Is there an economic theory that explains what happens when a market is saturated with a precious resource? The theoretical situation is this. What if a record breaking amount of platinum were discovered. What would happen to the economies that use, store, and/or produce platinum?

I would like to apply this theory to any kind of precious material or element. Other examples would be gold, uranium, or oil.
At the outset, discovery does not equate availability. Huge amounts of platinum (or the material at issue) might be discovered, but that does not necessarily mean that its extraction is feasible or practicable with the currently available techniques. See here and here.

Assuming that the discovered material is economically available, then supply would increase, thereby pushing prices down. At the same time, demand for that material would increase because agents (consumers) might deem that material a convenient substitute of other [now relatively costlier] alternatives. The net effect would be a higher quantity of that material being traded, and at a lower price.