The first part took place from November 11 to 17 and was due to take place again between Monday December 16 and Sunday December 22.
It has been brought forward, though, and the second week of work will now take place between November 25 and December 6.
The M8 was also closed between Junctions 1 and 2 on the night of November 12 to allow work to be completed.
The work will take place at M8 Junction 2 Claylands, near Ratho, to allow BEAR Scotland to carry out refurbishment work on two bridges carrying the motorway.
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It began on the night of Monday, November 11, when parapets will be removed, refurbished and reinstated on a bridge carrying the M8 motorway and another carrying the slip road exiting the M8 westbound onto the northbound M9.
The M8 Junction 2 westbound off-slip to the M9 will be closed between 8.3pm and 6am on the nights mentioned above over the course of the two weeks.
Diversions will be in place for traffic on the M8 westbound to join the M9 directing traffic to continue westbound on the M8 to turn at Junction 3, before returning eastbound on the M8 to exit via the Junction 2 eastbound off-slip which will add approximately 12 minutes affected journeys.
The parapets will be taken off-site to be refurbished. During this period, the hard shoulders on the main carriageway and the westbound off-slip at M8 Junction 2 will be closed.
David Bishop, BEAR Scotland’s South East Unit Bridges Manager, said: “The safety of road users and our workforce always comes first, therefore we have amended our plans.
“The size of the machinery that will be on site to remove the parapets means full closures of the slip road and the main carriageway are now required.
“We thank motorists in advance for their patience and understanding. We recommend that they check the latest travel updates, plan ahead and allow extra travel time for their journeys during these works.”
All work is weather dependent and subject to postponement or cancellation in the event of adverse conditions.
Real time journey information is available from Traffic Scotland on www.trafficscotland.org, or on X at @trafficscotland.