Anisotropy and redundancy governing undrained cyclic stress paths: closed-form modelling and micromechanical interpretation

Tokio Morimoto 

The undrained cyclic shear behaviour of sand leading to liquefaction cannot be predicted solely by traditional stress-dilatancy theories based on density and stress state; accounting for fabric, the microscopic structure of granular soils, is essential. This study develops a closed-form micromechanical model predicting increments in shear stress and mean effective stress during undrained cyclic simple shear across varied densities, stress states, and pre-shear histories. Building on Effective Medium Theory (EMT), which analytically links grain-scale properties and fabric to macroscopic moduli, the formulation incorporates stiffness degradation due to non-affine particle relaxation and contraction induced by contact sliding. We demonstrate that three internal variables, quantifying stiffness-weighted anisotropy, contact redundancy, and sliding-induced instability, govern the incremental shear modulus and dilatancy. Crucially, these variables are derived analytically from three quantities readily measurable in the Discrete Element Method (DEM): the contact normal fabric tensor, mechanical coordination number, and sliding contact fraction. Validated against DEM simulations across diverse packing states, the model provides a unified micromechanical interpretation of characteristic cyclic stress-path features, including phase transformation, pre-shear history effects, and anisotropic contraction.