Validity and Stability of Alternative Effective Stress—Specific Volume Relationship for Sands

Abstract

In this study a novel model based on the theory of compressible fluids is used to model the effective stress-specific volume response of granular materials during 1D compression, isotropic compression and critical state. Specifically, a modified Van der Waals equation for real gases is successfully validated against the experimental data obtained from few series of triaxial tests that were conducted over several decades. The proposed equation captures the experimentally observed response throughout the wide range of effective stress including elevated and high pressures. The excellent performance of the model is achieved without introducing any special provisions for grain crushing at elevated and high-pressures. Furthermore, features of the proposed isothermal equation of state are further illustrated by presenting it in different coordinate systems along with the experimental data. An additional characteristic of the proposed model is in that it contains thermodynamics-based stability criterion that describes the state of a granular material near the limit of its existence, i.e., in the extreme configuration. The nature of the stability concept is further investigated by presenting the experimental response of sand in triaxial tests observed during the initial stage of the shearing phase. It is found that the observed amount of lateral deformation increases with a decrease in effective confining pressure whereby no lateral deformation is observed initially at high pressures. This indicates that the amount of radial deformation is likely to further increase on approach to zero confining pressure, thus signifying the approach to instability induced collapse.