Formulation of a sand plasticity plane-strain model for earthquake engineering applications

The formulation of a sand plasticity model for geotechnical earthquake engineering applications is presented. The model follows the basic framework of the stress-ratio controlled, critical state compatible, bounding surface plasticity model for sand presented by Dafalias and Manzari, Journal of Engineering Mechanics, ASCE, 2004;130(6): 622-634. . Modifications to the model were developed and implemented to improve its ability to approximate the stress-strain responses important to geotechnical earthquake engineering applications. These constitutive modifications included: revising the fabric formation function to depend on plastic shear rather than plastic volumetric strains; adding fabric history and cumulative fabric formation terms; modifying the plastic modulus relationship and making it dependent on fabric; modifying the dilatancy relationships to provide more distinct control of volumetric contraction versus expansion behavior; providing a constraint on the dilatancy during volumetric expansion so that it is consistent with Bolton′s Géotechnique 1986; 36(1): 65-78. dilatancy relationship; modifying the elastic modulus relationship to include dependence on stress ratio and fabric history; modifying the logic for tracking previous initial back-stress ratios (i.e., loading history effect); recasting the critical state framework to be in terms of a relative state parameter index; and simplifying the formulation by restraining it to plane strain without Lode angle dependency for the bounding and dilation surfaces. Model responses to various loading conditions, including drained and undrained monotonic and cyclic loading, are used to illustrate the efficacy of the model modifications. Calibration and implementation of the model for practice are described in a companion paper.