Principal Surface Fault Rupture Hazard: Moving Beyond Aggregate Displacement Metrics
Structures crossing active faults are subjected to permanent ground deformation that can impose severe demands on infrastructure. Although probabilistic fault displacement hazard analysis (PFDHA) has advanced considerably, existing principal fault displacement models use aggregate displacement, implicitly assuming that overlapping rupture strands contribute simultaneously to site demand. This assumption is suitable for regional hazard characterization but does not represent finite structural dimensions, where only a subset of ruptures may intersect a structure. This study presents a probabilistic framework that reformulates aggregate principal displacement into a rupture-level representation for infrastructure-specific hazard assessment. Using the Fault Displacement Hazard Initiative (FDHI) database of 75 surface-rupturing earthquakes, principal rupture strands are reconstructed from mapped rupture geometries and displacement observations using event- and segment-based coordinate systems. The framework models three quantities: (1) the number of overlapping principal ruptures, (2) partitioning of aggregate displacement among individual rupture strands while preserving the aggregate displacement budget, and (3) the spatial distribution of rupture strands relative to the primary fault trace. These components are integrated into a generalized PFDHA formulation accounting for earthquake magnitude, style of faulting, rupture curvature, structural footprint, and fault-trace location uncertainty. Benchmark fault-crossing applications demonstrate the framework's ability to estimate the probability that individual rupture strands intersect a structure and the associated displacement demand. The framework provides a physically consistent extension of aggregate-based models and a basis for infrastructure-specific PFDHA that explicitly accounts for rupture geometry and finite crossing dimensions.