the only thing i could suggest is to dig up and seive the topsoil . Or rake them to the edge of the bed with a fine toothed rake.

And add more humus-containing material like compost or rotted-down manure or grow green manures to dig in?
The bits of pottery count as stones, so what you have is a very stony soil. It can be improved by feeding it more humus.

Pottery pieces are better than stones, because they hold water and nutrients. Continuing to add organic matter is the long term solution to the problems associated with this soil, and will help gradually break down the clay "pebbles" into smaller granules. If you want to grow root crops, dig it up to about 30 cm, and sift out everything larger than 1/2 cm.

Let me thank all for the solutions and interest in the problem.
Pottery pieces are mixed with the soil in appreciable percentage. I did try to sieve the pieces out a few years back, it is a costly operation and disposal of the pieces is tedious. Tugbrethil's solution is what is possible. In the second photo, the pieces are reduced in size and may not be as detrimental as the bigger pieces. Yes, the pottery pieces soak some water to release for the plants,

AR

I just thought of something, though. If many of those pieces are glazed, be aware that many older forms of pottery have lead in the glaze, so it may be worth while testing for lead. If a test isn't possible, put in some superphosphate to bind the lead, just in case.

Thanks , Not a single piece is glazed. It is pure baked earth, mainly thin pieces.

Likely to be safe, then.