Both pebble bed and thorium reactors belong in the generation 4 class of reactor, yet to be scaled up to commercial size and with safety problems unresolved. Both reactor "types" have been built and the Chinese are operating several prototypes of pebble bed reactor. The South African PBR has/is running short of funds while still largely at the design stage.
Nuclear reactors by their nature are highly dangerous and need to be designed to minimise every remotely possible accident. Once this has been done, the regulator must be satisfied that design, operation and supervision protocols reduce every accident scenario to near zero. A big ask with more to come. Construction and staff training must reach the safety benchmarks as well.
No wonder building nuclear reactors has become so expensive. If a problem can be imagined, design, construction and operation must reduce the probability to near zero. In the past, all reactors were essentially bespoke designs in the sense that every proposed reactor had run the safety gauntlet. In addition, many reactors were designed as essentially one off projects.
Generation3+ reactors are supposed to be different. Each type is supposed to have a fixed design with all the safety problems pre approved and reactor construction absolutely identical for each type. The Westinghouse AP1000 comes close to this ideal but the Brits have still managed to knock it back. I suspect the problem in large measure the the regulator rather than the design.
No generation 4 reactor has emerged from the regulator labyrinth and I expect it will be some time before one does. By way of example, the pebbles in the PBR will rub against each other as they move through the reactor. The attrition will create dust which must be accounted for. The paperwork for this accounting is incomplete along with hundreds of other "trivial" problems, We need to remember though that Three Mile Island started as a trivial problem too, a stuck venting valve as I recall.
I'm not sure this is what you asked for but it is where my research has been taking me lately. To get back to PBR and Thorium reactors we can look to the Chinese from now on for PBR unless the South Africans find another pile of money.
There is a whole spectrum of thorium reactors I've been looking into. Even some gen 2 reactors such as CANDU can handle thorium in the fuel mix but limited demand means limited supply for thorium. Even though it is several times as abundant as uranium and needs no enrichment, thorium ores are mostly left in the ground or even discarded
