Glue for marble

I think you'd put in some sort of dowel to carry the load. Simon.

That's a very tough call. If you can successfully drill and put in a reinforcing rod, and then use a suitable epoxy the right sort of color - I actually use microballoons in epoxy to get a flat white finish, you have a sporting chance.

Marble isn't terribly strong in tension: That probably why its broken already.

You can't make "beams" of marble, especially not that thin, it's too weak. Something like this should be attached along its length to a carrier beam (timber will do), and that should be carrying the load.

As suggested, use good epoxy to repair it. Something like West System and investigate the many fillers for it. If you ask around at a marble cutters, you might even be able to scrounge some stone dust in a matching shade.

Hoping that a 1 metre length of marble can be cantilevered out from a single end fixing is a big ask. I would doubt that the marble could ever be strong enough on its own.

If one side of the marble is always hidden, you could bond some sheet steel to the hidden side in addition to repairing the break, using an epoxy resin adhesive.

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??He clearly said supported at each end...

OTOH if the OP wants a sheet of marble to cut a new slice off, I've got rather a lot of scrap

Thanks..

What the others said, but on the effectiveness of adhesives on marble:

I have some offcuts from a marble hearth that the fitter trimmed to size. Wanting a flat surface to do some polishing on I had a go at getting a glued on strip of marble off the main flat piece. The 'glue' looked to be the hot melt sort, and there was the odd blob on the underside of the piece. It looked like a sharp tap would be enough to just knock off the blobs, but it was the stone that eventually gave, not the glue. There was no way I was ever going to get the complete glued backing strip off. Quite impressed I was!