Unified Evaluation of Slope Displacements Using Energy-Based Newmark Method for Arbitrary Earthquake Motions

Slope displacements (δ) have been shown to correlate uniquely with the earthquake energy (Eeq) contributing to slope sliding, regardless of input motion characteristics. Based on this principle, this study applies the Energy-Based Newmark Method to infinitely long slopes subjected to ten diverse earthquake records with stepwise scaled amplitudes. As the earthquake wave energy (Eᵤ) increases, the energy ratio (Eeq/Eᵤ) exhibits a distinct peak followed by a monotonic decrease. The peak values and corresponding Eᵤ levels strongly depend on the predominant frequencies (fp) of the motions, consistent with results from harmonic wave analyses. A unified design diagram is developed to correlate Eeq/Eᵤ with Eᵤ, incorporating fp and slope parameters. Since both Eᵤ and fp can be determined from design motions or empirically predicted using earthquake magnitudes and source distances, the slope displacement δ can be directly obtained from the diagram, eliminating the need for time-domain numerical simulations used in the conventional Newmark approaches. This method is recommended to conduct seismic zonation and hazard mapping in mountainous and hilly regions for regional authorities and infrastructure planners.