Stability of seismically loaded slopes using limit analysis

Numerical limit analysis is used to assess the stability of slopes subjected to seismic loading. The soil is assumed to follow the Mohr–Coulomb failure criterion. The lower and upper bound theorems are formulated as linear problems to be solved using linear programming techniques. Based on finite element discretisation of the slope, the velocity field is optimised to find the lowest upper bound, and the stress field is optimised to obtain the highest lower bound. Limit equilibrium computations and log-spiral upper bound solutions were also performed for comparison purposes. Additionally, finite element analyses were done for selected cases. Results from the limit equilibrium and finite element methods are in excellent agreement with the rigorous lower and upper bounds for all cases studied. The slip surfaces obtained from both the limit equilibrium and log-spiral upper bound methods lie within the plastic zones obtained for the slopes from both finite element and numerical limit analysis. Plots are presented of the horizontal pseudo-static acceleration ratio k_c = a_c/g required to cause collapse of simple homogeneous slopes as a function of the slope inclination and shear strength parameters.