Mohr-Coulomb failure criterion

Definition

The Mohr-Coulomb failure criterion is a mathematical model used to describe the shear strength of soil and rock materials based on their internal friction and cohesion. This criterion establishes the relationship between normal stress and shear stress, showing that failure occurs when the shear stress on a material reaches a critical value determined by its cohesion and internal friction angle. Understanding this criterion is crucial for analyzing stability in soil mechanics and evaluating the performance of earth structures under different loading conditions.

5 Must Know Facts For Your Next Test

1. The Mohr-Coulomb failure criterion is often represented in a linear equation of the form $$ au = c + an( heta) imes au_n$$, where $$ au$$ is the shear stress, $$c$$ is cohesion, $$ heta$$ is the internal friction angle, and $$ au_n$$ is the normal stress.
2. This criterion assumes that failure occurs when the applied shear stress exceeds the material's shear strength, which depends on both cohesion and the effective normal stress acting on a failure plane.
3. It is widely used in geotechnical engineering for analyzing slopes, retaining structures, and foundations, as it provides a simplified approach to predict when materials will fail under stress.
4. The Mohr-Coulomb model can be illustrated using Mohr's circle, which graphically represents the relationship between normal and shear stresses on different planes within the material.
5. Factors such as pore water pressure can influence the effective stress within soils, thereby affecting the applicability of the Mohr-Coulomb criterion in saturated conditions.

Review Questions

• How does the Mohr-Coulomb failure criterion apply to real-world geotechnical engineering scenarios, such as slope stability analysis?
  • The Mohr-Coulomb failure criterion is crucial for evaluating slope stability because it helps determine whether a slope will remain stable under various loading conditions. By analyzing the shear strength of soil at different depths along a potential failure plane, engineers can identify critical factors such as cohesion and internal friction angle that contribute to stability. This criterion allows engineers to calculate safety factors and design appropriate remedial measures if instability is detected.
• Discuss how changes in pore water pressure can affect the effectiveness of the Mohr-Coulomb failure criterion in predicting soil behavior.
  • Changes in pore water pressure significantly impact the effective stress within soil layers, which can alter their shear strength according to the Mohr-Coulomb failure criterion. When pore water pressure increases, effective normal stress decreases, leading to reduced shear strength and potentially increased risk of failure. Understanding this relationship helps engineers assess risks associated with saturated soils and implement measures like drainage to mitigate instability.
• Evaluate the limitations of the Mohr-Coulomb failure criterion when applied to complex soil conditions and suggest alternative approaches for better predictions.
  • While the Mohr-Coulomb failure criterion provides a useful framework for assessing soil behavior under simple conditions, it has limitations when applied to complex soils or situations involving non-linear behavior. For example, it does not account for effects like strain rate sensitivity or plasticity in clays. In these cases, alternative approaches such as the Lade criteria or more advanced constitutive models may be necessary. These alternatives allow for better predictions by considering factors like loading history and stress paths that influence material behavior beyond what is captured by Mohr-Coulomb.

Related terms

Shear Strength: The resistance of a material to shear deformation or failure, influenced by factors such as cohesion and internal friction.

Normal Stress: The stress component perpendicular to a given surface, which plays a significant role in determining shear strength according to the Mohr-Coulomb criterion.

Cohesion: The property of soil that describes its ability to stick together, contributing to its overall shear strength.