FLC DEVIATED FROM SID TOWARD TERRAIN.

Narrative

ACR WAS DEPARTING SLC ENRTE TO DAY. OUR CLRNC WAS SLC5- J154 MAINTAIN 8000; 135.5; SQUAWK XXXX. THE SLC 5 DEP STATES FOR RWY 34 -- FLY HDG 340 DEGS AND CROSS 7.5 N OF SLC VORTAC AT 8000 FT. EXPECT RADAR VECTORS ON COURSE 10 MINS AFTER DEP. AFTER TKOF WE WERE CLBING THROUGH 7500 FT S OF SLC VORTAC WHEN WE WERE CLRED TO FL230. AT THAT POINT WE READ BACK CLRNC AND I HEARD CLRED TO FL230 AND ON COURSE. THE FO AND FE WERE COMPLETING THE AFTER TKOF CHK AND I CROSSED THE VORTAC THROUGH 8000 FT AND AT 2.5 DME NE OF VORTAC TURNED TO JOIN J-154 ON COURSE CLBING THROUGH 12000 FT; GOING TO FL230. THEN DEP CAME ON FREQ AND ASKED IF WE WERE PROVIDING OUR OWN TERRAIN CLRNC AND WE SAID NEGATIVE AND THEN DEP TOLD US TO JOIN J-154 AND CONTACT CTR. WE WERE WELL ABOVE ALL SECTOR TERRAIN CLRNCS DEPICTED ON APCH CHARTS. CREW CAME OFF OF A REDUCED REST PERIOD PRECEDING 15 HR AND 45 MIN DUTY DAY DUE TO WX AND DE-ICING DELAYS IN DAY ON OUR FIFTH CONSECUTIVE DAY OF DUTY. SUPPLEMENTAL INFO FROM ACN 294647: THE FE AND I WERE COMPLETING THE AFTER TKOF CHKLIST WHEN I NOTICED THE CAPT WAS IN A R TURN AND ASKED THE CAPT 'ARE WE ON COURSE NOW?' HE REPLIED; 'YES.' I CHKED THE DEP RTE VISUALLY FOR TFC AND TERRAIN AND SAW WE WERE CLR; ALSO SEEING THAT WE WERE CLBING AT APPROX 2500-3000 FPM THROUGH 8000 FT. I FIGURED I HAD MISSED A XMISSION CLRING US ON COURSE. JOINING J-154 CLBING THROUGH 12000 FT APPROX 2.5 DME NE OF SLC VOR; ATC ASKED; 'ARE YOU PROVIDING YOUR OWN TERRAIN SEPARATION?' WE REPLIED; 'NO.' KNOWING THAT I HAD NOT HEARD ATC CLR US ON COURSE NOR HAD I READ BACK SUCH A CLRNC; I AGAIN ASKED THE CAPT IF WE HAD BEEN CLRED ON COURSE AND WE DISCOVERED OUR MISTAKES. ALTHOUGH THE SID WAS THOROUGHLY BRIEFED; TERRAIN NOTED AND PERFORMANCE DISCUSSED; WE DEVIATED FROM THE SID DUE TO POOR COM DUE TO FATIGUE. THE CAPT THOUGHT HE HEARD 'ON COURSE' BUT DID NOT VERIFY THE DEV FROM THE SID. I ASSUMED I HAD MISSED THE 'ON COURSE' DUE TO HIGH WORKLOAD AND FATIGUE; BUT DID NOT VERIFY THE DEP FROM THE SID.