Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Weak-Plane Anisotropic Failure Stress Formula

\sigma=\frac{2\sigma_c(S_w+\mu\sigma_c)}{[1-\mu\cot(\beta)]\sin(2\beta)}

Weak-Plane Anisotropic Failure Stress calculates anisotropic failure stress 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_c, S_w, mu_wp, 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, sigma_fail equals 31,283,806.247108 psi.

sigma_cpsi

2000

S_wpsi

5000

mu_wpdimensionless

0.3

beta_degdeg

Inputs

sigma_c

psi

Minimum Principal Stress

S_w

psi

Intact Rock Strength

mu_wp

dimensionless

Weak-Plane Internal Friction Coefficient

beta_deg

deg

Weak-Plane Angle to Maximum Principal Stress

Outputs

sigma_fail

psi

Anisotropic Failure Stress

D_wp

dimensionless

Weak-Plane Denominator Term

S_w

psi

Intact Rock Strength

Source and review

reviewed

Reservoir Geomechanics, Zoback, M.D.

Zoback, M.D. Reservoir Geomechanics. Cambridge University Press, Page 107.

source conflict

Source