re: is there a standard depth for house slabs

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That said, I don't want to go drilling concrete anchors in the slab and bust a pipe.

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This may be asking a lot of your slab guys, but if you have the safe and can get a pattern for the bolts needed to secure it to the slab, have them place them in the wet concrete when the slab is poured. That way they will be well incorporated in the concrete and offer the best hold, especially if the bolt heads are in the slab with just the threaded part above it.

If that is not an option and you have to do it yourself, drill about 3 inches into the slab and secure the threaded rods with epoxy to secure them or use some type heavy duty anchoring system. But definitely find out where your plumbing is before drilling just to be safe---pardon the pun.