• Slope of the critical state line in the plane
• Specific volume at the critical state when is 1.0 (or, ln is 0)
• Slope of the isotropic over-consolidation (swelling) line
• Slope of the isotropic normal consolidation line
• Specific volume
These five parameters are illustrated in Figure 7.1. The critical state line shown in the plane is the locus of critical states projected onto that plane. The critical state line has a slope of, , which is related to the angle of internal friction of the soil. For the case of triaxial compression, can be expressed as:
By definition, the specific volume, , is related to the void ratio, , through the following expression:
7.2 A standard triaxial specimen has dimensions of 50mm in diameter and 100mm height. Triaxial tests have been conducted on a Hong Kong marine clay. The following parameters have been obtained for two models:
Model 1: Mohr-Coulomb perfect elastic-plastic model: kPa, , , kPa, .
Model 2: The Modified Cam-Clay elastic-plastic model:,,,,.
Use a finite element program to do the following simulation:
(a) Use Model 1 and Model 2 to simulate the relationship of deviator stress vs. axial strain , vs. , and vs. of consolidated drained (CD) tests under isotropic consolidation stresses kPa and 200 kPa separately.
(1) Model 1, kPa
(2) Model 2 kPa
(3) Model 1, kPa
(4) Model 2, kPa
(b) Use Model 1 and Model 2 to simulate the relationship of deviator stress vs. axial strain , vs. , and vs. of consolidated undrained (CU) tests under isotropic consolidation stresses kPa and 200 kPa separately.
(1) Model 1, kPa
(2) Model 2 kPa
(3) Model 1, kPa
(4) Model 2, kPa
(c) Use Model 1 and Model 2 to simulate the relationship of vertical stress vs. vertical strain εz, σh vs. εz, and q vs. p’ of drained oedometer tests under initial stresses kPa and kPa up to vertical stress kPa.
(1) Mode 1
(2) Mode 2
For a rigid smooth strip footing of 2 m in width, use to Model 1 and Model 2 to calculate the curve of settlement vs. average vertical foundation pressure up to failure. Discuss the results (do drained analysis).
