What are the Mohr-Coulomb and Modified Mohr-Coulomb Models in GEO5 FEM?

In geotechnical engineering, the Mohr-Coulomb and Modified Mohr-Coulomb models are essential tools for analyzing soil and rock behavior under various stress conditions. These models are implemented in GEO5 FEM (Finite Element Method) software to simulate and predict the response of materials in different geotechnical structures.

1. Mohr-Coulomb Model in GEO5 FEM #

The Mohr-Coulomb Model is one of the most widely used constitutive models in geotechnical engineering. It describes the behavior of soils and rocks under shear stress, particularly focusing on failure due to shear. The model is defined by two key parameters:

• Cohesion (c): This parameter represents the inherent shear strength of the material.
• Friction Angle (φ): This represents the angle at which the material resists sliding along a plane.

The Mohr-Coulomb model assumes a linear failure criterion, expressed as:

$$\tau =c+\sigma \cdot \tan (\varphi )$$

Where:

• τ is the shear stress,
• c is the cohesion,
• σ is the normal stress,
• ϕ is the friction angle.

Advantages of the Mohr-Coulomb Model:

• Simplicity: Easy to implement and widely accepted in geotechnical engineering.
• Computational Efficiency: Suitable for large-scale simulations due to its simplicity.
• Adequate for Standard Problems: Works well for conventional geotechnical problems like slope stability, retaining wall design, and shallow foundation analysis.

Limitations of the Mohr-Coulomb Model:

• Inaccuracy in Tension: Does not handle tensile stresses effectively.
• Oversimplification: The linear failure envelope may not accurately represent complex stress conditions.
• No Dilatancy Consideration: Does not account for volumetric changes during shearing.
• Limited Strain Softening/Hardening: Does not capture changes in material properties with strain.

2. Modified Mohr-Coulomb Model in GEO5 FEM #

The Modified Mohr-Coulomb Model is an enhanced version of the basic Mohr-Coulomb model. It offers a more accurate representation of soil and rock behavior, especially under complex stress states involving both tensile and compressive stresses. Key features of this model include:

• Nonlinear Failure Envelope: Allows for better handling of tensile stresses and complex stress conditions.
• Tension Cut-off: Prevents unrealistic tensile strength predictions in weak materials.
• Dilatancy Angle (ψ): Accounts for volumetric changes during shear, improving deformation predictions.
• Strain Softening and Hardening: Can model changes in material strength post-yield.

Advantages of the Modified Mohr-Coulomb Model:

• Enhanced Realism: More accurate representation of soil and rock behavior under different stress states.
• Tension Cut-off: Ensures realistic failure predictions by limiting tensile strength.
• Consideration of Dilatancy: Better handles the volumetric changes during shear.
• Handling of Complex Stress States: Suitable for more complicated geotechnical problems like deep foundations.

Limitations of the Modified Mohr-Coulomb Model:

• Increased Complexity: Requires more parameters and a deeper understanding of soil behavior.
• Parameter Sensitivity: Performance depends on accurate parameter determination.
• Risk of Overfitting: More parameters can lead to overfitting to specific data sets.
• Higher Computational Demand: Nonlinear nature increases computational effort.

Conclusion #

Choosing between the Mohr-Coulomb and Modified Mohr-Coulomb models in GEO5 FEM depends on the specific needs of your geotechnical analysis. The Mohr-Coulomb model is ideal for standard problems requiring simplicity and computational efficiency. In contrast, the Modified Mohr-Coulomb model is better suited for more complex scenarios where realistic modeling of tensile behavior, dilatancy, and strain softening/hardening is essential.

For more detailed information on implementing these models in GEO5 FEM, refer to the relevant sections in the GEO5 FEM – Theoretical Guide.