Mohr-Coulomb Failure Criterion

Definition

The Mohr-Coulomb failure criterion is a mathematical model used to describe the conditions under which materials, particularly soils and rocks, fail due to shear stress. It combines the concepts of normal stress and shear stress to establish a failure envelope, helping to assess slope stability by identifying the maximum shear stress that a material can withstand before failure occurs.

5 Must Know Facts For Your Next Test

1. The Mohr-Coulomb failure criterion is defined by the equation: $$ au = c + an( heta) imes au_n$$ where $$ au$$ is the shear strength, $$c$$ is cohesion, $$ heta$$ is the angle of internal friction, and $$ au_n$$ is the normal stress.
2. This criterion is particularly useful in geotechnical engineering for analyzing slope stability and predicting landslides.
3. The failure envelope formed by the Mohr-Coulomb criterion shows how shear strength increases with normal stress up to a certain point, beyond which failure occurs.
4. It assumes that failure occurs when the shear stress on a plane reaches a critical value defined by both cohesion and internal friction.
5. Variations in water content and pore pressure can significantly affect cohesion and the angle of internal friction, influencing slope stability assessments.

Review Questions

• How does the Mohr-Coulomb failure criterion apply to evaluating slope stability in geotechnical engineering?
  • The Mohr-Coulomb failure criterion provides a framework for evaluating slope stability by establishing a relationship between shear stress and normal stress. By using this criterion, engineers can calculate the maximum shear stress a material can withstand before failing. This information is crucial when assessing potential landslides or failures in slopes, allowing for better predictions and design of safe structures.
• Discuss how changes in pore pressure impact the Mohr-Coulomb failure criterion and subsequently affect slope stability.
  • Changes in pore pressure can significantly influence both cohesion and the angle of internal friction in materials. As pore pressure increases, it effectively reduces the normal stress acting on soil particles, which decreases the overall shear strength according to the Mohr-Coulomb criterion. This relationship means that higher pore pressures can lead to an increased likelihood of slope failure, especially during heavy rainfall or rapid snowmelt.
• Evaluate the effectiveness of the Mohr-Coulomb failure criterion in predicting failures in various geological conditions, considering its limitations.
  • While the Mohr-Coulomb failure criterion is widely used due to its simplicity and ease of application, it may not always accurately predict failures in all geological conditions. For instance, it assumes homogeneity within materials and does not account for factors such as time-dependent behavior, anisotropy, or complex loading conditions. Therefore, while it provides valuable insights into slope stability, engineers must consider its limitations and complement it with more advanced models when necessary.

Related terms

Shear Stress: The component of stress that causes layers or particles to slide past each other in a material.

Cohesion: The internal forces that hold the particles of a material together, contributing to its overall strength.

Angle of Internal Friction: A measure of the resistance of a material to sliding along internal surfaces, crucial for determining slope stability.