极限平衡方法利用莫尔-库仑表达式来评价滑动面的抗剪强度。土体的剪切应力是指土的抗剪强度。当运动的剪切应力表示为剪切强度的分数时，极限平衡态存在。当临界状态达到时，在失效的时刻充分调动了抗剪强度。因此,剪切强度表达通常通过莫尔-库仑线性关系和ƮƮf定义为:Φ,c和a =摩擦角,凝聚力和吸引力在压力方面F =安全系数
The limit equilibrium methods use Mohr-Coulomb expression to evaluate the shear strength along with the sliding surfaces. The shear stress the soil fails is referred to the shear strengths of the soil. The limit equilibrium state exists when the mobilized shear stress is expressed as the fraction of shear strength. The shear strength is mobilized fully at the moment of the failure along with the failure surfaces when the critical conditions state is reached. Thus, the shear strength is expressed usually by the Mohr-Coulomb linear relationship and the Ʈ and Ʈf are defined by: Φ, c and a = friction angle, cohesion and attraction in stress terms F= factor of safety
The shear strengths rely on the effective normal stress and type of soil. The mobilized shear stress relies on the external forces that act on the soil mass. The factor of safety is the ratio of Ʈ and Ʈf in the limit equilibrium analysis. The factor of safety can be explained in three ways: moment equilibrium, force equilibrium and limit equilibrium. The first definition describes that the shear strength can be obtained in two ways: effective stress approach and total stress approach. The type of strengths relies on the loading condition, time elapsed after the excavation and type of soil. The total stress strength is commonly used for the short-term conditions in the clayey soils and the effective stress strength is commonly used in the long-term conditions in all types of soils. The second definition is based on the force equilibrium, and the third definition is based on the movement equilibrium. The second and third definition can be confusing sometimes whether the moment or force is a contribution on driving or resisting sides. For example, the force components along the sliding surface are considered on the resisting sides as the positive contribution as it increases the capacity of resistance against the movement. On the other hand, the component can be considered on the driving side as the negative contribution as it diminishes the driving tendency. The slices weights are situated at the tow and considered either on the driving side as the negative contribution or on the resisting side as the positive contribution.