Erratum for “Stress-Strain Response and Dilatancy of Sandy Gravel in Triaxial Compression and Plane Strain” by Andrew Strahler, Armin W. Stuedlein, and Pedro W. Arduino

During the analysis of additional true triaxial data, the authors identified some errors in the computation of the shear modulus and shear strain in this manuscript that require the updating of several figures and revision of some conclusions. Engineering shear strains were incorrectly calculated for the ${\mathrm{PSK}}_0\mathrm{CD}$ test specimens and did not reflect projection onto the deviatoric plane in accordance with Eq. (5). Accordingly, the previously published shear strains should be multiplied by $\sqrt{2}$ throughout the paper and in the original Figs. 7, 9, 11, 12, and 13. This error also requires adjustments to the ${\mathrm{PSK}}_0\mathrm{CD}$ dilation angles and initial shear modulus as presented in Figs. 4, 10, and 14. The dilation angles presented in the revised Fig. 4 are 30% lower than those previously reported and now range from 30 to 16°. The dilation angle at the smallest confining pressure was omitted from the trend fitting because of apparent influences of boundary conditions at low confining stresses.

As described above, the revised shear strains required updates to the reported shear modulus, $G_{{\mathrm{PSK}}_0\mathrm{CD}}$. $G_{{\mathrm{PSK}}_0\mathrm{CD}}$ must also be computed in the same manner as for the AICD stress path [i.e., $G=\mathrm{\Delta }q/(3\mathrm{\Delta }{\gamma }_s)]$ and, therefore, the revised ${\mathit{G}}_{{\mathrm{PSK}}_0\mathrm{CD}}$ must be 3$\sqrt{2}$ smaller than previously reported. The initial ${\mathrm{PSK}}_0\mathrm{CD}$ shear modulus presented in the revised Fig. 10 has been corrected for stress path and shear strain calculation errors. The revised $G_{{\mathrm{PSK}}_0\mathrm{CD}}$ values are lower than those measured in the AICD stress path, which is not consistent with the plane strain shear modulus reported by others [e.g., (Hatami and Bathurst 2005)].

To explore this finding, the consolidation-phase shear strains developed during the $K_0$ stress path were used to estimate the shear modulus near the end of the consolidation phase. The shear modulus calculated at the end of consolidation, presented alongside the $G_{{\mathrm{PSK}}_0\mathrm{CD}}$ in the revised Fig. 10, is similar to that measured at the onset of shearing. This confirms that the soil behavior is independent of the stress path. We conclude that the low magnitudes of the revised $G_{{\mathrm{PSK}}_0\mathrm{CD}}$ are attributed to the development of small magnitudes of ${\epsilon }_2$ strains that stem from the displacements in the load cells in the intermediate direction. During consolidation, ${\epsilon }_2$ was observed to be 0.03% on average and ranged from 0.02 to 0.06%. Therefore, the intermediate principal strains that develop within the UW-TTA system may not be small enough to accurately represent a true plane strain condition at small strains as a result of system compliance.

The revised Fig. 14 presents the corrected stress-dilatancy response of Kanaskat gravel, indicating that Bolton’s (1986) stress-dilatancy approximation underestimates the magnitude of dilation in well-graded gravelly soils by 22% on average. The revised comparison suggests that the plane strain stress-dilatancy response of well-graded gravelly soils at failure exhibits greater dilatancy than that predicted by Bolton’s (1986) approximation, which represents a new conclusion stemming from these data.