Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Hoek and Brown Criteria for Principal Stress Failure Formula

\sigma_a=\sigma_c+C_o\sqrt{m\sigma_c/C_o+s}

Hoek and Brown Criteria for Principal Stress Failure calculates maximum effective principal 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 (C_o, m, s, sigma_c) 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_a equals 17,696.938457 psi.

C_opsi

6000

mdimensionless

sdimensionless

sigma_cpsi

3000

Inputs

C_o

psi

Unconfined Compressive Strength of Rock

m

dimensionless

Hoek-Brown Rock Constant

s

dimensionless

Hoek-Brown Rock-Mass Constant

sigma_c

psi

Minimum Effective Principal Stress

Outputs

sigma_a

psi

Maximum Effective Principal Stress at Failure

m

dimensionless

Hoek-Brown Rock Constant

s

dimensionless

Hoek-Brown Rock-Mass Constant

Source and review

reviewed

Reservoir Geomechanics, Zoback, M.D. (2007)

Zoback, M.D. 2007. Reservoir Geomechanics. Cambridge University Press, Page 98.

Source