Seismic stability of slope considering material properties and geometric characteristics

Abstract

Earthquake is one of the main factors inducing landslide. By establishing a viscoelastic soil-elastic bedrock binary slope model, this research proposes a seismic stability evaluation approach that can consider the material properties and geometric characteristics of the slope. First, it is assumed that seismic waves vertically propagate from the base as harmonic waves. Second, the model satisfies the following boundary conditions: (1) the stress at the free surface is null; (2) the stress and displacement are continuous at the soil-bedrock interface. Third, the displacement and acceleration formulas for the viscoelastic soil-elastic bedrock binary slope model during earthquakes are derived. Finally, combining the limit equilibrium theory, a safety factor formula is developed, and a new modified pseudo-dynamic method (MPDM_E) based on the elastic bedrock assumption is proposed. The results show that the MPDM_E can reflect the dynamic response characteristics of slopes, and its seismic stability is related to the material properties and geometric characteristics. When the bedrock is elastic, the upper soil does not exhibit resonance due to the presence of impedance and damping ratios. If the impedance ratio is small, the acceleration in the soil reaches its maximum near ωH₀/vₛ = π/2. Sensitivity analysis indicates that the most sensitive parameters affecting the safety factor are the soil strength parameters, including the internal friction angle φ and cohesion c. These are followed by the slope angle α, soil unit weight γₛ, frequency f, and upward wave amplitude a_h1. The least sensitive parameters are the distance between the bedrock and the slope toe (H₀H), soil shear modulus Gₛ, and damping ratio D. Lastly, degradation verification shows that the safety factors calculated using pseudo-static method (PSM), modified pseudo-dynamic method (MPDM), and MPDM_E are consistent, indicating the stability and reliability of the new approach proposed in this study. This approach can provide a theoretical basis for seismic slope stability evaluation, engineering design and post-earthquake emergency rescue.