Abstract: The logarithmic spiral damage mechanism can fully meet requirements of soil velocity separation, so the logarithmic spiral is widely used in the upper limit analysis of slope stability.However, since the logarithmic spiral can′t be manifested in Cartesian Coordinate System, the current upper bound analysis method gives a perfect solution to the homogeneous slopes stability analysis although the research of heterogeneous slope stability is relatively rare.In order to disscus the application of upper limit analysis method in heterogeneous slope stability,the authors proposed a new method of logarithmic spiral fitting based on discrete algorithm, and applied this method to the engineering practice of upper limit analysis of slope stability in open-pit mine.At the same time, the most dangerous slip surface and the slope stability coefficient calculation cycle program was compiled based on energy balance condition, and the residual thrust method was used to evaluate accuracy of calculation result of upper limit analysis method from two angles of stability coefficient and the most dangerous slip surface.The results show that the logarithmic spiral discrete algorithm is highly consistent with the original curve, which can guarantee the requirement R2≥0.999 5.At the same time, the stability analysis results are highly accurate.The calculation result is analyzed from perspective of stability coefficient.From the perspective of stability factors, the calculation result is strictly the upper bound solution, and the calculation error is easy to estimate.From the perspective of the most dangerous slip surface,the most dangerous slip surface obtained by this method can fully satisfy the requirements of speed separation and has a stronger engineering practice significance.