Original synthetic study
How a stress sign convention changes an apparent failure result
Changing stress sign convention is harmless only when stresses, pressure terms and the failure equation are transformed together. Flipping one input alone can create a false failure indication.
By PetroCalcHub Team · Updated October 24, 2026 · Free to read and use
Define compression positive for the experiment
The reference uses compression-positive effective normal stress and strength |τ| ≤ c + μσn′. The same physical state can be written with tension-positive normal stress by changing the strength expression consistently.
The experiment includes a deliberately inconsistent column that flips the normal-stress sign without changing the envelope. That column is labelled as an error.
Pressure and shear need compatible treatment
Effective stress subtraction depends on the chosen total-stress convention. Shear sign can change with plane orientation, while a frictional envelope usually compares shear magnitude.
A positive or negative raw shear component is not by itself a failure criterion. Resolve the same physical plane and compare magnitude on the correct normal-stress basis.
Audit before interpreting a new failure result
If two implementations disagree, reconcile units, total versus effective stress, plane-angle definition and sign convention before changing strength parameters.
The study demonstrates bookkeeping, not a calibrated rock envelope. It does not establish stability of a real fault or wellbore.
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.
Effective compression (psi) = 2000. Correct compression-positive strength (psi): 1700; Correct tension-positive strength (psi): 1700; Wrong mixed-convention strength (psi): -700.
- Correct compression-positive strength (psi)
- Correct tension-positive strength (psi)
- Wrong mixed-convention strength (psi)
Worked example
Consistent and inconsistent sign transformations
Compression-positive effective normal stress varies. Cohesion 500 psi, friction coefficient 0.6. Tension-positive input is the negative of the same physical normal compression.
Relation and unit basis
strength+ = c + μσc; strength− = c − μσt, with σt = −σc
The deliberately wrong column uses c + μσt without transforming the envelope.
1. Define the baseline
Effective compression (psi) = 2000
Compression-positive effective normal stress varies. Cohesion 500 psi, friction coefficient 0.6. Tension-positive input is the negative of the same physical normal compression.
2. Select the relation
strength+ = c + μσc; strength− = c − μσt, with σt = −σc
The deliberately wrong column uses c + μσt without transforming the envelope.
3. Substitute the values
At σc = 2,000 and σt = −2,000: 500 + 0.6 × 2,000 = 500 − 0.6 × (−2,000) = 1,700 psi; wrong = −700 psi
Retain intermediate precision. The displayed values are rounded only after evaluation.
4. Read the result
Correct compression-positive strength (psi) = 1700; Correct tension-positive strength (psi) = 1700; Wrong mixed-convention strength (psi) = -700
A convention change preserves the physical result only when the equation is transformed too.
Result and interpretation
Correct compression-positive strength (psi) = 1700; Correct tension-positive strength (psi) = 1700; Wrong mixed-convention strength (psi) = -700
A convention change preserves the physical result only when the equation is transformed too.
The correct compression-positive and transformed tension-positive strengths agree; the mismatched column intentionally does not.
Study data and reproduction
Original synthetic teaching calculation. Equations and fixed controls are stated here; these are not field measurements.
| Effective compression (psi) | Correct compression-positive strength (psi) | Correct tension-positive strength (psi) | Wrong mixed-convention strength (psi) |
|---|---|---|---|
| 0 | 500 | 500 | 500 |
| 1,000 | 1,100 | 1,100 | -100 |
| 2,000 | 1,700 | 1,700 | -700 |
| 3,000 | 2,300 | 2,300 | -1,300 |
| 4,000 | 2,900 | 2,900 | -1,900 |
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. Can a sign-convention change alter the physical state?
Show the worked answer
No. If all equations and inputs are transformed consistently, the physical prediction should remain unchanged.
2. Reproduce the baseline Correct compression-positive strength (psi) without rounding intermediate values.
Show the worked answer
At σc = 2,000 and σt = −2,000: 500 + 0.6 × 2,000 = 500 − 0.6 × (−2,000) = 1,700 psi; wrong = −700 psi. Correct compression-positive strength (psi) = 1700. A convention change preserves the physical result only when the equation is transformed too.
3. Compare the first and last recorded scenarios. Which input changes?
Show the worked answer
Effective compression (psi) changes from 0 to 4000. Other controls remain as stated in the premise. Correct compression-positive strength (psi) changes from 500 to 2900.
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. The deliberately wrong column uses c + μσt without transforming the envelope. A convention change preserves the physical result only when the equation is transformed too.
Before using the result
- Declare the stress sign convention.
- Transform pressure and strength terms consistently.
- Use shear magnitude with the stated envelope.
A convention change preserves the physical result only when the equation is transformed too.
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.