PSI - Issue 78

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

1413

1. Introduction Earthquake loss assessment entails the quantification of losses (e.g., fatalities, financial costs, or functional downtime) associated with a given structural system. The most widely adopted framework for this purpose is Performance-Based Earthquake Engineering (PBEE). Loss assessment for existing structures involves a highly non linear and uncertain calculations, as it depends on several interrelated components, including the fragility assessment, which often requires non-linear time-history analysis (NLTHA). In contrast, loss-based design focuses on achieving a predefined acceptable level of loss for a structure to be built under a given seismic hazard scenario. Due to the non invertible nature of loss assessment, loss- or risk-based design approaches typically rely on iterative procedures, wherein successive trial designs are evaluated and adjusted until the desired performance criterion is achieved. These iterative schemes, while powerful, tend to be computationally intensive and time-consuming, making them more suitable for advanced stages of design rather than early-stage or conceptual design. To facilitate preliminary design, direct methods (e.g., (Gentile and Calvi, 2023)) have been proposed. These approaches aim to formulate explicit mathematical relationships linking decision variables (e.g., expected loss) to key design parameters. However, due to the inherent complexity of loss estimation, these formulations often involve a trade-off between methodological simplicity and solution accuracy (Gentile and Galasso, 2022). As an initial step toward enabling future, non-iterative, loss-based design of bridge structures, this study investigates the accuracy of a simplified loss-assessment methodology based on displacement-based assessment algorithms and the capacity spectrum method. The analysis is performed on a dataset comprising 18 case-study continuous-deck reinforced concrete (RC) bridges with single column piers, assumed to be located in a region of high seismicity. For each bridge, the expected annual loss (EAL) is estimated using the simplified approach and NLTHA, applied within cloud and multi-stripe fragility analysis methods. 2. Methodology 2.1. Loss assessment The estimation of expected losses for a given structure can be carried out using either a system-level approach, recommended by (Hazus-MH, 2011) and applied to bridges in (Nettis et al., 2025; Zanini et al., 2017) or through a more detailed component-by-component methodology, as described in (Federal Emergency Management Agency (FEMA), 2012) and implemented for bridges in (Perdomo et al., 2022). The component-based approach offers higher accuracy, while demands detailed input data and advanced calculations. In contrast, the system-level approach is more streamlined and has been effectively integrated into existing loss-based design frameworks (Gentile and Calvi, 2023; Rubini et al., 2025; Suarez et al., 2024). Accordingly, the present study adopts the system-level approach for loss assessment. This analysis focuses on direct economic losses associated with the repair or replacement of bridges. Indirect losses are not considered in the current work. The expected annual loss (EAL) is computed following Equation (1), where ( ) is the expected loss ratio, indicating a vulnerability function, and ( ) represents the seismic hazard curve, defined as the mean annual frequency of exceeding levels of a selected intensity measure (IM). The expected loss ratio functions ( ) quantify direct economic losses conditioned on a given IM. These functions are computed using Equation (2), where ( ) represents the probability that the structure being in damage state (DS) given an IM level and denotes the damage-to-loss ratio for that DS. The latter expresses the expected loss corresponding to a given DS normalised by the total cost of demolition and reconstruction. ( ) is derived from fragility functions ( | ) through Equation (3), where is the number of considered DSs. Fragility functions estimate the probability of reaching or exceeding a specific DS as a function of seismic IM, and can be developed using various methodologies available in the literature.