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 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 Computational Geotechnics Mohr-Coulomb Model

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

4 Basic Concepts of Mohr- Coulomb Model Bilinear approximation of triaxial test Basic law: for reversible elastic strain irreversible plastic strain f = yield function Computational Geotechnics Mohr-Coulomb Model

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

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

7 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 Computational Geotechnics Mohr-Coulomb Model

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

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

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

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

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

13 in which: Computational Geotechnics Mohr-Coulomb Model

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

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

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

17 Drained Simple Shear Test Computational Geotechnics Mohr-Coulomb Model

18 How to Understand   =  +  i or  =  -  i  i = inter particle angle of friction quartz sand:    – 30 o Computational Geotechnics Mohr-Coulomb Model

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