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

Figures & Tables

θ₀ [°]	A	A_min	A_max	A = 1
-30	23cosθ(2sinθ+1)sinϕ+3$\frac{2\sqrt{3}\cos \theta }{\left( 2\sin \theta +1 \right)\sin \phi +3}$	0.6	1.15	0.927
0	3cosθ3sinϕsinθ+3$\frac{3\cos \theta }{\sqrt{3}\sin \phi \sin \theta +3}$	0.67	1.22	0.969
30	23cosθ(2sinθ−1) sinθ +3$\frac{2\sqrt{3}\cos \theta }{\left( 2\sin \theta -1 \right)\sin\phi +3}$	1.0	3.0	1.49
−arctan(sinϕ/3)$-\arctan \left( \sin \phi /\sqrt{3} \right)\] $	3sin2ϕ+9cosθ(sin2ϕ+3sinθ+sinϕ)sinϕ+3$\frac{\sqrt{3{{\sin }^{2}}\phi +9}\cos \theta }{\left( \sqrt{{{\sin }^{2}}\phi +3}\sin \theta +\sin \phi \right)\sin \phi +3}$	0.6	1.0	0.897
4.22	3cos(θ)3(sin (θ) −0.0736) sin(ϕ) +2.99$\frac{3\cos \left( \theta \right)}{\sqrt{3}\left( \sin \left(\theta \right)-0.0736 \right)\sin \left( \phi \right)+2.99}$	0.7	1.3	1
-19.35	3cos(θ)3(sin (θ) +0.331) sin(ϕ) +2.83$\sin \phi \gt \sqrt{3}\tan \left( -\left( \theta +{{\theta }_{0}}\right)/2 \right)$	0.61	1.06	0.909