Fig. 10.
Two panels, a and b, present specific volume and stress relationships, critical state stress ratio plots and particle micrographs. Panel a plots specific volume e sub p vertically from 1.45 to 1.75 in intervals of 0.05 against mean effective stress p prime in kilopascals horizontally on a logarithmic scale from 1 to 1,000, with labelled values at 1, 10, 100 and 1,000. The legend identifies crosses as beginning of shearing T R X, open circles as end of shearing T R X 86 S, T R X 91 S and T R X 95 S, and plus symbols as end of shearing S S 86 S, S S 91 S and S S 95 S. Beginning-of-shearing T R X points occur across approximately 50 to 500 kilopascals and specific volumes of about 1.57 to 1.72. End-of-shearing points occur along horizontal and curved stress paths between approximately 3 and 800 kilopascals. The T R X paths include nearly horizontal initial portions followed by steep decreases in specific volume. The S S endpoints cluster mainly between approximately 40 and 200 kilopascals and specific volumes of about 1.52 to 1.66. Four critical state lines decrease with increasing mean effective stress. C S L superscript T R X subscript 86 S has a equals 1.725, b equals 0.060, c equals 0.40 and R squared equals 0.98. C S L superscript T R X subscript 91 S has a equals 1.655, b equals 0.040, c equals 0.40 and R squared equals 0.98. C S L superscript T R X subscript 95 S has a equals 1.618, b equals 0.030, c equals 0.40 and R squared equals 0.96. The dashed C S L superscript S S subscript unique has a equals 1.720, b equals 0.121, c equals 0.55 and R squared equals 0.97 and decreases more steeply than the other critical state lines. The fitted relation is e equals a minus b times p prime over p prime subscript ref raised to the power c, with p prime subscript ref equal to 100 kilopascals. Panel b contains a larger specific-volume plot with the same axes, ranges, symbols, shearing paths, fitted relation and four critical state lines and parameter values as panel a. To its 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 approximately from 0.8 to 1.5. The curve decreases from approximately 1.46 at negative 30 degrees to approximately 1.02 at 0 degrees and approximately 0.89 at 30 degrees. Circular markers occur at negative 30 and 0 degrees, and a vertical dashed line marks 0 degrees. Beside it, a polar plot presents 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. Its closed profile extends to approximately 1.0 at 0 degrees, 1.4 at 90 degrees, about 1.4 near 210 degrees and about 1.5 near 330 degrees, with circular markers near 0 and 330 degrees. Below the two critical state stress ratio plots are two particle micrographs containing irregular particles with varied sizes and angular forms. The left micrograph contains numerous closely packed smaller and larger particles and includes a 1 millimetre scale bar. Its annotations include det B S E D, H V 20.00 kilovolts, mag 100 times and W D 12.9 millimetres. The right micrograph contains fewer, generally larger irregular particles surrounded by finer material and includes a 400 micrometre scale bar. Its annotations include det B S E D, H V 20.00 kilovolts, mag 400 times and W D 12.9 millimetres.(a) Critical state lines (CSLs) in the υ–log p′ space for triaxial compression and simple shear tests – CoT. (b) CSL with SEM analysis and variation of the stress ratio M with the Lode angle θ