a. cut slab at back b. turn through 180 degrees c. drill the bit of slab under the step above and the broken end of the slab to take stainless steel rod or screws to guard against tipping d. fill holes with resin (or car body filler) and relay slab e. fill hole where bit broke off (or point in the bit that broke off if you have it)
If so, a quick fix would be to drill a couple of 12mm holes into the end of the slab, and matching ones into the broken bit, then use some concrete anchor resin[1] and some 8mm to 10mm threaded rod as a splint - setting the rod into pockets of resin as well as using it to "glue" the full area of the break. (over fill a bit, push tight and scrape off any excess.
[1] I have found this very effective@
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On a warm day it will set in 15 mins.
If you have not got the broken bit, then:
use a s SDS to break out the mortar at the back of the step under the step above. Rake out the mortar "grouting" and lift the slab.
If there is a solid bead of mortar under it, then flip it round 180, and resin bond it to the base. If the base is not that good, chip it out with the SDS and relay the slab on a fresh strong mortar mix with some SBR additive. Then point it all back in again with a dryish strong mortar mix. The broken edge now being hidden under the step above.
That would be my approach too. It looks as though there is next to no "overhang", so no significant bending moment on the joint.
In the absence of the missing bit, you could "square up" the failed area over the full slab width and let in a suitably cut portion, dowelling it in the same way. You might also let in a couple of vertical dowels in the brick, there is obviously a bit of a compromise with clearance somewhere to permit assembly.
Do most of the cut with an angle grinder for speed, finishing up the bits you can't do without damaging other slabs with a multi-tool
Car body filler works well as a "glue". After some advice on this group I experimented with fixing a broken concrete slab with car body filler
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The last picture shows the slab clamped to the arm of a garden bench with 4 house bricks on the over-hang being supported by the car body filler fillet.
The strength of the bond was however reliant on the surface of the break being sound concrete and with no flakiness at the joined edges.
I think you would need some support splints - so drilling holes and setting in some threaded rod, that you can then form the new bit around the ends of.
I expect they would work. Not cheap, but you don't need much volume. Maybe do a trial run to decide the amount of dye. Remember though that when filling a worn step the repair will be in compression when stood on. With an overhanging slab the top of the "crack" may be in tension some time. Adding one or two "dowels" as described (length of studing glued into hole in existing slab and protruding into cast repair) should help. Or you could let in a bit of steel plate into the mortar course below the slab, extending out to help support the new bit.
1) Remove the pointing mortar (stitch drill, angle grinder...).
2) Remove the piece.
3) Clean it.
4) Turn it around and put it back.
5) Replace the pointing with that something that goes off fast.
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