Probabilistic Capacity Function–Based Framework for Seismic Resilience Assessment of Liquefiable Embankments with Ground Improvement

This paper introduces a probabilistic framework for evaluating the seismic resilience of embankments on liquefiable soils, addressing key limitations of conventional empirical approaches that tend to underestimate failure risks. The proposed methodology combines nonlinear dynamic analysis using FLAC2D (version 8.0) with the point estimate method to systematically account for the variability of soil parameters treated as random variables. In contrast to traditional fragility-based approaches, the proposed framework enables a more comprehensive risk assessment by jointly quantifying the seismic fragility, vulnerability, and postearthquake restoration potential. The embankment capacity is characterized based on settlement thresholds, and uncertainty is propagated through a suite of ground motion simulations. Both reinforced and unreinforced embankment systems were investigated by comparing their performance in terms of variability reduction, response stability, and seismic resilience. The effectiveness of different mitigation strategies, including deep mixing, steel sheet piles (SPs), and stone columns, in improving seismic resilience was assessed. The results indicate that steel SP reinforcement leads to the smallest variability in limit state capacities while achieving the most stable performance, which in turn contributes to enhanced seismic resilience. The proposed framework provides a robust foundation for selecting and optimizing liquefaction countermeasures in performance-based seismic design.