Identifying Thresholds of Resilience Dimensions for Alternative Regimes of Flood-Control Facilities: A Conceptual Framework

Climate change and aging infrastructure are undermining the resilience of urban flood management systems, reducing their reliability and increasing the likelihood of systemic failure that may culminate in regime shifts. This study develops a conceptual and practitioner-oriented screening framework based on a quantitative mathematical model to examine facility-level resilience and identify threshold conditions that may trigger regime transitions under external disturbances and varying pre-disturbance facility conditions. The framework adopts the composite sigmoid function (CSF) to capture nonlinear performance trajectories of infrastructure systems. Building on this model, this study extends its application by developing a parameterization scheme directly linked to four resilience dimensions: robustness, redundancy, rapidity, and resourcefulness (4Rs), which can be derived from field investigations or expert surveys. The normalized 4R scores are mapped to the CSF parameters, thereby converting static resilience assessment results into degradation and recovery curves. To search for threshold conditions, a parametric analysis was conducted by systematically varying the 4R values across their defined ranges. Rather than indicating a single universal threshold value, the results revealed critical threshold regions formed by specific combinations of the 4R dimensions. Lower robustness reduced the initial performance buffer, and low redundancy accelerated and extended performance degradation, while insufficient rapidity and resourcefulness delayed or limited recovery, increasing the likelihood of transition into an alternative degraded regime. For example, even when R1 and R2 were set to relatively high normalized values of 0.90, and R3 was set to its maximum value of 1.00, full recovery could not be achieved when R4 decreased below approximately 0.20. An illustrative application was conducted using preliminary 4R assessment results for flood-control facilities in three districts of Seoul, Korea. The model-derived trajectories were qualitatively compared with reported historical vulnerability patterns. While this comparison was intended as a contextual assessment rather than an event-specific empirical validation, our framework supports comparative, scenario-based screening of potentially vulnerable facilities for preliminary maintenance and investment prioritization.