ORIGINAL PAPER A quantitative approach for the evaluation of rockfall risk on buildings Valerio De Biagi 1 • Maria Lia Napoli 1 • Monica Barbero 1 Received: 12 December 2016 / Accepted: 26 April 2017 Ó Springer Science+Business Media Dordrecht 2017 Abstract A quantitative rockfall risk analysis at local scale is a complex and difficult task because it should consider both the randomness in the natural phenomenon and the vari- ability of the response of the elements at risk. In engineering systems, such difficulties can be tackled with logical trees. In particular, event trees allow the determination of a set of outcomes of a given event in a probabilistic manner. Following recent publications on the estimation of rockfall risk on infrastructures (roads) by means of the event tree approach, a novel framework for the quantitative evaluation of the effects of the impact of a falling rock block on a building is presented. The method considers the occurrence of a given rockfall event, the kinetic energy of the falling block, the structural response of the impacted elements and the possibility of damage propagation within the building. An example is proposed to show the capabilities of the proposed approach. Keywords Risk analysis  Structural response  Building  Impact  Rock falls  Event tree  Vulnerability 1 Introduction The ability to identify the causes of particular natural events or to be able to predict the likelihood of occurrence of certain phenomena is a critical element in risk analyses and management processes (Danaher 1995; De Biagi et al. 2016). Probabilities associated with complex events are difficult to assess directly, and it is therefore often useful to decompose these events into components and to determine the overall event likelihood by assembling the components’ probabilities using standard probability calculus (Ezell et al. 2010). & Valerio De Biagi valerio.debiagi@polito.it 1 Department of Structural, Geotechnical and Building Engineering, Politecnico di Torino, C.so Duca degli Abruzzi 24, 10124 Turin, Italy 123 Nat Hazards DOI 10.1007/s11069-017-2906-3