The building hit by the fire at the back of the site has now been declared by West Midlands Fire Service as structurally unsafe, as well as full of asbestos.
When the fire broke out on Thursday at about 6pm it forced the closure of the busy Mucklow Hill causing traffic delays for commuters.
Watch commander Thomas Bell, from Woodgate Valley Cross fire station, said: “When we arrived we found a big pile of rubbish that was well alight.
"The whole of the back was well alight and was about 30m by 20m deep.
“The building has been classed now as a derelict shed and they are in the process of clearing the soil to get rid of all the rubbish at the landfill.”