ACR WDB BLEW DUST AND DIRT ON CONSTRUCTION WORKERS TURNING INTO GATE AT LAX.

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CONSTRUCTION IN PROGRESS ON 2 HIGH SPD TXWYS S OF SATELLITE AT LAX. ATIS ADVISED TXWYS CLOSED. LNDG ON RWY 24R; UNABLE TO ACCOMMODATE ARR ON S COMPLEX; CLRING RWY 24R WAS CLRED TAXI UNIFORM; TXWY 49 HOLD SHORT OF KILO; LATER CLR TO TAXI KILO TO GATE B SATELLITE. ARRIVING AT SAID GATE CAPT OBSERVED NUMEROUS CATERING TRUCKS AND AIRLINE GND VEHICLES BEING MOVED INTO SAFETY ZONE OUT OF TXWY KILO ADJACENT TO GATES. ALSO; SOME GND VEHICLES TRANSITING COMPANY GATE SATELLITE. HAD TO SLOW ACFT TO ALLOW TRANSIT. VERY TIGHT 140 DEGS TURN REQUIRED TO ALIGN ACFT TO DEPLANING AREA. UTILIZED MINIMUM THRUST ON ENG 4 AND MINIMUM SPD (5 KTS) TO ENTER AREA. ALL WENT WELL UNTIL GND CTLR ANNOUNCED; 'USE MINIMUM THRUST; YOU ARE BLOWING DUST ALL OVER CONSTRUCTION WORKERS AND RWY.' MINIMUM THRUST WAS IN USE! LAX SHOULD EITHER ARRANGE TO SHUT DOWN ON KILO AND TOW IN OR CLEAR AREA AND STOP CONSTRUCTION ACTIVITIES WHILE WDB ACFT AT GATE. AFTER DOCKING CAPT PHONED BOTH LAX TWR SUPVR AND LAX CITY OPS TO DISCUSS. WAS ASSURED NO DAMAGE OR INJURY; BUT WOULD LIKE TO AVOID TERSE COMMENTS BY GND CTL AND VERY CONCERNED FOR SAFETY OF GND PERSONNEL IN SUCH CLOSE PROX TO PARKING AREA. WAS ADVISED OF SEVERAL SUCH INCIDENTS--AN MLG AT IDLE THRUST AND WDB X.