Skew Adjustment Factors for Fragilities of California Box-Girder Bridges Subjected to Near-Fault and Far-Field Ground Motions

Past reconnaissance studies revealed that bridges close to active faults are more susceptible to damage and more than 60% of the bridges in California are skewed. To assess the combined effect of near-fault ground motions and skewness, this paper evaluates the seismic vulnerability of skewed concrete box-girder bridges in California subjected to near-fault and far-field ground motions. The relative risk of skewness and fault-location on the bridges is evaluated by developing fragility curves of bridge components and system accounting for the material, geometric, and structural uncertainties. It is noted that the skewness and bridge site close to active faults make bridges more vulnerable, and the existing modification factor in HAZUS cannot capture the variation in the median value of the fragilities appropriately. A new set of fragility adjustment factors for skewness coupled with the effect of fault location is suggested in this paper.

💡 Research Summary

This paper investigates the seismic vulnerability of skewed concrete box‑girder bridges in California, focusing on the combined effects of near‑fault (NF) and far‑field (FF) ground motions. Recognizing that more than 60 % of California bridges are skewed and that roughly three‑quarters of them lie close to active faults, the authors aim to quantify how skew angle and fault proximity together influence bridge fragility.

A comprehensive suite of ground motions is assembled: 120 pairs of recorded NF motions (Dabaghi 2014) and 120 pairs of FF motions (Baker et al., 2011). Each record is scaled by factors of 1.5 and 2.0 to ensure sufficient intensity coverage, yielding a total of 360 motions per suite. Spectral acceleration at a 1‑second period (Sa‑1.0 s) is adopted as the intensity measure (IM) to maintain consistency with HAZUS, although the suitability of Sa‑1.0 s for NF motions alone is noted as an area for future validation.

The bridge modeling framework is built in OpenSees. The study selects three‑span, single‑column‑bent, post‑1970 concrete box‑girder bridges with either diaphragm or seat abutments—representative of more than 25 % of the state inventory. Superstructures are modeled as elastic beam‑column elements; columns are represented by fiber‑type displacement‑based elements to capture nonlinear flexural behavior. Rigid elements enforce moment and force transfer between deck and columns. Abutment behavior incorporates bilinear bearings, trilinear shear keys (with gap), and pounding modeled after Muthukumar & DesRoches (2006). Soil‑pile springs are rotated to reflect abutment skew, and the stiffness/strength variation due to skew follows the empirical relation 0.3·tan(α)/tan 60°, capped at 0.3 for α = 60°.

Uncertainties in geometry, material properties, and system characteristics are captured through probabilistic distributions (means, standard deviations, and distribution types) derived from a review of over 1,000 bridges (Mangalathu 2017). Latin Hypercube Sampling (LHS) generates 320 bridge instances, each paired randomly with the 360 ground motions, resulting in 115,200 nonlinear time‑history analyses (NLTHA). Outliers beyond 1.96 σ are truncated to maintain realistic samples.

Seven engineering demand parameters (EDPs) are extracted: maximum column drift (θc), residual column drift (θR), maximum passive abutment displacement (δp), maximum active abutment displacement (δa), maximum tangential abutment displacement (δt), maximum deck unseating (δu), and maximum bearing displacement (δb). For each EDP, a probabilistic seismic demand model (PSDM) is derived via log‑log linear regression: ln(D) = a + b·ln(IM), where a and b are regression coefficients and the dispersion βD|IM is computed from residuals. Assuming lognormal distributions for both demand and capacity, component fragility functions are expressed as cumulative lognormal distributions.

The results reveal a pronounced skew effect: as the skew angle α increases, especially beyond 30°, the median demand (θ50) under NF motions drops substantially, indicating higher vulnerability. Under FF motions the skew influence is milder but still noticeable. Existing HAZUS skew modification factors (generally ranging 0.8–1.2) fail to capture the observed shifts in median values, leading to under‑ or over‑estimation of risk.

To address this gap, the authors propose new skew‑adjustment factors ψ(α, type), where “type” distinguishes NF from FF ground motions. ψ decreases approximately linearly with α for NF cases, while for FF cases the decline is gentler. Applying ψ as a multiplicative correction to the HAZUS median fragility values aligns the adjusted curves with the simulation‑based fragilities across all skew angles and motion types.

The study also introduces demolition (demolition fragility) criteria based on residual drift: bridges exhibiting residual column drift exceeding 1.75 %—a threshold observed in post‑Kobe demolition decisions—are assigned higher demolition probabilities, particularly under NF excitations.

In conclusion, the paper demonstrates that skewness and proximity to active faults jointly exacerbate seismic risk for California box‑girder bridges. The conventional HAZUS modification factors are insufficient, and the newly derived ψ(α, type) factors provide a more accurate, implementable means to adjust fragility curves for regional risk assessments, emergency response planning, and retrofit prioritization.