This is what I have growing in cracks between stones around my pond. Rosettes with yellow flowers.It has no runners. At age 15 years it has spread to about 2’ wide feet, 2" high - maybe too large for your use but a very slow grower that starts
out really small. Handles drought summers and wet winters. Can be mowed. Because of liner, roots get no moisture from the pond. Nothing bothers it. 
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I have that growing in a dry corner of our front yard, any idea what it’s called?
It would be a good idea for around the periphery of the patio for sure, but probably not in the cracks for the reasons you mentioned.
It’s Sedum Immergrunchen.
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Well, the neighborhood raccoons forced my hand on this one! As described in this post, they pulled out the pipe that circulated water to the upper pond from the lower one, and I had no easy way to snake it back through, so it became a fig planter.
Some photos of the transition:
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