PSI - Issue 78

Ataklti Gebrehiwet Gebrekidan et al. / Procedia Structural Integrity 78 (2026) 1665–1672

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OpenSeesPy to determine the pier drift ratio values at which pre-defined material strain limits were exceeded (Pinto et al., 2024). Although the analysis is deterministic, the dispersion at each damage state was assumed, in a simplified manner, as that provided by Perdomo and Monteiro (2020) for the same cross-section of the as-built configuration. 5. Application of the multi-criteria decision-making framework 5.1. Decision variable selection and estimation Decision Variable (DVs) define the baseline parameters that influence the preference of retrofit alternatives. They represent different economic, social, technical, and environmental aspects. According to Gebrekidan et al. (2025) and the specific context, the selected DVs, the estimation steps and assumptions are as follows: • C 1 - Direct Expected Annual Losses (D-EAL): The D-EAL are obtained based on the procedure described in the FEMA P-58 guidelines. Although the procedure was originally developed mainly to assess specific buildings, it has also been successfully used to assess bridge structures (see e.g. Ozsarac et al. (2023)). • C 2 - Mean Annual Frequency of Collapse (MAFC): The collapse fragility curve and the site hazard curve were integrated to provide the MAFC values (Couto et al., 2024). • C 3 - Installation Costs: The total cost of installation includes all materials and labour needed to complete the work. The unit cost of the activities was estimated using unit cost data available in A.N.A.S. S.p.A. (2024). • C 4 - Maintenance Costs: The cost of maintenance over the structure's 50-year lifespan was estimated following the rationale by Caterino et al. (2008) in combination with engineering judgment. • C 5 - Disruption of use during retrofitting: The duration of works is obtained by estimating the duration of retrofitting activities associated with traffic disruption. The structural intervention works duration for each phase was estimated using the data from Homewyse (2024) and engineering judgment. • C 6 - Need for Specialised Labour: The AHP approach was used to qualitatively rate the options according to the need for specialized labour. The Authors' judgment served as the foundation for the pairwise comparison. • C 7 - Foundation Intervention: The Authors' judgment and the AHP were used to determine the values. In this case, the judgement of the Authors was supplemented by estimates the increment of base-shear capacity of the retrofitted against the foundation capacity to horizontal loads (Rubini et al., 2024). • C 8 - Expected Annual Environmental Impacts (EAEIs): This variable is obtained based on the procedure described in (Clemett et al., 2022; Huang and Simonen, 2020). The EEIOLCA process was used to estimate the EIs of the repair activity, each cost component was disaggregated into the appropriateindustrial sectors and combined with the United States Environmentally Extended Input-Output (USEEIO) database. The EI metric is express as kilograms of carbon dioxide (kgCO 2 e). • C 9 - Installation EIs and C 10 - Maintenance EIs: The EEIOLCA process was used to estimate both the metrics. According to Caterino et al. (2008), the decision matrix (D) that has to be used within the MCDM framework is normalised since each DV may be expressed in different units. The DV normalised value ( r ij ) is calculated by dividing the value of a single retrofit by the square root of the sum of the squares of all values of the retrofitting in the same decision variable. For the analysed case study, the DV normalised values ( r ij ) are shown in Figure 4. 5.2. Determination of the weight vectors Two combinations have been considered: Comb1 and Comb2 for each seismic hazard level. Comb1 does not consider EI (thus, it includes the variables C1 to C7). Matrices associated with Comb2 consider, instead, also all the EI-related variables (i.e. C8, C9, and C10). For what concerns the weight vector values for each decision matrix, they were determined using the AHP approach and the Authors' judgment (Caterino et al., 2008). During the pairwise comparisons, several assumptions were made and in the low seismic hazard location, the seismic performance related DVs were given minor weight; however, in the high seismic hazard location, they became as important as the cost variables. Expenditure and duration of works were assumed, instead, to be of high importance with a slight preference given to maintenance costs. Additionally, EI-related DVs were considered almost as significant as cost-related