This reference says that you need to add prohibitive amounts of sand to remediate clay soils. And if you don't get it right, you get a soil like concrete
The problems occur when sand and clay are mixed in incorrect proportions. An ideal soil has 50% pore
space (with the remainder consisting of minerals and organic matter). The pore spaces in a clay soil are
all small, while those in a sandy soil are all large. When one mixes a sandy and a clay soil together, the
large pore spaces of the sandy soil are filled with the smaller clay particles. This results in a heavier,
denser soil with less total pore space than either the sandy or the clay soil alone. (A good analogy is the
manufacture of concrete, which entails mixing sand with cement - a fine particle substance. The results
are obvious.) A soil must consist of nearly 50% sand by total volume before it takes on the
characteristics of a sandy soil. For most sites, it would be prohibitively expensive to remove half the
existing soil and add an equal volume of sand and then till it to the necessary 18-24". Mineral
amendments of large particle size, such as perlite, may provide some benefit but can also be costly
depending on the size of the site. (Reducing this task to amending only the planting hole is a recipe for
plant failure and perhaps will be addressed in a separate column.)
If you're going to add organic matter to your clay soil, make sure it's evenly distributed and not just in one area.
The wrong thing to do is to dig planting holes and fill them with organic soil amendment since that creates pockets of soggy ground that fill up with water and rot roots. Also roots will think they are in a container and go around and around inside the amended plant hole and never get out into the surrounding soil.
Planting pits are used in Africa in clay soils to catch precipitation but that's a different situation
And rich planting pits are a different matter again, and are not done in clay soils.