https://www.thespruce.com/how-to-plant-and-grow-asparagus-1402814

https://modernfarmer.com/2015/04/how-to-plant-asparagus/#:~:text=Dig%20a%20trench%2012%20inches,a%204%2Dfoot%20wide%20bed.

Pretty deep and pretty wide. These are not shallow rooted plants.

And now enjoy the ensuing female/male crown argument, too. :-)

Depending on your locale, it may or may not be realistic to box-plant these even in a 2x2x2' box for each plant (listed depth is 12" for the roots at minimum, it's smart to give them room to grow just in case [ETA and get planted with crowns 4" down to begin with /ETA]). Zone 3? Almost certainly not as a raised box will get too cold. Zone 4-6a? Variable. Zone 6b-8? Go for it, you'll be fine.

There's a thread about this, and a really good answer there: https://www.houzz.com/discussions/1402312/how-deep-do-asparagus-roots-go-down

It's written better there, but happy asparagus can get roots 10-15' deep once they are goodly established.

Maybe asparagus won't work too well for your concrete yard, even with planters a few feet deep. But you might want to consider alternatives that you can grow in planters on concrete.

Some broccolis are supposed to be a good flavor sub- I'm afraid I can't tell you what varieties since I haven't tried this, but I would imagine some of the more sprouting/flowering kinds meant to be picked tender might work.

Beans, particularly the pole bean known as asparagus beans are surprisingly asparagus like in taste to me, more asparagus than bean sometimes. Asparagus beans are from the Asian yard long beans, and are more noted for their asparagus taste than other yard long beans. Yes, the beans do grow very long as their name suggests. They don't replace asparagus exactly, but can really work nicely if you don't have asparagus. Also kind of nice in later summer when fresh picked asparagus is months gone.

Looks like I either have to just live with the short lifespan of putting them in planter box or just don't grow altogether 😔.

But overall, thank you for answering my question. Now I know what to expect instead of guessing.

I have dug them out and it is quite a workout. Mine weighed well over 100 pounds. It was almost impossible to get them out of the hole once dug. I would not ever do it again. To top it off they did not survive the winter as winter came early that year.