Rigorous limit equilibrium methods of slices should be used in slope stability analysis

especially for general slip surfaces. However

different assumptions regarding the inter-slice forces have resulted in different calculating formulations for the factor of safety of slope stability

thereby rendering the calculation process complicated and concealing the advantages and disadvantages of different procedures.

In this paper

the assumptions regarding the inter-slice forces that made by the existing rigorous limit equilibrium methods of slices are expressed into the unified formulation for the first time

the simple and clear recurrence equations of the inter-slice forces and inter-slice moments are derived based on force equilibrium and moment equilibrium. Based on the recurrence equations of the inter-slice forces and inter-slice moments

the unified calculating formulation for the factor of safety based on rigorous equilibrium in the context of conventional methods of slices is developed by Newton-Raphson method. The relevant derivatives that it needs can be computed by using recurrence formulas

and its nature is analytic solution

therefore its computer formulation is of the good stability and convergence. All of its formulas are algebraic expressions. It facilitates the application and dissemination in engineering.