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I could take a better photo on the inside. Take into consideration two things:
1. this is a garden, most of it was dug, turned over, enriched;
2. that particular place was used to make fire, ashes and coals was mixed there.
About the bottom I reached soil fine, smooth enough to call it clay. Actually it is quite fine. I considered to dig up some and smear the walls of the pit over with it. But then the bottom would be lower then the opening of the vent. And that should be as close to the bottom as possible.