The trust’s chief operating officer, Julie Sharman, said the investigations were complicated because the damage to the canal embankment had been significant and earth structures could be complex.
Asked for a time-scale for the investigation, the trust said it was likely to take weeks rather than months.
It also said the immediate focus would be on recovering the remaining trapped narrowboats.
A tracked winch was brought in from Leicestershire just before Christmas to rescue one which had been hanging over the edge of the breach.
Dams were put in place on either side of the affected area so that other boats could be re-floated.
But the trust said an excavator would be needed to flatten the steep side of the breach hole, to create a gradual slope for the remaining boats to be winched out.
Campbell Robb, chief executive of the Canal and River Trust, said: “This has been a deeply distressing time for these boat owners in particular.”
He thanked people who had contributed £100,000 an online fundraising appeal for the owners of the three worst-affected boats.
Robb added: “Thankfully, breaches of this scale are relatively rare, but, when they do occur, they’re expensive and complicated to fix.”