A complete φ-ν inequality and its applications

Geotechnical stability has long been a central topic in geotechnical engineering research, and the strength reduction method based on displacement finite element analysis has been one of popular stability analysis methods. When performing the geotechnical stability analysis, it is also essential to properly interpret the plastic zone distribution in the soil or rock mass, apart from evaluating the factor of safety and the location of the slip surface. Non-physical (or spurious) plastic zone distributions may lead to misinterpretations of the failure mechanism and potentially result in inappropriate engineering remedial measures. According to Zheng et al.¹⁵, keeping the Poisson's ratio unchanged during the strength reduction process, which may violate the requirement of the φ-ν inequality, could be a primary cause of such non-physical plastic zones. In this study, it is proved that the φ-ν inequality proposed by Zheng et al. ¹⁵ only provides a lower bound for Poisson’s ratio. Furthermore, an upper bound is derived here, and then it is integrated with the lower bound, so a complete φ-ν inequality is established. Based on an embankment slope and a slope with stabilization pile, it is validated that the lower bound of the φ-ν inequality effectively eliminates non-physical plastic zones in deep soil layers, while the upper bound successfully constrains the non-physical expansion of plastic zones in shallow regions.