journal article
Open Access
Jul 29, 2025
Insights on the experimental dynamic behaviour and energy losses of rocking blocks under free vibration
Abstract
Abstract
This study focuses on the experimental response of free-standing hard limestone blocks under free vibration. The campaign includes 120 tests, varying the block’s height-to-width ratio and considering multiple specimens to account for the aleatoric variability of the phenomenon. The study offers full reconstruction of the three-dimensional free-rocking motion, giving insights into the influence of unintended geometrical asymmetries, as well as material and interface irregularities on the response. The paper revisits the experimental estimation of the angular Coefficient of Restitution (CoR) through different methodologies based on the angular velocities, potential energy, and potential and frictional energies. The results are compared with Housner’s theoretical model. Due to the sensitive nature of rocking motion, a statistical approach is employed. The findings indicate that Housner’s model provides statistically accurate predictions of energy losses for blocks of medium-to-high slenderness (i.e. with aspect ratio
$$5 \le {H \mathord{\left/ {\vphantom {H B}} \right. \kern-\nulldelimiterspace} B} \le 10$$
while it becomes statistically inaccurate for very slender
$${H \mathord{\left/ {\vphantom {H B}} \right. \kern-\nulldelimiterspace} B} > 10$$
and very stocky
$${H \mathord{\left/ {\vphantom {H B}} \right. \kern-\nulldelimiterspace} B} < 5$$
blocks. Importantly, the study demonstrates that all three experimentally estimated CoRs statistically depend on the aspect ratio. Finally, the CoRs extracted from the potential energy and potential and frictional energies are found statistically dependent on the rocking amplitude, while the CoR extracted from the angular velocities show statistical independence. Overall, this study offers a pathway for more systematic analyses and improved predictions of energy losses during impacts.
This study focuses on the experimental response of free-standing hard limestone blocks under free vibration. The campaign includes 120 tests, varying the block’s height-to-width ratio and considering multiple specimens to account for the aleatoric variability of the phenomenon. The study offers full reconstruction of the three-dimensional free-rocking motion, giving insights into the influence of unintended geometrical asymmetries, as well as material and interface irregularities on the response. The paper revisits the experimental estimation of the angular Coefficient of Restitution (CoR) through different methodologies based on the angular velocities, potential energy, and potential and frictional energies. The results are compared with Housner’s theoretical model. Due to the sensitive nature of rocking motion, a statistical approach is employed. The findings indicate that Housner’s model provides statistically accurate predictions of energy losses for blocks of medium-to-high slenderness (i.e. with aspect ratio
$$5 \le {H \mathord{\left/ {\vphantom {H B}} \right. \kern-\nulldelimiterspace} B} \le 10$$
while it becomes statistically inaccurate for very slender
$${H \mathord{\left/ {\vphantom {H B}} \right. \kern-\nulldelimiterspace} B} > 10$$
and very stocky
$${H \mathord{\left/ {\vphantom {H B}} \right. \kern-\nulldelimiterspace} B} < 5$$
blocks. Importantly, the study demonstrates that all three experimentally estimated CoRs statistically depend on the aspect ratio. Finally, the CoRs extracted from the potential energy and potential and frictional energies are found statistically dependent on the rocking amplitude, while the CoR extracted from the angular velocities show statistical independence. Overall, this study offers a pathway for more systematic analyses and improved predictions of energy losses during impacts.
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Universidade do Minho
Cite This Article
Carla Colombo, Georgios Vlachakis, Anastasios I. Giouvanidis, et al. (2025). Insights on the experimental dynamic behaviour and energy losses of rocking blocks under free vibration. Bulletin of Earthquake Engineering. https://doi.org/10.1007/s10518-025-02224-8
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