Mohr-Coulomb (MC)
Given the fact that traditional soil mechanics and partially also the rock mechanics are based on this model, the Mohr-Coulomb model represents one of the most commonly applied material models in engineering practice. In GEO5 FEM the corresponding yield surface is defined with the help of three limit functions, which display in the principal stress space as an irregular hexagon. Similarly to the Drucker-Prager model the yield function depends on the mean effective stress σmeff. From the projection of the yield surface fMC into the deviatoric plane it is obvious that individual edges intersect at a point of triaxial extension θ = - 30° and triaxial compression θ = 30°. Because the yield surface also dependence on the Lode angle θ, the model is able to provide predictions which are in better agreement with the real soil behavior in comparison to the Drucker-Prager model.
a) yield surface in principal stress space, b) projection into deviatoric plane c) stress-strain law
The stress-strain diagram also suggests that the Mohr-Coulomb model, similarly to the Modified elastic model, allows for modeling a different response of the soil in primary loading and subsequent unloading and reloading by introducing the modulus of unloading/reloading Eur.
Similarly to the Drucker-Prager model, the Mohr-Coulomb model makes possible to take into account the soil dilation (evolution of positive volumetric plastic strains during plastic shearing). Analogous is also the solution of a given task under drained and undrained conditons. Further information including the list of the required material parameters can be found in the description of the Drucker-Prager model.
A number of illustrative examples, which compare numerical predictions with the real soil behavior on the bases of simple laboratory tests, is available here. An example of modeling undrained conditions is provided here. Further details describing the implementation of drained and undrained conditions is available in the theoretical manual.
Unlike the Drucker-Prager model the Mohr-Coulomb model, similarly to the Hoek-Brown model, allows for limiting the tensile strength either by directly prescribing the tensile strength σt < ccotφ, where c, φ are shear strength parameters of the soil, or by introducing the tensile strength reduction factor TsRF. In such a case we get 
. The reduction of tensile strength is numerically driven by the Rankin yield surface fR. A graphical representation is evident from the following figure.
a) yield surface in principal stress space, b) projection into deviatoric plane c) projection of Mohr-Coulomb and Rankin yield surface into σ1 - σ3 plane
The Mohr-Coulomb model allows, similarly to the Drucker-Prager model, for performing the stability analysis. Both the standard slope stability analysis and stability analysis within a given construction stage can be carried out. In both cases, this task is solved by gradually reducing the shear strength parameters c, φ by introducing the reduction parameter ζ such that
where c, φ are the actual shear strength parameters and cd, φd are the reduced parameters. The Factor of safety FS is then given by
Similarly we reduce the dilatancy angle ψ providing ψ ≠ 0.
Implementation of the Mohr-Coulomb material model into the GEO5 FEM program is described in detail in the theoretical manual.