Modified lade criterion

Input(s)

$S_{a}$: Principle Stress (psi)

$S_{b}$: Intermediate Stress (psi) $S_{c}$: Minimum Stress (psi)

$P_{a}$: Pressure $(\mathrm{psi})$

m: Material Strength Constant (dimensionless)

Output(s)

$I_{a}$: First Invariant of Stress Tensor (psi)

$I_{c}$: Third Invariant of Stress Tensor (psi3)

$\eta$: Lades Coefficient (dimensionless)

Formula(s)

$$ \begin{gathered} \mathrm{I}_{\mathrm{a}}=\mathrm{S}_{\mathrm{a}}+\mathrm{S}_{\mathrm{b}}+\mathrm{S}_{\mathrm{c}} \\ \mathrm{I}_{\mathrm{c}}=\mathrm{S}_{\mathrm{a}} * \mathrm{~S}_{\mathrm{b}} * \mathrm{~S}_{\mathrm{c}} \\ \eta=\left(\left(\frac{\mathrm{I}_{\mathrm{a}}^{3}}{\mathrm{I}_{\mathrm{c}}^{3}}\right)-27\right) *\left(\left(\frac{\mathrm{I}_{\mathrm{a}}}{\mathrm{P}_{\mathrm{a}}}\right)^{\mathrm{m}}\right) \end{gathered} $$

Reference(s)

Mark D. Zoback, Reservoir Geomechanics, Cambridge University Press, UK, Page: 99.