no, it is best to put unfinished compost in the soil. two reasons: no nitrogen loss if it is well buried, and earthworms will further grind the soil as they access the material and digest it. it is not you breaking the soil, it is the worms. Fungi will contribute too, if you put in large chunks of rotten wood. the latter technique is called hugelkultur.

I have heavy clay and have been adding composted manure and wood chips. I also use cover crop like oats, clovers and oilseed radish. They all leave the soil better than the clay it was. I especially like the oats. I till them in right before they go to seed and they make a nice fluffy soil. I have a section of mostly gravel and I have had nice results there with manure and cover crops.

Bury whatever you've got. Dig an area that you estimate the plant roots will spread to and refill the area with half the soil you dug out and half whatever organic matter you have, composted or no. Do that over a few years and you'll have lovely soil. Set the extra native soil aside to either build a basin around your plants or to add to the area as the organic matter decays and the soil sinks down.

I've been trench composting in my heavy clay soil since we bought this place last year, and it's going quite well. You can mix greens and browns, just like you would in a compost pile, or just bury the greens. I'm also planning to sow Daikon as a cover crop to try and break up my worst bed. We shall see...

I add alfalfa pellets to my clay soil...purchased in large bags from the feed store in town.

When people say they have clay soil, we understand that they have stiff, heavy, and lumpy soil that clods up. Actually, most of this 'clay' soil is a mixture of clay, silt, and sand, but the clay portion is too high for good friabilty and is is not much fun to work.

Adding organic matter regularly from outside sources and cover crops is a main way to 'loosen' that soil up some and put more life into the soil. Also these clayey soils can usually be helped by additions of sand and peat moss. These are instant texture additions that can go along with improving the soil in the usual good ways.

Add any plant/organic material you can get your hands on, "sheet" or "trench" composting works wonders. Your goal is to improve the soil friability, you can worry about adjusting for specific N-P-K later. IMHO, it's an old "somebody's" tale that green material, grass clippings, etc. leach nitrogen and other essential plant nutrients.

I have heard that the critters that break down wood chips do the leaching of that which the plants need to grow. I have stopped all form of wood anything for my gardens.

Did you have the soil tested? Looks can be deceiving. Clerks at an extension office can help you figure out what to add.

If you need massive quantities then I would get it all at once and use a rototiller. (Then, never use a rototiller ever again, it is destructive)

What is it with "friable" soil? Do you fry it with butter or olive oil? Will it make a good topping next time I poach an elephant?

It is nice that so many people are now in favor of compost in place. Traditional composting is good for exercise, like going out in midwinter to turn a pile, and bad for nitrogen content. It is also negative for earthworms and fungal flora, which are deprived of the food they need, and which are the two best friends a gardener has.

I do sheet composting I would say...adding rotted horse manure with a lot of hay in it...leaf mulch,...and the crop residues chopped up in situ.

I even till these things in and have added other texture improving material to my silty clay soil to improve friability [looseness and workability].