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To minimise any disruption the patching works will take place at night between Sunday 22 May and Wednesday 1 June.
As a result, the road from Ashey Lane up to and including New Road will be closed between 8pm and 6am on those days, apart from Thursday the 26th and the weekend of Saturday the 28th and Sunday the 29th when no work will be taking place and the road will remain open.
The works are in preparation for surface dressing which is due to take place in early July.
Anyone travelling between Bristol and Somerset on the nights of the road closure is advised to go via the A370.
"The night-time road closures are necessary to ensure the work can be carried out safely," said North Somerset Council's executive member for transport and highways Cllr Steve Hogg.
"Our contractors Milestone will be liaising with residents on a nightly basis and traffic marshalls will be on hand to help with any queries."
The council is taking the opportunity of the road closures to remove some ash trees adjacent to the road which are suffering from Ash Dieback, a fungal disease which is often fatal. A rapid decline in the health of these trees means urgent action is needed to remove them for safety reasons.
For more information about the A38 works visit www.n-somerset.gov.uk/roadworks.
For updates on social media follow North Somerset Travel and Roads on Facebook (@NStravelandroads) and Twitter (NStravel_roads).