Seismic slope permanent displacement calculation based on improved Newmark model using upper bound solution of plastic mechanics

Based on a review of the fundamental principles of the Newmark sliding displacement method, this paper proposes an improved approach based on the upper bound solution of plastic mechanics, drawing on the theory of Academician Zuyu Chen, which states that "during a given time period t, whenever velocity V > 0 occurs, the integration domain must be determined based on the varying distributions of acceleration a." The improved Newmark program integrates four main categories and eight subcategories of conditions into its framework through C + + programming. By employing the inclined strip method to construct velocity fields, the program enables more precise calculations of permanent slope displacements. To validate the effectiveness and accuracy of the improved method, calculations were conducted on both ideal slope models and real-world slope models. For the ideal soil and rock slope models, the results from the improved Newmark program were consistent with those obtained using the pseudo-static method and commercial software, demonstrating its strong applicability and accuracy. Furthermore, normalized artificial seismic waves, the Loma Prieta earthquake wave, and the Wenchuan earthquake wave, each with varying amplification factors, were input into the actual slope model of a colluvial deposit at the C₁ hydropower station in Tibet. A comparison of these results with existing data revealed that the improved Newmark program produced calculations that closely matched real-world observations. This further validates the method's reliability and accuracy in practical applications. In conclusion, the improved Newmark program can more accurately calculate permanent displacements under seismic loads, which has far-reaching significance for the design and safety assessment of slope engineering.