Closed-form dimensionless median-capacity models for RC bare frame seismic fragility derivation

Machine-learning surrogate models offer a computationally efficient alternative to Incremental Dynamic Analysis (IDA) for seismic fragility derivation, but adoption is limited by opaque black-box behaviour and validation practices that rarely test generalisation beyond a model’s own training distribution. This study presents a transparent, factor-informed framework through derivation of closed-form median-capacity equations from 176 randomised RC frame archetypes undergoing a total of 11k NLTHA under both fixed-base and soil-structure interaction (SSI) conditions in ETABS. To ensure interpretability and scale independence, the equations use three dimensionless macro-parameters as inputs (normalised period T ¯ , stiffness ratio SR, and effective slenderness λ eff ) to predict fragility medians for damage states DS1–DS4. Seven black-box architectures were first trained as benchmarks to test whether these inputs carry enough signal to predict the medians. They achieve R 2 = 0.67–0.86 at DS1–DS2 (5-fold cross-validation) but only 0.17–0.44 by DS3. Four sparse-regression methods reproduce this accuracy in explicit closed-form equations, with the final equations selected by repeated cross-validation and then subjected to internal robustness checks. A targeted ablation shows that one additional global variable, foundation flexibility χ f , recovers much of the DS3–DS4 signal (R 2 gains of +0.178 and +0.290), indicating a limitation of the superstructure-only feature set rather than a physical ceiling. Assessed against 63 configurations from ten independent studies, R 2 reached 0.408 at DS1 but was near-zero or negative at DS2–DS4, against an inter-study coefficient of variation of 65–97%; disaggregation revealed that even nominally compatible sub-groups diverge sharply in transferability. These results show that published fragility behaviour is more heterogeneous across studies, sub-types, and functional forms than any compact formulation can fully capture, and that internal robustness alone does not guarantee external transferability. The framework nonetheless delivers practical, engineer-readable equations with an explicit, externally tested account of their limits.