•A quantitative method to study spatial-temporal evolution of fire-related domino effects is developed.•The temporal change of escalation vectors in domino propagation is investigated.•The burnout state of process units is introduced to carry out a dynamic risk assessment of domino effects.•High-risk units are identified by a posterior probabilities analysis, and are validated by graph theory. Domino effects are typically high impact low probability (HILP) accidents, whereby escalation effects triggered by fires are most frequent. The evolution of fire-related domino effects depends on synergistic effects and the performance of safety barriers, but those factors usually are time-dependent. In the present study, a methodology is developed to provide more accurate probabilities related to domino effects, by considering the temporal evolution of escalation vectors caused by time-dependent factors. The Dynamic Bayesian Network (DBN) approach is applied both to model the spatial-temporal propagation pattern of domino effects and to estimate the dynamic probabilities of domino chains. The methodology is illustrated with a case study to determine the dynamic aspect of the probabilities of domino effects considering the impact of add-on (active and passive) safety barriers and taking into account synergistic effects. The critical units for facilitating domino propagation have been identified by the analysis of posterior probabilities, and further validated using graph theory. The methodology will be helpful for risk management and emergency decision-making of any chemical industrial area.