Earthquake-induced displacement of cohesive-frictional slopes subject to cracks

The upper bound theorem of limit analysis together with Newmark's method are employed to evaluate the displacement of soil slopes subject to cracks. The pseudo static approach has been routinely used in the literature to estimate the seismic displacement of soil slopes. However, the effect of cracks on the slope displacement has yet to be tackled. In this paper, a new technique is proposed to estimate the horizontal displacement at the slope toe due to a given earthquake postulating rough estimation of real time crack formation. Rotational failure mechanisms for intact slopes exhibiting the formation of cracks as part of the failure process and the case of cracks which are pre-existing in the slope were considered. On the basis of Newmark's method, the seismic-induced displacement is calculated by incorporating a stepwise yield acceleration corresponding to the cracks occurring in the slope. Results of the proposed technique can reasonably bridge the gap between the conservatism of assuming the slopes subject to the most detrimental cracks, and the overestimation of slope stability resulted from the neglect of crack formation. An example illustrating the procedure for a given earthquake is presented. Also, charts providing the values needed to calculate the stepwise yield accelerations are proposed.