Andrea Penna

Equivalent‐frame modeling is a common approach for assessing the seismic response of unreinforced masonry buildings, given its ability to capture the main failure mechanisms of masonry panels without the complexity of micro‐modeling techniques and the associated computational burdens. Typically, the equivalent‐frame strategy assumes that the out‐of‐plane response of walls is negligible, and the analysis focuses on the global building response governed by in‐plane panel mechanisms, reproduced through macroelements corresponding to vertical piers and horizontal spandrels. However, there might be cases where accounting for the coupled in‐plane and out‐of‐plane response is essential for a comprehensive description of the nonlinear behavior of the structure, even when local out‐of‐plane overturning mechanisms are inhibited through adequate structural details. For this reason, this paper presents a two‐node three‐dimensional macroelement that enhances the capabilities of the well‐established bidimensional formulations already implemented in computer programs, effectively and efficiently capturing the bidirectional axial‐flexural response in both elastic and nonlinear regimes. Two sectional integration approaches are proposed for the axial‐flexural response: a stripe formulation that optimizes computational efficiency through bidimensional analytical stress integrations, and a fiber discretization that allows versatility in defining constitutive laws. Three independent shear failure criteria are also implemented. The presentation of the macroelement is completed by an explicit demonstration of the energetic equivalence with a force‐based beam‐column element and by a detailed discussion on the inclusion of second‐order geometrical effects. The capabilities of the proposed macroelement are validated through the simulation of in‐plane and out‐of‐plane quasi‐static cyclic shear‐compression tests on masonry piers characterized by different masonry typologies, aspect ratios, and axial‐load ratios, demonstrating its accuracy and reliability. Moreover, numerical simulations carried out with the proposed formulation demonstrate the opportunity of including in‐ and out‐of‐plane interaction in numerical simulations.

Reliable displacement reconstruction from acceleration measurements is a persistent challenge in shaking-table testing because sensor noise and baseline drift can accumulate through numerical integration, biasing the inferred kinematic response. This study investigates and compares two complementary strategies for noise suppression and displacement estimation: (i) an optimized signal-processing workflow that combines band-limited integration with systematic parameter tuning, and (ii) a data-driven approach based on a Long Short-Term Memory (LSTM) neural network trained to map acceleration time histories to displacement. For the signal-processing workflow, filter parameters are selected through a multi-objective search using Latin Hypercube Sampling (LHS) to minimize reconstruction error against reference displacement measurements while limiting drift and spurious low-frequency content. For the LSTM approach, model hyperparameters are selected via Bayesian optimization to balance accuracy and generalization across excitation phases. The methods are assessed on shaking-table records from an instrumented experimental campaign, using displacement transducers as reference. Results indicate that both approaches substantially reduce integration drift and noise-induced artefacts compared with conventional fixed filtering and detrending. The optimized signal-processing pipeline provides a transparent, physically interpretable baseline with strong accuracy, whereas the LSTM model can achieve comparable performance with reduced need for manual tuning and improved robustness to non-stationary noise characteristics. The proposed framework offers a reproducible benchmark for computational-intelligence methods in vibration data post-processing and supports more reliable displacement estimation in experimental structural dynamics.

This paper investigates the seismic performance of a multi‐span masonry arch bridge using an advanced modeling approach based on the Distinct Element Method. Located in Italy and constructed of regular stone masonry, the bridge features three consecutive arch vaults with similar geometry. The three‐dimensional structure of the bridge is modeled using the commercial software 3DEC, as an assembly of discrete blocks including all its different structural and nonstructural components, such as piers, abutments, arch vaults, backing, spandrel walls, and backfill material. Masonry is represented as an assembly of rigid blocks connected by zero‐thickness interfaces, while the backfill is modeled as a continuum mesh based on plasticity theory. The bridge geometry and material properties are derived from available in‐situ surveys. Sensitivity analyses on the level of detail of the model are conducted to balance numerical accuracy and computational effort. A Maxwell damping model is employed to further reduce the time window required by dynamic simulations. Multi‐stripe nonlinear time‐history analyses are carried out, applying 200 three‐component ground‐motion records. The results are presented and discussed in terms of observed damage patterns and relationships between a case‐specific engineering demand parameter (EDP) and typical intensity measures. Thresholds for various performance levels (PLs), including usability preventing damage and global collapse, are defined based on a statistical correlation between the selected EDP and the damage observed in each time‐history analysis. Fragility curves are then generated for each of the considered PLs. Finally, model uncertainties are explored by introducing geometric variations in bridge components, highlighting their impact on the seismic vulnerability of the structure.

The behavior factor, which represents the force reduction that a structure would experience if its response was completely elastic compared with the seismic forces used for design, is defined in seismic design codes for common construction techniques and materials. A specific assessment is needed when novel construction materials are adopted. The lack of accurate structural performance estimations limits the use of green construction materials because building codes only allow the use of minimum values for the behavior factor. This research aims to verify the reliability of the proposed capacity-demand-based (CDB) method for the estimation of the force reduction factor and behavior factor, by comparison with other procedures such as demand-based, capacity-based and formula-based approaches. The main characteristic of the proposed approach is that the ductility-FRF curve is obtained numerically for the building natural period, instead of imposing an analytical FRF-ductility-period relationship. The advantage of the CDB-method is its efficiency from a computational point of view without restrictions concerning the construction material and structural typology. The results are compared in the case where dynamic analyses are performed for a three-dimensional (3D) building model (considered as a reference) and for an equivalent single-degree-of-freedom system which reduces the computation time. The CDB-method yields safe results compared with the N2 method, and it is consistent with a capacity-based approach applied to the 3D building model.

This paper explores the performance of different ground motion intensity measures in observational fragility studies, using damage data from the 2009 L’Aquila earthquake and leveraging physics-based numerical simulations (PBS) to calibrate fragility functions. The dataset included masonry and reinforced concrete (RC) buildings representative of the Italian building stock. The optimality (efficiency, proficiency and practicality) of a wide set of ground motion intensity measures was assessed with two methodologies introduced specifically in this work for such purpose. Results from both methodologies are consistent, highlighting the superior performance of average spectral acceleration, particularly for RC buildings. On the other hand, peak ground acceleration was found to perform well especially for masonry buildings. Among integral intensity measures, Housner intensity emerged as the most effective, while Arias intensity and cumulative absolute velocity displayed weaker correlations with damage. Although based on a single case study, these findings offer initial insights into the optimality of different intensity measures for observational seismic fragility studies and underscore the potential of PBS in enhancing region- and site-specific seismic risk assessments.