A Generalized Limit Equilibrium-Based Platform Incorporating Simplified Bishop, Janbu and Morgenstern–Price Methods for Soil Slope Stability Problems

Abstract

Limit equilibrium (LE) method is the most widely used method for slope stability analysis. Different methods based on the LE technique for the analysis of the stability of the slope have been developed. Some are based on satisfying the force equilibrium condition of the failing mass (Janbu’s method), while some focus on satisfying the moment equilibrium condition (Bishop’s method). Among these methods, the most accurate result is provided by the Morgenstern–Price method as it not only satisfies both moments as well as a force equilibrium condition but also considers the interslice shear forces (V_i) and interslice normal forces (E_i), which are neglected by most of the LE methods to avoid the condition of indeterminacy. To accommodate these forces, Morgenstern–Price (MP) gave a relation between the V_i and E_i which depends upon a scaling multiplier (λ). Thus, it becomes necessary to evaluate λ value along with the factor of safety (FS). There is barely any work discussing the detailed methodology of evaluation of λ along with FS. Method for obtaining λ along with FS have been developed and elaborated in details here. While calculating FS (MP method), evaluation of E_i is a must which is dependent upon the values of normal force at the base of each slice (N_i) and FS, which itself is dependent upon the value of E_i, making it a loop of interdependent variables. To avoid this interdependency of above stated variables, a separate formulation of E_i is given which reduces the calculations (run-time) involved. A VBA code-based platform has also been developed incorporating the generalized LE method, including Bishop’s, Janbu’s, and Morgenstern–Price methods which are represented in the form of flowcharts in this work.