OK, Ed. There are true barrel tiles, and they are extruded clay, a
two piece overlap system.

Then there are barrel shaped cement tiles. These are not actual
barrel tiles, but concrete manufactured tiles manufactured to have the
appearance and coloration of real clay tiles.

Here's a hint. If the tiles are "U" shaped and very fragile, about
16" long and about 7 - 8" across, they are true barrel tiles. They
will not be uniform in shape or dimension.

If they are uniform in shape and dimension and actually look like
tile, no matter what the profile (barrel, half barrel, striated,
smooth, rough, etc.) they are probably concrete.

So which do you have?

Robert