Rational selection of critical acceleration factors for sliding stability

• Compute exceedance probability of sliding displacement due to seismic excitation.
• Calculations use the previously published Urzúa–Christian model for seismic sliding.
• Find acceptable critical acceleration for prescribed displacement and probability.

The horizontal seismic loading coefficient is an essential input in evaluating the seismic adequacy of slopes, such as those in open-pit mines and natural slopes. In some cases, the coefficient is established through dynamic finite element analyses, which are time-consuming and require a new analysis for each facility, including a new suite of accelerograms. The values of the coefficient are sometimes incorporated in design manuals, but the procedures for establishing the values are seldom transparent. The usual situation is that the values arise from consensus, experience, and previous practice. In this paper, the Urzúa–Christian model for normalized sliding displacement has been extended to develop the critical acceleration value corresponding to the probability of observing prescribed amounts of sliding displacement. The method has been applied to two sets of data based on probabilistic seismic hazard analyses. The results show that, to satisfy the criterion that there must be 0.1 probability of the sliding displacement exceeding 100 cm if a maximum credible earthquake (MCE) occurs, the critical acceleration must be approximately 0.13 g. This means that a slope with these parameters in this environment must be stable enough that a horizontal acceleration of 0.13 g is necessary to put it in a state of sliding motion. In the case of the operational basis earthquake (OBE), which is a much smaller ground motion, the criterion of 0.1 probability of 100 cm of sliding is achieved for a slope with a critical acceleration of 0.35 g.