If you have lots of shade then Vinca Minor is perfect. It stands up well to our dogs and isn't real invasive like ivy. When you talk soft all I can think of is moss or that tiny thyme I think it is. not sure how good these are with dogs.
"In Him we are chosen, having been predestined according to the plan of Him who works out everything in conformity with the purpose of His will" Eph.1:11 *****Barbara**** Arkansas central time
My suggestion is rather than suggesting a particular kind of plant is to visit a local nursery if you have one and see what's recommended for your area. An evergreen ground cover for sure rather than seasonal.
In northern PA we used to visit and there was a very very soft plush evergreen ground cover that would have survived dogs.
In NJ I had violets fill the yard instead of grass with hosta as edging but don't have dogs that might tear it up.
Much depends not only on your zone but plants that would thrive locally.
-:|:- Dee -:|:- Joy is a state of being regardless of our circumstances. Find a way.
I am considering making a big change in my backyard. I am allergic to most of the grasses that are common here. I would love to get rid of the grass and use some alternative ground cover. I am looking for something that can control erosion, of course, but I want something that is soft under foot and maybe has a little color. I have three dogs that have full access to the backyard. I want something that is not dangerous to them and something that can withstand their running around on it and their "use" of it. Also, because I am in Georgia, I need something that can handle our varied climate. I have some red clay in the yard, but there is a pretty good layer of topsoil.
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