21.5. Fault Mechanics and Stress Analysis

The behavior of faults under stress is analyzed using the Mohr-Coulomb failure criterion:

$\tau = c + \sigma_n \times \tan(\phi)$

Where:

• $\tau$ = shear stress
• $c$ = cohesion
• $\sigma_n$ = normal stress
• $\phi$ = angle of internal friction

The Mohr-Coulomb failure criterion is used to analyze how faults behave when they are subjected to stress. In this equation, shear stress ($\tau$) refers to the force that causes the layers of rock to slide against each other. Cohesion ($c$) is the intrinsic strength of the rocks that helps hold them together. Normal stress ($\sigma_n$) is the force acting perpendicular to the fault plane, and the angle of internal friction ($\phi$) reflects how the rocks resist sliding against each other. Together, these elements help determine when the shear stress on a fault will exceed the strength of the rock, resulting in fault movement and potentially causing an earthquake.

Imagine pushing two stacked books on a table. The force you apply is similar to shear stress, trying to slide them against each other. The friction between the books is akin to cohesion. As you push harder (adding shear stress), at some point, the force will overcome the friction, causing the books to slide suddenly. This is similar to how faulting occurs in the Earth; once the stress exceeds frictional resistance, rocks will rupture or slip, releasing stored energy.

When shear stress exceeds the rock strength, faulting occurs. Stress accumulation over time results in elastic deformation, eventually released as seismic energy during fault rupture.

Shear stress builds up in rocks near faults due to tectonic forces. When the stress becomes too great, it exceeds the strength of the rock, causing it to fail and rupture. This sudden release of accumulated stress results in seismic energy that we feel as an earthquake. Before the fault movement, the rocks may experience elastic deformation, meaning they bend or stretch without breaking until the stress threshold is reached.

Think of a rubber band. If you stretch it slowly, it can deform without breaking—this is similar to the elastic deformation in rocks. However, if you stretch it too far, it snaps, releasing all that stored tension instantly. This snapping is analogous to faulting: when rock deformities become excessive due to build-up of stress, the sudden release leads to an earthquake.

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