I have done under ground splices several times. I bought the splice kits that the others have talked about. They are basically a clamp type connector and a extra heavy duty shrink tube with special sealer in them. I added another layer of protection. I took a piece of PVC pipe that had the ID big enough to go over the splice connectors went they where installed with the kit. I slide the pipe over the wire before I used the splice kit. I then slide the PVC pipe over the splice. When it was finished. I then filled each end with silicone. It takes about a caulking tube of silicone sealer to seal both ends up.
One of these I had to add wire to it about 4 years after the original repair. So I dug up the splice. I cut the PVC pipe open and the inside was dry with zero moisture even to the shrink tubing.