Work to replace and repair sections of the current drain east of Stainmore Cafe is expected to be completed in early June.
A 40mph speed limit will be in place past the road works with any work – often requiring single lane closures - taking place between 9.30am and 3.00pm in the day and between 8pm and 6am overnight.
The work will reduce incidents of carriageway flooding.
Members of the public should contact the Highways England customer contact centre on 0300 123 5000.
Journalists should contact the Highways England press office on 0844 693 1448 and use the menu to speak to the most appropriate press officer.