The line is closed between Linlithgow and Haymarket and ScotRail has said it is expecting disruption until the end of the day today (Thursday).
As a result train services between Glasgow Queen Street and Edinburgh via Falkirk High will be cancelled or terminated at, and started back from, Linlithgow.
However a bus replacement service is in place between Linlithgow and Edinburgh Park.
And services between Dunblane and Edinburgh have been suspended.
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In a statement on its website, ScotRail said: “Due to severe weather during Wednesday 24th January we have a landslip in the Winchburgh area.
“We anticipate that services will be altered as a result of this until the end of service today, Thursday 25th January, however our staff are on site working hard round the clock to move the debris from the line and carry out neccessary repairs so we may be able to start running services sooner if the work is completed.”
Trains from Glasgow Queen Street to Edinburgh will operate between Queen Street and Linlithgow only, calling at Croy, Falkirk High and Polmont.
They will depart Queen Street at XX00 and XX30, while trains from Linlithgow will depart at XX48 and XX18.
Buses will leave Linlithgow for Edinburgh Park at 25 and 55 minutes past the hour, and will return from Edinburgh Park at 15 and 48 minutes past the hour.
ScotRail’s website states that a bus shuttle service will run between Stirling and Edinburgh Park calling at Larbert, Camelon, Falkirk Grahamston, Polmont and Linlithgow in both directions.
It said: “We are also planning to run buses from Dunblane to Haymarket calling at booked stations, departing Dunblane at the following times; 06.29, 07.08, 07.23, 07.58 and 08.28.
“Following this time we are intending to introduce an hourly bus shuttle service between Dunblane and Haymarket (calling at stations).
“These will depart at XX30 past the hour, starting from 0930.
“We intend to depart buses as close as possible to train times, but delays are possible due to road traffic.”