PSI - Issue 78

Alessandro Contento et al. / Procedia Structural Integrity 78 (2026) 1975–1982

1978

although more expensive and complex, provide valuable insights under realistic conditions, including interaction with the structural frame and real-life operational scenarios. Notably, studies such as those by Frost and Cacciola (2023) have used forced rocking tests to calibrate nonlinear models based on the Hunt and Crossley (1975) impact model, highlighting the importance of detailed experimental data. Additionally, the development of advanced sensors and in situ monitoring technologies enables the collection of data on NSE behavior during actual seismic events, supporting

a continuous model validation approach and refinement of predictive methods. 3. Modeling the dynamic behavior of isolated blocks and base-block interaction 3.1. Seismic isolation strategies for NSEs

Seismic isolation is one of the most effective strategies for protecting NSEs from damage during seismic events. This technique is based on inserting isolating devices at the base of the elements, such as elastomeric bearings or innovative rolling-ball systems, which attenuate the accelerations transmitted from the building to the component, thereby reducing induced stresses. Elastomeric bearings, available in various types, including natural or synthetic rubber bearings with steel inserts and high-damping rubber bearings (HDRBs), offer different characteristics in terms of stiffness, energy dissipation capacity, and durability. The choice of isolator depends on multiple factors, such as the weight of the element to be protected, the expected seismic hazard level, and the required degree of isolation. Innovation in the field of isolation devices has led to the development of low-cost, easy-to-install solutions, such as the system proposed by Di Martino et al. (2023), which uses rolling balls to allow smooth and controlled motion, reducing the energy transmitted to the block. When properly calibrated and integrated with active control systems, these devices can significantly limit or prevent rocking phenomena, enhancing the safety of NSEs. Furthermore, seismic isolation not only mitigates transmitted forces but also helps reduce uplift and overturning effects - phenomena that are particularly critical for rigid blocks and culturally or historically valuable objects. 3.2. Basic models for isolation analysis and dynamic behavior The analysis of the seismic behavior of isolated elements relies on models that describe the interaction between the block, the isolation system, and ground motion. Traditionally, the isolation base has been modeled as a rigid body, with instantaneous impacts characterized by restitution coefficients to represent contact and rebound phenomena during rocking. This approach, used in many classical studies (Caliò & Marletta, 2003; Contento & Di Egidio, 2009), simplifies the analysis but does not always faithfully represent the real behavior of the isolator. Some studies have introduced compliant models, which consider the base as a deformable element with nonlinear behavior. In particular, the Hunt and Crossley impact model (1975) has been adopted to describe the dynamic interaction between the block and the isolating base, incorporating energy dissipation and nonlinear response to impacts. Frost and Cacciola (2023, 2024) developed models based on this theory, validating them experimentally through forced harmonic tests and demonstrating their improved accuracy. These more advanced models also allow for consideration of mass and stiffness eccentricities and can be integrated with active control systems, paving the way for innovative engineering solutions to protect rigid and sensitive elements. 3.3. Active control systems integrated with base isolation In recent years, beyond traditional passive isolation systems, there has been growing interest in integrating active or semi-active control systems with base isolation. These systems aim not only to dissipate seismic energy but also to proactively intervene to prevent or delay overturning of rigid elements. Several studies (Di Egidio et al., 2020; Simoneschi et al., 2018; Venanzi et al., 2020) have demonstrated that adding active control using linear control algorithms - such as pole placement (PP) and linear quadratic regulator (LQR) - can significantly improve the stability of elements during seismic events. The effectiveness of such systems has been highlighted in sensitive fields such as the protection of artworks and delicate electronic equipment, where reducing motion and acceleration translates into a lower likelihood of damage. However, the practical implementation of active systems requires proper integration with the isolation system and a careful assessment of cost-benefit ratios.