A Generalized Flow Theory for Sand
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Within the framework of certain concepts presented nearly two decades ago a constitutive law for sand is established which is capable of describing the mode of deformation experienced during quite complicated loading paths of the generalized stress space. The proposed law assumes the existance of a yield surface and a bounding surface and as such is a two surface model. It is a consistent isotropic-kinematic hardening law which, in view of its general nature, can be readily incorporated in a suitable numerical code ; the finite element code for example. The paper provides a detailed mathematical formulation concerning the virgin loading process as well as stress-reversal histories during which the stress paths penetrates the interior of the bounding surface. The formulation is based on the theory of plasticity incorporating a non-associated flow rule and the concept of reflected plastic potential. The mathematical description is followed by a discussion concerning the performance of the model. In particular, the concept is applied to simulate a number of complex 'triaxial' loading programs carried out on a typical granular medium. The emphasis is placed on modelling of liquefaction and cyclic mobility phenomena. For a number of tests, the performance of the model is compared with experimental results. The predictions, although restricted to triaxial configuration only, are quite encouraging and indicate that the applicability of the model extends to a quite wide spectrum of initial void ratios, ranging from a very loose sand to a very dense one.