The calculated value of safety factor of a slope directly determines the design of slope engineering. However

the limit equilibrium method can not yield a single value of safety factor; thus the study of multiple solution of safety factor helps in justifying the reasonableness of the computation results and selecting the range of possible values of safety factor. The initial distribution of normal stresses over the slip surface is assumed

which is then modified by a Lagrangian function involving three parameters to satisfy the complete equilibrium conditions of the sliding body. Solving the equilibrium equations yields values of the three parameters associated with a series of prescribed safety factors

and the reasonable range of safety factor of a slope is justified according the reasonableness of the normal stress distribution over the slip surface. Example studies show that the reasonable range of safety factor for a circular slip surface is within 5 %; however

for non-circular slip surfaces

this range would be as large as 15 %.