Correlating Circular Failure Charts, Limit Equilibrium and Finite Element Method Based Safety Factor for Circular Failure Type Landslides

Landslides in the form of circular failures often occur in homogeneous geomaterials like soil, debris and highly weathered or fragile rocks. In slope engineering practices, Factor of Safety (FoS) is commonly determined using Circular Failure Charts (CFCs), Limit Equilibrium Methods (LEM) and Finite Element Methods (FEM). The present study is an attempt to assess the disparities and inter-relationships in FoS using CFCs, LEM and FEM. FoS calculations were performed manually and using an automated Windows-based open-source tool FS Calculator 1.0. Pertinent geomechanical (cohesion, friction, unit weight) and geometrical properties (slope angle and height) of fifty-one slopes from nine case records were considered in the present analysis. A linear correlation occurs in FoS using CFC and LEM i.e., \({\text{FoS}}\left({{\text{CFC}}}_{{\text{FS}}}\right)= 2.7592\times {\text{FoS}}({\text{LEM}})- 2.2082\) , with the coefficient of determination of 0.99. However, the linear relationship between SRF and FoS (LEM) is \({\text{FoS}}\left({{\text{CFC}}}_{{\text{FS}}}\right)=0.889\times {\text{SRF}}\left({\text{FEM}}\right)+0.0438\) having coefficient of determination of 0.63 only. It connotes that FoS using CFCs and LEM is relatively well in comparison to FoS from CFCs and FEM. It is also evident that CFCs provide relatively more conservative FoS than FEM and LEM. Among all three proxies, FEM relies on a wider set of geomechanical parameters and evaluates stability under static and dynamic conditions with capability of applying wider range of remedial measures. Since, most of the FEM tools are commercial, open-source CFCs based FS Calculator may be used and proposed relationships may be utilized as correction factor.