A pseudo-static approach to the seismic bearing capacity of eccentrically loaded footing lying on rock obeying a generalized Hoek–Brown strength criterion

The ultimate seismic bearing capacity problem of strip foundations under eccentric loading is investigated within the framework of limit analysis theory. Referring to the kinematic approach formulated in the context of pseudo-static method, the analysis aims to assess the reduction in bearing capacity induced by the combined effects of load eccentricity and seismic loading. At the material level, the generalized Hoek–Brown failure criterion is adopted for modeling the nonlinearity of the strength properties. At that respect, derivation of closed-form expressions for the support functions associated by duality with such a failure condition is a fundamental component for the implementation of the kinematic approach. At the structure level, elaboration of two specific failure mechanisms allows deriving rigorous upper bound estimates for the ultimate bearing capacity. The approach is then applied to assess the effects of relevant geometry, strength, and loading parameters controlling the stability conditions. The accuracy of the analysis is evaluated by comparison with a series of lower and upper finite element solutions, thus emphasizing effectiveness of the approach to predict the reduction in ultimate bearing capacity associated with the particular loading conditions.