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Abstract Based on the assumption of the modification of normal stress over the slip surface，the solution to the factor of safety is derived by iteration，according to the equilibrium conditions of the slope. Regarding the slip surface as a curved surface yielded from a family of power function rotating on y-axis，slip surfaces of different shapes are obtained by changing the values of the power function′s power. Accordingly，by discussing the impact of the slip surface′s shape on the factor of safety，the results reveal that the factor of safety is the single-valued function of power and its minimum value exists as well. As a result，the critical slip surface is obtained by optimizing the value of power，and the change law of the relationship between the value of power and the length of the sliding mass is analyzed. At last，the end effect of 3D slope is also discussed. It is demonstrated that the presented method can derive smaller factor of safety；the value of power corresponding to the critical slip surface decreases slightly and then increases gradually with the increase of length of the sliding mass. The analysis reveals that the end effect can be neglected when the length of the sliding mass is bigger than the height of the slope by 10 times，and it is proportional to the internal friction angle，inversely proportional to the cohesive stress and does not has close relation with the change of the slope inclination.
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Received: 19 May 2009
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