# 5 Tresca

The Tresca model is essentially a special case of the Mohr-Coulomb model where the cohesion is set equal to the undrained shear strength, c'=c_u, the friction angle is set equal to zero and Poisson's ratio is set equal to \frac{1}{2}. The Tresca model implicitly assumed undrained conditions with the stresses being the total stresses. As such, the Tresca model should not be linked to other models, e.g. Mohr-Coulomb, making use of effective stresses.

• E_u: undrained Young's modulus (see Section Elasticity for relation to drained modulus)

• c_u: undrained shear strength

Isotropic elasticity defined by E_u is used (see Section Elasticity).

The Tresca failure surface is given by

F = |\sigma_1-\sigma_3| - 2c_u \tag{5.1}

where c_u is the undrained shear strength.

Some possible depictions of the Tresca failure surface are shown in Figure 5.1.

The flow potential is associated:

\dot{\boldsymbol\varepsilon}^p = \dot\lambda\frac{\partial F}{\partial\boldsymbol\sigma} \tag{5.2}