Abstract: Determining the stress state of sliding surface and the sliding direction of slope is the key to analyzing the stability of slope using the method of vector sum. The stress of any point on fixed sliding surface of arbitrary shape is ascertained based on the principle of minimum potential energy, and the normal stress and shear stress of sliding surface are obtained through the virtual displacement which produces minimum potential energy. Meanwhile, the slide-resistance direction of micro-unit is calculated by regarding the overall motion trend of the slope as in the opposite direction of the vector sum of the slide-resistance direction. Moreover, the ratio of slide-resistance to sliding stress which are acquired from projecting all the forces on the slope in the sliding direction is defined as the safety factor of slope. Compared to previous researches, the present method does not need to assume a major slide surface, and therefore, avoids the confirmation of initial sliding direction. The method is applied to calculating the safety factor, slide direction and normal stress of two classical calculation examples and also in a practical project. The results of two calculation examples verify the rationality of the present method; in practical engineering, the calculation result is also consistent with those of other methods.

Key words: slope, sliding direction, stability, vector sum, safety factor