Engineering lesson
Effective stress versus total stress and the Biot coefficient
Total stress includes the overall load; effective stress subtracts the pore-pressure contribution under a stated convention. For an isotropic Biot model with compression positive, σ′ = σ − αp.
By PetroCalcHub Team · Updated October 24, 2026 · Free to read and use
State the sign convention first
This lesson treats compressive normal stress as positive. Increasing pore pressure at fixed total stress then lowers effective compression. A tension-positive implementation needs a consistently transformed equation.
The Biot coefficient α = 1 − Kd/Ks relates drained frame and solid-grain bulk moduli on the stated poroelastic assumptions. Kd is not the saturated bulk modulus.
Keep moduli and pressure compatible
Kd and Ks must use the same units for their ratio. Total stress and pore pressure must also share units before subtraction.
The explorer holds total stress and pore pressure fixed while varying α. It isolates the coefficient effect rather than simulating a coupled depletion stress path.
A constitutive coefficient is not a complete stress model
Depletion can change total stress through boundary constraints as well as changing pore pressure. Holding total stress fixed is one defined scenario, not every reservoir's response.
For anisotropic rocks or more general constitutive models, a scalar α may be inadequate. Keep the assumed material model with the result.
Explore the example
Original synthetic teaching calculation. Equations and fixed controls are stated here; these are not field measurements.
Select one of 5 recorded scenarios. Intermediate states are not interpolated.
Biot coefficient α = 0.8. Effective compression (psi): 5600.
- Effective compression (psi)
Worked example
Biot coefficient in a fixed-load sensitivity
Compression positive; total normal stress 8,000 psi and pore pressure 3,000 psi. Only α varies.
Relation and unit basis
σ′ = σ − αp
α is dimensionless. A coupled reservoir stress path could also change total stress and is not represented here.
1. Define the baseline
Biot coefficient α = 0.8
Compression positive; total normal stress 8,000 psi and pore pressure 3,000 psi. Only α varies.
2. Select the relation
σ′ = σ − αp
α is dimensionless. A coupled reservoir stress path could also change total stress and is not represented here.
3. Substitute the values
8,000 − 0.8 × 3,000 = 5,600 psi
Retain intermediate precision. The displayed values are rounded only after evaluation.
4. Read the result
Effective compression (psi) = 5600
Higher α gives a larger pore-pressure contribution at fixed total stress.
Result and interpretation
Effective compression (psi) = 5600
Higher α gives a larger pore-pressure contribution at fixed total stress.
Only α varies in the compression-positive effective-stress balance.
Exact scenario data
Original synthetic teaching calculation. Equations and fixed controls are stated here; these are not field measurements.
| Biot coefficient α | Effective compression (psi) |
|---|---|
| 0 | 8,000 |
| 0.25 | 7,250 |
| 0.5 | 6,500 |
| 0.8 | 5,600 |
| 1 | 5,000 |
Scroll the table to see all columns. The highlighted row is the worked baseline. Downloads retain full numerical precision.
Test your understanding
Work through the question before revealing its answer. Use the stated assumptions and include units in every numerical step.
1. At total compression 8,000 psi, pore pressure 3,000 psi and α = 0.8, what is effective compression?
Show the worked answer
5,600 psi, from 8,000 − 0.8 × 3,000.
2. Reproduce the baseline Effective compression (psi) without rounding intermediate values.
Show the worked answer
8,000 − 0.8 × 3,000 = 5,600 psi. Effective compression (psi) = 5600. Higher α gives a larger pore-pressure contribution at fixed total stress.
3. Compare the first and last recorded scenarios. Which input changes?
Show the worked answer
Biot coefficient α changes from 0 to 1. Other controls remain as stated in the premise. Effective compression (psi) changes from 8000 to 5000.
4. What would be needed to apply this example to a different physical system?
Show the worked answer
Replace the synthetic controls with compatible documented inputs and check the relation's assumptions. α is dimensionless. A coupled reservoir stress path could also change total stress and is not represented here. Higher α gives a larger pore-pressure contribution at fixed total stress.
Before using the result
- Declare compression or tension positive.
- Use drained frame modulus in α.
- Separate fixed-total-stress sensitivity from a stress path.
Higher α gives a larger pore-pressure contribution at fixed total stress.
Continue learning
Start with the broader workflow guide
Sources and method
The explanation and synthetic examples are original PetroCalcHub teaching material. The references below support the definitions and model context. They do not supply field validation for the synthetic scenarios.