Critical height and stability of two-layered homogeneous slopes

Based on the plastic limit theory of slopes, the critical height equation for a two-layered homogeneous slope is derived directly by using the sectioned logarithmic spiral failure mechanism. Through the strength reduction method, the slope is gradually placed in the limit equilibrium state, and then the factor of safety of slope stability is obtained. This method integrates the external power directly without using numerical methods, and displays the critical height of the slope. In view of the dependence of the initial values on the optimal calculation in the process of strength reduction, using the logarithmic spiral parameters of the upper bound limit analysis of the homogeneous slope, an estimation method for the initial values is proposed to make the slope stability analysis more efficient through the focus search in key optimization space. By vertifying and comparing the results of examples, the computational accuracy and stability are demonstrated, the problem of the upper bound method in local stability analysis of layered slopes is pointed out, and the objective function which can be used for various failure modes is derived. Finally, taking a loess slope in Lanzhou as the background, the stability of the slope is analyzed by using several methods. The results show that the proposed method is stable and reliable, with little dependence on the initial values, and can be applied to projects quickly and effectively. © 2023 Chinese Society of Civil Engineering. All rights reserved.