Limit equilibrium analysis: The kinematic approach of limit analysis is explored in three-dimensional 2D stability analysis of slopes. The stability of the slope can be calculated by analyzing the possible sliding surface and simplifying the stress on the sliding surface to a uniform distribution, and then calculate the stability coefficient of the slope. Alternatively, the kinematic approach yields the lower estimate of the stability factor cu/λH.
The limit equilibrium methods use the Mohr-Coulomb expression in order to identify the shear strength along the sliding surfaces. Thus, the shear stresses which the soil fails in the shear are referred to the shear strength of soil. The limit equilibrium state exists when the mobilized shear strength is expressed as the fraction of shear strength. The shear strength at the moment of the failure is mobilized fully along with the failure when the critical conditions state is reached. It is expressed usually by the Mohr Coulomb linear relationship. The shear strength relies on the effective normal stress and type of soil and the mobilized shear stress relies on the external forces that act on the soil mass. The factor of safety is defined as the ratio of the Ʈf to Ʈ in the limit equilibrium analysis. The factor of safety can be defined in three ways: moment equilibrium, force equilibrium and limit equilibrium. The first definition relies on the shear strength that can be in obtained from two ways: effective stress approach and total stress approach. The strength type depends on the type of the soil and the time elapsed after the excavation and loading conditions. The total stress strength is utilized for the short term conditions in the clayey soils and effective stress strength is utilized in the long term conditions in types of soils and conditions where the pressure pore is known. The third and second definitions are based on the movement equilibrium and force equilibrium conditions to resist and drive moment and force components. The definitions are sometimes confusing but the moment or force components contribute on driving and resisting slides.