Fig. 11.
Two panels, a and b, present specific volume against mean effective stress, shearing paths, critical state stress ratio against Lode angle, a polar representation and particle micrographs. Panel a plots specific volume e sub 0 vertically from 1.50 to 1.90 in intervals of 0.05 against mean effective stress p prime in kilopascals horizontally on a logarithmic scale from 10 to 1,000, with labelled values at 10, 100 and 1,000. The relation is e equals gamma minus lambda times natural logarithm of p prime. Crosses identify beginning of shearing T R X. Open circles identify end of shearing T R X 86 S, T R X 91 S and T R X 95 S. Plus symbols identify end of shearing S S 86 S, S S 91 S and S S 95 S. Several T R X paths begin with horizontal or nearly horizontal segments and then curve downwards. The upper T R X 86 S paths extend from specific volumes near 1.85 and 1.80 and descend towards approximately 1.74 and 1.70. T R X 91 S paths occur around specific volumes of 1.75 to 1.56, while T R X 95 S paths occur around 1.71 to 1.56. S S endpoints are distributed mainly between approximately 30 and 250 kilopascals and specific volumes of approximately 1.63 to 1.82. A straight C S L subscript unique descends across the plot from approximately 1.88 at 10 kilopascals to approximately 1.54 near 1,000 kilopascals. Its parameters are gamma equals 2.053, lambda equals 0.074 and R squared equals 0.95. Panel b contains a larger version of the specific-volume plot with the same axes, logarithmic scale, equation, marker categories, shearing paths and C S L subscript unique. Multiple T R X paths occur at progressively higher mean effective stresses. Horizontal or nearly horizontal portions are followed by downward curved portions terminating at open-circle endpoints. Plus-symbol S S endpoints lie among these paths at different specific volumes and mean effective stresses. To the right, a line graph plots critical state stress ratio M theta vertically against Lode angle theta in degrees horizontally. The horizontal axis ranges from negative 30 to 30 degrees, with labelled values at negative 30, negative 15, 0, 15 and 30. The vertical axis ranges from approximately 0.8 to 1.5 in intervals of 0.1. A dashed curve decreases from approximately 1.40 at negative 30 degrees to approximately 0.99 at 0 degrees and approximately 0.86 at 30 degrees. Circular markers identify values at negative 30 and 0 degrees. A vertical dashed reference line passes through 0 degrees. The adjacent polar plot is labelled Lode angle theta in degrees around its circumference, with angular labels from 0 through 330 degrees in 30-degree intervals. Critical state stress ratio M theta forms the radial axis, ranging from 0 to 1.6 in intervals of 0.2. A dashed closed profile extends from approximately 1.0 at 0 degrees to approximately 1.4 at 90 degrees, approximately 1.4 near 210 degrees and approximately 1.5 near 330 degrees before returning towards 0 degrees. Circular markers occur near 0 and 330 degrees. Below the plots are two particle micrographs. The left micrograph contains numerous densely packed irregular, angular and elongated particles of varying sizes, including many fine particles between larger grains. It has a 1 millimetre scale bar. The annotations include det B S E D, H V 20.00 kilovolts, mag 100 times, W D 13.0 millimetres and Inspect F 50. The right micrograph contains larger irregular, angular and elongated particles with finer particles occupying spaces between them. It has a 400 micrometre scale bar. The annotations include det B S E D, H V 20.00 kilovolts, mag 352 times, W D 13.0 millimetres and Inspect F 50.(a) Critical state line (CSL) (unique) in the υ–log p′ space for triaxial compression and simple shear tests – CoP. (b) CSL with SEM analysis and variation of the stress ratio M with the Lode angle θ