The Mohr-Coulomb yield criterion takes on the simplest form in the Mohr stress space

which has thus been most extensively applied in limit analysis and limit equilibrium methods because of its accuracy. However

the Mohr-Coulomb yield surface in the stress space is non-smooth

causing huge troubles to the constitutive integration in the deformation based finite element plasticity analysis. In addressing strength problems

meanwhile

solvers based on the load controlled method (LCM) are hard to bring the finite element model to the limit equilibrium state. Aiming at these issues

the solution schemes are proposed as follows. First

an algorithm named GSPC is designed for the constitutive integration for plasticity with non-smooth yield surfaces. GSPC is always convergent for arbitrary large strain increments

with far more excellent numerical properties than the return-mapping methods available. A solver based on the displacement controlled method (DCM) is developed for the finite element plasticity analysis. The DCM solver is able to bring easily the finite element model into the limit equilibrium state

with no convergence issue

and far more efficient and robust than any LCM solvers. At last

combined with the strength reduction method

the secant method for the factor of safety of slopes is developed

and the location and depth of tension cracks at the slope top are proposed.Keywords: constitutive integration for plasticity; Mohr-Coulomb yield surface; displacement controlled method; slope stability; tension cracks