A "gap" that opens in the ground is called a "fissure":
fissure (n): A long, narrow opening or line of breakage made by cracking or splitting, especially in rock or earth.
"Fissure" is also a verb:
fissure (v): Split or crack (something) to form a long, narrow opening.
However, while something can be "fissuring", this is not common -- my online spell checker actually marks it as wrong, despite it being a valid word. Instead it's more common to use one of split, split open, or just open:
Look, a fissure is opening in the ground!
Other words like fissure: crack, cleft, crevice, cleavage, gap.
There are other words used with other materials. Fabric can be rent, ripped, torn, or various others. A pizza can be split, cut, sliced into wedges. Various things can be severed.
And so on. If you provide a specific context, I can tell you the most appropriate options.