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Top1. Introduction
Stability of slopes poses a significant problem in the fields such as geotechnical engineering, mining engineering etc. At present, the assessment of the stability of earthen slope is performed with several available techniques such as limit equilibrium technique, finite element method, probabilistic methods etc. Application of limit equilibrium technique (LET) is most popular among engineers and researchers for slope stability analysis because of its simplicity, reliability and robustness in formulation. The evaluation of factor of safety (FOS) corresponding to failure surface has been performed using several available limit equilibrium techniques (Bishop, 1955; Fellenius, 1936; Janbu, 1975; Lowe & Karafaith, 1960; Morgenstern & Price, 1965; Spencer, 1967). Some researchers (Burman, Acharya, Sahay, & Maity, 2015; Smith, Griffiths, & Margetts, 2015) have successfully applied strength reduction technique using finite element method to solve slope stability problems. This method has lately emerged as a reliable alternative to already popular limit equilibrium-based slope analysis methods.
Stability analysis of heterogenous slopes having week layer sandwiched between two successive strong layers is a complicated geotechnical problem. The formulation of general non-circular failure surfaces requires the condition of kinematic admissibility as well as concave upward pattern should be satisfied. The slope analysis with general non-circular failure surfaces yields continuous solution of the objective function over the domain of interest. Analysing a slope with concave upward failure surfaces in presence of weak soil layer yields discontinuous solution. The discontinuity referred here is related to identical failure surfaces with substantial change in FOS value. A significant change in the values of FOS is usually observed for a failure surface trapped inside a weak layer with that lying outside it. The impracticality in application of concave upward failure surface using general method of formulation potential failure surface needs refinement. Basic engineering knowledge dictates considerable portion of the failure surface should lie within the weak layer when the analysis of slopes with weak layer is performed. Whenever the failure surface is predominantly trapped inside the weak layer, it renders the failure surface non-concave with seemingly straight-line appearance. This modification maintains the requirement of kinematic admissibility and makes the objective function continuous over solution domain. Many researchers analysed the slope problem having a layer of poor geotechnical properties sandwiched between two strong layers. Bolton, Heymann, & Groenwold, (2003) considered slope problem having a weak layer with horizontal as well as inclined geometric layout. However, the method of generation of failure surface in the slope analysis by Bolton et al., (2003) has not been described in detail. Later, two different slopes with different geometry and weak layer embedded between successive strong layers have been analysed by Zolfaghari, Heath, & McCombie, (2005). The researcher explained a novel technique of generating non-circular failure surfaces with eleven different categories based on change in base angles 
. In recent past, Cheng, Li, & Chi, (2007); Cheng, Li, Chi, & Wei, (2007) analysed the soil slope with another new technique of generation of non-circular failure surface efficiently. Cheng, Li, & Chi, (2007); Cheng, Li, Chi, et al., (2007) described the method of generation of non-circular failure surface in details and demonstrated its efficiency for the homogeneous as well as heterogenous slopes. But, did not describe the modifications required for generating non-circular failure surfaces (i.e. non-concave in nature) for the slopes having sandwiched weak soil layer. However, the reported non-circular failure surface and corresponding FOS values by Cheng, Li, & Chi, (2007); Cheng, Li, Chi, et al., (2007) showed that the method worked very efficiently.