The vector sum method (VSM) based on real stress state has been applied recently for analysing the slope stability

considering its clear physical meaning. However

the factor of safety (FoS) defined by VSM could be negative in the case where total normal force vector projection is negative

and its absolute value is larger than total shear force vector projection. Moreover

deduced by Pan’s Principle

the direction of shear resistance stress vector of every point on potential slip surface is currently defined to be opposite to that of the projection of the potential slip direction of the possible slip mass on the tangential surface through this point. However

according to the definition of VSM safety factor and Pan’s Principle

the direction of the projection of the potential slip direction on the tangential surface through this point is opposite to that of the total resistance stresses including shear and normal ones. In this study

a vector-sum-based slip surface stress method for analysing slip mass stability was proposed to overcome these two disadvantages above of VSM. The slip surface was treated as a thin slip band

and forces undertaken by an arbitrary element of the slip band was analysed. The direction of the limit resisting shear stress of an arbitrary element was defined as the opposite direction of the real shear stress

and the possible slip direction was defined as the opposite direction of the resultant limit resisting shear force. Finally

FoS was defined as the ratio of the projection of the limit resisting shear force vector sum in the opposite possible slip direction to that of real dynamic shear force vector sum in the possible slip direction. Compared with the limit equilibrium method

the proposed method satisfied the force and moment equilibrium equations and compatibility conditions without any assumption. Compared with the shear strength reduction method

the proposed method defined that the FoS was explicit form avoiding iteration. The classic two-dimension static slope case was used to verify the proposed method with comparisons among main methods for slope stability analysis

which indicated that the proposed method was feasible. Additionally

the proposed method was applied to a three-dimensional engineering case to study its stability during the excavation process

which showed the proposed method could be used for practical application.