Upper-bound analysis of centrifuge modeling for embankment stability on soft soil accounting for linearly varying acceleration and optimal effective radius selection

In centrifuge modeling, the linearly varying centrifugal acceleration field distorts the internal stress state relative to uniform-gravity prototypes. Practice commonly represents this field with a uniform surrogate at an effective radius selected by vertical-stress matching. However, the effective radius should be determined based on the response of interest (e.g., the critical stability factor) rather than stress matching alone. This paper develops a rigorous upper-bound limit analysis for centrifuge modeling of embankments on soft soil foundations with linearly increasing undrained strength. Using a deep-seated rotational failure mechanism, analytical solutions are derived for the critical stability factor and the associated slip surface that explicitly account for the linearly varying acceleration. The solutions are validated against gravity-field analyses and centrifuge test data, showing good agreement. A parametric study reveals that using a conventional stress-matching effective radius can introduce systematic model–prototype discrepancies of up to about 14% in the critical stability factor, despite nearly identical slip surfaces. To minimize this discrepancy, an optimal effective radius is derived, which is found to lie at a depth of 0.42–0.52 times the embankment height below the crest. Practical design charts and recommendations for the optimal effective radius are provided to support test design and data interpretation.