Developing time-dependent fragility curves for cube-armored breakwaters: stochastic modeling and experimental quantification

Cube-armored breakwaters progressively deteriorate under long-term water wave action due to the instability of armor layers. However, quantifying deterioration process remains challenging due to the probabilistic characteristics of damage. This study proposes a method for establishing time-dependent fragility curves that account for stochastic deterioration in armor units through theoretical modeling and experimental quantification. First, a Markov chain model is employed to describe the stochastic deterioration of cube-armored breakwaters with the introduction of conditional transition matrices. Subsequently, comprehensive experimental quantification involving 288 two-stage wave flume tests on cube-armored breakwaters with a 1:1.5 slope was conducted to derive general fragility curves and conditional transition matrices. The time-dependent fragility curves considering breakwater deterioration are then established by integrating initial damage with the temporal progression of deterioration via a Markov chain. Application of the framework highlights differing structural vulnerabilities under distinct wave regimes, showing progressive vulnerability with deterioration and heightened sensitivity at lower damage levels. Minor discrepancies of diverse modeling approaches indicate the practical viability of a homogeneous Markovian deterioration model. The proposed framework advances probabilistic damage assessment of coastal infrastructures, offering referable insights for maintenance strategies and resilience assessment.