Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Failure Criteria - Mohr-Coulomb Stress Components Formula

\tau=0.5(\sigma_a-\sigma_b)\sin(2\beta)

Failure Criteria - Mohr-Coulomb Stress Components calculates shear stress on the plane 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 (sigma_a, sigma_b, beta_deg) 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 1,299.038106 psi.

sigma_apsi

8000

sigma_bpsi

5000

beta_degdeg

Inputs

sigma_a

psi

Principal Stress

sigma_b

psi

Second Strongest Stress

beta_deg

deg

Angle Between Fault and Principal Stress Direction

Outputs

tau

psi

Shear Stress on the Plane

sigma_n

psi

Normal Stress on the Plane

Source and review

reviewed

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

Source