1. Mohr-Coulomb Model Short Course on Computational Geotechnics + Dynamics Boulder, Colorado January 5-8, 2004 Stein Sture Professor of Civil Engineering University of Colorado at Boulder

2. Mohr-Coulomb Model Computational Geotechnics Contents • Idealized and Real Stress-Strain Behavior of Soils • Basic Concepts of Mohr-Coulomb Model • Mohr-Coulomb Model Modeling • Friction Angle • Influence of Intermediate Principal Stress on Friction Angle • Drained Simple Shear Test • How to Understand  • Drained Triaxial Test

3. Mohr-Coulomb Model Computational Geotechnics Idealized and Real Stress-Strain Behavior of Soils

4. Mohr-Coulomb Model Computational Geotechnics Basic Concepts of Mohr-Coulomb Model Bilinear approximation of triaxial test Basic law:

5. Mohr-Coulomb Model Computational Geotechnics Mohr-Coulomb Soil Modeling

6. Mohr-Coulomb Model Computational Geotechnics Mohr-Coulomb Soil Modeling Flow rule for plastic strain: This means: , , etc.

7. Mohr-Coulomb Model Computational Geotechnics Mohr-Coulomb Soil Modeling a multiplier that determines the magnitude of plastic strains determines the direction of plastic strains Classical associated plasticity: g = f General non-associated plasticity: g  f M-C model: f r – s sin– c cos : yield function g r – s sin– c cos : plastic potential function

8. Mohr-Coulomb Model Computational Geotechnics Mohr-Coulomb Soil Modeling Nonlinear Failure Envelope Representation

9. Mohr-Coulomb Model Computational Geotechnics Mohr-Coulomb Soil Modeling Friction Angle Definitions

10. Mohr-Coulomb Model Computational Geotechnics Mohr-Coulomb Soil Modeling Strength Envelopes for a Range of Soil Types

11. Mohr-Coulomb Model Computational Geotechnics Mohr-Coulomb Soil Modeling Versus Relative Density and Unit Weight

12. Mohr-Coulomb Model Computational Geotechnics Friction Angle Dilatancy Angle Relationships

13. Mohr-Coulomb Model Computational Geotechnics in which:

14. Mohr-Coulomb Model Computational Geotechnics for NC Clays vs. PI

15. Mohr-Coulomb Model Computational Geotechnics Influence of Intermediate Principal Stress on Friction Angle

16. Mohr-Coulomb Model Computational Geotechnics Influence of Intermediate Principal Stress on Friction Angle

17. Mohr-Coulomb Model Computational Geotechnics Drained Simple Shear Test

18. Mohr-Coulomb Model Computational Geotechnics How to Understand y

19. Mohr-Coulomb Model Computational Geotechnics Drained Triaxial Test (identical to biaxial test)