Modified lade criterion

Input(s)

SaS_{a}: Principle Stress (psi)

SbS_{b}: Intermediate Stress (psi) ScS_{c}: Minimum Stress (psi)

PaP_{a}: Pressure (psi)(\mathrm{psi})

m: Material Strength Constant (dimensionless)

Output(s)

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

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

η\eta: Lades Coefficient (dimensionless)

Formula(s)

Ia=Sa+Sb+ScIc=Sa Sb Scη=((Ia3Ic3)27)((IaPa)m)\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.

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