Critical Filling Height of Embankment over Soft Soil: A Three-Dimensional Upper-Bound Limit Analysis

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This paper investigates the critical filling height of embankments over soft soil using three-dimensional (3D) upper-bound limit analysis based on a rotational log-spiral failure mechanism. Soft soils are characterized by low shear strength and high compressibility, making the accurate determination of critical filling height essential for evaluating embankment stability. Unlike conventional two-dimensional (2D) analyses, the proposed 3D method captures the true failure mechanism of embankments, providing more realistic and reliable results. The upper-bound analysis equations are derived using the principle of virtual work and solved efficiently through the genetic algorithm (GA), which avoids the limitations of traditional loop and random searching algorithms. The proposed solution is validated by comparing it with existing studies on slope stability and demonstrates higher accuracy and computational efficiency. Parametric studies are conducted to evaluate the influence of the depth–height ratio (the ratio of soft soil depth to embankment height) on the failure width of the embankment, the critical failure surface, and the critical filling height. Results show that the critical failure surface is tangential to the bottom of the soft soil layer and the critical filling height increases as the depth–height ratio decreases. The findings provide a set of critical filling heights calculated under various soft soil depths, strength parameters, and embankment geometries, offering practical guidance for embankment design.