Refinements to the Silvestri’s theory for the evaluation of the seismic actions in flat-bottom silos containing grain-like material

The seismic behavior of flat-bottom silos containing grain-like material still presents strong uncertainties and current design codes tend to provide too conservative formulations for the estimation of the seismic actions. Over the years, some researchers focused on the dynamic behavior of such silos mainly through numerical investigations. Analytical formulations for the evaluation of the pressures exerted by the ensiled grain on the silo wall under seismic excitation were developed by Younan and Veletsos (J Struct Eng ASCE 124(1):62–70 1998) and, more recently, by Silvestri et al. (Bull Earthq Eng 10(5):1535–1560 2012). Experimental shaking-table tests were performed on silo specimens (Silvestri et al. EESD 2015, submitted), which showed good agreement with the Silvestri’s analytical formulations, even if some theoretical limits of validity were not satisfied. This has encouraged a complete revision and refinements of the theoretical framework, which is the object of this paper. In detail, the static and the dynamic actions exchanged between different grain portions and between the grain and the silo wall are idealised in a more physically consistent way. The analytical developments are carried out by means of simple free-body dynamic equilibrium equations. The refinements yield to a significant extension of the theoretical limits of validity and to a new set of analytical formulas for the wall pressures and for the wall shear and bending moment. A comparison of the analytical formulas with (i) the consolidated Janssen (Zeitschrift des vereines deutcher Ingenieure 39:1045–1049 1895) and Koenen (Centralblatt der Bauverwaltung 16:446–449 1896) theory for static design of silos and (ii) with the Eurocode 8 provisions for seismic design of silos and with the experimental results is also performed in order to (i) check the updated theoretical model in static conditions and (ii) verify the reliability of the different formulations in accelerated conditions, respectively. The refined theory confirms that the portion of ensiled material that interacts with the silo wall is significantly smaller than the effective mass suggested by Eurocode 8.