Try Gorilla glue, don't wipe the ooze off until it sets up then cut it away.
Gorilla Glue is sold just about everywhere it is a moisture cure ureathance. Duct tape or tire tube rubber bands make a good clamp.

Gorilla glue is a great idea. If you are in a freeze/thaw environment than you want to make sure that no water will get in there ans settle. BTW polyureathane glue expands quite forcefully so take heed in the advice to use the duct tape or band and clamps.
Good Luck!

Sounds like a job for two part epoxy to me, the kind you mix with a catalyst. You can get it at most hardware chains. I used it to repair the broken bowl on my inlaws birdbath and it was about 4" thick. It works wonders

alternatively tile adhesive is very good for a weather situation

I would go with the two part epoxy. AKEMI is what we use here at work. I subscribe to Stone World magazine because of the type of work I do, they have an advertiser's listing and the web site for AKEMI is www.akemina.com. There phone is 1-877-GO-AKEMI. It is really easy to use and is what the pros use.