Gardening

like hostas, elephant ears, caladiums. Seeds will definitely wash away but well rooted plants should stay put. They will also help keep the soil in place. Hostas should winter over if your elevation is not too cold in winter. Elephant ears are so large they can easily be dug up and winter over in the garage then replanted.
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SInce you want children to be able to play there, how about smooth pebble stones? I have sheet mulched a garden but not a playspace.

LOL back in the 50s, we would just turn it into a mudpie factory! My grandmother had a little corner which was too shady for anything to grow. We kept it that way by hosing it down and making all sorts of cool mud delights. She had a concrete block wall that held it in and we sat on that instead of in the mud.