONS NOT TO USE THE L SIDE OF THE ACFT AND AIRSTAIRS. 107 PEOPLE EXITED THROUGH THE 2 SVC DOORS IN ABOUT 1 MIN. NO INJURIES TO PAX OR CREW WERE INCURRED OR NOTED.