Rocking podium isolation systems have gained significant research interest as a method of limiting seismic demands on superstructures and eliminating residual post‐earthquake drifts through self‐centring behaviour. However, while numerous models of varying complexity, including analytical, phenomenological, and physical formulations, have been proposed, implementing them for the analysis of rocking systems poses significant challenges. Analytical models, though simple and efficient, are difficult to integrate with detailed non‐linear superstructure response. In contrast, detailed numerical models are often computationally expensive due to the large number of elements required and the complex material and geometric non‐linearities they capture. Therefore, this study introduces and validates a novel simplified lateral spring formulation for rocking systems that balances ease of implementation with robust integration into non‐linear structural models, which may be utilized in both open‐source and commercial software. The proposed formulation enables accurate prediction of the distribution of maximum rocking displacement, a key engineering design parameter for rocking isolation systems. Model performance is validated through a planar numerical study against the benchmark Housner piecewise model, as well as through three‐dimensional simulations calibrated to experimental results from rocking‐column, rocking‐frame, and rocking‐podium studies. These investigations demonstrate the reliability of the proposed model while also showing improved motion‐specific predictive consistency relative to unenhanced rocking systems, highlighting the advantages of simplified modelling strategies for practical application to controlled rocking systems.
The rocking motion resembles the dynamic behaviour of various structures, and therefore, it is fundamental for many earthquake engineering applications. Despite its importance, modelling the rocking motion remains an open and challenging topic owing to its highly non‐linear and sensitive dynamic behaviour. Several rocking models have been proposed in the scientific literature, yet, in most cases, with limited or partial validation against experimental results. To this end, this study proposes a novel compliant contact model for simulating the response of block‐type rocking structures. The model is calibrated using data from an experimental campaign on dry‐joint interfaces and features a hysteretic, rate‐independent term that captures the joint‐closure tests. Moreover, the model includes a non‐linear viscous damping term calibrated to match energy dissipation for any angular coefficient of restitution value. Subsequently, the proposed model is validated against an extensive experimental campaign of more than 400 free‐rocking and forced‐rocking shaking‐table tests of limestone blocks with various geometries.
G. Vlachakis, Carla Colombo, S. Saloustros et al.· Earthquake Engineering &...· 0 citations
This study focuses on the capacity design of earthquake-resistant steel structures incorporating knee bracing systems, which serve as dissipative elements. It also presents the development and validation of a numerical model for simulating the behavior of these systems. The proposed model accurately captures the response of the fuse element by accounting for the interaction among axial force, shear, and bending moment, including second-order effects, while maintaining low computational demands. Model validation was performed through comparison with two independent experimental campaigns: (1) three-point bending tests on isolated fuses to characterize their local behavior, and (2) cyclic push-over tests on a full-scale, single-story frame to evaluate the global response of the system under lateral loading. Following the validation, an extensive parametric study was carried out via nonlinear static analyses on a multi-story, multi-bay steel frame with semi-rigid joints equipped with knee bracing systems. The investigation examined the influence of the axial forces in the fuses, the fuse cross-sectional typology, the joint rotational stiffness, and the lateral load distribution. The proposed model provides a practical and computationally efficient tool to support performance-based design and optimization of energy-dissipative devices in steel frame structures. The paper also provides a series of design recommendations for practitioners involved in designing earthquake-resistant structures with knee bracing systems.
R. Piazzon, F. Gusella, P. Zampieri· Bulletin of Earthquake Engin...· 0 citations
Underground railway systems provide a vital solution to urban spatial constraints, yet their construction in weak rock formations poses severe geotechnical challenges. Issues such as ground settlement and tunnel deformation under dynamic train loads can compromise structural integrity and operational safety. This study addresses these complexities by integrating a novel two-dimensional Finite Element model with a complementary viscoelastoplastic analytical framework. This dual approach effectively correlates global dynamic responses with localised continuum effects. A detailed parametric study reveals that axle loads exert a more pronounced effect on the track structure than the tunnel lining, increasing track displacement by 23.9% compared to only 12.3% for the lining. At high operational speeds, the numerical analysis identifies a stability plateau attributed to radiation damping, while the analytical model predicts a conservative upper-bound response. The analysis further demonstrates that increasing the Young’s modulus of the surrounding rock beyond 1000 MPa reduces vertical displacement to negligible levels. Geometrically, while circular cross-sections offer superior radial confinement, they exhibit an 18.5% increase in localised invert settlement compared to horseshoe profiles due to a punching shear mechanism. By establishing a mechanical hierarchy, this study provides engineers with a strategy to use analytical methods for safety baselines and numerical modelling for realistic serviceability limits.
Hafsa Farooq, Sanjay Nimbalkar· Geotechnical and Geological...· 0 citations
Reliable settlement predictions require a consistent representation of both soil behavior and evolving structural stiffness. While advanced soil models are available in geotechnical analyses, reinforced concrete structures are commonly represented by linear elastic elements, neglecting stiffness reductions caused by cracking and creep. This paper presents a practical workflow for incorporating load- and time-dependent structural stiffness into geotechnical settlement analyses. An equivalent linear elastic foundation slab stiffness is derived from nonlinear structural analyses considering cracking and creep and transferred construction-stage-wise into the geotechnical model. The methodology is validated against nonlinear reference analyses and investigated through parametric studies and a three-dimensional case study. The results show that isolated local cracks have little influence on the global equivalent stiffness. A pronounced reduction occurs only when cracked regions expand and progressively interconnect across the foundation slab, demonstrating that the spatial development of cracking is more relevant than its first occurrence. In the reference analysis, the cracked area increases from approximately 11% at the end of construction to 26% under the settlement load combination. Subsoil stiffness and reinforcement ratio show the strongest influence on stiffness evolution, while concrete strength and construction duration are less significant. The proposed methodology predicts the maximum differential settlement within approximately 3% of the nonlinear reference analysis, compared with approximately 6% using a constant 50% stiffness reduction. The presented results refer to building-load-induced settlements and the investigated structural and parameter ranges.
Efficient and practical seismic control of structures-particularly through isolation systems-remains a significant challenge due to high implementation costs and construction complexity. Moreover, their application in retrofitting existing structures often requires extensive modifications.To address these challenges, this study proposes a novel and cost-effective seismic control system, termed the Ridge-Isolated Tuned Mass Damper (RITMD), which integrates the advantages of tuned mass damping and seismic isolation. A reduced-order two-degree-of-freedom (2DOF) model is developed to capture the coupled dynamic behavior of the primary structure and the RITMD system. An optimization framework based on the Particle Swarm Optimization (PSO) algorithm is employed to determine the optimal tuning parameters. Subsequently, closed-form design expressions are obtained using nonlinear regression analysis to facilitate practical engineering applications .The proposed approach is further extended to three-dimensional structural systems, and its performance is evaluated through nonlinear time-history analyses under bidirectional earthquake excitations. The results demonstrate that the RITMD system significantly reduces structural responses, including displacements, accelerations, inter-story drifts, torsional demands, and their corresponding root-mean-square (RMS) values.Overall, the proposed system provides an efficient, practical, and versatile solution for enhancing the seismic performance of both new and existing structures.
This study develops two parallel seismic design frameworks—spectrum based iterative design (SBID) and spectrum based direct design (SBDD)—for free‐standing slender systems subjected to base excitation, founded on the principles of dimensional analysis. The formulation establishes an intrinsic relationship between the two approaches, demonstrating that they are fundamentally interlinked through consistent non‐dimensional parameters governing rocking response. Within the SBID framework, design is achieved through the combined and iterative use of stability coefficient spectra (SCS) and rocking spectra (RS), which together capture acceleration demand and rotational response. In contrast, the SBDD approach employs constant rotation spectra (CRS) to directly relate excitation intensity to a prescribed permissible rotation (implicitly ensuring stability). As such, SBDD obviates the need for iterations and enhances computational efficiency. The spectra are constructed for both idealized pulse‐type and recorded seismic excitations, illustrating their applicability across a range of loading scenarios. The methodology is further extended to bidirectional excitations, where coupled rotations about orthogonal axes are considered. It is shown that the proposed methodology can explicitly incorporate the effects of base flexibility and incidence angles of loading. Overall, the study provides a unified and efficient framework, especially for preliminary assessment and design of rocking systems.
Arghyadeep Banerjee, R. Roy· Earthquake Engineering &...· 0 citations