Generalised Kinematic Single-Impact and Multi-Impact Models for Rocking Structures

Abstract

The rocking motion is fundamental in earthquake engineering, as it reflects the dynamic behaviour of many structural systems. However, simulating the impacts during rocking motion remains a challenging topic, as they occur in a very short time, generate high impulsive forces, cause sudden changes in velocities and result in rapid energy losses. Several non-smooth and continuous impact models have been proposed in the literature to describe such complex phenomena, yet the notable experimental variability of the angular coefficient of restitution is not adequately interpreted. This study introduces novel single-impact and multi-impact models tailored to the dynamic peculiarities of rocking motion. The proposed single-impact model effectively captures a wide range of impact conditions of the contact interface and demonstrates notable versatility as it uniquely combines the strengths and features of available models in the rocking literature. Subsequently, the model is extended into a multi-impact model, enabling the effective simulation of consecutive impacts and possible free-flights. This enhancement increases the model's efficacy and broadens its scope of application. Importantly, the proposed models are calibrated and validated against an extensive experimental campaign of 120 free rocking tests on blocks with various aspect ratios, demonstrating enhanced predictive capabilities. Finally, a series of comparative numerical analyses reveals the influence of the proposed impact models on the dynamic response of rocking blocks.