arch failure criteria

guideonl

I am a mechanical engineer, trying to understand the stones arch structure. I found out the basic forces but I could not able to determine the failure criteria (keeping the arch stable and not collaps even without external loads).
I looked for information in tne internet but i did not find something that could satisfy me.
If there are civil engineers at this forum I would be glad to get simple ideas that will help me to understand the concept (directing to sites/articles that explain it basicaly, figures and computations, forces and failure criteria definitions).

note: i am not intend to build an arch, just for better understanding of the concept.

Thanks, Guideon