Beech have surface rooting tendancies, but nowhere near as bad as willow.
There is some problem with foundations and clay soils in that they are dynamic ith the wet/dry cycle. You've probably seen this with the cracks in the lawn when in drought season.
As stated above the construction of the foundation means more then the tree. If the backfill is sand or gravel then there is little worry of the roots exacerbating the soil movement of the wet/dry cycle. If they backfilled with just cay, then there can be some added stress to the structure.
As for actual damage by roots them selves, one must look at how trees grow; adding a thin layer of cells under the bark layer to add another "cylinder" to the stem, branch or root.
If there is a rock, fence or wall that that root grows against, then it will form around it vs moving it. If there are defects in the structure then the root can take advantage of them, but they need to be severe.
The there are the limiting factors involved with root propigation. Water is the most obviouse, but free oxygen is the biggest. So if we have a well compacted base and seemless slab, then the root's not going to grow under it due to the lack of O2. If the base was not preped properly and the slab cracked then roots may get in and take advantage of the room to grow, and maybe cause the cracks to propigate.
This has been shown with city sidwalks, where there is marked increase of roots under the seams and cracks as aposed to the solid areas.
Another good example is how trees grown down to cracked and old-clay sewer tile. you have a plumb of nutrien rich, aerated water coming up into which the tree root grows. If it were not for the seams and cracks, the rotots would never grow down into unaerated soil.
