Study on the Dynamic Response of Large Slopes Under Non-Uniform Seismic Excitation Considering the Slope Scale

In the existing studies of slope stability under seismic excitation, the non-uniform spatiotemporal dynamic response and amplification effect caused by the slope scale are often overlooked. In order to analyze the dynamic response of large-scale slopes under non-uniform seismic excitation, this study presents an analytical model based on the Hilbert’s best approximation problem (BAP), taking into account the scale of slopes under seismic incidence. A methodology for differentiating between the plane wave assumption of Huygens’ principle and BAP principle is proposed. A Stoneley equation considering the scale of the slope on the interface is proposed to analyze the non-uniform spatiotemporal dynamic response. Meanwhile, the Knott equation is subjected to non-uniform seismic waves and adopted to describe the amplification factor of spectral response accelerations (SRA). To visually represent the non-uniform spatiotemporal dynamic response and amplification effect, numerical models based on the finite difference method (FDM) are established to simulate the non-uniform incidence of seismic waves. The numerical simulation results show that the non-uniform dynamic response cannot be disregarded in cases where L/h>4:20. Slopes of this scale subjected to seismic wave incidence satisfy the BAP principle. Conversely, the dynamic response exhibits uniformity in cases where L/h<1:20, which is in accordance with the plane wave assumption of Huygens’ principle.