Investigation on the inclination angle of undrained shear slip surface in saturated soils based on mixture theory

TL;DR

This paper analyzes the inclination angle of undrained shear slip surfaces in saturated soils using mixture theory, energy conservation, and thermodynamics, revealing its dependence on permeability and effective stress.

Contribution

It introduces a novel theoretical framework linking slip surface inclination to soil permeability and effective stress, integrating mixture theory and thermodynamics.

Findings

Inclination angle varies with soil permeability.

Uncoupled analysis applies when permeability is infinite.

Fully coupled analysis applies when permeability is zero.

Abstract

The inclination angle of the undrained shear slip surface in saturated soils is analyzed based on mixture theory. First, starting from the property that the bulk strain of soil skeleton is equal to the flow ratio of water discharged from soil skeleton, the energy conservation equation of saturated soil is obtained. According to state variables of energy equation and non-equilibrium thermodynamics, the mechanical mechanism underlying effective stress principle is revealed that Gibbs free energy of saturated soil is only expressed as a function of effective stress under isothermal process. Consequently, the deformation and strength of saturated soil are uniquely determined by the effective stress and not directly related to Newton's equilibrium equations, which governs the movements of solid-fluid two-phase components. The instability of soil skeleton is related to the applied forces and requires analysis based on the Newtonian equilibrium condition. The interaction between the solid-water components and the equilibrium equation of solid component are investigated under two working conditions: when permeability tensor equals zero and when it equals infinity. Combined with the Mohr-Coulomb strength theory, the inclination angle of the undrained shear slip surface is explored under Rankine's passive earth pressure in saturated soil. The results indicate that, when the permeability equals infinity, the uncoupled hydro-mechanical analysis is recommended, and the inclination angle of slip surface is ; when the permeability equals zero, the fully coupled hydro-mechanical analysis is recommended, and the inclination angle of slip surface is . The permeability of actual saturated soil falls between the two extremes, the inclination angle of slip surface must be analyzed on a case-by-case basis.