Several; the best-known are Chinkapin Oak (Quercus muhlenbergii) and Bur Oak (Q. macrocarpa). For others, have a look at the search results below.

Oak roots can go deep, but they also have plenty of shallow surface roots. All trees do; they need them for water and nutrient uptake.

Resin

Here is a link that might be useful: Flora of North America: Oaks recorded on limestone

Thank you so much for the input-- I kept reading that Oaks need acidic soil, but I will look into those types.

The question I really should have asked (& forgive my newbiness) is what trees, if any, will tolerate a raised bed around them? My old house had a beautiful (though PITA) huge Silver Maple with a gorgeous raised bed of Hostas around it (about 1' tall, circle bed about 4' diameter around the Maple). It looked magnificent. And I'd love to recreate something like this in the long run at my new house, but I'm reading that most trees can't tolerate a raised bed around their roots.

They'll tolerate it no problem if the raised bed is built before the tree is planted. It is the change in soil levels over existing roots that does the damage. A new tree planted in the middle of a raised bed will be fine.

Resin

Great to know! Thank you so much.

I have an Shumard oak tree I planted as a dug up sprout which after it was about 7 years old, I installed a 2 feet high and 3 feet wide berm that stretched past the east side of the oak. The berm's west side was only five feet away from the oak.

Within two years after installing the berm, and when I planted new things to finish landscaping the berm, during the planting I often encountered some of the oak's roots which had spread into the berm.

It amazed me to see how well the tree had adapted to such a drastic changed elevation of soil only 5 to 7 feet away from its trunk.

Of course, the tree most likely would not have done so well if I had raised the soils elevation that high all around the tree.

Now a Silver Maple tree on the other hand is different story. I created a one foot high raised bed about 30 feet away from a neighbor's Silver Maple tree. After less than 6 months the Silver maple envaded that bed so badly that it killed my 6 foot tall Nyssa sylvatica tree I had planted in the raised bed. The silver maple robbed my tree of the water and soil nutrients it needed, even when I paid attention to check my tree daily and found I had to water often because every time I checked, I would discover that the maple had caused the bed to dry out too quickly

Shumard Oak or Shumard Red Oak adapts to alkaline soils quite nicely. After Live Oaks, they are the most used oak tree down here.
The Bur Oak is considered sort of a plains tree. It is not unusual for it to have more mass below ground than above.
It is, along with Cottonwoods and Eastern Red Cedars, a tough pioneer tree that can survive and thrive under harsh prairie conditions.
The only Chinkapins I have seen in the wild have always been along sheltered creek or river areas.

Shummard Oak from the Western 1/3 it's native range is indeed quite adaptable to alkaline soils. The problem is that Shummard Oak from the Eastern 2/3 (of course this is a rough estimation) aren't nearly as alkaline tolerant. Shummard Oak in Kansas, Oklahoma, and Texas grows in limestone derived soils and often times on drier rocky hills, while further East it's more typical of a lower rich bottomlands. I suspect there might be either the beginnings of or already are 2 species, which are morphologically almost indistinguishable, lumped into Shummard Oak. Kind of like Laurel Oak (Quercus laurifolia) and Darlington Oak (Quercus hemisphaerica) were. Only genetic studies can probably prove or disprove this theory of mine. Sooo....if you can find Shummard Oak being sold that is from a tree farm in say Oklahoma(there are several large ones supplying the Wichita and Kansas City markets with Shummard Oak native to Southern Oklahoma and North Texas) being sold by a nursery in Nebraska, it will be alkaline tolerant.

Also, Texas Red Oak (Quercus buckleyi) will grow well in alkaline soils. I've seen it growing very well in places like Amarillo, TX, Wichita, KS, and Salina, KS all of which either have alkaline soils or large parts of them have alkaline soils. Gambel Oak(Q. gambelii) also grows well on alkaline soils and is often a smaller growing Oak. Shrub Live Oak (Q. turbinella) also does well on alkaline soils and is more a large semi-evergreen shrub rather than a tree. It's also quite cold hardy, well into zone 5 and it does very well in the Denver area as well as apparently in Kalamzoo, Michigan(Oikos tree crops has said it's doing well for them).

If you're interested at all in some exotic Oaks, English Oak(Q. robur), Mongolian Oak(Q. mongolica), Oriental White Oak(Q. aliena)(this and English Oak are both just as alkaline tolerant as Chinquapin Oak), Daimyo Oak(Q. dentata), and I believe Hungarian(sometimes called Italian) Oak(Q. frainetto) do well on alkaline soils. Many of these are usually available through many mail-order nurseries and some are usually available through larger local nurseries.

Chinquapin and Bur Oak are both excellent very well adapted Oaks to alkaline soils and harsh great plains conditions(to areas with annual rainfall as low as about 15"(380mm) or so) like the other posters said. In the Southwestern part of it's range, Chinquapin Oak does tend to grow in more sheltered and moister areas, but in the NW part of it's range it's often growing on dry rocky South and West facing slopes as well, so should do well for you no matter where you planted it.

Our soils are quite alkaline and Bur and English have proven the most tolerant with Shumard, Chinkapin next and oddly Shingle are doing O.K.

I found a website that listed recommended trees for Nebr. Recommended oak rees are Bur, Red, Shingle, and Swamp White. Not sure what part of Ne. you are in but we have huge oak trees in the eastern half growing in alkaline soil. Only problem is they produce lots of acorns that attract squirrels and grow new oak trees in flower beds. That may or may not be a problem for your circumstance.

Thanks for all of the info! (I'm in Omaha. Just obviously not very knowledgable yet lol).