A possible continuum theory for densification and liquefaction of saturated sand

A previously developed continuum theory of granular media is applied to the problems of densification and liquefaction of saturated sand. An expression for the free energy of saturated sand is developed. The process of densification of sand subjected to cyclic shear stress is studied and several expressions for an increase of the solid volume fraction are obtained and discussed. The problem of the initial liquefaction of saturated sand samples under cyclic shear stress is then considered and several criteria relating the shear stress amplitude, over-burden pressure, time to liquefaction, and physical properties of the sand sample are established. Some semiempirical relations for field applications are also presented.