The fate of cities under natural hazards depends not only on hazard intensity but also on the coupling of structural damage, a collective process that remains poorly understood. Here we show that urban structural damage exhibits phase-transition phenomena. As hazard intensity increases, the system can shift abruptly from a largely safe to a largely damaged state, analogous to a discontinuous phase transition in statistical physics. Higher diversity in the building portfolio smooths this transition, but multiscale damage clustering traps the system in a highly volatile regime that suppresses the emergence of predictable Gaussian statistics. The observed phenomenological patterns are interpreted through an effective random-field Ising model, with its key parameters translated into tangible engineering variables such as hazard demand, structural diversity, and modeling uncertainty. These insights establish a phase-aware description of collective damage, revealing that common engineering simplifications can distort the inherent phase of real urban portfolios. Critically, such phase distortions can substantially bias hazard loss estimates, producing relative errors of up to 50% in exceedance probabilities under moderate earthquakes---equivalent to a several-fold gap in anticipated repair costs. The phase-aware description turns the collective behavior of civil infrastructure damage into actionable diagnostics for urban risk assessment and planning.

翻译：暂无翻译