PSI - Issue 78

Besim Yukselen et al. / Procedia Structural Integrity 78 (2026) 1943–1950

1945

where x̅ is the design vector representing the retrofitting configuration, f( x̅ ) is the vector of objective functions, and Ω is the feasible solution space defined by code-compliance constraints. A solution is considered feasible only if all structural members satisfy Eurocode 8 performance criteria, such that cj( x̅ )=0. The design vector x̅ encodes the presence or absence of RC jacketing for each beam and column, the inclusion of seismic gaps via infill-frame separation, and the selected retrofitting parameters, including jacket thicknesses drawn from discrete values (75, 100, 150, and 200 mm). To simplify the problem and reflect construction practice, all jacketed members in a solution are assumed to have the same thickness. RC jacketing uses 30 MPa concrete and 450 MPa steel reinforcement, with columns using four-sided jackets and beams using three-sided ones. Longitudinal reinforcement consists of 20 mm bars with a minimum ratio of 1%, while 10 mm stirrups spaced at 100 mm provide transverse confinement. Further details on the adopted retrofitting technique are provided in Yukselen et al. (2025a). The Non-dominated Sorting Genetic Algorithm II (NSGA-II) is used to solve the optimisation problem, offering a diverse set of Pareto-optimal solutions without requiring predefined weights for each objective. Infeasible solutions encountered during the evolutionary process are penalised and excluded, ensuring that all proposed retrofitting strategies satisfy structural code requirements. For each candidate solution, the four objective functions are evaluated. The cost is calculated by aggregating the quantities and unit prices of all required actions. At the same time, the environmental impact is quantified in terms of embodied carbon emissions during the material production stage (A1 – A3), in accordance with EN 15978 (European Committee for Standardization (CEN) 2011) . Equivalent CO₂ values are sourced from the EC3 database or regional manufacturers, and average values are used to maintain consistency and reduce computational effort. The unit costs and equivalent carbon emissions adopted for each action are summarised in Table 1.

Table 1: Adopted cost and equivalent CO 2 values per action for RC jacketing

Retrofitting technique

Cost (€) 5.12 2270 36.3 32.6 11.46 13.1 200.89

EI (kg,eqCO 2 )

Action

Unit

Dowel insertion Reinforcing steel Concrete casting

ea

0.37 801 299

tonnes

m 3 m 2 m 2 m 2 m 2

RC Jacketing

Scaffolding

0 *

Addition of plaster and paint infill demolishing Concrete cover removal

0.386 3.85

0 **

* The scaffolding is assumed to be reused, so its environmental impact (EI) is neglected. ** The EI of concrete cover removal is considered part of the infill demolition process, as the scale of the work makes it negligible.

To estimate the Expected Annual Loss (EAL) and downtime for each retrofitting design candidate, the nonlinear structural responses were obtained through a multiple-stripe analysis (MSA) approach. Ground motions were selected based on conditional spectra for twelve intensity levels corresponding to return periods ranging from 30 to 4000 years. Probabilistic seismic hazard analysis and disaggregation were performed using the ESHM20 (Danciu et al. 2021) via the OpenQuake engine (Silva et al. 2014), considering AvgSa in the 0.15 – 2.25 s period range. To reduce computational demands, nonlinear static pushover analyses were conducted in both principal directions, considering positive and negative loading in each case, using modal load patterns and scaled ground motions. The Capacity Spectrum Method (CSM) (Federal Emergency Management Agency 2005) was used to identify performance points; in cases of multiple performance points, the one minimising the absolute difference between the geometric mean spectral displacement (AvgS dk ) and the displacement at each performance point was selected, following Nettis et al. (2021). Collapse fragility curves were modelled as lognormal distributions fitted via the maximum likelihood method (Baker 2015), with total dispersion incorporating both record-to-record and epistemic uncertainties (Mucedero et al. 2022). Peak inter-story drift (PID) values were obtained at the performance point, while peak floor accelerations (PFA) were estimated using the formulation by (Merino et al. 2020; 2024), based on the derived drift. EAL was then computed using the FEMA P-58 (FEMA 2018) component-based assessment framework via the Pelicun tool (Zsarnoczay et al. 2025). The building inventory was defined through structural and architectural layouts, supplemented by informed assumptions, while the most suitable component fragilities and