Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Modified Lade Failure Criterion Formula

\eta=\left(\frac{I_1^3}{I_3}-27\right)\left(\frac{I_1}{P_a}\right)^m

Modified Lade Failure Criterion calculates modified lade coefficient 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_a, S_b, S_c, P_a, m_lade) 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, eta equals 6.871781 dimensionless.

S_apsi

8000

S_bpsi

6000

S_cpsi

4000

P_apsi

14.7

m_ladedimensionless

0.1

Inputs

S_a

psi

Major Principal Stress

S_b

psi

Intermediate Principal Stress

S_c

psi

Minor Principal Stress

P_a

psi

Atmospheric Reference Pressure

m_lade

dimensionless

Material Strength Exponent

Outputs

eta

dimensionless

Modified Lade Coefficient

I_1

psi

First Stress Invariant

I_3

psi^3

Third Stress Invariant

P_a

psi

Atmospheric Reference Pressure

m_lade

dimensionless

Material Strength Exponent

Source and review

reviewed

Reservoir Geomechanics, Zoback, M.D.

Zoback, M.D. Reservoir Geomechanics. Cambridge University Press, Page 99.

source conflict

Source