The ongoing work has closed part of Princes Street and Shandwick Place in the city centre over several days since Sunday night – but trams have not been disrupted.
Edinburgh Trams said defects in the concrete had “degraded” and repairs were required “to ensure safe operation of the system”.
They are believed to include a 1m-long section beside St John’s Church at the west end of Princes Street.
Another is thought to be on the other side of the road, near a crossing beside the Johnnie Walker Princes Street attraction in the former House of Fraser department store.
Further work is also being done on the two streets to replace life-expired “track sealant”.
Three sources told The Scotsman the concrete cannot cope with being driven over by vehicles and is crumbling.
‘Falling to bits’
It is claimed this has been happening since shortly after the line was completed in 2014 and the wrong grade of material may have been used.
One source said: “The bases are falling to bits next to the tram tracks.
"The line has only been open seven years and it’s already breaking up.”
Another source said: “Several slabs have cracked quite severely and have had to be patched up.
"It’s been in a completely dire state.”
Part of Princes Street was being closed overnight from 11:30pm to 5am for three nights up to and including Thursday night, as well as all day on Thursday.
The city council’s travel news service described it as “tram track maintenance”.
Shandwick Place, immediately to the west, was closed for the same hours overnight on Sunday and Monday night, and all day on Tuesday until 11:30pm.
The closure also covered the northbound carriageway of adjacent Queensferry Street.
Edinburgh Trams said there had been no planned disruption to services for the duration of the maintenance works.
A spokesperson said: “Currently, there are two streams of essential work taking place at Shandwick Place and the West End.
"Firstly, we are carrying out scheduled maintenance to replace track sealant which has come to the end of its life.
"Secondly, reactive maintenance to repair concrete track form defects which have degraded and now require repair to ensure the safe operation of the system.”
‘Cracking from bus weight’
Four years ago, the Edinburgh Tram Inquiry into the delayed and over budget scheme heard that cracks developed in the tram line after work in Princes Street was stopped in 2009 before it was finished because the city council firm running the project wanted the road re-opened in time for Christmas.
Martin Foerder, project director for the construction consortium involved, said they did not have time to install joint filler along the tram rails, which led to cracking because of the load from buses.
In 2013, less than a year before the eight-mile Edinburgh Airport-York Place line opened, cracks were found in the concrete under an elevated section near Edinburgh Park tram stop.
The discovery was made shortly after the first tram test runs.
Experts said at the time the cracks could become an ongoing maintenance headache.
One said the cracking was "most likely associated with shrinkage after casting the concrete".
A council spokesperson said at the time: "Cracking within concrete is common and the majority of cracks, such as this one, have no structural influence on performance.”