Rocking response of inverted pendulum structures under blast loading

Abstract

We investigate the dynamics of inverted pendulum structures under fast-dynamic excitations arising from an explosion. We model blast actions using established empirical models and best-fit interpolations of existing experimental tests. We focus attention on pure rocking response mechanisms. We present moment balance equations and overturning conditions. Inspired by previous works in the frame of earthquake engineering, we derive new analytical, closed-form solutions for the rocking response and the overturning domain of slender blocks due to explosions. The analytical findings and assumptions are validated through existing experimental tests and detailed three-dimensional numerical simulations, which consider the full interaction between the blast waves and the structure. We show that unilateral rocking response and overturning are predominant mechanisms compared to sliding and uplifting. Finally, we develop design charts to be used as a straightforward decision making tool for determining the critical stand-off distance between the explosive source and the target in order to prevent overturning. Our model can be easily applied for the design of protective devices to preserve artefacts, secure buildings and humans, as well as for devising energy absorbing systems based on rocking.

Resistance of museum artefacts against blast loading

“…Drag and diffraction phenomena are neglected. The effects of induced ground shocks [24,25] is discussed in Appendix B and an exhaustive discussion and validation can be found in [6]. In particular, it is shown that the minimum distance that has to be assured between the explosive source and the target, such that toppling is avoided, is in good agreement and on the safety side with the one determined by the full and detailed numerical model.…”

“…These parameters are functions of the distance R and the explosive weight (conventionally expressed in TNT, trinitrotoluene, equivalent). Herein we consider only the positive phase of the blast wave (safety approach, see [6]).…”

“…For a more detailed description of the fluid-structure interaction phenomena and their modelling, we refer to [21,22,23,20]. Further details can also be found in [6].…”

“…The rocking and overturning of artefacts is investigated using the well-established model of the inverted pendulum structures [1,2,3,4,5]. An analytical approach to compute the rocking response and the overturning domain of slender, rectangular blocks, formerly developed by the authors [6], is here adopted. In particular, moment balance equations and overturning conditions are used to determine the critical (minimum) standoff distance between the source and the target to prevent toppling.…”

“…Section 3.2 focuses on the overturning response mechanism of rectangular, slender blocks subjected to an explosion. We present an analytical approach, formerly developed by the authors [6], to be used as a straightforward engineering tool to derive the critical stand-off distance between the target and the explosive source to avoid toppling. In Section 3.3, the analytical model is applied to museum artefacts and some emblematic examples of existing statues are presented.…”