A new Drucker-Prager criterion for geomaterials under conventional triaxial stress condition

With the increasing attention paid to three-dimensional numerical limit analysis, there is an urgent need to develop a new Drucker-Prager (DP) criterion suitable for geomaterials under conventional triaxial stress condition. Yet, an exact DP criterion for geomaterials under conventional triaxial stress condition does not exist. Instead, an approximate equal-area-circle DP-3₁ criterion has been used traditionally, which is relatively safe. This study developed a new DP-3₂ criterion for geomaterials under conventional triaxial stress condition based on the tri-shear energy yield criterion. The theoretical formulation was derived to determine the highest point of the criterion (i.e., the tangent point between the criterion and the Mohr-Coulomb criterion). Then, the conventional triaxial DP-3₂ criterion was established through the highest point. Thereafter, this new criterion was used to determine the ultimate load of soil under conventional triaxial condition and slope stability analysis. The ultimate load of soil under conventional triaxial condition determined by the DP-3₂ criterion was found to be about 87%–97% of the measured value. Moreover, the maximum ratio of ultimate load computed by the DP-3₂ criterion to the DP-3₁ criterion was 1.19, and it increased with decreasing confining pressure, increasing cohesion <i>c</i>, or increasing internal friction angle <i>φ</i>. The factor of safety (FOS) of soil slopes determined by the DP-3₂ criterion was approximately 1.01–1.04 times that determined by the DP-3₁ criterion. Furthermore, the difference increased at larger slope angles. These results suggest that the DP-3₂ criterion is suitable for numerical limit analysis of geomaterials under conventional triaxial stress condition.