Optimum design of rocking wall coupled with building under stochastic seismic ground motion

Coupling with rocking walls is a possible approach to protect buildings against earthquakes. In fact, previous studies have demonstrated that such strategy can mitigate the seismic damage and can also prevent soft-story collapse mechanisms due to excessive displacements. In this regard, the use of special devices connecting the building and the rocking wall can further enhance the dissipation of the input seismic energy. Within this framework, the present work aims at providing some insights about the optimum design of rocking walls for seismic protection of buildings. To this end, the dynamics of the building is reduced to a linear elastic and viscously damped single-degree-of-freedom system. A linear elastic spring and a linear viscous device provide the coupling between the main system and the rocking wall, which is pinned at the mid-width through a linear elastic rotational spring and a rotational dashpot. The dynamics of such coupled system under earthquake is analyzed by simulating the seismic ground motion as time-modulated filtered white Gaussian noise. Once the differential equations governing the dynamics of the resulting coupled system are derived, the optimum design problem is formulated. Final numerical results highlight the performance of this seismic protection strategy and provide useful information for its preliminary optimum design.