PSI - Issue 78

Andrea Nettis et al. / Procedia Structural Integrity 78 (2026) 1412–1419

1415

Cloud analysis represents a computationally efficient alternative to the multi-stripe fragility analysis, primarily because it does not require scaling of input ground motions and can be applied directly using large suites of natural records. Nevertheless, the cloud analysis may introduce inaccuracies in the estimation of fragility functions due to the reliance on pre-defined functional forms, which may not adequately capture the actual trend of EDP as a function of the IM for the specific structural system under investigation. In addition, the homoscedasticity assumption, i.e., constant dispersion across IM levels, can be inaccurate since in some structures the dispersion in seismic demand due record-to-record variability increases by increasing the IM value. Therefore, while the cloud method is more efficient and suitable for preliminary fragility assessments or parametric analyses, the multi-stripe method is appropriate for detailed risk assessment where high accuracy is required. In bridge-level loss assessment, fragility functions are typically derived from a series of simulations capturing the structural response to seismic excitation across a range of IM levels. The most rigorous methodology involves conducting NLTHA of a detailed structural model subjected to the ground motion records (Baker, 2015; Jalayer et al., 2017b). However, as noted in the Introduction, the application of NLTHA across multiple tentative design configurations in a loss- or risk-based design context is computationally prohibitive. This limitation underscores the necessity of employing approximate fragility analysis methodologies that represent a trade-off compromise between efficiency and accuracy. The simplified loss assessment strategy adopted in this study is based on a nonlinear static analysis procedure employing displacement-based assessment (DBA) approach (Gentile et al., 2020; Şadan et al., 2013). These methods are aimed to compute the equivalent SDoF force–displacement response of the bridge under investigation. DBA involves a series of analytical calculations that can be implemented by using computationally efficient programming routines. DBA algorithms adopt a simplified modelling strategy in which the bridge is idealised as an equivalent elastic beam with inelastic supports. These supports are assigned force–displacement relationships representative of the substructure components (i.e. the piers and the abutments) as equivalent cantilevers, including the contribution of bearings, shear keys, and foundations. The equivalent SDoF force–displacement response, referred to as the displacement-based pseudo-pushover in (Gentile et al., 2020) and herein, is obtained through iterative equivalent elastic (eigenvalue or static) analyses with updated secant stiffness of the supports, progressively increasing the displacement at a control node (Gentile et al., 2020; Nettis et al., 2023). As a simplified alternative of NLTHA, the capacity spectrum method (CSM) is applied for computing the seismic demand of the bridge under a given seismic excitation represented by an elastic response spectrum (Nettis et al., 2021). The hysteretic energy dissipation associated with the cyclic response of the structure is accounted for using spectral reduction factors and equivalent viscous damping coefficients. This approach enables the direct estimation of seismic demand in terms of the equivalent SDoF displacement. Nevertheless, additional EDPs can be computed by tracking their evolution as the effective displacement increases throughout the pseudo-pushover analysis. Previous applications show that the combined DBA and CSM approach yields more accurate results for bridges whose seismic response is predominantly governed by the first mode of vibration and for which inelastic deformation does not significantly alter the elastic modal shape. The primary sources of approximation in this simplified approach coupling DBA and CSM stem from simplified analytical formulations used to compute the equivalent cantilever response of bridge piers, the simplified model adopted in the algorithm, as well as the assumptions embedded in the equivalent viscous damping models. The CSM enables the derivation of cloud or multi-stripe EDP-vs-IM observations, which can then be used for fragility analysis. 3. Parametric analysis 3.1. Case-study bridge realisations The dataset used for the parametric analysis comprises 18 realisations of straight, continuous-deck RC bridges with single-column piers (Gentile et al., 2020). In the transverse direction, pinned connections are assumed between the 2.3. Seismic analysis strategies