A continuous-time Markovian framework for performance-based earthquake engineering: integrated seismic risk and resilience assessment

Sat, 01 Aug 2026 00:00:00 +0000

Abstract

Assessing the seismic reliability of structural systems increasingly requires models that jointly represent damage evolution and recovery. Yet, the traditional PEER PBEE formulation does not capture the temporal dynamics of post-event repair, and modern reliability analyses often rely on scarce or uncertain recovery data, motivating the need for tractable methods. We reformulate the PEER PBEE framework using a continuous time Markov Chain (CTMC) Monte Carlo approach, which naturally models probabilistic transitions among damage and recovery states under time-invariant seismic hazards. Transition rates incorporate metamodel-based state-dependent fragility functions, as well as recovery processes, yielding a unified representation of hazard effects and system evolution. Leveraging the analytical properties of CTMCs, we compute steady-state performance statistics, such as mean time to failure and time spent in degraded states, and define a resilience index adapted from the classical reliability index β. The approach is tested on a simple yet representative example, showing that the CTMC-enhanced PBEE framework captures the temporal progression from damage to recovery in a computationally efficient and data-flexible manner.

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PEER PBEE Framework |

A continuous-time Markovian framework for performance-based earthquake engineering: integrated seismic risk and resilience assessment