A note on the differences between Drucker-Prager and Mohr-Coulomb shear strength criteria

A systematic approach to measure the differences between Mohr-Coulomb (MC) and Drucker-Prager (DP) shear strength criteria used commonly in soil and rock mechanics is presented. It is shown that the DP criterion generates a shear strength between 0.6 and 3 times the MC strength, for the same friction angle and cohesion parameters. The appropriate conditions for obtaining equal shear strengths are given. Moreover, some new DP failure surfaces are proposed which minimize the differences relative to the MC predictions. The equivalence of the DP and MC criteria under plane strain conditions is also examined.