Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Linearized Mohr Failure Line Formula

\tau=S_o+\sigma_n\mu_i

Linearized Mohr Failure Line calculates shear stress at failure for in-situ stress and rock mechanics workflows in geomechanics and fracturing.

Calculate

How engineers use this formula

Use this formula when the listed inputs (S_o, sigma_n, mu_i) are known and the assumptions behind the cited in-situ stress and rock mechanics relationship match the engineering case being checked.

Assumptions

Input values are representative for the well, reservoir, fluid, or equipment case being evaluated.
The declared units match the field-unit constants used in the formula.
The cited formula applies to the selected petroleum engineering workflow.

Limitations

The calculation does not replace a full engineering model or operating procedure.
Accuracy depends on the source correlation, assumptions, input quality, and unit consistency.

Common mistakes

Mixing unit systems without converting the inputs.
Using default example values as field recommendations.
Applying the formula outside the source assumptions.

Default example

Using the default inputs, tau equals 4,000 psi.

S_opsi

1000

sigma_npsi

5000

mu_idimensionless

0.6

Inputs

S_o

psi

Cohesive Strength or Failure-Line Intercept

sigma_n

psi

Normal Stress

mu_i

dimensionless

Internal Friction Coefficient

Outputs

tau

psi

Shear Stress at Failure

S_o

psi

Cohesive Strength or Failure-Line Intercept

sigma_n

psi

Normal Stress

mu_i

dimensionless

Internal Friction Coefficient

Source and review

reviewed

Zoback, M.D. 2007. Reservoir Geomechanics, Cambridge University Press, Page 89.

Source