Mohr-Coulomb Failure Criterion

Definition

The Mohr-Coulomb failure criterion is a mathematical model that describes the shear strength of soil and other materials based on their internal friction and cohesion. This criterion helps engineers predict when materials will fail under stress by relating shear strength to normal stress through a linear relationship defined by the cohesion intercept and the angle of internal friction.

5 Must Know Facts For Your Next Test

1. The Mohr-Coulomb failure criterion uses the equation $$ au = c + an( heta) imes ext{N}$$, where $$ au$$ is the shear strength, $$c$$ is cohesion, $$ heta$$ is the angle of internal friction, and $$N$$ is the normal stress.
2. This criterion can be represented graphically using Mohr's circle, allowing for easy visualization of stress states and failure conditions.
3. The criterion is applicable to both drained and undrained conditions, but different values for cohesion and angle of internal friction are used depending on drainage conditions.
4. It plays a vital role in analyzing slope stability and earth pressures, as it provides insight into how materials behave under different loading scenarios.
5. Factors such as soil type, moisture content, and previous loading history can significantly influence the parameters used in the Mohr-Coulomb failure criterion.

Review Questions

• How does the Mohr-Coulomb failure criterion relate to factors affecting shear strength in soil mechanics?
  • The Mohr-Coulomb failure criterion directly connects to factors like drainage conditions, soil type, and stress history by defining how these aspects influence shear strength. For instance, different soil types have varying cohesion values and angles of internal friction, which are critical parameters in the criterion. Additionally, drainage conditions determine whether drained or undrained shear strengths are used, impacting the overall stability analysis.
• Evaluate the importance of the Mohr-Coulomb failure criterion in analyzing active and passive earth pressure states.
  • The Mohr-Coulomb failure criterion is crucial in determining active and passive earth pressures because it helps predict when soil will fail under lateral loading. By using the values of cohesion and angle of internal friction, engineers can calculate the forces acting on retaining structures. Understanding these pressures allows for effective design and safety evaluations against potential failures or slides.
• Discuss how the Mohr-Coulomb failure criterion can be applied in rotational slope stability analysis methods like Bishop's method.
  • In rotational slope stability analysis methods such as Bishop's method, the Mohr-Coulomb failure criterion is used to assess the stability of potential slip surfaces by calculating the factor of safety. By integrating shear strength parameters derived from this criterion into stability equations, engineers can analyze different slip circles. The method allows for a more accurate representation of the forces acting on a slope, factoring in variations in cohesion and internal friction at different depths within the soil layers.

Related terms

Shear Strength: The resistance of a material to shear deformation, which is crucial in determining stability in geotechnical engineering.

Cohesion: The component of shear strength that is independent of the normal stress; it reflects the material's ability to stick together.

Effective Stress Principle: A principle that describes how the effective stress acting on a soil mass influences its behavior, particularly in saturated conditions.