Fig. 9.
The line graph and polar plot present critical state stress ratio M theta against Lode angle theta for C o T and C o P. In the line graph, the horizontal axis is Lode angle theta in degrees, ranging from negative 30 to 30, with labelled values at negative 30, negative 15, 0, 15 and 30. The vertical axis is critical state stress ratio M theta, ranging from 0.8 to 1.5 in intervals of 0.1. The C o T curve decreases from about 1.46 at negative 30 degrees to 1.02 at 0 degrees and about 0.89 at 30 degrees. The C o P curve decreases from about 1.40 at negative 30 degrees to 0.99 at 0 degrees and about 0.86 at 30 degrees. Circular markers identify C o T and C o P values at negative 30 and 0 degrees. A vertical dashed line marks 0 degrees. The equation below the curves reads M theta equals M c times the quantity 2 alpha to the power of 4 over the quantity 1 plus alpha to the power of 4 minus the quantity 1 minus alpha to the power of 4 times sine 3 theta, all raised to the power of one quarter. The polar plot represents Lode angle theta around the circumference from 0 to 330 degrees in 30 degree intervals and critical state stress ratio M theta radially from 0 to 1.6 in intervals of 0.2. The C o T and C o P profiles form approximately triangular closed paths, extending to about 1.4 at 90 degrees, about 1.4 near 210 degrees, about 1.45 near 330 degrees and about 1.0 at 0 degrees. Circular C o T and C o P markers occur near 330 and 0 degrees.Variation of the stress ratio M with the Lode angle θ. The lines represent the interpolation using the g(θ) method proposed by Sheng et al. (2000), calibrated with experimental data from triaxial compression (TXC) and simple shear (SS) tests