[zh3]

A close approximation should arguably include collapses/slides, which happen spontaneously because the pile organises itself to a critical angle; then an incredibly small event can trigger a large slide of salt/sand/whatever/rocks (or whatever else the pile is made of). Even working out something like "What's the biggest and smallest slides that could occur given a pile of some particular substance?".

Every approximation will by definition deviate from what really happens - I suppose that's why we talk of "working approximations", i.e. they work well enough for a given purpose. So it probably comes down to what the approximation is being used for.

There is the idea that we are all living in a simulation; if so maybe if we look closely enough at the detail all the way from the universe to atoms then we'll start to see some fuzziness (well, of course there's quantum physics....).