Plane strain instability of saturated elasto-plastic soils

The two-phase instability of saturated elasto-plastic soils is investigated under plane strain conditions. This type of material instability is characterised by a non-homogeneous field of solid deformation with vortex-like patterns, which grows rapidly and is accompanied by a non-uniform flow of interstitial water exhibiting source-sink flow patterns. Three simple criteria are established to define the conditions for the onset of two-phase instability within elasto-plastic soils saturated with an incompressible fluid and subjected to plane-strain undrained loadings. The simplest criterion states that the onset of instability almost coincides with the peak deviator stress during undrained loading. This analysis shows that two-phase instability in elasto-plastic soils is different from strain localisation, strain softening and constitutive singularities. Two-phase instability is likely to emerge before shear bands in contractant elasto-plastic soils of the Mohr-Coulomb type. The study suggests that two-phase instability may disrupt numerical liquefaction analyses using elasto-plastic soil models, and thus prompts the need for further analytical and experimental investigations.