Widebody; Low Wing; 2 Turbojet Eng
Flight Crew Air Transport Pilot (ATP)
Flight Crew Total 15432; Flight Crew Type 9633
Workload; Situational Awareness; Fatigue; Distraction; Confusion
Aircraft Equipment Problem Less Severe; Deviation - Altitude Excursion From Assigned Altitude; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter Weather / Turbulence
Flight Crew Became Reoriented; Flight Crew FLC Overrode Automation; Flight Crew Returned To Clearance; Flight Crew Took Evasive Action; General Maintenance Action
Aircraft; Airport; Human Factors; Procedure; Weather
On arrival into SFO we were planning an RNAV approach to Runway 10L as was stated on the ATIS. We started briefing the approach about an hour out of SFO using the Approach Briefing Guide. As we approached SFO; NORCAL changed the approach to the RNAV (RNP) Z 10R approach. We advised NORCAL that we were unable an RNP approach and we requested the RNAV approach 10L which he granted.NORCAL gave us a vector to intercept the 10L Final Approach Course (FAC) inbound to NORMM. After intercepting the FAC in LNAV and acquiring ALT CAP at 3500 feet; we selected 100 feet in the altitude window; opened VNAV (it engaged in VNAV PTH); and selected our speed of 180 knots in the speed window. I thought we met [company] requirements so we selected TDZE. We were in VMC with the airport in sight the altimeter was 29.32' and the winds were 030/16kts. Prior to arriving over NORMM the airplane started a slow descent with the autopilot on. We disconnected the autopilot and tried to climb back to 3500 feet at NORMM to intercept the proper glide slope. We continued the approach in VMC with the airport in sight. Approaching XATTU we got low again and received one 'Terrain Warning'. We immediately got back on glideslope and landed.  The approach was just before daylight so we should of executed the proper Ground Proximity Warning System (GPWS) profile starting with 'max thrust; stow speed brakes' when we received the 'Terrain Warning'.A contributing factor was the PAPI on 10L not being turned on. Tower said it showed on but the only PAPI working was for 10R.
In hindsight; since it was still dark; the correct procedure would have been an escape maneuver. We continued and landed uneventfully.
An international flight crew reported the aircraft started to descend early on the SFO RNAV 10L approach after setting 100 feet in the altitude window. After returning to the glideslope; the aircraft descended again followed by a TERRAIN WARNING.