Question
looks like our highly shaded yard is mostly silt (and tree roots) and that the correction is to add clay. Where do ya get that, how much, etc?  

Answer
Hi Tom
Clay? what are you trying to acomplish? most topsoil is a mix of clay silt and sand a good balance. if you are trying to fix the yard just cover the area with topsoil and then sod or seed with a fescue mix. the moisture level will have to be monitored because water does not evaporate fast in shade
the tree will take what it needs and then the rest will drain away. the topsoil will retain moisture enough to supply both the tree and your yard.  Good Luck Larry  ;-)