A new approach, named the Vector Sum Method (VSM), is proposed to analyze the anti-sliding stability problems for slope, dam foundation, etc. It is well known that the strength reduction method is generally applied in this field. But the stress state due to the strength reduction is a virtual state rather than a real one. So the safety factor calculated based on a virtual stress state is not physical sound. Some disadvantages of slope and dam foundation stability analysis methods based on strength reduction principle are discussed. To overcome the limitation of the strength reduction method, the VSM uses the real strength parameters rather than the reduced parameters to compute the stress field. The safety factor is computed based on the real stress state and the vector sum algorithm. Several typical examinations calculated by the vector sum method are presented. The comparison between results shows that theVSM is reasonable. The safety factor is calculated by an explicit formula in 2D case while by iterative computation in 3D case after the stress fields are acquired by finite element method or other methods. The VSM can be well applied to 3D problems for its simplicity and efficiency.

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