Determination and application of the nonlinear safety factor for high arch dams based on energy index and Pearson coefficient

High arch dams are complex statically indeterminate structures， and the nonlinear safety factor of high arch dams represents the extent of overload safety factor as the structural state transitions from overall elastic behavior to a nonlinear working condition. This factor is crucial for the safety assessment of arch dams. By integrating geomechanical model tests with nonlinear numerical analyses， this study investigates the failure evolution characteristics of arch dams under overload conditions and elucidates the physical implications and diagnostic significance of the nonlinear safety factor. The overall nonlinear state of an arch dam is essentially characterized by accelerated cracking damage and rapid energy dissipation occurring after the yield state is exceeded by a certain threshold. By analyzing the variation of the plastic complementary energy （PCE） during the overloading process of multi-arch dam projects， a nonlinear safety determination method based on Pearson coefficient is proposed. The plastic residual energy paradigm effectively quantifies energy dissipation during crack formation and damage progression in rock structures， while the the Pearson coefficient indicates the linear correlation between the plastic residual energy paradigm and the overload multiplier. Considering six engineering analogies， the Pearson coefficient criterion rw corresponding to the nonlinear safety factor Kn is determined as 0.90. Accordingly， the nonlinear safety factor of Dongzhuang Arch Dam is calculated to be 6.54. Furthermore， the substitutability of energy index， and the discount effect of long-term water storage on the nonlinear safety factor are investigated.