Shear Strength for Unsaturated Soil

The unsaturated soil shear strength theory, in the form of an extended Mohr-Coulomb envelope. The Mohr circle corresponding to failure can be plotted in a three-dimensional graph. The three-dimensional graph has the shear stress, τ, as the ordinate and the two stress state variables, (σ-u_a) and (u_a-u_w), as the abscissas. For a saturated soil, the matric suction (u_a-u_w) is zero and the pore-water pressure becomes equal to pore-air pressure. Therefore, there is a smooth transition in the shear strength equation from unsaturated soils to saturated soils. 

Extended Mohr-Coulomb failure envelope for unsaturated soil, Fredlund and Rahardjo 1993

Relationship between soil-water characteristic curve and shear strength for the clayey sand, Rahardjo et al 2007

References

1. Fredlund, D. G., Rahardjo, H. and Fredlund, M. D. (2012). Unsaturated soil mechanics in engineering practice, John Wiley & Sons, Inc., New York, 926 pages (ISBN 978-1-118-13359-0). doi 
2. Rahardjo, H., Krisdani, H., Leong, E. C., Ng, Y. S., Foo, M. D., Wang, C. L., (2007). “Unsaturated soil mechanics for solving seepage and slope stability problems.” KEYNOTE LECTURE. Proceedings of Twelfth International Colloquium on Structural and Geotechnical Engineering. Ain Shams University, Cairo, Egypt, 10–12 December, 1-38.
3. Fredlund, D. G. and Rahardjo, H. (1993). Soil mechanics for unsaturated soils, John Wiley & Sons, New York, 517 pages (ISBN 0-471-85008-X). doi
4. Fredlund, D. G. and Morgenstern, N. R. (1977). “Stress state variables for unsaturated soils”. Journal of the Geotechnical Engineering Division, 103(5), 447-466.