Where c and φ refer to the cohesion and the friction angle of the ground, respectively, L is the length of the slice’s base, and N’ is the effective normal force acting at the base of the slice. Moreover, the Mohr-Coulomb failure criterion is utilized to derive the shear strength of the ground, hence, the ultimate shear force that can be developed in a single slice i is: In addition, a correction factor f 0 is incorporated in the analysis and will be further discussed in the Calculations section below. Janbu’s method satisfies horizontal force equilibrium for the entire failure mass, as well as vertical and horizontal equilibrium for each slice.
Janbu’s method suggests that the normal interslice forces are equal and can be neglected. Forces acting on a single slice: i) the weight of the soil above the failure surface W, ii) the interslice reactions from the adjacent slices X i-1, X i+1, V i-1, V i+1, iii) the reaction of the stable ground which consists of a normal effective N’ and a shear component T, respectively, and iv) the boundary water force U. Examples of typical non-circular failure surfaces including: (a) a failure surface that passes through a sheared zone, and (b) a failure surface that begins as circular but is then interrupted by a stronger geological formation (bedrock)The assumptions made by the Janbu’s method are that the interslice forces acting at each slice are equal and can be neglected ( Figure 2).įigure 2. Examples of such surfaces are illustrated in Figure 1a and 1b.įigure 1. Non-circular failure surfaces are more common in nature (due to the existence of soil layers with different properties or due to geometrical restrictions). Moreover, Janbu’s Method can be used for both circular and non-circular failure surfaces. However, a major difference between the two is that Janbu’s Method satisfies force equilibrium as opposed to Bishop’s Method that satisfies moment equilibrium. The method has similar features with the Bishop Method of Slices regarding the assumptions made on the inter-slice forces. Janbu’s Method was developed by the Norwegian Professor N.