Rubus pentalobus (syn. R. calycinoides) or creeping raspberry. Creeping Raspberry trails along the ground, forming a thick mat of dark, leathery leaves that are adorned by snowy white flowers in early summer and will often produce a smattering of golden raspberries in midsummer. It is a thornless plant, but does have small hairs that can be a little rough on the hands. Plants are a favorite for bees and are very adaptable. Shade to sun, happy in well drained clay and are drought tolerant when established and easily pruned if necessary. Tolerates foot traffic well

Rubus calycinoides

Sorry........will not let me attach link. Check out Annie's Annuals for a good photo.

I have dymondia margaretae, which looks like this:

It's not in a place where we walk on it much, but I can say that despite various websites saying it needs full sun, that ours has done great in mostly shade, as well. We are on clay as well in No. San Diego County zone 10a for reference. I believe the only watering it gets is that it's next to some lawn and maybe there's enough moistness from the lawn to keep it going? Our landscaper recommended it and there aren't any drips nearby, so I'd say that's very low maintenance and low water.

@gardengal48 (PNW Z8/9) How would Rubus pentalobus do in an area that floods in Winter rains?

@gardengal48 (PNW Z8/9) After a few days of continuous rain, the area might have a few puddles of water. During rain, the area would be underwater continuously.