Understanding Mohr-Coulomb Failure Criteria in Rock Mechanics

What is the Mohr-Coulomb Theory?

The Mohr-Coulomb theory is a widely used model in rock mechanics to predict when rocks will fail under stress. It describes how shear stress (τ) and normal stress (σ) interact within materials, particularly rocks, to determine their strength. The theory was developed by Adhémar Jean Claude Barré de Saint-Venant and later refined by Hubert Henry Mohr and André Coulomb.

The key idea is that the material will fail when the shear stress acting on a plane exceeds the maximum shear stress (τ_max) that can be supported by the normal stress (σ_n) and cohesion (c). This relationship is described by the equation: τ = c + σ_n * tan(φ), where φ is the friction angle of the material.

How Does It Work?

The Mohr-Coulomb theory operates on a stress circle, or Mohr circle, which visualizes the state of stress at any point within a rock. The horizontal axis represents normal stress (σ), and the vertical axis represents shear stress (τ). As you rotate a candidate fracture plane through this stressed rock block, the Mohr circle dynamically updates to show how these stresses change.

The theory predicts that failure occurs when the applied shear stress exceeds the frictional strength of the material. This is represented by the angle at which the normal stress and shear stress intersect on the Mohr circle, known as the Coulomb angle.

Why Does It Matter?

Understanding the Mohr-Coulomb theory is crucial for predicting landslides, earthquakes, and other geological hazards. Engineers use this knowledge to design stable structures such as dams, tunnels, and foundations that can withstand the forces exerted by rock masses.

In mining operations, it helps in planning safe extraction methods and preventing cave-ins or collapses of mine walls.

Real-World Applications

The Mohr-Coulomb theory is applied in various fields including civil engineering, geotechnical engineering, and petroleum engineering. For instance, it aids in the design of retaining walls that prevent soil movement, ensuring safety in construction projects.

In mining, engineers use this principle to predict potential failure points in rock formations, helping to avoid catastrophic collapses.

Frequently asked questions

Try it live

Everything above runs in your browser — open Mohr-Coulomb Faulting Simulator and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.