Aerial views have highlighted the extent of damage on the line between Llandudno and Blaenau Ffestiniog, Network Rail said.
A tree fell on the line and disturbed line-side vegetation on the rock face at Blaenau Ffestiniog when Storm Doris struck on Thursday 23 February.
Clean-up and repairs began on Monday.
The line had to be repaired last winter when flooding caused damage at 100 separate locations.
Chris Howchin, route programme manager for Network Rail Wales, said: "We are working closely with our partners, Arriva Trains Wales, to keep passengers moving during the closure of the line, and a rail replacement bus service will be in operation until it reopens."
A bus timetable has been published online operating Monday to Saturday.
A rail replacement bus service will continue "until further notice" as repair work continues on the storm-hit Conwy Valley line.