The idea of Phase Field Method (PFM) is introduced to depict the dynamic shear modulus degradation of saturated soil revealed in the undrained triaxial tests. The order parameter in PFM is adopted to govern the liquefaction process. Then the inherent and generalized constitutive relation among shear stress, shear strain, shear modulus and confining pressure is derived. It more complies to thermodynamics in comparison to conventional empirical model following a phenomenological description. By comparing to existed empirical model, the presented four-parameter model is validated to be of robustness and efficacy to various soil types and confining pressure levels under monotonic and cyclic loading. The simulated pore pressure varies simultaneously with modulus degradation, which is consistent with observations and energy consideration. The presented method makes it possible to apply to deformation prediction in deep excavation and other engineering practice, whilst without loss of physical interpretations.

The present study is devoted to the investigation of the dilatancy behaviour of a fine sand based on hollow cylinder tests. Medium and dense samples were tested at a constant average stress by applying torsional angles for shear strains gamma = 1, 2, 3 and 4%. Dilatancy curves along with shear wave velocity measurements to investigate the influence of the shear strain amplitude gamma(ampl) in the shear modulus degradation curve are presented and discussed. The measured stress and strain paths were used to compare the performance of four advanced constitutive models especially in describing the dilatancy behaviour of sand. From the perspective of their constitutive equations, the differences between the simulations with various material models are examined. It may be concluded that all four models allow a proper prediction of torsional shear tests as long as a proper calibration of the material parameters is secured.