Markovian modeling of seismic damage accumulation

Analysis of civil structures at the scale of life-cycle requires stochastic modeling of degradation. Phenomena causing structures to degrade are typically categorized as aging and point-in-time overloads. Earthquake effects are the members of the latter category this study deals with in the framework of performance-based earthquake engineering (PBEE). The focus is structural seismic reliability, which requires modeling of the stochastic process describing damage progression, because of subsequent events, over time. The presented study explicitly addresses this issue via a Markov-chain-based approach, which is able to account for the change in seismic response of damaged structures (i.e. state-dependent seismic fragility) as well as uncertainty in occurrence and intensity of earthquakes (i.e. seismic hazard). The state-dependent vulnerability issue arises when the seismic hysteretic response is evolutionary and/or when the damage measure employed is such that the degradation increment probabilistically depends on the conditions of the structure at the time of the shock. The framework set up takes advantage also of the hypotheses of classical probabilistic seismic hazard analysis, allowing to separate the modeling of the process of occurrence of seismic shocks and the effect they produce on the structure. It is also discussed how the reliability assessment, which is in closed-form, may be virtually extended to describe a generic age- and state-dependent degradation process (e.g. including aging and/or when aftershock risk is of interest). Illustrative applications show the options to calibrate the model and its potential in the context of PBEE.