A stress–strain description of saturated sand under undrained cyclic torsional shear loading

A constitutive model to describe the cyclic undrained behavior of saturated sand is presented. The increments in volumetric strain during undrained loading, which are equal to zero, are assumed to consist of increments due to dilatancy and increments due to consolidation/swelling. This assumption enables the proposed model to evaluate increments in volumetric strain due to dilatancy as mirror images of increments in volumetric strain due to consolidation/swelling, thus simulating the generation of excess pore water pressure (i.e., reduction in mean effective principal stress) during undrained cyclic shear loading. Based on the results of drained tests, the increments in volumetric strain due to consolidation/swelling are evaluated by assuming that the quasi-elastic bulk modulus can be expressed as a unique function of the mean effective principal stress. On the other hand, in evaluating the increments in volumetric strain due to dilatancy, a normalized stress–plastic shear strain relationship is employed in combination with a novel empirical stress–dilatancy relationship derived for torsional shear loading. The proposed stress–dilatancy relationship accounts for the effects of over-consolidation during cyclic loading. Numerical simulations show that the proposed model can satisfactorily simulate the generation of excess pore water pressure and the stress–strain relationship of saturated Toyoura sand specimens subjected to undrained cyclic torsional shear loading. It is found that the liquefaction resistance of loose Toyoura sand specimens can be accurately predicted by the model, while the liquefaction resistance of dense Toyoura sand specimens may be slightly underestimated. (i.e., the liquefaction potential is higher). Yet, the model predictions are conservative.