Abstract: Expanding the applicability of traditional limit equilibrium (LE) methods in slope stability analysis under complex conditions has been a research hotspot in geotechnical engineering field. It is recognized that the shear failure of geotechnical body of slope is typically governed by nonlinear strength criteria, while the traditional LE method is only applicable to the slope stability analysis under the linear strength criterion. Pre-stressed anchors, as an active protection measure, are widely used in the reinforcement of medium and large-scale slope projects because they can greatly and instantly improve the stability of slopes. However, the long-term stability characteristics of slope reinforced by the pre-stressed cables, including stress relaxation, creep, and the effects of corrosion, are often overlooked. To address these issues, an approach based on the Morgenstern-Price (M-P) has been developed. This method incorporates the nonlinear Mohr-Coulomb (M-C) criterion and integrates the pre-stress loss model of the cables under stress relaxation and creep effects, as well as the performance deterioration model of the cables under the influence of corrosion. In order to tackle the challenge of solving implicit nested formulas under the nonlinear strength criterion, the initial value of the inter-slice normal force is set to zero, and an iterative loop calculation strategy is applied. Subsequently, the approximation of the real theoretical results of slope stability can be realized by introducing the criterion of the allowable error of loop termination. Through comparison and analysis of various examples, the feasibility and rationality of this method have been verified. Furthermore, the variation patterns of long-term stability of slope reinforced by the pre-stressed cables under different pre-stressed loss rates and different corrosion environments are also studied.

Key words: slope, limit equilibrium M-P method, nonlinear M-C strength criterion, reinforced by pre-stressed cables, long-term stability