The concept at the heart of the paper is seismic uplift fragility, defined as the conditional probability that pile uplift will occur given a particular ground motion intensity measure. Fragility analysis is a cornerstone of modern earthquake engineering because it converts the messy, uncertain physics of soil-structure interaction into probabilistic statements that can feed directly into risk assessment and design codes. Previous research had established that scour removes overburden soil around the pile cap, amplifies pile-cap rotations during shaking, and can trigger uplift of the piles themselves. But the authors note that the seismic uplift behavior of scoured pile-group foundations had never been probabilistically quantified, leaving a significant gap in multi-hazard bridge assessment.

To close that gap, the team built an extensive numerical modeling campaign. They established 49 archetype bridge configurations by varying twelve structural and geotechnical parameters, including pile length, pile spacing, axial load ratio, and the longitudinal reinforcement ratio of the piles. The bridges were founded in cohesionless soils, meaning sandy, non-clayey sediments of exactly the kind that scour attacks most aggressively and that are common beneath river and coastal crossings. Each archetype was subjected to suites of ground motions, and the resulting simulations were mined for the quantities that best track uplift behavior.

A central technical contribution of the study is the careful selection of the response metrics used in the probabilistic demand models. The researchers systematically compared candidate engineering demand parameters and intensity measures, and concluded that the peak rotation of the pile cap is the optimal engineering demand parameter for quantifying uplift, while the Housner intensity, a measure based on the energy content of the ground motion, is the optimal intensity measure. Crucially, they found that pile-cap rotation is more efficient and more practical than the pile cap’s lateral displacement for characterizing uplift demand. Rotation, it turns out, directly captures the rocking mechanism that precedes uplift, whereas lateral displacement conflates rocking with sliding and bending responses, diluting the statistical relationship.

With demand quantified, the team then turned to capacity. Uplift capacity models were derived from the pile-cap rotations at the onset of uplift, effectively defining the rotation threshold beyond which part of the pile group begins to pull free of the surrounding soil. When a rocking foundation reaches this point, load redistributes to the remaining compressed piles, soil resistance on the uplifted side vanishes, and the energy dissipation and recentering behavior of the foundation change fundamentally. Combining the probabilistic demand models with these capacity models yielded the study’s headline output: seismic uplift fragility curves for scoured pile-group foundations in cohesionless soils.

The numbers are sobering. For the base bridge model, the probability of uplift reaches 82 percent under a seismic hazard level associated with a 475-year return period, the design-level event around which many modern seismic codes are organized. In other words, a bridge whose foundations have been scoured has a very high likelihood of experiencing pile uplift when struck by an earthquake of the magnitude engineers already plan for. Because uplift initiates the transition from a ductile rocking response toward potentially uncontrolled foundation movement, an 82 percent probability at the design event represents a serious vulnerability, particularly for the aging river and coastal bridges that dominate many transportation networks.

The parametric analysis that followed is where the study becomes most directly useful to practitioners. The fragility decreases as pile length increases, as pile spacing increases, and as the axial load ratio rises, while it increases as the longitudinal reinforcement ratio of the piles decreases. Among all the parameters examined, pile length was identified as the single most influential factor. Each of these trends has an intuitive physical basis. Longer piles provide deeper embedment and greater resistance to pullout. Wider spacing reduces the overlapping stress zones between adjacent piles, letting each pile mobilize more of the surrounding soil. Higher axial load on the foundation provides a stabilizing, self-weight-driven resistance to rocking and uplift. Conversely, less longitudinal reinforcement weakens the capacity of individual piles to sustain the tension that develops during rocking, making uplift and its consequences more damaging.

These findings resonate with a broader body of experimental work on rocking foundations. Quasi-static tests and shaking table studies by the same research group and by others in recent years have shown that scoured pile-group foundations exhibit distinctive uplift behavior and energy dissipation mechanisms, and that rocking can sometimes even be harnessed as a deliberate design strategy when the foundation is detailed to recenter after shaking. The new study adds the probabilistic layer that such experimental work lacks, translating deterministic observations into fragility statements that can be integrated into regional risk models, resilience assessments, and retrofit prioritization for bridge stocks exposed to both flood scour and seismic hazard.

Recognizing that running full nonlinear finite element simulations of 49 archetype bridges is impractical for routine design offices, the authors also distilled their results into practical tools. They established and validated multivariate linear regression models that allow rapid estimation of uplift fragility from the key design parameters, without the need for expensive simulation. This surrogate modeling approach mirrors a wider trend in earthquake engineering, in which machine-learned and regression-based approximations of physics-based analyses are used to bring probabilistic assessment within reach of everyday engineering workflows. For a bridge engineer wondering whether a scour-critical crossing needs longer piles, wider spacing, or enhanced reinforcement, the regression models offer a first-order answer in seconds.

The broader significance of the work lies in its treatment of concurrent hazards. Flood-induced scour and earthquakes are usually assessed separately, yet they are physically coupled in ways that can dramatically worsen outcomes. Scour weakens exactly the soil-foundation system that must resist seismic demands, and climate-driven changes in flood frequency suggest that more bridges will spend more of their service lives with compromised foundations. By delivering the first probabilistic quantification of seismic uplift fragility for scoured pile-group foundations in cohesionless soils, the Fuzhou University and Tongji University team has given the engineering community both a warning and a toolkit: multi-hazard assessment is not optional for river and coastal bridges, and the levers that most reduce uplift risk, above all pile length, are already in the hands of designers.

Subject of Research: Seismic uplift fragility analysis of scour-affected bridge pile-group foundations in cohesionless soils

Article Title: Seismic uplift fragility of scoured bridge pile-group foundations in cohesionless soils

Article References: Wang, J., Luo, H., Wang, X., & Gu, Y. (2026). Seismic uplift fragility of scoured bridge pile-group foundations in cohesionless soils. Bulletin of Earthquake Engineering. https://doi.org/10.1007/s10518-026-02686-4

Image Credits: AI Generated

DOI: 10.1007/s10518-026-02686-4

Keywords: bridge scour, pile-group foundation, seismic fragility, pile uplift, cohesionless soils, Housner intensity, pile-cap rotation, probabilistic seismic demand, multi-hazard assessment, sensitivity analysis, regression surrogate model, earthquake engineering

The research is rooted in performance-based earthquake engineering, a framework that treats structures not as objects that simply stand or fall, but as systems whose performance can be predicted probabilistically. At the heart of this framework sits the intensity measure, a scalar descriptor of ground shaking, such as peak ground acceleration or spectral acceleration at a given period, that serves as the bridge between hazard analysis and structural response prediction. The quality of an intensity measure is judged by its efficiency, meaning how tightly it correlates with the engineering demand parameters that describe structural and operational damage, and by its sufficiency, meaning how well the predicted response remains independent of other ground-motion characteristics. An intensity measure that is both efficient and sufficient allows engineers to build accurate probabilistic seismic demand models with fewer costly simulations, which is precisely where the new study makes its contribution.

The particular system the researchers examined, known as the simply-supported-bridge-vehicle coupled system, is among the most common bridge forms on high-speed railway networks, especially on challenging routes such as the Sichuan-Tibet Railway, where lines must cross regions laced with active strike-slip faults. Simply supported spans rest on bearings that allow rotation and, to a degree, translation, which makes them economical and constructible but also vulnerable when the ground beneath them lurches in two directions at once. When a train is present, the problem becomes even more intricate, because the vehicle, the track, and the bridge form a dynamically coupled system in which the running safety of the train depends on the deformation of the deck, and the vibration of the deck is in turn influenced by the moving masses of the vehicles above it. Past investigations by these and other research groups have shown that near-fault pulse-type ground motions can compromise derailment resistance and that fault rupture itself imposes permanent, quasi-static displacements that no amount of dynamic damping can absorb.

Strike-slip faulting introduces a uniquely punishing combination of effects. As the fault ruptures, the ground on either side shears horizontally past the other, and a structure crossing the fault trace is forced to accommodate the offset. In the near-fault zone, two signature phenomena dominate: the fling step, a permanent, often unidirectional displacement pulse produced by tectonic deformation, and forward directivity, a strong long-period velocity pulse that arrives when the rupture front propagates toward the site at nearly the speed of the shaking itself. These effects are inherently directional, aligned with the fault-parallel and fault-normal orientations, so the structural response depends critically on the angle at which the bridge crosses the fault. Compounding the challenge, recorded ground motions close to strike-slip surface ruptures are scarce, forcing analysts to work with limited datasets in which the choice of intensity measure carries outsized consequences for the reliability of the resulting risk estimates.

To tackle this problem, the team developed a modified intensity measure selection framework for cloud analysis, a widely used statistical technique in which a family of ground motion records, each scaled or unscaled, is run through the structural model and the resulting demands are regressed against candidate intensity measures in logarithmic space. The innovation lies in the normalization of the intensity measures, which sharpens the comparison of efficiency across candidates whose raw numerical ranges differ by orders of magnitude. By normalizing before evaluating statistical performance, the framework reduces distortions that can arise in regression diagnostics and produces a fairer ranking of alternatives. The researchers then applied the framework across a battery of candidate measures drawn from the standard toolbox of earthquake engineering, including peak ground velocity, peak spectral displacement, peak spectral velocity, and measures defined from individual ground motion components as well as geometric-mean combinations, testing each against six representative engineering demand parameters spanning the bridge and the running vehicles.

The verdict from thousands of coupled dynamic analyses is strikingly clear: under the coupled fling-step and forward-directivity demands of crossing strike-slip faulting, velocity- and displacement-based spectral measures outperform the acceleration-based measures that have traditionally dominated fragility studies. Specifically, the peak spectral displacement, SDmax, and peak spectral velocity, SVmax, emerged as the top performers for constructing probabilistic seismic demand models of the coupled system. This makes physical sense. Long-period velocity pulses and permanent displacement offsets, the hallmarks of near-fault strike-slip motion, resonate most directly with displacement-type demands such as bearing displacement, pier drift, and the deck deformations that govern train running safety. Peak ground acceleration, by contrast, emphasizes high-frequency content that is relatively less consequential for these long-period, quasi-static-dominated failure modes, and its correlation with demand weakens accordingly.

Equally important is the finding about directionality. The study shows that intensity measures computed from the fault-parallel component of ground motion perform consistently well in integrated assessments across all six engineering demand parameters, reflecting the dominant role of the shearing displacement imposed along the fault trace. When the researchers turned to specific engineering scenarios defined by the fault-bridge crossing angle, they identified scenario-specific optima: for a 90-degree crossing, the geometric mean of peak spectral displacement across the two horizontal components, SDmax,GM, proved best, while for a shallower 45-degree crossing, the fault-parallel peak spectral displacement, SDmax,FP, took the top spot. In both cases the chosen measures delivered a balanced combination of efficiency and sufficiency, giving engineers a defensible, defensible-to-auditor basis for record selection and fragility construction tailored to the actual geometry of a proposed crossing.

The practical implications reach well beyond academic statistics. High-speed rail corridors in tectonically active regions, from southwest China to Turkey, California, and Taiwan, increasingly must traverse fault zones because alternative routings are economically or geographically impossible. The 1999 Kocaeli and Duzce earthquakes in Turkey and the Chi-Chi earthquake in Taiwan famously collapsed or displaced simply supported spans whose unseated girders traced the fault rupture across their alignments. By identifying which ground-motion descriptors most faithfully capture the demand imposed on a coupled bridge-train system, the new framework enables more economical and more trustworthy fragility assessment, supporting decisions about bearing seat widths, restrainers, isolation systems, and operational speed limits during seismic events. Because cloud analysis with unscaled records is computationally expensive, the improved efficiency of the recommended measures also translates directly into fewer simulations required for a given confidence level, a meaningful saving when each coupled vehicle-track-bridge analysis involves extensive nonlinear computation.

Methodologically, the study also contributes a reusable template. The normalization-based cloud analysis framework is not tied to any particular bridge form, and the authors’ evaluation metrics, which weigh efficiency, sufficiency, and practicality across multiple demand parameters simultaneously, can be redeployed for continuous girders, cable-stayed spans, and suspension bridges crossing faults, where prior work by the same community has documented severe track-bridge interaction and long-span dynamic amplification. The research was supported by the National Natural Science Foundation of China, the Department of Education of Guangdong Province, the Foshan Science and Technology Bureau, and Hunan University of Science and Technology, and drew on the strong-motion database of the Pacific Earthquake Engineering Research Center’s Next Generation Attenuation-West2 project. As high-speed rail networks push deeper into seismically hostile mountains and basins, the humble task of choosing the right number to describe a ground motion, once treated as a technical footnote, now stands revealed as one of the decisive levers for keeping trains, bridges, and passengers safe when the ground itself refuses to hold still.

Subject of Research: Selection of optimal seismic intensity measures for railway simply-supported-bridge-vehicle coupled systems subjected to crossing strike-slip faulting.

Article Title: Analysis and selection of seismic intensity measures for railway simply-supported-bridge–vehicle coupled systems subjected to crossing-strike-slip faulting

Article References: Zhou, T., Li, Z., Jiang, L., & Wen, T. (2026). Analysis and selection of seismic intensity measures for railway simply-supported-bridge–vehicle coupled systems subjected to crossing-strike-slip faulting. Bulletin of Earthquake Engineering. https://doi.org/10.1007/s10518-026-02676-6

Image Credits: AI Generated

DOI: 10.1007/s10518-026-02676-6

Keywords: seismic intensity measures, railway bridge, strike-slip fault, vehicle-bridge interaction, probabilistic seismic demand, fling step, forward directivity, cloud analysis, running safety, high-speed railway, fault crossing, earthquake engineering