Three-dimensional rigorous upper-bound limit analysis of soil slopes subjected to variable seismic excitations

Abstract

In the present study, a semi-analytical model that couples the three-dimensional (3D) kinematical approach of limit analysis and the modified pseudo-dynamic method was developed. The model was used to assess the critical safety factor of slopes from a realistic and wholistic perspective. Time-space dependent sinusoidal-cosinusoidal waves were introduced to represent cyclic effects of seismic waves, and the shaking amplitude and damping effect were incorporated. A 3D discretized failure mechanism comprising a series of kinematically admissible triangle meshes was generated. This failure mechanism is superior compared with conventional mechanisms as the normality condition required by the plastic theorem is fully met and variable seismic excitations can be directly incorporated. The work-rate of the external forces and the internal dissipation rates were numerically acquired to explicitly determine critical safety factors. Accuracy of the proposed model was determined through numerical simulations and dynamic safety factors and plastic zones were compared. Comparisons and parametric analyses showed the importance of accounting for the third dimension of slopes, damping ratios, the relationship between shaking frequency and natural frequency. Testing of proposed model was performed through seismic stability analysis of the Longnan slope located in an earthquake-prone zone.