Deterministic analysis does not provide a comprehensive model for concrete dam response under multi-hazard risk. Thus, the use of probabilistic approach is usually recommended which is problematic due to high computational demand. This paper presents a simplified reliability analysis framework for gravity dams subjected to flooding, earthquakes, and aging. A group of time-variant degradation models are proposed for different random variables. Response of the dam is presented by explicit limit state functions. The probability of failure is directly computed by either classical Monte Carlo simulation or the refined importance sampling technique. Next, three machine learning techniques (i.e., K-nearest neighbor, support vector machine, and naive Bayes classifier) are adopted for binary classification of the structural results. These methods are then demonstrated in terms of accuracy, applicability and computational time for prediction of the failure probability. Results are then generalized for different dam classes (based on the height-to-width ratio), various water levels, earthquake intensity, degradation rate, and cross-correlation between the random variables. Finally, a sigmoid-type function is proposed for analytical calculation of the failure probability for different classes of gravity dams. This function is then specialized for the hydrological hazard and the failure surface is presented as a direct function of the dam's height and width.