Teton Dam is the classic example. The core material was low-plas silt placed dry of optimum, which is not inherently problematic if one designs for it. (Not exactly what you'd prefer, but you have to build with the materials that are available.)
Nobody knows exactly how erosion initiated, but one of the credible explanations is that the relatively narrow, vertical-sided trench in fissured volcanic bedrock allowed the fill to arch. This meant that the weight of overlying fill was carried by the trench walls, rather than as vertical stress in the core backfill. When the reservoir filled, this could have introduced 150(?) feet of pressure head in an area of the cutoff trench where there was little vertical stress in the fill, much less than 150*62.4. (Finite element analysis for the failure investigation indicated that Sigma-v was pretty low.) Water seeping in could have hydrofractured (wedged open horizontal fractures), which would allow the water to flow through, cause erosion, etc., eventually causing 11 fatalities. There was no filter on the downstream side, and the discontinuities in bedrock were not sealed by grout or concrete. There was a thread about this a few months back that had some pictures to go with it.
I see that you were part of that. The pictures might be worth 1000 words.
The portion of the cutoff in alluvium had flatter slopes, and probably would never have been a problem.
Not sure about clay, but clayey sand can arch, as can low-plasticity silt. Clay might be able to if not placed wet of optimum.
Concrete and soil-cement are, of course, not so easily erodible, but they aren't always economically viable. Sand, by itself, would not make a good cutoff, but modern practice often includes a sand filter to back up the cutoff.
Did I answer the question?
