Building bridges between disciplines: a generalized mathematical framework for talking quantitative risk assessment

Different perspectives of risk and approaches to risk assessment exist, which complicate communication, methodological advances and management across disciplines. To help building bridges, we have developed, tested and applied a generalized mathematical framework for risk assessment in a unique community effort, involving researchers from various fields. We present the derivation of the risk equation, which is tailored to civil and environmental engineering risk assessment of spatially-distributed and dynamic systems. We start off with a general framing and then refine individual parts of the equation as much as needed. The individual terms of the unified risk equation explicitly relate to concepts of frequency, intensity, duration, exposure, vulnerability and asset worth. Our approach takes a new perspective on facilitating communication across disciplines by exploiting mathematical formalism: filling our equation with life enforces a clear definition of the relevant terms and thereby helps in ‘translating’ between different terminology in the involved disciplines. For the sake of clarity and accessibility, we keep the framework simple in terms of additive effects and neglect failure cascades or nonlinear multi-hazard impact functions. Hence, while the framework is not designed to provide a one-fits-all-mathematical solution, it can help carve out the specific properties of a system that potentially violate these assumptions, and this is very valuable when talking risk assessment across disciplines. We demonstrate the utility of our proposed framework with ten selected examples from various domains, ranging from groundwater protection through seismic risk assessment to reliability analysis of critical infrastructure. The structured discussion between all involved researchers has greatly improved mutual understanding, which makes us confident that the proposed framework can serve as a catalyst for interdisciplinary advances in communicating and treating risk.