Finite-element upper-bound analysis of seismic slope stability considering pseudo-dynamic approach

The present study presents a novel procedure to assess the seismic slope stability, using the finite-element upper-bound method combined with the pseudo-dynamic approach. A pioneering work is performed to incorporate the pseudo-dynamic accelerations into the finite-element upper-bound analysis which combines the advantages of upper bound and finite element methods. The finite element method is principally used to discretize the domain of soil mass into finite elements, aiming to construct a kinematically admissible failure mechanism based on which the external and internal rates of work can be expressed. Based on the upper bound theorem, the upper bound formulations are derived from the virtual work rate equation, in the form of slope safety factor and limit surcharge acting on the slope crest. The problem of seeking the optimal upper bound solution is transformed to solve a linear programming problem within numerous kinematically admissible velocity fields, and this is achieved by using the interior-point algorithm implemented into the MATLAB. Pseudo-dynamic solutions are calculated and compared with the pseudo-static, limit equilibrium and FLAG results. The proposed procedure is versatile in considering the homogeneity and non-homogeneity of soil strength properties in seismic slope stability analysis. A benchmark problem with 0.5 m thick weak interlayer is discussed.