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

Marek Wojciechowski

Marek Wojciechowski

Faculty of Civil Engineering, Architecture and Environmental Engineering, Technical University of Łódź, AlŁódź, Poland
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Wojciechowski, Marek
  
20 oct 2018
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Categoría del artículo: Research Article
Publicado en línea: 20 oct 2018
Páginas: 163 - 169
Recibido: 31 ene 2018
Aceptado: 18 may 2018
DOI: https://doi.org/10.2478/sgem-2018-0016
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© 2018 Marek Wojciechowski, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Figure 1

Variability of Drucker-Prager shear strength vs. Mohr-Coulomb shear strength with respect to Lode angles θ0 and θ and the friction angle ϕ. The qDP=qMC line represents the equivalent friction angles for the case of the DP criterion.
Variability of Drucker-Prager shear strength vs. Mohr-Coulomb shear strength with respect to Lode angles θ0 and θ and the friction angle ϕ. The qDP=qMC line represents the equivalent friction angles for the case of the DP criterion.

Figure 2

Deviation of coefficient A from unity for selected θ0 values with respect to Lode angle θ and friction angle ϕ.
Deviation of coefficient A from unity for selected θ0 values with respect to Lode angle θ and friction angle ϕ.

Figure 3

Integral A¯=1$\bar{A}=1$with respect to the θ0 angle for different integration areas Ω.
Integral A¯=1$\bar{A}=1$with respect to the θ0 angle for different integration areas Ω.

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

θ0 [°]AAminAmaxA = 1
-3023cosθ(2sinθ+1)sinϕ+3$\frac{2\sqrt{3}\cos \theta }{\left( 2\sin \theta +1 \right)\sin \phi +3}$0.61.150.927
03cosθ3sinϕsinθ+3$\frac{3\cos \theta }{\sqrt{3}\sin \phi \sin \theta +3}$0.671.220.969
3023cosθ(2sinθ−1) sinθ +3$\frac{2\sqrt{3}\cos \theta }{\left( 2\sin \theta -1 \right)\sin\phi +3}$1.03.01.49
−arctan(sinϕ/3)$-\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}$0.61.00.897
4.223cos(θ)3(sin (θ) −0.0736) sin(ϕ) +2.99$\frac{3\cos \left( \theta \right)}{\sqrt{3}\left( \sin \left(\theta \right)-0.0736 \right)\sin \left( \phi \right)+2.99}$0.71.31
-19.353cos(θ)3(sin (θ) +0.331) sin(ϕ) +2.83$\sin \phi \gt \sqrt{3}\tan \left( -\left( \theta +{{\theta }_{0}}\right)/2 \right)$0.611.060.909
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4 veces al año
Temas de la revista:
Geociencias, Geociencias, otros, Ciencia de los materiales, Compuestos, Materiales porosos, Física, Mecánica y dinámica de fluidos
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