geomechanics · stress
Effective Stress (Terzaghi/Biot)
σ' = σ − α × Pp
click formula to derive ↑
Inputs
psi
psi
—
Description
Calculates the effective stress acting on the rock matrix by removing the pore-pressure-supported portion of total stress. Effective stress, not total stress, governs rock deformation, compaction, and failure — it is the working stress term used throughout geomechanics, including the Mohr-Coulomb failure check.
Variables
| Symbol | Unit | Description |
|---|---|---|
| σ' | psi | Effective Stress |
| σ | psi | Total (overburden or other) stress acting at the point of interest — typically the output of the Overburden Stress calc, but any total stress component may be used. |
| Pp | psi | Pore (formation fluid) pressure at the point of interest — typically the output of the Eaton Pore Pressure calc or a direct measurement (RFT/MDT). |
| α | — | Poroelastic (Biot) coefficient describing how efficiently pore pressure offsets total stress. α=1 recovers Terzaghi's original soil-mechanics assumption; stiffer, lower-porosity rock (tight carbonates, well-cemented sandstone) typically has α well below 1. |
Assumptions
- Isotropic, homogeneous porous medium over the interval being evaluated
- Pore pressure is in equilibrium (not actively dissipating in a transient state)
- α applies uniformly to the stress component being evaluated (no direction-dependent anisotropy in this simplified scalar treatment)
Limitations
- Assuming α=1 (pure Terzaghi) in stiff, low-porosity rock overstates how much pore pressure reduces effective stress — this can materially understate failure risk in tight carbonates and well-cemented sandstones
- Naturally fractured or strongly anisotropic rock may have direction-dependent effective stress behavior not captured by this single scalar α
- Does not account for thermal or chemical (e.g. osmotic) stress contributions sometimes significant in shale
Use Cases
- → Mohr-Coulomb failure input: Feed the resulting effective stress directly into the Mohr-Coulomb Failure Criterion calc to assess shear-failure risk.
- → Reservoir compaction / subsidence screening: As a reservoir depletes and Pp falls, effective stress rises — track this rise to flag compaction or subsidence risk in weakly cemented reservoirs.
- → Sanding risk during drawdown: Increasing effective stress at the wellbore during production drawdown is a key driver of near-wellbore rock failure and sand production.
Related Calculations
Region Notes
Permian Basin
Wolfcamp shale/carbonate intervals are commonly modeled in published geomechanical studies with α in the 0.7-0.9 range rather than the simplified α=1 — using α=1 in these lithologies will overstate the effective-stress reduction from pore pressure.
Global
α=1 (Terzaghi) is a reasonable default for soft, high-porosity, unconsolidated sediment; always recalibrate α from lab core data or published correlations for cemented or low-porosity rock before relying on this calc for failure analysis.
References
Primary source
Primary source
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