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, will fail under shear stress. This criterion combines the effects of normal stress and shear stress to predict when a material will yield or fracture, providing valuable insights into the elastic and plastic behavior of materials in various engineering applications.

5 Must Know Facts For Your Next Test

1. The Mohr-Coulomb failure criterion is expressed mathematically as $$ au = c + an( heta) \sigma$$, where $$ au$$ is the shear stress at failure, $$c$$ is the cohesion of the material, $$ heta$$ is the friction angle, and $$\sigma$$ is the normal stress.
2. This criterion assumes that failure occurs along a plane where the shear stress exceeds the material's strength, taking into account both cohesion and internal friction.
3. It applies to both elastic and plastic behavior, making it essential for understanding how materials respond under various loading conditions.
4. The Mohr-Coulomb failure envelope is linear for many materials, which simplifies analysis and design in geotechnical engineering applications.
5. Understanding this criterion helps engineers assess the stability of slopes, foundations, and other structures that rely on the mechanical behavior of soils and rocks.

Review Questions

• How does the Mohr-Coulomb failure criterion help in understanding the elastic and plastic behavior of materials?
  • The Mohr-Coulomb failure criterion provides a framework for analyzing when materials will yield or fail under different stress conditions. By incorporating both cohesion and friction angle into its formulation, it allows for predictions about how materials transition from elastic behavior, where they return to their original state after loading, to plastic behavior, where permanent deformations occur. This understanding is critical for designing structures that can withstand various loads without failing.
• Discuss how the laws of dry friction relate to the Mohr-Coulomb failure criterion in practical applications.
  • The laws of dry friction govern how surfaces interact when subjected to normal and shear forces. In practical applications, the Mohr-Coulomb failure criterion uses these laws to establish a relationship between normal stress and shear stress at failure. Understanding these interactions helps engineers predict when materials will fail due to sliding or slipping along interfaces, which is crucial in fields such as civil engineering and construction.
• Evaluate how knowing the Mohr-Coulomb failure criterion can influence engineering decisions regarding soil stability and structure design.
  • Knowing the Mohr-Coulomb failure criterion allows engineers to accurately assess soil stability under various loading conditions. This understanding can influence decisions related to foundation depth, slope stability, and retaining wall design. By predicting potential failure points based on shear stress and normal stress relationships, engineers can create safer designs that mitigate risks associated with soil movement or structural collapse, ultimately leading to more reliable infrastructure.

Related terms

Shear Stress: A type of stress that acts parallel to the surface of a material, causing layers to slide against each other.

Cohesion: The property of a material that describes its ability to stick together due to intermolecular forces, playing a significant role in the strength of soils.

Friction Angle: The angle that defines the relationship between normal stress and shear stress, representing the slope of the failure envelope in the Mohr-Coulomb failure criterion.