OK, thanks to all for the data.
But when I build handrails into a slab or existing concrete sidewalk, I'm limited since the "base" is already solid.
What " works" - but I emphasize! not analyzed - is to core drill the sidewalk all the way through the concrete to dirt. If a slab, go down no more than 6 inches - since the core drill jams out any deeper. I've had no problems with holes only 4 inches deep, but prefer to go further if the sidewalk allows it.
On porches or wlakways in the open air, sometimes I can only go 3 inches deep before I bore through. If so, then I have to fill/plug/block off the bottom of the hole so the concrete doesn't just slide through the opening.
Plan on a 1-1/4 dia pipe (or equal) as the vertical, and get a 3.5 inch core drill. 4 dia if you can find one. The bigger the hole the easier it is to force the grout/concrete around the pipe without making a mess. Build and install the handrail pipe so it goes 5+ inches deeper than the surface, but doesn't hit any dirt.
Pour/insert/tamp the "expanding" grout/concrete around the post so you slightly over-fill the hole to force water runoff.
Keep the post supported overnight. Test the top of the handrail at 200 lbf the next day.
Note again: This is not a designed solution, but a construction "solution" report.