I have no experience with breaking up clay soil but this place sells seeds. They are a family operation no online ordering and slow to get their catalog up. I order from them every year. Scroll down for the soil improvement things.

Here is a link that might be useful: Sand hill preservation

Is there such a thing as a non-mechanical way? I think the owners here, (we are renting) used a Maddox. It is hanging in the garage. Luckily they did all that grunt work, so there are some nice raised beds here.

Get out the Shovel , Double dig your bed to start dig it two shovels deep turning the top to the bottom adding any organic matter to the middle or you can dig a trench same depth and fill it with dead pcs of wood soft wood if possible like maple, cottonwood etc. hardwoods like oak or cedar take to long to break down fill it to the top then cover it back up and water it down plant any kind of cover crop the wood will rot in one season and the mound will shrink then dig it again to turn the cover crop in. this will really help with the hard clay.

am wanting to expand my garden in a couple of years and am looking for non-mechanical options to break up clay soil and add organic matter.

Your best way is "lasagna gardening" ... lay out your planned expansion beds and paths, then layer stuff on top of the place you plan to expand into and let it sit and decompose. Make several layers of manure, dead leaves and compost over the location of the new beds, keep it moist and mulched to keep the weeds down and moisture even.

Use thick cardboard and wood chips where you want paths for longer-lasting weed control.

When you start planting , just move the mulch back and add your transplants.

Deep-rooted annual plants, such as okra, are great for breaking into clay soil. Let them grow, then cut them off at the roots at the end of the season and leave the roots to decay ... they will leave tiny channels where the roots decompose.

I went from desert silted-clay hardpack I had to dig with a pick to a veggie bed I can dig with a hand trowel by this method.

As fall planting to keep the soil loose I plant a root crop I use Turnips , I like the greens and the bottoms when their young but leave what I don't use in over winter most will freeze out by spring some of the roots get 10-12 inches and keep the ground loose for spring

There's a fellow over on the Oklahoma Gardening forum. His screen name is JohnnyColman. I bet, if you ask him, he'll have some great input. He likes to start really large gardens for other people. I'm sure he's doing something like you have in mind. Personally, I'd consider a pretty thick planting of cowpeas, after the weather warms up. In the fall, I'd consider a cover crop like Austrian Peas and or Hairy Vetch.

I have never refrained from mechanically breaking up the soil. But I have seed plants and worms do an awful lot and I'm about ready to try this.

George
Tahlequah, OK

Thanks for the responses so far! Some good ideas.
I'm not opposed to using mechanical means ( i have access to a small track hoe) but wanted to try to something that would break up that hard pan to REALLY deep level while incorporating organic matter at the same time.

I have had good luck on grassy sod using the modified lasagna method. I only used what I had on hand: A layer of very wet newspapers (several thicknesses), a layer of old alfalfa hay and some straw. During the winter I would lift a section and layer in my kitchen waste which was mostly coffee grounds and egg shells with some green stuff. By spring (did this in the fall) I could dig in the sod with my hands by lifting the mulch and then planting. I only did this with roses and tomato plants and some daylilies. I didn't use it for seeds.

Of course I don't have hard pan or clayey soil or even very rocky ground....I lucked out in that department.

It has been several years ago and I now need to layer some flakes of the old hay back in place again just to keep things neat.

If you have access to more organic matter such as grass clippings and manure that will speed up the process.
You could also first plant a green manure crop shallowly and then begin layering right over it. once it gets some size.

Good luck. I am curious why you want to go so deep?

suggest researching 'no till' methods. my favorite method is easy but takes time. two seasons before you want to plant an area cover it to a depth of a couple feet with wood ashes, manures, straw, compost, dry shredded leaves, blood from animal processing, rock dust, etc. in other words, all the organic matter you can lay your hands on. the pile will shrink over time, when you finally pull back the organic layer grass and other weeds are gone, earth worms are numerous, ground is soft and ready to plant. i farmed for a living for over two decades in the ozarks, this is a tried and true method i used many times with good results.