Micromechanics-based stress-dilatancy relationship for granular materials

From the perspective of micromechanics, the formulas for the average contact force and contact displacement in the granular are derived based on the true stress tensor, then the stress-shear dilatancy relationship considering the fabric anisotropy and its evolution is obtained through the macro-micro energy conservation. In addition, the physical meaning of dilatancy parameters and their influence on dilatancy are analyzed. Finally, the proposed formulation is compared with the classical Cambridge flow law, Rowe dilatancy equation and test results to calibrate its reasonableness and applicability. The proposed stress-dilatancy relationship with clear physical meaning can describe the initial dilatancy (contraction) behavior for granular materials, considering the anisotropic evolution of fabric and the influence of the density on the dilatancy. Moreover, the proposed stress-dilatancy equation can reflect that the stress ratio at the phase transition point is less than the critical stress ratio and the peak stress ratio emerges behind the maximum dilatancy ratio. It is in good agreement with the test results and can better predict the anisotropic stress-dilatancy relationship of granular materials.