A unified monotonic model for sand based on modified hyperbolic equation and state-dependent dilatancy

Abstract

Accurate prediction of the state-dependent shearing behaviors of sand in a rational way is a challenging task of the development of constitutive models. In the present study, a deformation type model is proposed based on a modified Duncan-Chang hyperbolic equation, which provides a simple and efficient way to characterize the stress–strain relationship. The hyperbolic equation is improved to tackle the limitations when predicting the strain-softening behavior of sand. By coupling with a flow rule, the volumetric response under a drained condition and excess pore pressure generation under an undrained condition can be modeled as well. An empirical state variable, known as the relative dilatancy index, is implemented in the modified hyperbolic equation and the flow rule to model the state-dependent shearing behaviors in a unified way. The flow rule evolves with the state of soil during shearing and provides realistic simulations of dilatancy-related response. The calibration process for dilatancy and hyperbolic equations is suggested. The model is validated by drained and undrained triaxial compression tests of two silica sand, showing a fairly good capability of unified modeling of the sand behaviors with a wide range of densities and stress levels.