The seismic safety assessment of large concrete dams remains a significant challenge in dam engineering, as it requires appropriate analysis methods, modern performance criteria, and advanced numerical models to simulate the dam seismic behavior. This paper presents a method for seismic safety assessment of arch dams based on Endurance Time Analysis (ETA), using tensile and compressive damage results from a robust formulation for seismic analysis considering joint opening/sliding and concrete non-linear behavior (finite element program DamDySSA, under development in LNEC). The seismic performance is evaluated by controlling the evolution of the damage state of the dam, according to predefined performance criteria, to estimate acceleration endurance limits for tensile and compressive damage. These acceleration limits are compared, respectively, with the peak ground accelerations prescribed for the Operating Basis Earthquake (OBE) and Safety Evaluation Earthquake (SEE), aiming to evaluate the dam seismic performance relative to both earthquake levels efficiently, using a single intensifying acceleration time history. The ETA-based method is applied to the cases of Cabril Dam (132 m-high) and Cahora Bassa Dam (170 m-high), confirming its usefulness for future seismic safety studies, while the potential of DamDySSA for non-linear seismic analysis of arch dams is highlighted.