As exposed in Mohr coulomb criteria for fragile materials, the equation that calculates when yield takes places is:
K2 will be equivalent to the maximum stress in the Rankine criteria. Taking a value for the frictional angle of 0.2 (c = 0.2), the cohesive value should be 0.61152, so as the stress takes a value equivalent to the Rankine criteria.
For the Drucker Prager criteria, the equivalent octahedral stress for the maximum Rankine stress should be calculated. The octahedral stress is the stress in the direction with cosines equal to 1/√3. This stress correspond to,
This is the value to use in the Drucker-Prager criteria equation. In the graphic below, the graphical representation of the Drucker-Prager criteria part of the cruve is inside the yield curve of the Mohr Coulomb criteria. But there is other part of the curve, for negative stresses, that yield curves of both criteria intersect.
To obtain a better fit (so as the Drucker Prager yield curve remains inside the Mohr Coulomb yield curve, the following equivalent expression for the Drucker Pracker criteria will be used
With the following values for a and K,