State-dependent strength of sands from the perspective of unified modeling

Abstract

This paper discusses the state-dependent strength of sands from the perspective of unified modeling in triaxial stress space. The modeling accounts for the dependence of dilatancy on the material internal state during the deformation history and thus has the capability of describing the behavior of a sand with different densities and stress levels in a unified way. Analyses are made for the Toyoura sand whose behavior has been well documented by laboratory tests and meanwhile comparisons with experimental observations on other sands are presented. It is shown that the influence of density and stress level on the strength of sands can be combined through the state-dependent dilatancy such that both the peak friction angle and maximum dilation angle are well correlated with a so-called state parameter. A unique, linear relationship is suggested between the peak friction angle and the maximum dilation angle for a wide range of densities and stress levels. The relationship, which is found to be in good agreement with recent experimental findings on a different sand, implies that the excess angle of shearing due to dilatancy in triaxial conditions is less than 40% of that in plane strain conditions. A careful identification of the deficiency of the classical Rowe's and Cam-clay's stress-dilatancy relations reveals that the unique relationship between the stress ratio and dilatancy assumed in both relations does not exist and thereby obstructs unified modeling of the sand behavior over a full range of densities and stress levels.