A probabilistic analysis framework for stochastic dynamic damage of arch dams considering parameters spatial variability subjected to stochastic earthquake excitation

A new framework is proposed for the stochastic dynamic response and seismic fragility analysis of arch dams to obtain accurate probabilistic information under small-sample-size conditions. This framework integrates the coupling effects of material spatial randomness and seismic randomness into seismic fragility analysis of arch dams. Key components include: the Karhunen-Loève Expansion combined with the Cholesky decomposition method for efficiently modeling spatial correlation and variability of material parameters; the improved Clough-Penzien power spectral model for accounting for non-stationarity in ground motion frequency and intensity; and the velocity divergence-generalized adaptive probability density evolution (VD-GAPDE) method for solving random seismic responses. The VD-GAPDE method incorporates both shape and location information of the joint transfer probability density of representative points, enabling precise probabilistic analysis with small sample sizes, and its efficiency is validated through comparisons with Monte Carlo simulation and generalized probability density evolution (GPDE) method. The theoretical derivation demonstrates the compatibility of the VD-GAPDE equation with the Fokker-Planck-Kolmogorov and GPDE equations, confirming its applicability to stochastic dynamic systems. A case study of the Baihetan Arch Dam evaluates the impacts of seismic randomness, material spatial randomness, and their coupled effects. The results highlight the importance of accounting for material parameter correlation in reliability analysis.