The soil in my backyard has very few rocks but the clay is so hard and dense it may as well be a brick wall.

When it's wet, but not saturated - like 1-2 days after a rain - you can decompact the soil with a strong metal broadfork and leave the soil in large block aggregates. This keeps the soil structure and maintains some fungal web connections. Add nutrients, wood chips, stick and sand below aggregates and in cracks. Cover with compost and plant clover to cover.

This is amazing info thank you.

What is the purpose of planting clover?

Really good advice above. But if you want to cheat a bit, I used https://www.thompson-morgan.com/p/vitax-clay-breaker--25-kg-... on my heavy clay garden and it helped a lot, in combination with extra organic material etc.

this is just gypsum in case anyone was wondering

Clover is a nitrogen fixing plant - used to be that you’d plant clover for a year in between other crops to make your soil fertile again.

(It’s the bacteria in the roots that do the actual nitrogen chemistry.)

Clover fixes nitrogen and roots help stabilize the voids in the soil. They sell seed mixes called "ground cover mix" that includes other plants and will help keep the soil from recompacting when it rains and keeps weeds at bay.

Are you sure it is just clay? Sandy clay packs even tighter than just clay: https://www.uaex.uada.edu/farm-ranch/crops-commercial-hortic...

"If you mix sand into clay, the clay particles will fill in all the open spaces between the sand particles and often the clay will act as a ‘glue’ sticking all particles together, ultimately resulting in a more dense soil."

A friend of mine retired from the military and moved to my neck of the woods in the Ozarks. Having lived in Eastern North Carolina for most of his 20 years in, he had gotten used to sandy soil with nary a rock. Prior to that, he was in the Twin Cities of Minnesota, and I don't think he dug many holes there.

After closing on their new house he asked me for a shovel, for which to install a mailbox. Of course I'd help my friend out. "Sure, buddy!" I said. "Here's a shovel, post-hole digger, pickax and a rock-bar. That should get the job done." After I explained to him that yes, you need a 20 pound pointy chunk of steel to dig any sizable hole around here, he still didn't quite believe me. However, once he got the mailbox planted, he adjusted his beliefs accordingly.

On the rare occasion that I have to dig a hole somewhere with actual dirt, I always find myself amazed at how easy it is. Those times help me understand scenes in TV or movies that include someone digging a hole. Those scenes don't ever depict someone deciding to move whatever it is they're putting in the ground because they hit a massive stone at 8 inches into a 24 inch hole, and there ain't any getting through it. The scenes don't depict the Herculean effort required to just plant a tree. Those shows don't show the absolutely back-breaking labor it takes to be a landscaper around here. And before I had the chance to do the same kind of work in actual soil, those scenes just didn't make sense.

Our house sits on a small basalt volcanic plug and the solid dark rock lurks not very far under our garden - 100m north of us and its sandstone, 100m south and it is limestone.

Digging a hole of any depth would probably require explosives!

Hard pass. Karst limestone is bad enough.

I'd save a fortune on concrete and rebar if I had high quality bedrock so close.

I suppose I shouldn't be surprised that complaints of rocks where you expect soil invite other Ozarkians. That was something that shocked me about the Midwest in comparison; even with a concerted effort, I couldn't find enough of a rock to fill a slingshot.