Austin houses are rife with foundation issues. This seems chiefly due to the clay content our homes are built upon. This 1905 soil survey of Austin suggests that, at least as of century ago, most of central Austin is covered with Austin Clay, Houston Black Clay, and Travis Gravelly Loam, with “Rock Outcrop” to the west and Houston Gravelly Clay to the east. Anecdotally, the annual cycle of contraction and expansion the clay soil undergoes wreaks havoc on foundations — especially the 1950s and 1960s slab foundations with cast-iron plumbing in Brentwood, Crestview, and surrounding neighborhoods.
I overlayed the soil survey on top of a map of Austin. This makes it a little easier to tell which neighborhoods are built on which types of soil. Caveat emptor — I have no idea how current the soil survey data is, although it seems likely to me that things are mostly unchanged.