2.2 Types of Factors of Safety
There are basically three methods to determine the factor of safety for stability analysis：the strength factor method，the load factor method，and the dimension factor method，which are given as follows：
①Strength factor method：The method considers the soil strength involving much uncertainty and has the strength reduced by a factor of safety.If the factor of safety for the strength factor method is represented as FSs，the parameters for the effective stress analysis are as follows：
the parameter for the undrained analysis is
After conducting a force equilibrium or a moment equilibrium analysis with the after⁃reduction parameters c′m，φ′m or su，m derived as above，we can design the penetration depth.The method locates the factor of safety at the source where the largest uncertainty arises and is therefore quite a reasonable method.Since the after⁃reduction parameters will lead to a smaller Kp and a larger Ka，the distribution of earth pressures on the retaining wall will be skewed.As a result，the method is applicable only to stability analysis and cannot be applied to deformation analysis or stress analysis.
②Load factor method：The factor of safety for the load method，FSl，can be defined as follows：
where R represents the resistant force and D is the driving force.R and D can be either the resistant moment and the driving moment，or the bearing force and the external force.FSl considers uncertainty arising from the soil strength，the analysis method，and external forces synthetically.The factors of safety adopted in this chapter are mainly derived from the load factor method.
③Dimension factor method：Suppose that retaining walls are in the limiting state and the soil strengths are fully mobilized.With the force equilibrium（the horizontal force equilibrium，the moment equilibrium or other type of force equilibrium），the penetration depth of retaining walls in the limiting state can be found.The penetration depth for design is
where FSd＝factor of safety for the dimension factor method；Hp，cal＝penetration depth computed from the limit equilibrium.
The factor of safety is usually defined as a ratio of the resistant force to driving force or as a factor to reduce the strength.Eq.2.4 is too much empirically oriented and cannot properly express the meaning of the factor of safety，leading to unreasonable results and is not recommended.If applied，cross checking by other methods is necessary.