τ = c + σ tan φ

Definition

The equation τ = c + σ tan φ represents the Mohr-Coulomb failure criterion, which is used to describe the shear strength of materials, particularly soils and rocks. In this equation, τ is the shear strength, c is the cohesion, σ is the normal stress acting on the failure plane, and φ is the angle of internal friction. This relationship helps predict when a material will fail under applied stress, providing crucial insights into stability and failure mechanisms in geotechnical engineering.

5 Must Know Facts For Your Next Test

1. The Mohr-Coulomb failure criterion is foundational for analyzing the stability of slopes, foundations, and retaining structures in geotechnical engineering.
2. Cohesion (c) can vary significantly depending on soil type and moisture content, affecting the overall shear strength.
3. The angle of internal friction (φ) influences how granular materials behave under loading; higher values indicate greater resistance to sliding.
4. This equation assumes linear behavior, making it applicable for many types of soils but not all conditions such as heavily saturated or highly plastic soils.
5. Understanding this criterion helps engineers make informed decisions about design and safety measures for earth structures.

Review Questions

• How does the Mohr-Coulomb failure criterion apply to real-world scenarios in geotechnical engineering?
  • The Mohr-Coulomb failure criterion is crucial for assessing the stability of various structures like slopes, embankments, and retaining walls. Engineers use this criterion to calculate the shear strength of soil based on existing stress conditions. By applying this equation, they can predict failure conditions and make necessary adjustments in design and construction practices to ensure safety.
• Discuss how changes in cohesion and internal friction angle affect the shear strength according to the Mohr-Coulomb failure criterion.
  • Changes in cohesion (c) and internal friction angle (φ) directly impact the shear strength (τ) as described by the Mohr-Coulomb equation. An increase in cohesion typically raises shear strength, providing more resistance against failure. Conversely, a decrease in internal friction angle reduces frictional resistance among soil particles, making the material more susceptible to sliding under stress. Understanding these relationships helps engineers evaluate different soil types under varying conditions.
• Evaluate how the Mohr-Coulomb failure criterion might be limited when applied to complex soil behavior in geotechnical projects.
  • While the Mohr-Coulomb failure criterion provides a fundamental framework for analyzing soil behavior, it has limitations when dealing with complex scenarios like saturated soils or soils exhibiting plastic behavior. For instance, this model assumes linear elasticity and does not account for pore water pressure effects adequately. Therefore, engineers often need to incorporate additional factors or alternative models to capture non-linear behavior accurately and ensure safe design practices in challenging geotechnical situations.

Related terms

Shear Strength: The resistance of a material to shear forces, which is essential for understanding how materials behave under stress.

Cohesion: The component of shear strength that depends on the interparticle forces in a soil or rock mass, independent of external loads.

Internal Friction Angle: The angle that characterizes the frictional resistance to sliding between particles in a material, contributing to its overall shear strength.