Mohr-Coulomb Faulting Simulator

Faulting Regime

Stress State

Max principal stress σ₁ 150 MPa

Min principal stress σ₃ 40 MPa

Cohesion C₀ 20 MPa

Friction angle φ 30°

Fracture plane angle θ (from σ₁) 45°

STABLE — plane below envelope

Normal stress σₙ

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Shear stress τ

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Envelope τ at σₙ

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Coulomb-optimal θ

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Mohr Circle

How it works

On any plane inclined at angle θ to the maximum principal stress σ₁, the normal and shear stresses are given by the Mohr circle equations (σ₁, σ₃ compressive, σ₁ ≥ σ₃):

σn = (σ1+σ3)/2 + (σ1-σ3)/2 · cos(2θ)
τ  = (σ1-σ3)/2 · sin(2θ)

The rock fails on that plane once τ reaches the Mohr-Coulomb failure envelope, a linear function of the cohesion C₀ and the internal friction angle φ:

τ_failure = C0 + σn · tan(φ)

Maximising τ − σn·tanφ over θ shows failure first occurs on the plane at the Coulomb-optimal angle:

θ_opt = 45° − φ/2   (measured from σ1)

Real crustal rock typically has φ ≈ 25–35°, so shear fractures form in conjugate pairs about 25–35° from σ1 — not at 45°, the classic textbook departure from simple maximum-shear intuition.

Regime — Anderson's theory of faulting: which principal axis is vertical decides the fault style. σ1 vertical → normal faults (steep, ~45+φ/2° dips). σ1 horizontal, σ3 vertical → reverse/thrust faults (shallow, ~45−φ/2° dips). σ1 and σ3 both horizontal → strike-slip faults (near-vertical).
θ slider — rotates the candidate fracture plane (and its Andersonian conjugate, mirrored about σ1) through the stress field; the 3D planes and the point on the Mohr circle move together.
Snap to optimal — jumps straight to θ_opt, the angle real rock actually breaks along.

σ₁ (max compression) σ₃ (min compression) candidate fracture plane conjugate plane

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