The trench appeared after a weekend of heavy rainfall
There are no plans to fill in County Durham's "Grand Canyon", the land's owners have said.
The massive trench was created by floodwater in a field belonging to Houghall College near Durham City after torrential rain in July.
Several hundred metres in length, 14ft deep, and measuring more than 80ft at its widest point, it has become an unlikely visitor attraction.
The college has now put up notices warning people not to approach it.
It is thought the site was once a branch of the River Wear, diverted in the 15th Century by Durham monks to prevent the city's cathedral and castle becoming waterlogged.
Alistair Cummings-McLeod, marketing manager for East Durham and Houghall College, said: "The current situation is that the canyon is going to remain there.
"It is not a field under insurance, so we wouldn't be looking to fill it back in.
"However, we have taken the decision not to encourage people to come down there for their own safety.
"We have put up notices warning them not to approach or go into the canyon."
He added that he thought one of the reasons it had captured the public imagination was because it had appeared overnight.
"We are used to landscapes being millions of years old," he said.
"The novelty with this is that it wasn't there on Saturday and then all of a sudden on Sunday it was."