An improved morgenstern-price method using gaussian quadrature

The Morgenstern-Price (MP) method is an effective solution to compute the factor of safety (FOS) of a slope against sliding that has been used extensively for decades. In the MP method, the soil mass above the slip surface needs to be tediously divided into vertical slices to compute the force and moment integrals. The proposed research improves the computational efficiency of the MP method by employing the Gaussian quadrature for the integrals, where the soil mass division into a significant number of vertical slices is improved by aligning a few Gauss points along the slip surface. Consequently, the computational efficiency can be dramatically improved, resulting in a reduction in calculation efforts. Moreover, this research further refines the iteration scheme to satisfy the equilibrium conditions for the FOS using a robustly stable numerical algorithm with two initial scaling factors. The critical slip surface was determined by the simulated annealing algorithm. Finally, the proposed method was thoroughly validated via a series of benchmark examples. This research could improve the traditional MP method by enhancing its robustness and efficiency and provide an informative technique for force integrals that may be motivated by other problems in geotechnical engineering.