Series of semi-Markov processes to model infrastructure resilience under multihazards

Civil infrastructure systems are subjected to multiple hazards, including natural and anthropogenic, that disrupt their function or the level of service offered. Estimating the function recovery of these systems (or how soon normalcy of operations will be restored) when subjected to repeated hazard events by considering the inter-event dependencies is an important problem in multihazard infrastructure resilience. However, this problem has been less addressed in the field. This paper proposes a series of semi-Markov processes model to capture the inter-event dependencies in infrastructure recovery when subjected to successive hazard events. Recovery after each new hazard event is represented by a unique semi-Markov process that models the reduced recovery rates and the increased recovery times caused by the system's incomplete recovery from the preceding event. Two novel formulations of the inter-event dependency modeling, namely Maximal Effects Dependency (considers the worst impact of two successive hazard events) and Cumulative Effects Dependency (considers the aggregated impacts of two successive hazard events), are proposed and discussed. The model is demonstrated by considering the following applications: Three-state system subjected to deterministic and random occurrences of identical hazard events; and Multihazard resilience of a building in Charleston, SC, considering earthquake and hurricane hazards. Results indicate that considering inter-event dependencies in recovery modeling can lead to lesser-predicted resilience, thereby affecting resilience-based decision-making.