Modeling monotonic and cyclic behavior of granular materials by exponential constitutive function

It is still an open problem to develop a model with a uniform theoretical treatment under various loading conditions. This paper aims to formulate such a model for describing both monotonic and cyclic behaviors of granular materials. An exponential function was adopted to reproduce the stress-strain relation. Within the framework of endochronic models, the shear strain component was enriched with an absolute term to account for a reverse loading effect during shearing. The capacity of the basic model with four parameters for reproducing the basic features of granular materials was examined. Three numerical schemes for simulating undrained triaxial tests, drained triaxial tests under constant p' or under constant confining stress, and under both monotonic and cyclic loadings were established. Then, three modifications were carried out to enhance the model by introducing a nonlinear elasticity, a nonlinear stress dilatancy, and the critical state concept with four additional parameters. The enhanced version of the model showed good performances in simulating triaxial tests on Toyoura sand under various loading conditions: drained, undrained, constant p', constant confining stress, and monotonic and cyclic loadings.