Instability of sands under axisymmetric proportional strain and stress loadings

Abstract

This paper compares the pre-failure instability of sands under axisymmetric proportional strain and axisymmetric proportional stress conditions. Based on a deviatoric hardening plasticity model, the critical hardening moduli under both conditions were obtained by the second-order work criterion. In the proportional strain condition, the instability of sands depends on the stress–dilatancy relationship and the imposed strain proportion ratio. Loose sand is prone to instability; dense sand maintains stable behaviour under the undrained condition, butit may become unstable in expansive loading. In the proportional stress condition, dense sand shows stable behaviour; loose sand can be stable as long as the stress proportion is at a sufficient distance from zero. A material state-dependent elasto-plasticity model was used to predict the instability of sands in triaxial tests under the proportional strain condition, constant mean stress condition, and constant shear stress condition; the predicted instability behaviour agrees well with the experimental data.

Keywords:

• Diffuse instability
• sands
• axisymmetric condition
• state-dependent plasticity
• second-order work criterion