title: Closed-form rocking overturning conditions for a family of pulse ground motions.
abstract: This paper characterizes the stability of a rigid rocking block subjected to a family of multi-lobe pulse ground motions. It unveils a counter to intuition plurality of overturning (OT) modes despite the short duration and bounded energy of the examined ground motions. Accordingly, it describes with original closed-form expressions the critical conditions of all OT modes involving a finite number of impacts. It also proposes pertinent semi-analytical, exact analytical and approximate analytical solutions with respect to the determination of the (unknown) times of impact, as appropriate. The analysis reveals that thefirst, orlower bound, critical OT mode is in most cases toppling during free rocking after one impact specifically before the end of the pulse. For this case, it elucidates the physical mechanism behind the timing of impact that producesminimumamplitude andmaximumamplitudecriticalOT, respectively, and proposes pertinent closed-form approximations. Finally, the study derives, in 'universal' terms, global 'safety walls' against rocking OT considering a large number of different pulse shapes.
authors.affiliation: Department of Civil and Environmental Engineering , The Hong Kong University of Science and Technology , Kowloon Bay, Hong Kong.
authors.forename: Elias G
authors.identifier: 0000-0003-0341-9512
authors.initials: EG
authors.lastname: Dimitrakopoulos
authors.affiliation: Department of Civil and Environmental Engineering , The Hong Kong University of Science and Technology , Kowloon Bay, Hong Kong.
authors.forename: Edwin Dat Win
authors.initials: ED
authors.lastname: Fung
keywords: closed-form solutions; earthquake engineering; overturning; rocking; rocking resonance