A Constitutive Model with a Historiotropic Yield Surface for Sands

A simple, yet versatile yield surface in the stress space is combined with a hypoplastic equation to simulate the influence of recent deformation history on the mechanical behaviour of sand. This yield surface is used to describe the intensity of anelastic flow. In the model, the state is fully described by the current stress, the void ratio and a novel back stress-like tensor. This new state variable determines the shape and size of the yield surface and accounts for recent deformation/stress history. The direction of the anelastic flow upon shearing is obtained from a generalization of the Taylor’s dilatancy rule. As a distinctive feature of the model, this dilatancy is able to reproduce the strong contractancy upon reversals observed in experiments without the need of additional state variables. The model corrects some known shortcomings of previous hypoplastic models like overshooting and the excessive accumulation of stress/strain upon strain/stress cycles of small amplitude (ratcheting). Laboratory tests are simulated to show the capabilities of the model to reproduce the soil behaviour under monotonic and cyclic loading conditions after different deformation histories.