Critical state concepts

Critical state soil mechanics ties together strength and volume change. When a soil is sheared far enough, it reaches a critical state in which it keeps deforming at constant shear stress, constant effective stress and constant volume. All samples of the same soil, whatever their starting density, end on one line in stress space, the critical state line, where the ratio of deviator stress to mean effective stress is a constant, M.

Where a sample starts relative to that line decides how it gets there. Loose sands and normally consolidated clays are on the wet side: they contract as they are sheared, and in undrained tests positive pore pressures build up and reduce effective stress. Dense sands and heavily overconsolidated clays are on the dry side: they dilate, show a peak strength above the critical value, and soften towards it; undrained, they develop negative pore pressures.

The parameter M is linked to the critical-state friction angle. In triaxial compression, M equals 6 sin φ over 3 minus sin φ. This angle is a property of the soil grains and their arrangement and does not depend on density, which makes it a reliable design parameter for large strains, for example in slopes that have already slipped.

The Cam clay and modified Cam clay models build on these ideas, adding a yield surface that grows with consolidation, and are widely used in numerical analysis of embankments on soft clay, excavations and foundations. They explain why the undrained strength of a normally consolidated clay is roughly proportional to its consolidation stress.