Ensuring dam safety is paramount because it directly impacts the protection of lives, critical infrastructure, and the environment. In engineering practice, dams are usually designed based on a deterministic "safety factor," which is a concept rooted in a particular mathematical model that predicts the dam's physical behavior. However, this method often fails to adequately consider the complex uncertainties inherent in dam systems and does not extend to calculating the probability of failure that correlates with the determined safety factor. Uncovering potential relationships between safety factors and the probability of failure could significantly aid engineers in performing more comprehensive risk analyses. In this paper, we propose a novel strategy to generate two equivalence functions for the seismic assessment of dams. The first function correlates the sliding safety factor with the return period of the seismic load. The second function links the safety factor directly to the associated probability of failure. Our methodology addresses epistemic and aleatory uncertainties by focusing on the spatial variability of strength and loading parameters.