geomechanics · failure criteria
Mohr-Coulomb Failure Criterion
σ1' = Nφ·σ3' + 2C0√Nφ , Nφ = tan²(45° + φ/2)
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Inputs
psi
psi
°
Description
Applies the linear Mohr-Coulomb shear-failure criterion to determine the critical effective maximum principal stress at which a rock with given cohesion and friction angle fails in shear, given its effective confining (minimum principal) stress. Also reports the equivalent unconfined compressive strength (UCS).
Variables
| Symbol | Unit | Description |
|---|---|---|
| σ1'crit | psi | Critical Max. Principal Stress |
| UCS | psi | Unconfined Compressive Strength |
| σ3' | psi | Effective minimum (confining) principal stress acting on the rock — typically the output of the Effective Stress calc, evaluated for the relevant stress direction. |
| C0 | psi | Intrinsic shear strength of the intact rock at zero normal stress, from triaxial testing or log-derived rock-strength correlations. |
| φ | ° | Angle of internal friction of the rock, from triaxial testing. Typically 25-35° for shale, 30-45° for sandstone and carbonate. |
Assumptions
- Rock behaves as a linear Mohr-Coulomb material with constant C0 and φ over the stress range evaluated
- Intact rock — no pre-existing fracture or weak plane being reactivated (a slip-tendency analysis on a known plane orientation would be needed for that case)
- Effective stresses (already pore-pressure corrected) are used as inputs, not total stresses
Limitations
- Mohr-Coulomb is a linear approximation of rock strength — real failure envelopes are often curved (e.g. Hoek-Brown fits better at high confining stress, especially in shale and weak rock)
- Does not capture failure along pre-existing natural fractures or faults, which fail at lower stress than intact rock via friction on the existing surface, not new shear failure
- Does not capture tensile failure (a different mode entirely, relevant to hydraulic fracturing/breakdown, not shear-driven breakout)
Use Cases
- → Wellbore breakout risk screening: Compare a computed near-wellbore effective stress state against this critical threshold to flag shear-failure (breakout) risk before committing to a mud-weight program.
- → Estimating UCS from log-derived strength parameters: Where direct lab UCS testing is unavailable, estimate it from log-correlated cohesion and friction angle for drilling, cementing, and sand-control parameter sensitivity.
- → Casing/perforation strategy in weak rock: Identify intervals with low cohesion or friction angle as higher risk for sand production or perforation-tunnel collapse.
Related Calculations
Region Notes
Permian Basin
Wolfcamp shale/carbonate intervals are commonly characterized in published geomechanical studies with φ≈30-35° and C0 in the 10-20 MPa range — always calibrate to local core/log data rather than relying on these as defaults.
Global
Typical friction angles run ~25-35° for shale and ~35-45° for well-cemented sandstone/carbonate; cohesion is highly variable (near 0 for unconsolidated sand up to tens of MPa for strongly cemented rock) and should be measured, not assumed.
References
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