Evaluating the abutment stability of high arch dams is crucial for ensuring their safe operation under complex and evolving environmental conditions. The material properties of the dam and foundation vary significantly over time, and the randomness of these time-varying parameters introduces uncertainties into dam stability analysis. However, traditional methods often rely on deterministic parameters, neglecting the time-varying and uncertain nature of dam and foundation materials, potentially leading to inaccurate or misleading assessments. To address these limitations, a probabilistic evaluation methodology is developed that explicitly incorporates the time-varying characteristics and uncertainties of material parameters into abutment stability analysis. A novel reliability metric, termed the assurance rate, is introduced. It is defined as the cumulative probability that the safety factor exceeds a specified threshold, providing a more realistic and dynamic measure of structural reliability. The method incorporates a time-dependent reliability analysis, considering the probability of failure as a function of time, alongside the assurance rate. To capture the temporal variability of material behavior, an inversion method is established by integrating empirical mode decomposition, response surface methodology, and intelligent optimization algorithms into a unified framework. To further incorporate parameter uncertainty, the inverted parameters and their statistically derived probability distributions are embedded into Monte Carlo simulations. Application to the Dagangshan (DG) arch dam shows that the reliability indicators show clear time-varying characteristics, ranging from 4.62 to 5.01 for the left abutment and 4.70–5.03 for the right. And the probability of exceeding the allowable safety factor (K = 3.5) consistently remains above 99.99%, confirming the dam’s structural reliability. The proposed method overcomes the limitations of traditional approaches that rely solely on a single safety factor to evaluate abutment stability, offering a more comprehensive and dynamic framework for rational assessment of dam abutment stability.
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