<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></abstract>

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.

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

Studia Geotechnica et Mechanica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

A systematic approach to measure the differences between Mohr-Coulomb (MC) and Drucker-Prager (DP) shear strength criteria used commonly in soil and rock...

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

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

Article Category: Research Article

Pubblicato online: 20 ott 2018

Pagine: 163 - 169

Ricevuto: 31 gen 2018

Accettato: 18 mag 2018

DOI: https://doi.org/10.2478/sgem-2018-0016

Parole chiave
Mohr-Coulomb, Drucker-Prager, elasto-plasticity, shear strength, plane strain conditions

© 2018 Marek Wojciechowski, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Figure 1

Figure 2

Figure 3

Expressions for coefficient A and its minimum, maximum and average values for the selected values of θ0 parameter.

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

Article Category: Research Article

Pubblicato online: 20 ott 2018

Pagine: 163 - 169

Ricevuto: 31 gen 2018

Accettato: 18 mag 2018

DOI: https://doi.org/10.2478/sgem-2018-0016

Parole chiaveMohr-Coulomb, Drucker-Prager, elasto-plasticity, shear strength, plane strain conditions

© 2018 Marek Wojciechowski, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Figure 1

Figure 2

Figure 3

Expressions for coefficient A and its minimum, maximum and average values for the selected values of θ0 parameter.

Parole chiave
Mohr-Coulomb, Drucker-Prager, elasto-plasticity, shear strength, plane strain conditions