PSI - Issue 70

Edavalath Nadeem et al. / Procedia Structural Integrity 70 (2025) 19–26

22

km, reflecting diverse rupture scenarios and propagation paths. The response spectra of the selected ground motion records, illustrating their spectral acceleration characteristics across a range of periods, are presented in Figure 2.

Fig. 2. Response spectrum of selected ground motion records with their mean spectra.

3. Definitions of Damage States and Corresponding Analysis Outcomes A nonlinear time history analysis (NLTHA) is performed on the adopted RC bridge model to assess its seismic performance. The structure exhibits a fundamental mode period of 0.74 seconds. Given that bridge columns are typically the most seismically vulnerable components, both µ ϕ -m and µ ϕ -r are selected as the EDPs, as discussed in the preceding section. The µ ϕ -m is defined as the ratio of the maximum attained nonlinear curvature to the yield curvature ( ϕ y ), representing the peak inelastic deformation capacity. Conversely, the µ ϕ -r is defined as the ratio of the residual curvature, recorded after seismic shaking, to the yield curvature, providing insight into the permanent damage and self-centering capability of the column. Using a strain-based bilinear approximation method, the ϕ y of the RC bridge column is determined to be 1.32 × 10⁻³ m⁻¹ , with the corresponding yield moment ( M y ) calculated as 23,684.84 kNm. Structural performance is categorized into four distinct damage states (DS), as outlined in the Caltrans Seismic Design Criteria (Caltrans, 2019). DS1 denotes slight damage, DS2 moderate damage, DS3 extensive damage, and DS4 corresponds to collapse. These damage states represent a progressive degradation of structural integrity. Specifically, DS1 involves minor cracking and superficial spalling of the concrete cover. DS2 indicates more pronounced shear cracking and the initial exposure of the core reinforcement. DS3 corresponds to the yielding of longitudinal reinforcement, signifying the onset of significant inelastic behaviour. DS4 represents a near-collapse condition, characterized by crushing of core concrete, buckling of longitudinal bars, and loss of confinement, often accompanied by substantial residual deformations. Each damage state is associated with a corresponding maximum column curvature ductility threshold. These thresholds, adopted from prior studies (Ramanathan, 2012; Mangalathu, 2017; Srivastava et al ., 2022; Srivastava et al ., 2024), are set as 1.0, 4.0, 8.0, and 12.0 for DS1 through DS4, respectively. These ductility limits are subsequently utilized as the median capacity values of µ ϕ -m for developing the component fragility curves. 4. Interrelation among EDPs Based on the results of the nonlinear time history analysis, the relationship between the µ ϕ -m and µ ϕ -r are established, as illustrated in Figure 3. µ − = 1.58( µ − )−3.42 (1) Table 1. DS values of µ ϕ -m and µ ϕ -r µ ϕ -m µ ϕ -r µ ϕ -m µ ϕ -r DS1 1 0.03 DS3 8 1.48 DS2 4 0.39 DS4 12 3.23 The derived regression equation, applicable for µ ϕ -m values up to 20, effectively captures the observed trend within this range. Beyond this threshold, the reduced number of data points introduces increased uncertainty, limiting the reliability of extrapolated predictions. The goodness-of-fit for the developed model is evaluated using the coefficient of determination ( R² ), with a value of 0.82, indicating a strong correlation between the two EDPs. Given the established literature and the availability of various damage states (DSs), µ ϕ -m is adopted as the primary EDP. Using the developed