Quasi-steady state: a real behavior?: Discussion

Abstract

When loose sands are sheared undrained from relatively low initial effective stress conditions, hardening is observed following quasi-steady state in laboratory testing. The authors stated that the hardening is mainly due to the end restraint of the specimen and not a true behavior of sand. Although the writer agrees with the authors’ opinion that the hardening during an actual flow failure in the field is doubtful, the writer suspects that the hardening observed in the laboratory after quasi-steady state is the real behavior of sand if it is sheared under purely monotonic loading condition without any cyclic disturbance. Figure D1 shows the results of undrained simple shear tests on Toyoura sand using a hollow cylinder torsional shear apparatus. The testing device and the testing procedure were the same as described by Yoshimine et al. (1998) except the fact that the height of the specimens was shorter (13 cm) to allow larger shear strain. The outer and inner radii of the specimen were 10 cm and 6 cm, respectively. As the dimensions and the shape of the sample were not changed and only torsional shear was applied to the sample under undrained simple shear condition, there should not be any end restraint due to the friction between the specimen and the porous stones on the top and the bottom of the sample. The torsional shear deformation was very uniform from the bottom through to the top edge of the sample without any sign of restraint. The observed hardening behavior following quasi-steady state in the simple shear condition which is free from end restraint (Fig. D1) indicates that the restraint was not the main reason of the hardening. The simple shear tests on the specimen with larger height (20 cm) exhibited the same tendency (Yoshimine et al. 1998). In Fig. 13 of the original paper, test results by Uthayakumar (1996) was sited. In this test, b value was fixed to zero and a sand was sheared undrained with various maximum principal stress inclinations from the vertical (ασ value) using a hollow cylinder torsional shear apparatus. If ασ = 0° and b = 0, the outer and inner cell pressures are equal, while larger ασ value results in larger outer cell pressure. The combination of ασ = 90° and b = 0 is the most severe condition for hollow cylindrical specimens where the outer cell pressure could be more than three times higher than the inner cell pressure at large deformation. As a result, the radial contraction of the specimen is the largest, and the effect of end restraint might be the maximum under the condition of ασ = 90°, which is contrary to the assumption of the authors. The hardening behavior following quasi-steady state can be systematically understood from the test results by Verdugo (1992). In Fig. D2, the state of phase transformation and the ultimate steady state during undrained triaxial compression on Toyoura sand were plotted on the e ! p′ plane. The points of ultimate steady state form an unique ultimate steady state line (USSL) and the little scatter confirms the accuracy of the measurement (Verdugo and Ishihara 1997). Phase transformation is the point of minimum effective mean stress including quasi-steady state. In this figure, phase transformation points from the same initial confining stress (pc′) are connected and phase transformation lines (PTL) are drawn. Quasi-steady state exists on the upper part of each PTL. As can be seen in the figure, when the initial stress level becomes high enough, PTL converged into USSL, since the “minimum” stress can not be larger than the