I finally got around to digging some holes around my yard to collect soil samples for a soil test.
http://www.youtube.com/watch?v=LKe9c0oVrKY
90% of the yard is covered in various grasses and sedges (St. Augustine, Bermuda, nutsedge and at least two others). So there's typically maybe a inch of organic material by the roots, but directly under that is a thick layer of reddish-orangish-brown clay, with 1-2 inch rocks scattered throughout. That generally goes down to about a foot, but then past that the soil is more sandy and crumbly (this video only goes down to the clay layer). The hole is about a foot in diameter and two feet deep. I didn't find one earthworm.
Some history: The land here was once part of a large citrus grove. That went on for about 50 years, until it was purchased and cleared by developers. Then in the 80s, the area that is now my back yard was dug up completely and an underground drainage channel was installed (see here for photo:
https://permies.com/t/26157/trees/drainage-channel-running-backyard). So the soil profile is probably all screwed up.
That said, all the trees in the backyard seem to like the soil just fine. So long as the soil remains moist I think the trees have no problem growing their roots in and through the clay. I found some grass/sedge roots up to 1.5 ft down.