You can't dent it because it's dry. To successfully dig and/or plant in clay and other soils, those soils should be evenly moist, such that a handful forms a lump but doesn't ooze water.

Then either mix in the compost or heap it on top. Mixing in gives fastest results.

Disclaimer - your milage may vary.

In my hardpacked adobe clay, I have the best results with sheet composting on top (gotta keep the moisture level right), then tilling that in to break up the top 6" or so, more composting, then dig it in as much as possible with a digging fork. In areas where I've sheet composted only, the soil will have a definite layered effect with about 3-6" of good stuff on top, then pure clay below. It's much nicer where it's been tilled or dug.

Cheers,
Michelle

tilling in coarse sand will help too.

About that coarse sand: It will help only if it increases total sand content to 60 percent.

Adding little bit of sand won't do any good. A moderate amount may make things worse. Would still need compost anyway.

covering the spots with mulch/leaves compost etc will probably help. What are you hoping to do with these patches if/when you improve them? If you want to do a little gardening, perhaps building a bit of a raised bed over top of them would be easier than trying to get the area dig-able. I've heard putting some gypsum down before the sheet composting can help loosen up some types of clay (perhaps sodic clay?) but not all types.

Cover it now with several inches of mulch and by next spring you will have soft soil underneath. What your soil needs to soften is a lot of healthy fungi. The mulch will moderate the moisture and allow the fungi to grow.

Most of the clay soil I have seen in New York will be easily changed simply by building a compost pile, or a lasagna garden on top of it and allowing the Soil Food Web to work that organic matter into the soil for you.

Here is a link that might be useful: Lasagna Gardening 101

Thank you all. I don't have a hose back there but I guess I can use a watering can to keep my lasagna compost moist. And bty, the only thing I want to plant in those spots is grass.

After you build it you don't need to water the compost much unless it is really hot and dry. Compost only needs to be moist, not wet.