Concrete – Double expansion concrete anchor

Epoxy is required in home building. Especially when attaching a wooden stud to an adjacent concrete wall. Architects and Engineers will usually specify a rod depth and that they are set with epoxy into the wall. The epoxy can be rolled onto the rod extensively and then placed into the hole. You usually allow the rod to set with the epoxy for 24 hours before attaching any hardware to the rods such as 2x4 pressure treated plates with 2 inch washer and nut. You can buy All-Thread rod that you simply cut to length. If you are concerned about the dust, then use an air compressor to blow out the hole prior to inserting the rod. When I added on a room to my house, it was specified that the rods must be epoxied into the hole. I used Loctite Metal/Concrete Epoxy.

You should be able (with a cheap metal-drilling bit you don't love much) to drill those out and try again. Drill them out, use a correctly-sized masonry bit to drill the holes larger, vacuum all the dust out of the holes, and set new anchors. Perhaps set the anchors a bit deeper to compensate for the slight spalling at the surface here. You can use "hydraulic cement" to patch the surface, but don't expect the patch to take much of the load, so just put the anchors in a bit below the surface in the correctly-sized holes.

If you choose to abandon and move up the wall, that looks like plenty of room so that the old holes won't bother the new ones. Drill the anchors out and patch the whole area with hydraulic cement, in that case.