Development of Bishop and Diagram Methods in order to Slope Stability Analysis Considering the Intermediate Principal Stress

The recent studies have shown the importance of the role of intermediate principal stress in design process of geomechanics projects. Therefore in this paper, considering the triaxial unified strength failure criterion, the Bishop method was developed. Moreover, based on the numerical modeling results, two diagrams for slope stability analysis were presented. In large-scale open pit mines, one of the major issues during design is maximizing the net present value of the mine. One of the most important factors in this regard is the optimum slope angle of the mine. Generally, in rock slope stability analyses, the considered failure criteria are biaxial, thus in analysis process, only the maximum and minimum principal stresses of medium are considered. Actually, in most cases, the effect of intermediate principal stress is ignored completely, while recent researches have shown that the design and calculation of safety factor, regardless of the intermediate principal stress effect, is conservative and can have a significant effect on the economic conditions of the project. One of the triaxial failure criteria is the unified strength failure criterion. It consists of a wide range of solutions based on different failure criteria such as the Mohr-Coulomb failure criterion and Generalized Twin Shear Stress yield. In reality, based on this failure criterion, considering the intermediate principal stress effect, the amount of geomechanical properties of rock mass; such as internal friction angle and cohesion are increased and consequently, the safety factor of stability condition will be larger than the obtained safety factor from biaxial failure criterion. Therefore, the main purpose of this paper is development of a slope stability analysis method that considers the effect of intermediate principal stress. In this research, considering the circular failure conditions for soil and rock slopes, the Bishop's equilibrium method was extended based on the triaxial unified strength failure criterion. Also, for analyzing the stability and calculating the optimum slope angle, new diagrams were presented. The results showed that, without the intermediate principal stress effect, calculation of safety factor for investigating the slope stability condition is conservative and the net present value of mine is decreased consequently. Moreover, the sensitivity analyses showed that the amount of intermediate principal stress effect on the safety factor is not a function of the resistance properties of rock and soil.