I am trying to make a floor mat where the base is wood and the top are pebble stones. The bonding must be strong and permanent as it needs to withstand the force of people walking in it.
What glue or other material is used for this?
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A project often seen on video resources is similar to your objective. One places objects on a flat surface, usually surrounded by a tray structure. The objects are then immersed in an epoxy casting liquid, which cures in a matter of hours or days. Table tops are a common project.
In your case, having the surface covered with the casting material would result in disfiguring scratches. One could, however, ensure the stones are as tightly packed as possible and pour the liquid just short of the surface of the assembly. Additionally, colorant can be added to the casting liquid to "accept" any scratches that would result from use as a floor mat.
I'd consider to add a sand or smaller pebble material between the stones to provide additional traction. The smaller material may become sacrificial in use, but could easily be refreshed as needed.
If liquid casting is not your selection, conventional epoxies would also work. Note that long duration cure time epoxies are going to be stronger than the often-advertised five-minute cure epoxy.
The resin method suggested by fred_dot_u is probably the most secure approach. A less expensive variation is to press the stones into a bed of mortar or cement. The stones will be very secure if more than half the thickness is embedded.
But if you want the appearance to be more like a pattern of loose stones than a bed with stone tops showing through, there's another approach that will work. You can glue the individual stones to the wood with an appropriate adhesive.
Wash and thoroughly dry the stones so their surface is clean.
Paint the wood a suitable background color because spots are likely to be visible between the stones. Black or a dark color is generally better because it is less visible and total coverage isn't needed. Use a thin paint that soaks into the wood rather than a thick layer that can peel off. Ideally, you want some wood texture and porosity to bond to. The wood won't be very visible, so more of a tint than a paint shell will be fine. Stain would also work as long as it doesn't leave an oily surface and is totally dry.
You can either do this freehand as you go, or lay out the stones to position them where you want them, then one-by-one, remove a stone, put down a good blob of adhesive, and press the stone into it, or put a good blob on the back of the stone and press it into place. You want enough adhesive to cover a good area on the back of the stone, and enough thickness so the stone is well supported and won't want to roll if weight is put on an edge.
Clear silicone caulk (or a color matched to the painted wood; black is readily available), is a good adhesive for this. The clear or color-matched silicone won't be very visible. Silicone will adhere well to both surfaces and can flex if needed when you step on the stones so it doesn't break or come off (which will also be comfortable to walk on). You can also use construction adhesive (typically comes in a caulking tube; polyurethane-based is good for this). Just paint the wood to match the color of the adhesive.
The method described above assumes the stones are big enough to be glued individually. If by "pebble stones" you mean something like pea gravel size, you can use a "bulk" variation.
You won't need to paint the wood. Spread a layer of the silicone caulk roughly half the thickness of a typical stone (construction adhesive won't be practical for this). You might want to temporarily place a frame around the mat to keep stones and silicone from being squeezed off the edges (although you could cut away excess later if you don't). To make the frame non-stick for the silicone, wax it or line it with strips of HDPE (you can cut these from milk jugs).
Spread a single layer of the clean, dry pebbles over the surface and press them into the silicone. Put another piece of wood over the whole mat and stand on it to press the pebbles into the silicone, which will make a more uniform level.