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.