What this research found
After an earthquake, inspectors must decide which bridges to visit first. Reconstructing that decision for the magnitude 6.0 South Napa earthquake of 24 August 2014, K-Dense interpolated the USGS ShakeMap onto every California bridge, kept the 156 that experienced Modified Mercalli intensity VI or greater, and ran a 10,000-trial Monte Carlo simulation through FEMA Hazus fragility and restoration curves to estimate expected closure time weighted by daily traffic. Those 156 bridges carry 19,025,725 expected vehicle-days of lost function, of which the 20 highest-ranked structures account for 81.29%.
- Inspection effort concentrates sharply. The top 20 of the 156 exposed bridges — about 13% of them — capture 81.29% of expected network disruption (15,465,162 of 19,025,725 vehicle-days), while the top 5 alone carry 45.01% and the top 50 reach 96.97%.
- Damage from a magnitude 6.0 event is limited but not negligible. Averaged over the 156 bridges the probability of no damage is 0.806, with 0.030 for extensive and 0.024 for complete damage, implying roughly 4.7 extensively and 3.8 completely damaged structures.
- Expected closure times span three orders of magnitude, from 0.001 days to 150.5 days, with a median of 1.74 days and a network total of 1,242 bridge-days.
- Two different mechanisms drive the ranking. The top-ranked structure combines 45,000 daily vehicles with about 80 expected closure days, whereas another enters the top five almost entirely on traffic exposure — 133,000 daily vehicles despite only 6.56 expected closure days.
- The priority list is geographically tight, with 18 of the top 20 bridges in Napa County and the other two in Solano County. Most exposed structures also predate modern seismic design: 101 of the 156 were built before 1975.
How it was done
The reviewed USGS ShakeMap Atlas grid for the event — 168,633 cells at roughly 1 km spacing — was bilinearly interpolated to each bridge's coordinates for peak ground acceleration, spectral acceleration at 0.3 and 1.0 seconds, shaking intensity, and their lognormal dispersions. The 2014 Federal Highway Administration National Bridge Inventory for California was cleaned from 25,406 records to 24,880, of which 8,991 fell inside the ShakeMap footprint and 156 saw intensity VI or above. Each of those was mapped to one of the 28 FEMA Hazus highway-bridge classes from material, span configuration, structure length, and year built, with fragility medians adjusted for deck skew. A 10,000-trial Monte Carlo per bridge sampled both ground-motion demand and structural capacity to produce damage-state probabilities, which were converted to expected downtime using Hazus restoration times of 0.6 to 230 days and multiplied by average daily traffic. The work was written up as a 19-page paper with 39 references.
Data sources
- USGS ShakeMap Atlas — reviewed ground-motion field for the 2014 South Napa earthquake, 168,633 grid cells with per-cell uncertainties
- FHWA National Bridge Inventory, 2014 California file — 25,406 raw records cleaned to 24,880
- FEMA Hazus 6.1 — lognormal fragility curves and restoration times for 28 highway-bridge classes
- 39 DOI-verified references spanning seismic fragility, ShakeMap uncertainty, liquefaction, and transport network resilience
Limitations
The fragility model represents ground shaking only, omitting liquefaction, lateral spreading, and seismically induced slope failure, which likely under-ranks bridges founded on soft or saturated ground. Weighting each bridge by its own traffic count also ignores network topology, over-stating the impact of busy crossings with good detours and under-stating that of low-traffic but sole-access links.
Figures from this analysis
How this research was produced
K-Dense Web planned and ran this engineering investigation end to end — gathering the sources, carrying out the analysis, producing the figures, and drafting the report. The full session transcript, including every intermediate step, is available to view.
