Displacement-based seismic design of a shallow strip footing positioned near the edge of a rock slope

•Seismic performance of a shallow strip footing placed near the edge of a rock slope.•Influence of geometrical factors, rock strength parameters and seismic loadings.•Displacement-based seismic design by iterative procedure.•Design example for the bridge foundation.

This paper presents a displacement-based dynamic design of shallow strip footings located close to the edge of homogeneous and isotropic rock slopes. The analysis is conducted using the “generalized tangential” technique in which the Hoek–Brown strength is replaced by an “optimal” tangential Mohr–Coulomb domain within the framework of the kinematic approach of limit analysis theory. In order to better understand the influence of these factors including geometrical features, rock strength parameters and seismic loading, a parametric study is carried out. An expression is derived and used to obtain a least upper bound solution for the bearing capacity of a footing on a rock slope considering a kinematically admissible log-spiral failure mechanism. In addition, a similar expression of the horizontal yield seismic coefficient is derived for a given load acting on the foundation.The assessment of earthquake-induced permanent displacement is performed by a simplified procedure. This requires the knowledge of a ground motion parameter that can be evaluated by site-specific seismic hazard analyses or ground motion prediction equations and that considers the actual sliding surface. The calculated displacement should not be greater than a selected limiting tolerable displacement for the specific case. An example is presented illustrating the application of the design procedure for the bridge foundations.

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