Numerical Stability Analysis of Canal Embankment Using Hill’s Second-Order Work Criterion

Natural disasters are becoming increasingly frequent, causing both human suffering and economic setbacks. The prediction of these risks, especially regarding catastrophic landslides, is crucial. While slope stability analysis is a classic problem in geotechnical engineering, some landslides with low (less than 14°) to very low (less than 8°) slope angles cannot be explained by classical empirical methods or traditional limit analyses (plasticity theories). This paper introduces Hill’s sufficient condition of stability, based on the sign of the second-order work, as a potential criterion for predicting failures that occur before the Mohr-Coulomb criterion is met. The paper details the formulations of both local and global second-order work used in finite element (FE) programs. A plane strain FE analysis of an idealized canal embankment, composed of gravelly sand and considering unsaturated hydro-mechanical coupling behavior, was conducted during excavation and water rise. The results confirm that the second-order work criterion effectively predicts potential instability in the embankment at both local (material) and global (domain) scales.