Use of Linear Extrapolation to Estimate Critical State Void Ratio from Drained Triaxial Shear Tests on Dense Cohesionless Soil

Abstract

Within the strain level attainable in drained triaxial tests, it is not uncommon for dense cohesionless soil to be sheared insufficiently to reach the critical state. Linear fitting of the correlative data from the maximum stress ratio or minimum dilatancy to the end of the test, and then extrapolating these fitted lines to the critical stress ratio or zero dilatancy has been frequently used to estimate the critical state void ratio. However, the linear extrapolation method is empirical and involves different choices of correlative test data, which leads to different estimates. Therefore, a series of simulations of drained tests on dense Toyoura sand are performed using a state-dependent model. Multiple data sets are generated, including void ratio e, volumetric strain εv, stress ratio η, and dilatancy D. The linear extrapolation accuracy of the e–η, e–D, and εv–D data sets is examined. It turns out that the e–η data set is best suited. The goodness of the e–η data set is examined against 18 sets of experimental data on dense sand. In addition, the selection of the start point for extrapolation is shown to influence the estimates. The latter 50% of the post-peak data is found to be reliable.