Natural state parameter for sand

Abstract

Based on the frictional state concept, the natural state parameter for sands is defined as an extension of the state parameter defined by Been and Jefferies. The proposed definition of the natural state parameter is the sum of the distance between the normalised difference of the current stress ratio and the critical frictional stress ratio and the difference between the current and critical frictional state void ratio for the same mean principal stress. Therefore, it combines the difference between the current and critical frictional state in the q ‒ p’ and e ‒ p’ planes and can be treated as an extension of Been and Jefferies’ definition of the state parameter in the e ‒ p’ plane. The results of drained triaxial compression tests for Toyoura sand and Dog’s Bay sand, presented in the literature, are analysed. The values of the natural state parameter at failure for these sands are equal to zero. Therefore, the critical state in the q ‒ p’ and e ‒ p’ planes can be determined by analysing the conditions at failure. At failure, the deformations of the samples are almost homogeneous, and the stresses and deformations (void ratios) can be correctly determined. Additionally, the critical frictional state and critical state are very similar for these sands. The relationship between the dilatancy and the state parameter at failure, similar to that given by Been and Jefferies, was obtained directly by using the frictional state concept and the proposed definition of the natural state parameter. The natural state parameter, like the state parameter, can be used for modelling of sands in the future.