7.2.1 Formulation of the Mohr⁃Coulomb model
The Mohr⁃Coulomb yield condition is an extension of Coulomb's friction law to general states of stress.In fact，this condition ensures that Coulombs friction law be obeyed in any plane within a material element.The full Mohr⁃Coulomb yield condition consists of six yield functions when formulated in terms of principal stresses（see for instance Smith Griffiths，1982）：
The two plastic model parameters appearing in the yield functions are the well⁃known friction angle y and the cohesion c.The condition f＝0 for all yield functions together（where fi is used to denote each individual yield function）represents a fixed hexagonal cone in principal stress space as shown in Figure 7.1.
Figure 7.1 The Mohr⁃Coulomb yield surface in principal stress space（c＝0）
In addition to the yield functions，six plastic potential functions are defined for the Mohr⁃Coulomb model：
The plastic potential functions contain a third plasticity parameter，the dilatancy angleψ.This parameter is required to model positive plastic volumetric strain increments（dilatancy）as actually observed for dense soils.A discussion of all of the model parameters used in the Mohr⁃Coulomb model is given in the next section.
When implementing the Mohr⁃Coulomb model for general stress states，special treatment is required for the intersection of two yield surfaces.Some programs use a smooth transition from one yield surface to another，i.e.the rounding⁃off of the corners（see for example Smith Griffiths，1982）.For a detailed description of the corner treatment，readers can refer to relevant literature（Koiter，1960；van Langen and Vermeer，1990）.
For c＞0.The standard Mohr⁃Coulomb criterion allows for tension.In fact，allowable tensile stresses increase with cohesion.In reality，soil can sustain none or only very small tensile stresses.Mohr circles with positive principal stresses are not allowed.The tension cut⁃off introduces three additional yield functions，defined as
When this tension cut⁃off procedure is used，the allowable tensile stress，σt is，by default，taken equal to zero，but this value can be changed by the user.For these three yield functions an associated flow rule is adopted.